tag:blogger.com,1999:blog-83987970883916067522024-03-14T02:10:48.036-07:00PLEKTIXA blog on complex systems, and by extension, life.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.comBlogger87125tag:blogger.com,1999:blog-8398797088391606752.post-940329890334960792020-10-05T11:31:00.006-07:002020-10-05T13:33:46.460-07:00Does mathematics carry human biases?<p>This week, a conversation flared up on Twitter on whether mathematics can carry human biases, and what such a possibility could even mean. <br /></p><p>The spark was a statement by the Committee on Minority Participation in Mathematics of the <a href="https://www.maa.org/">Mathematical Association of America</a> (MAA), responding to actions the Trump administration has taken to disparage and de-fund the academic discipline of <a href="https://en.wikipedia.org/wiki/Critical_race_theory">Critical Race Theory</a>. The committee's <a href="https://www.mathvalues.org/masterblog/anti-science-policy-censure-of-discourse-on-race-and-racism">statement</a> pointed out that the attack on Critical Race Theory has a potentially chilling effect on all academic disciplines, including mathematics:</p><blockquote><p>As mathematicians, we notice patterns - this is something we are all
trained to do. We bring these Executive actions to our community’s
attention for several reasons: we see the pattern of science being
ignored and the pattern of violence against our colleagues that give
voice to race and racism. We need to fight against these patterns. As
educators, we also recognize the threatening pattern of banning
education and withdrawing education funding to suppress conversations on
race and racism, extending from elementary to postsecondary
institutions to the workplace and research spheres. <br /></p></blockquote><p> The MAA tweeted out this statement, highlighting the following quote:<br /></p><blockquote class="twitter-tweet"><p dir="ltr" lang="en">"It is time for all members of our profession to acknowledge that mathematics is created by humans and therefore inherently carries human biases. Until this occurs, our community and our students cannot reach full potential." -CMPM <a href="https://twitter.com/hashtag/MathValues?src=hash&ref_src=twsrc%5Etfw">#MathValues</a> <a href="https://t.co/vVBUnXf1TL">https://t.co/vVBUnXf1TL</a></p>— MAA (@maanow) <a href="https://twitter.com/maanow/status/1312377160938774528?ref_src=twsrc%5Etfw">October 3, 2020</a></blockquote><p>The resulting conversation appears to have focused in particular on the idea that "mathematics is created by humans and therefore inherently carries human biases", largely disregarding the rest of the committee's statement. One biologist in particular felt so provoked by this statement that she felt it should be dis<span>qualifying for the whole field:
</span></p><blockquote class="twitter-tweet"><p dir="ltr" lang="en"><span>If you truly believe that math is created by humans, you have no business in math.<br /><br />The ways that we *describe* math are, no doubt, a social construct, but math itself is the discovery of underlying reality. <a href="https://t.co/z5ce8hLCTZ">https://t.co/z5ce8hLCTZ</a></span></p><span>— Heather E Heying (@HeatherEHeying) <a href="https://twitter.com/HeatherEHeying/status/1312464832512229378?ref_src=twsrc%5Etfw">October 3, 2020</a></span></blockquote><p>First off, let me say clearly: Dr. Heying's tweet is reprehensible. No one should be dictating who does or does not have business in math, let alone someone from outside the field. She also seems completely ignorant of the <a href="https://www.pbs.org/wgbh/nova/article/great-math-mystery/">centuries-old debate on whether mathematics is discovered or invented</a> (most mathematicians feel it's some combination of both). And while I do not know if her comment was intended to be racist, the fact that she is saying the Committee on Minority Participation in Mathematics has "no business in math" is absolutely racist in its effect. She should apologize immediately, but instead she is <a href="https://twitter.com/HeatherEHeying/status/1312569435819929600?s=20">doubling down</a>.<br /><br />Leaving aside Dr. Heying's offensive remark, the statement itself raises some interesting questions. What could it mean for mathematics to "carry human biases"? I think part of the issue here is that the word "mathematics" could be understood in several different ways:</p><ol style="text-align: left;"><li>Mathematics as a collection of relationships (discovered or not) among numbers and other mathematical objects,</li><li>Mathematics as the human body of knowledge regarding these relationships,</li><li>Mathematics as a discipline and profession devoted to understanding and describing these relationships</li></ol><p>For an example of mathematics in the first sense, let's take the theorem that <a href="https://en.wikipedia.org/wiki/Euclid%27s_theorem">there are infinitely many primes among the natural numbers</a>. This is one of the most famous results in elementary number theory, with a number of beautiful proofs dating back to Euclid in ancient Greece. Within the universe of math, such a statement is not contestable. This is the point--and the beauty--of proofs in mathematics: they reveal truths that are universal, regardless of who discovers or uses them.</p><p>Many of those responding to the committee's statement assumed that they were using "mathematics" in this first sense, as if theorems like the inifinitude of primes could carry human bias. But I see this as an exceedingly ungenerous interpretation, with no support in the rest of their statement. Indeed, the people leaping to this interpretation seem to be all too eager to paint the committee's statement in the worst possible light, as if any statement calling for greater diversity and inclusion in mathematics is automatically considered suspect.<br /><br />If "mathematics" is understood in the third sense, as a discipline and profession, then absolutely it can carry human bias. Ronald Fisher, who pioneered the study of statistics, was a <a href="https://en.wikipedia.org/wiki/Ronald_Fisher#Eugenics">notorious racist and eugenicist</a>, and he was <a href="https://en.wikipedia.org/wiki/Francis_Galton">not alone</a> in these views. Moreover, until recent decades, women and minority groups were systematically excluded from studying and practicing higher mathematics. Because of this systematic exclusion, most of the "great figures" of Western mathematics are white men, and this perception that "math is for white men" becomes self-reinforcing. This is not merely a historical legacy: nonwhite mathematicians continue to face <a href="https://www.nytimes.com/2019/02/18/us/edray-goins-black-mathematicians.html">bias and isolation</a>, and in some cases <a href="https://twitter.com/kareem_carr/status/1292273338736349185?s=20">harassment</a>.<br /><br />What about the second sense, mathematics as a human body of knowledge? Could this carry bias? Here I think the question is much more nuanced, but the example of <a href="https://en.wikipedia.org/wiki/Negative_number#History">negative numbers</a> is instructive. They first appeared in the Han Dynasty of ancient China (202 BC - 220AD). It has been <a href="https://www.springer.com/gp/book/9783540337829">suggested</a> that the idea of duality in Chinese philosophy made negative numbers more intuitive for them. Indian mathematicians in the 7th century AD were using negative numbers to represent debts. Yet in Western mathematics, negative numbers were dismissed as absurd and nonsensical until calculus came along in the 18th century.<br /><br />I like the example of negatives, because it shows that what gets accepted as legitimate mathematics is indeed a social construct. Cultural biases can come into play when determining which ideas gain legitimacy, even in the abstract world of pure mathematics. Relationships among numbers are not biased, but our process of understanding and discovering these relationships may be. And I agree with the committee's statement that understanding how human biases influence our thought--even within the ivory tower of mathematics--is key to achieving greater inclusion and equity for all people.<br /></p><span> <script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script> </span><p></p>Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com2tag:blogger.com,1999:blog-8398797088391606752.post-61320691528055636312020-01-01T09:14:00.001-08:002020-03-02T10:52:20.153-08:00How do we mourn human civilization?<div dir="ltr" style="text-align: left;" trbidi="on">
2019 was a lot of things. But for what I want to say here, 2019 was the year that I realized we might not save ourselves.<br />
<br />
Just on its face, 2019 was a terrible year if you care about climate change. Arctic permafrost may have <a href="https://www.washingtonpost.com/weather/2019/12/10/arctic-may-have-crossed-key-threshold-emitting-billions-tons-carbon-into-air-long-dreaded-climate-feedback/" target="_blank">reached a tipping point</a>. Antarctic ice <a href="https://earther.gizmodo.com/antarctic-ice-melt-may-have-hit-an-all-time-high-on-chr-1840679498" target="_blank">melted at record pace</a>. The <a href="https://www.nytimes.com/2019/08/21/world/americas/amazon-rainforest.html" target="_blank">Amazon burned</a>. Meanwhile, carbon emissions <a href="https://www.nytimes.com/2019/12/03/climate/carbon-dioxide-emissions.html" target="_blank">continued to rise</a>, and COP-25, the major UN forum for international climate policy, ended with <a href="https://www.vox.com/energy-and-environment/2019/12/18/21024283/climate-change-cop25-us-brazil-australia-japan" target="_blank">essentially no progress</a>.<br />
<br />
But for me personally, 2019 was the year I allowed myself to consider that we might not work it out. Not only will we not stop the first effects of climate change, we might not even stop any of them. Faced with an existential threat to our entire civilization, we might just drive ourselves right off the fucking cliff.<br />
<br />
<i>Surely we will do something to stop it</i>. Consciously or not, this thought had always been in the back of my head when thinking about climate change. Yes, the science looks bleak, the politics look intractable, and some level of crisis is probably unavoidable. But <i>surely, at some point, human civilization will come together, face the danger ahead, and do something to stop it.</i><br />
<br />
This year, I allowed myself to pluck this voice from the back of my head, hold it to the light, and examine it. <i>Will we do something to stop it?</i><br />
<br />
Well, what does our track record show? Climate change was officially identified by NASA as a severe global threat <a href="https://www.nytimes.com/1988/06/24/us/global-warming-has-begun-expert-tells-senate.html" target="_blank">in 1988.</a> Since then, we've had 31 years of scientific research, policy debates, and international agreements. Every international scientific and policy-making body recognizes climate change as an urgent and existential threat. And yet emissions have continued to rise, essentially without pause. <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRWmral-_YZp3SfEVPfc5PsFnHuoCQmzeW10bpJMPTtNYoo3zbBxz_rIege_xJncxaY9Y0vJEOlwI-m66TNICI8PC-HJwo-u-SiBtt-KKpszsyIROLDUdox0m1h3OFE5Q343wIFIAxNAC9/s1600/Presentation2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="540" data-original-width="720" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRWmral-_YZp3SfEVPfc5PsFnHuoCQmzeW10bpJMPTtNYoo3zbBxz_rIege_xJncxaY9Y0vJEOlwI-m66TNICI8PC-HJwo-u-SiBtt-KKpszsyIROLDUdox0m1h3OFE5Q343wIFIAxNAC9/s640/Presentation2.png" width="640" /></a></div>
<br />
I'm an optimist at heart. I always try to look at things in the best possible light. But at this point, it's starting to look like, if we were going to save ourselves, we would have done it by now.<br />
<br />
<i>Surely we will stop it. We might not stop it. What if we don't stop it?</i><br />
<br />
What happens if we don't take drastic action? Here is where I think that the scientific and journalistic institutions have failed to properly communicate the danger. Because the headline numbers—3 or 4 degrees Celsius, 2 meter sea-level rise by 2100—might not sound that bad at first. Why, exactly, are these numbers so scary?<br />
<br />
First of all, with a 4°C temperature rise, 74% of the Earth's population would experience <a href="https://www.nature.com/articles/nclimate3322" target="_blank">deadly heat waves every year</a>. <a href="https://www.nytimes.com/2019/08/08/climate/climate-change-food-supply.html" target="_blank">Multi-breadbasket failures</a> are possible, leading to mass famine. As much as 5% of the world's population could be <a href="https://www.pnas.org/content/111/9/3292" target="_blank">flooded every year</a> by 2100. These and other catastrophes could lead to as many as a <a href="https://www.unccd.int/sustainability-stability-security" target="_blank">billion climate refugees</a> by 2050.<br />
<br />
What would this level of disruption mean for human civilization? With one tenth of the world's population displaced, can nations still maintain their borders or their identities? Can governments survive if they can't provide food or <a href="https://e360.yale.edu/features/how-phoenix-is-preparing-for-a-future-without-colorado-river-water" target="_blank">freshwater</a> to their people? When "natural disasters" turn into <a href="https://www.phi.org/news-events/1339/climate-change-is-making-natural-disasters-worse-and-more-likely-how-do-we-protect-the-most-vulnerable" target="_blank">commonplace occurrences</a>, will the <a href="https://www.theonion.com/u-s-economy-grinds-to-halt-as-nation-realizes-money-ju-1819571322" target="_blank">collective fiction</a> known as "money" retain its value?<br />
<br />
Questions like these defy quantitative predictions, but based on these an other considerations, researchers have described increase of 5°C or more as posing "<a href="https://www.pnas.org/content/114/39/10315" target="_blank">existential threats to the majority of the population</a>". And while it is probably still possible to avoid this level of warming, doing so would require unprecedented economic transitions and global cooperation—and our track record so far does not give much reason for optimism.<br />
<br />
<i>We might not stop it.</i><br />
<br />
2019 is the year I started to mourn. The year I let myself consider that the civilization we have right now might be—likely will be—the best we will ever get. That our current society—for all its wonders and flaws—could be revealed as fossil-fueled mirage that collapses before we ever build something better to replace it. That, even if <i>homo sapiens</i> as a species survive, what we know of as human civilization could go up in smoke, fire, and water.<br />
<br />
Of course, the destruction will not be spread evenly, nor fairly. The countries most vulnerable to climate change, such as <a href="https://www.nationalgeographic.com/environment/2019/01/climate-change-drives-migration-crisis-in-bangladesh-from-dhaka-sundabans/" target="_blank">Bangladesh</a> and <a href="https://www.theguardian.com/environment/climate-consensus-97-per-cent/2015/dec/17/haitians-are-noticing-climate-change-impacts-on-extreme-weather-and-agriculture" target="_blank">Haiti</a>, are among those least responsible for creating it. Still, there is reason to doubt that the political and economic systems of the West will survive extreme climate change. Already, mass migration from the Middle East and Central America (<a href="https://www.nationalgeographic.com/news/2015/3/150302-syria-war-climate-change-drought/" target="_blank">driven in part</a> by <a href="https://www.nytimes.com/2019/04/13/world/americas/coffee-climate-change-migration.html" target="_blank">climate change</a>) have fueled the rise of the Far Right in Europe, Brexit in the UK, and the election of Donald Trump in the US. Currently, the US is holding thousands of these migrants in <a href="https://www.thenation.com/article/immigration-kids-trump-flores-concentration-camps/" target="_blank">concentration camps</a>, forcibly separated from their families. What will happen when migrants swell to 10% of the world's population, compounded with greatly increased fires, flooding, hurricanes, <a href="https://www.newscientist.com/article/2219981-how-deadly-disease-outbreaks-could-worsen-as-the-climate-changes/" target="_blank">epidemics</a>, and food shortages? How much strain, exactly, can our political and economic institutions take?<br />
<br />
What had you pictured for yourself and your loved ones in 2050? I had hoped to be rounding out my career as a mathematician, with a satisfying record of scientific accomplishment and well-taught students behind me. I had hoped to be watching my son thrive in the world with at least some of the advantages that had helped me succeed. But now I'm letting myself ask, what if my college, the university system, the country, the entire economy, are gone by then? What if all we leave the next generation is a command to survive, survive at all costs?<br />
<br />
I am not telling you to despair. Despair saps the will to act, and there is too much work to be done. The difference between 2°C vs 3°C, or between 3°C vs 4°C, is so great that we must be out in the streets causing disruption, fighting for our futures and our lives. We must also join with each other to become resilient, to form networks of preparedness, to help the most vulnerable, and to strategize how we will adapt to whatever change will come. I am not telling you that we cannot make a difference. I believe we can and we will, and I invite you to join me, and help me, in this struggle.<br />
<br />
But I also invite you to mourn. We can't truly grasp the urgency for action unless we emotionally grapple with the consequences of inaction. What, in human civilization, will you miss most? What will you wish we had fought harder to preserve? What imagined future will you be most heartbroken to discard?<br />
<br />
I wish you a joyous 2020, but also a mournful one. We must be clear-eyed about what we will lose, if we are to fight to preserve what we can.</div>
Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com0tag:blogger.com,1999:blog-8398797088391606752.post-89147601314135570792019-06-25T08:17:00.002-07:002019-06-26T10:08:42.915-07:00Andi's Factor Game<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="background-color: white; color: #1d2129; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; margin-bottom: 6px;">
Two weeks ago, my friend Andi messaged me about a mathematical game she had invented. She was so excited to share it. She had coded up a "proof of concept" version in html, and had come up with a mathematical proof about its winning strategies. She was enthusiastic about its potential to make math fun even for non-math people, and full of ideas for next steps.<br />
<br />
Then two days ago, I learned that Andi died. It seems that this game is one of the last things she put into the world. Although I didn't know her as well as I might have, her excitement about sharing this game seems to typify the passion and determination with which she approached all her projects. Andi was an uncompromising advocate for social justice with a poetic eye and a keen sense of humor. Also, she was a transgender woman; I say this because visibility matters and because I believe she would not want this aspect of her identity to be erased.<br />
<br />
The best way I can personally think of to honor Andi's memory is to share her final game with the world. Like any well-designed game, it is easy to play but difficult to master. The rules are deceptively simple:</div>
<div style="background-color: white; color: #1d2129; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; margin-bottom: 6px; margin-top: 6px;">
<br />
<ol style="text-align: left;">
<li>A large whole number, called the Magic Number, is specified and known to both players (it could be randomly generated by computer, for example). All factors of the Magic Number are listed out, including 1 and the number itself.</li>
<li>Two players take turns choosing factors of the Magic Number. Every time one player chooses a factor, that factor <i>and all multiples of it</i> are crossed out. Once a factor has been crossed out, neither player can choose it.</li>
<li>Whoever chooses 1 loses. In other words, the goal is to eliminate the factors in such a way that the other player is forced to choose 1.</li>
</ol>
</div>
<div style="background-color: white; color: #1d2129; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; margin-bottom: 6px; margin-top: 6px;">
<br />
For example, let's say the Magic Number is 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. These are all the numbers that can be chosen.<br />
<br />
Say player 1 choses 12 itself. Then 12 is eliminated, so the "board" looks like this:<br />
<br />
1 2 3 4 6 <strike><b>12</b></strike></div>
<div style="background-color: white; color: #1d2129; font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px; margin-bottom: 6px; margin-top: 6px;">
<br />
Now player 2 chooses 3. So 3 and all multiples of 3 are crossed out:<br />
<br />
1 2 <strike><b>3</b></strike> 4 <strike>6</strike> <strike>12</strike><br />
<br />
Next player 1 chooses 2. So 2 and all multiples of 2 are crossed out:<br />
<br />
1 <strike><b>2</b></strike> <strike>3</strike> <strike>4</strike> <strike>6</strike> <strike>12</strike><br />
<br />
Only the number 1 is left. Player 2 is forced to choose 1, so Player 1 wins.<br />
<br />
To visualize what's happening in this game, it helps to draw a diagram like this:<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYUgZY72IUuelh1e1YsIy90ZOSLTm5nEngcKDmlFAtMJ5_zzTIWgfh11VejbYPFfx0qvcWoF5Np1r0Yo4YO_A5dcxz-1XTbh9TYbFlQFjqI_Sr6O0kGIVKB1dyRZLS4esyT7STtQZu4GvS/s1600/FactorGame.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="720" data-original-width="720" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgYUgZY72IUuelh1e1YsIy90ZOSLTm5nEngcKDmlFAtMJ5_zzTIWgfh11VejbYPFfx0qvcWoF5Np1r0Yo4YO_A5dcxz-1XTbh9TYbFlQFjqI_Sr6O0kGIVKB1dyRZLS4esyT7STtQZu4GvS/s320/FactorGame.png" width="320" /></a></div>
Every time you a player picks a number, that number and all numbers downstream of it are eliminated. (Here "downstream" refers to the direction the arrows are pointing, which is visually upwards.) So, if 2 is picked, that eliminates 2, 4, 6, and 12. <br />
<br />
To mathematicians, a diagram like this is called a <a href="https://en.wikipedia.org/wiki/Lattice_(order)" target="_blank">lattice</a>. The game-play for a given Magic Number is determined by the structure of the lattice, which in turn is determined by the Magic Number's prime factorization, as you can see in this <a href="https://en.wikipedia.org/wiki/Partially_ordered_set?fbclid=IwAR1GlUevEZ_YeVgshzqfSQuhsWHst9Ffv228785tBV9gKQs3NatoPsqjKEA#/media/File:Birkhoff120.svg" target="_blank">lattice for 120</a>.<br />
<br />
But enough theory, go ahead and play! Here's a <a href="http://plektix.fieldofscience.com/p/factor-game-this-list-gets-expanded.html" target="_blank">link to the "proof of concept" version</a> that Andi coded up. You play against the computer, who goes first. To try again with a different Magic Number, click "New Game". You can put in whatever Magic Number you choose, or have the computer randomly pick one.<br />
<br />
Did you win? No, you didn't. But don't feel bad: Andi proved that, with optimal play, Player 1 will always win the game.<br />
<br />
It's a <a href="https://en.wikipedia.org/wiki/Proof_by_contradiction" target="_blank">proof by contradiction</a>. Assume, for the sake of contradiction, that for some particular Magic Number, Player 2 has a winning strategy. In other words, Player 2 has a winning response to any first move that Player 1 might make. In particular, if Player 1 chooses the Magic Number itself, Player 2 must be able to choose some other number—call it <i>n</i>—which puts them in a winning position. But then Player 1 could have chosen <i>n</i> as their first move, which would have put Player 1 in this same winning position. This contradicts our assumption that Player 2 has a winning response to any first move of Player 1. Therefore, by contradiction, Player 1 must win if both sides play perfectly.<br />
<br />
The interesting thing about this proof is that it's <a href="https://en.wikipedia.org/wiki/Constructive_proof#Non-constructive_proofs" target="_blank">non-constructive</a>. It says that there exists a winning strategy for Player 1, but gives no indication of what this winning strategy might be!<br />
<br />
Andi designed her code to search through all possible game outcomes for a winning one. While this guarantees that the computer always wins, it doesn't give much insight into how one <i>ought</i> to play, or why certain strategies might work better than others.<br />
<br />
There are many interesting open questions here: Can the winning strategy be described concisely? Is there a <a href="https://en.wikipedia.org/wiki/Time_complexity" target="_blank">polynomial-time algorithm</a> to find the winning strategy for a given Magic Number? And can the game be generalized to other kinds of lattices?<br />
<br />
Andi's final gift to the world is a good one. Her code is <a href="https://github.com/AndiBurns/Factor-Game" target="_blank">available on GitHub</a>; please use it and build on it if you are inspired. I hope she is remembered for this and for everything else she put out into the world.<br />
<br />
I'll close with this mathematical meditation, which was one of Andi's last Facebook posts:<br />
<br />
<div class="_1dwg _1w_m _q7o" style="font-family: inherit; padding: 12px 12px 0px;">
<div style="font-family: inherit;">
<div class="_5pbx userContent _3ds9 _3576" data-ft="{"tn":"K"}" data-testid="post_message" id="js_cfs" style="border-bottom: none; font-family: inherit; line-height: 1.38; margin-top: 6px; padding-bottom: 12px;">
<div style="display: inline; font-family: inherit;">
The set of rational numbers is continuous, in the sense that between any two distinct rational numbers, there exist more distinct rational numbers. If you only look at the rationals, you'll miss uncountably many reals. If you insist on defining reals in terms of rationals, you'll need to take rationals to their limits.</div>
</div>
</div>
</div>
<br />
Rest in Power.</div>
</div>
Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com1tag:blogger.com,1999:blog-8398797088391606752.post-73472284751092864952016-11-18T12:18:00.000-08:002016-11-18T13:43:00.651-08:00You can win the Electoral College with 22% of the vote<div dir="ltr" style="text-align: left;" trbidi="on">
Donald Trump is poised to become the next US president, despite the fact that Hillary Clinton received over a million more votes than him (and <a href="https://www.thenation.com/article/hillary-clintons-popular-vote-victory-is-unprecedented-and-still-growing/">counting</a>). This would mark the second time in sixteen years, and either the fourth or fifth time in history (<a href="https://en.wikipedia.org/wiki/List_of_United_States_presidential_elections_where_winner_lost_popular_vote">depending on how you count</a>) that the Electoral College winner has lost the popular vote.
<br />
<br />
How is it possible to win the Electoral College but lose the popular vote? The answer lies in a combination of two factors. The first is the winner-take-all nature of the state contests. All states except for Maine and Nebraska deliver all their electors to the candidate with the plurality of votes. This means that if you win by slim margins in a sufficient set of states, you can lose badly in all other states and still secure an Electoral College victory.<br />
<br />
The second factor is the disproportionate representation of small states. Each state has a number of electors equal to its total number of congresspeople (senators plus representatives). The number of representatives is roughly proportional to population size, but adding in the two senators per state gives the smaller states more per-capita representation. For example, Wyoming has approximately 7 electors per million elligible voters, while California has 2 per million. So a Wyomingite has more over three times the Electoral College representation of a Californian (calculations <a href="https://docs.google.com/spreadsheets/d/1Yr7QpSXdwBOtesfay5VKFSgvjY2pBKi0ZlwZOcuSV_w/edit?usp=sharing">here</a>).<br />
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So if you want to become president without winning the most votes, your strategy is to aim for narrow victories in a set of smaller states that add up to 270, while ceding the other states to your opponent. This begs the question: what is the smallest popular vote percentage one could receive while still winning the presidency?<br />
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The answer—according to my best calculations—is 22%. You could capture the Electoral College, and become President of the United States, with only 22% of the vote.<br />
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I got this number by starting with the states with the most electors per elligible voter (Wyoming, Vermont, Delaware, Alaska, ...). For each of these, I gave 50.1% of the vote to "Team Red", and the remaining 49.9% to "Team Blue". I continued down the list of states with the most electors per capita, giving 50.1% to Team Red, until the total electoral votes exceeded the 270 needed to win. I then gave Team Blue 100% of the vote for all other states. It turns out Team Red didn't need New Jersey, so I threw that over to Team Blue as well. The result: Team Blue captures 77.7% of the popular vote, but Team Red wins the Electoral College vote 270 to 268. You can check my math in <a href="https://docs.google.com/spreadsheets/d/1Yr7QpSXdwBOtesfay5VKFSgvjY2pBKi0ZlwZOcuSV_w/edit?usp=sharing">this spreadsheet</a>. My answer agrees with a <a href="https://web.archive.org/web/20111206194438/http://blog.cgpgrey.com/the-electoral-college">similar calculation</a> done in 2011.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitt0HWLGhiOj5HBHMAYK2u9REblhwyt-2MeHWTLIX_Qfxv_RU6o3OGPVy3BlE5I9PSrUZ6uFs6MtXg-gSjcByVBM0OzBix-uN7BdpSblhKp2lwKg_0DfLXvmoTZCuYjzlQF7sly5HL-YRF/s1600/Electoralmap.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="464" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitt0HWLGhiOj5HBHMAYK2u9REblhwyt-2MeHWTLIX_Qfxv_RU6o3OGPVy3BlE5I9PSrUZ6uFs6MtXg-gSjcByVBM0OzBix-uN7BdpSblhKp2lwKg_0DfLXvmoTZCuYjzlQF7sly5HL-YRF/s640/Electoralmap.png" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 1: One can capture the Electoral College with only 22.3% of the vote, by receiving 50.1% of the vote in the red states above and 0% in the blue states. </td></tr>
</tbody></table>
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<div class="separator" style="clear: both; text-align: center;">
</div>
It makes sense that the 22.3% figure is close to one quarter. If all states were equal in both population and electoral votes, one could tie the electoral college with slightly more than one quarter of the vote, by winning slightly more than half the vote in half the states, while losing the others completely (see below). The fact that one can win the US electoral map with <i>less</i> than 25% is due to the disproportionate representation of small states.<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVM0i-MXXdzZvNmwLIi-_8YRMZYkVNmEc8V4_85qWjUeuVIomBE_xr2n8imhGxhJexFT9JBevu6HpE7NLYSAou_V3p6tatxjM1UVgGhuoLecF7sx5wXN7smUxC7wFEdnaQqsRRG6IbuCvV/s1600/4statecollege.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgVM0i-MXXdzZvNmwLIi-_8YRMZYkVNmEc8V4_85qWjUeuVIomBE_xr2n8imhGxhJexFT9JBevu6HpE7NLYSAou_V3p6tatxjM1UVgGhuoLecF7sx5wXN7smUxC7wFEdnaQqsRRG6IbuCvV/s200/4statecollege.png" width="200" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 2: A hypothetical electoral map of four states with equal populations and electoral votes. Pie charts show the popular votes in each state. One can tie the electoral college with slightly more than 25% of the vote, by winning narrow majorities in two states and receiving no votes in the other two. </td></tr>
</tbody></table>
The above calculations assume that there are no third party candidates, and that voter turnout is the same in each state. Dropping these assumptions can lead to even more lopsided possibilities. For instance, with one third-party candidate, we only need to give Team Red 33.4% in the red states of Figure 1, while Team Blue and the third party each get 33.3%. This leads to an Electoral College win for Team Red with 14.9% of the vote. Alternatively, suppose that the turnout in the red states of Figure 1 is half that of the blue states. Then Team Red wins with 14.3% of the vote.<br />
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Of course, possible is not the same as likely. It would be very unlikely, for instance, for a candidate to receive 50.1% of the vote in Oklahoma but 0% in Texas. What does <i>not</i> seem unlikely, on the other hand, is that the Electoral College winner loses the popular vote. This has happened in <a href="https://en.wikipedia.org/wiki/List_of_United_States_presidential_elections_where_winner_lost_popular_vote">at least</a> 4 out of 58 elections, or 6.8%, which is not that rare of an occurrence. What we need to decide, as a country, is whether we support an electoral system that does not always align with the majority of votes.</div>
Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com6tag:blogger.com,1999:blog-8398797088391606752.post-60541803672553270622014-10-24T12:46:00.000-07:002014-10-26T14:58:23.875-07:00Information and Structure in Complex Systems<div dir="ltr" style="text-align: left;" trbidi="on">
Eight years ago, I had finished my first year of graduate school in math, and I was at a loss as to what to research. My original focus, differential geometry, was a beautiful subject to learn about, but the open research questions were too abstract and technical to sustain my interest. I wanted something more relevant to the real world, something I could talk to people about.<br />
<br />
Looking for new ideas, I took a course in complex systems, run by the<a href="http://necsi.edu/" target="_blank"> New England Complex Systems Institute</a>. The director, <a href="http://www.necsi.edu/faculty/bar-yam.html" target="_blank">Yaneer Bar-Yam</a>, had pioneered a new way of representing structure in a systems. I was fascinated by this idea but also puzzled. As a mathematician, I wanted to understand the basis of this idea. What assumptions does it rely on? How are its basic concepts defined? <br />
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My attempt to answer these questions turned into one of the longest and most demanding projects I’ve worked. After an eight-year collaboration Yaneer and my friend <a href="https://www.sunclipse.org/" target="_blank">Blake Stacey</a>, we finally have a <a href="http://arxiv.org/abs/1409.4708" target="_blank">preliminary manuscript</a> up on the web. It is currently under review for publication. And to my pleasant surprise, we got a nice <a href="https://www.sciencenews.org/blog/context/there%E2%80%99s-new-way-quantify-structure-and-complexity" target="_blank">write-up in ScienceNews</a>.<br />
<br />
So what is this project all about? The idea is that we're using <a href="http://en.wikipedia.org/wiki/Information_theory" target="_blank">information theory</a> (which I've <a href="http://plektix.fieldofscience.com/2008/03/information.html" target="_blank">written about</a> <a href="http://plektix.fieldofscience.com/2008/04/information-part-deux.html" target="_blank">previously</a>) as a tool to represent and quantify the structure of a system.<br />
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Before I explain what any of this means, let's consider some motivating examples. Here's a system (call it system <b>A</b>):<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs-JVnFU7YMSnRcoGkS4I1GsWWzM1L10yJqZngg3NHjECcIb1jkl-G6xH2GLlAZKbGOniPGyvQeS1pnd0ecbLSp82yc0DmIcChDRqEpag9Q-tmtB_Ky4voSJGARLHzMVyI1_-qvSUEGhEO/s1600/Ball.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgs-JVnFU7YMSnRcoGkS4I1GsWWzM1L10yJqZngg3NHjECcIb1jkl-G6xH2GLlAZKbGOniPGyvQeS1pnd0ecbLSp82yc0DmIcChDRqEpag9Q-tmtB_Ky4voSJGARLHzMVyI1_-qvSUEGhEO/s1600/Ball.gif" height="232" width="320" /></a></div>
You wouldn't really call this a <i>complex</i> system. It has only one component (a ball) that bounces around in a fairly simple way. Since there's not much to see here, let's turn to system <b>B</b>:<br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinx1jre-u7pwALZ34XY9Koo5CcCJnnwar5AWx8DuTUeMl9otCSJnRbYZS-VTkqcC12GeS6FSnPek99Vq0iFhoquXpzV9-rrlY2tniplOjh0ZylZ59o8hvhSk0vabBz8jhhYyj4PenwYUMC/s1600/Translational_motion.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEinx1jre-u7pwALZ34XY9Koo5CcCJnnwar5AWx8DuTUeMl9otCSJnRbYZS-VTkqcC12GeS6FSnPek99Vq0iFhoquXpzV9-rrlY2tniplOjh0ZylZ59o8hvhSk0vabBz8jhhYyj4PenwYUMC/s1600/Translational_motion.gif" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Source: <a href="http://commons.wikimedia.org/wiki/File:Translational_motion.gif" target="_blank">Wikimedia Commons</a></td></tr>
</tbody></table>
This system has many particles, which bounce around and bump into each other. In one sense, this system is quite complex: it is very difficult to describe or predict its exact state at any given time. But looking beyond the level of individual particles reveals a kind of simplicity: since the particles behave independently of each other, overall measures such as the average particle velocity or the rate of collisions are relatively stable. In other words, the individual complexity "averages out", so that on the whole, the system behaves quite simply.<br />
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Contrast that to the behavior of system <b>C</b>:<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK3QWZ3jJmmwfESwLZPSuXwO0bJQWen5x-P0MgYm09gbY3Dq7NWQ5r5BXNvlMjyK4qiVQP02q82bkLuwtzuctNMCW9I200LflyPo9W2c7b1_hOVUp8k4Tcsc3qyJow0RRYehuDCCzSMlyF/s1600/murmuration.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK3QWZ3jJmmwfESwLZPSuXwO0bJQWen5x-P0MgYm09gbY3Dq7NWQ5r5BXNvlMjyK4qiVQP02q82bkLuwtzuctNMCW9I200LflyPo9W2c7b1_hOVUp8k4Tcsc3qyJow0RRYehuDCCzSMlyF/s1600/murmuration.gif" height="132" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Source: <a href="http://vimeo.com/58291553" target="_blank">A Bird Ballet by Niels Castillon</a></td></tr>
</tbody></table>
This is a <a href="http://www.wired.com/2011/11/starling-flock/" target="_blank">murmuration of starlings</a>. The starlings fly in a semi-coordinated, semi-independent way, creating intricate shapes and patterns that you would never observe in systems <b>A</b> and <b>B</b>. This is a prototypical "complex system"—the kind that has intrigued researchers since the 70's. <br />
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It is intuitively clear that systems <b>A</b>, <b>B</b>, and <b>C</b> have entirely different kinds of structure. But it is surprisingly difficult to capture this intuition mathematically. What is the essential mathematical property of system <b>C</b> that can allow us to differentiate it from <b>A</b> and <b>B</b>?<br />
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We try to answer this question using information theory. Information theory was first invented by mathematician <a href="http://en.wikipedia.org/wiki/Claude_Shannon" target="_blank">Claude Shannon</a> in 1948 to address problems of long-distance communication (e.g. by telegraph) when some signals may be lost along the way. Shannon's ideas are still used, for example, in the development of cell phone networks. But they also have found applications in physics, computer science, statistics, and complex systems. <br />
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To explain the concept of information, let's look at a system consisting of a single blinking light:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLhQRmrMBorkSrGzrO1En0A5N4r3JrXeKqeOEWUWb-ZXYCXnDZU39y4i8PYyY8y6CcdTtSUHiPdg8IRvQrZl_J9T-BiRppq7PmsWV2LIbRm7S-yzjTIb9wS7B6iNnlDFz56ThBsCQVRi_7/s1600/Lights1blinking.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjLhQRmrMBorkSrGzrO1En0A5N4r3JrXeKqeOEWUWb-ZXYCXnDZU39y4i8PYyY8y6CcdTtSUHiPdg8IRvQrZl_J9T-BiRppq7PmsWV2LIbRm7S-yzjTIb9wS7B6iNnlDFz56ThBsCQVRi_7/s1600/Lights1blinking.gif" height="100" width="67" /></a></div>
This is one of the simplest systems you could possibly imagine. In fact, we can quantify this simplicity. To describe the state of the system at any given time, you only have to answer one yes/no question: "Is the light on?"<br />
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The amount of information conveyed in one yes/no question is called one <i>bit</i>. "Bit" is short for "binary digit", and is the same unit used to quantify computer memory. In other words, the state of this light can be described in one binary digit, 0 for OFF and 1 for ON.<br />
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Now let's add another light:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgspMz8mN85gXpyMzWjosOX2ikiURDWwByVbHV6bYGrsgXZ8kRiILdL4PIrbNOmmYXpQaSho01jS9KVbDvSBnBT4oSQZnhhbKhNin9XRZxEnNBmYuVju6xFkkuGz_DXEX1b0Njsn6Us6PBI/s1600/Lights2indep.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgspMz8mN85gXpyMzWjosOX2ikiURDWwByVbHV6bYGrsgXZ8kRiILdL4PIrbNOmmYXpQaSho01jS9KVbDvSBnBT4oSQZnhhbKhNin9XRZxEnNBmYuVju6xFkkuGz_DXEX1b0Njsn6Us6PBI/s1600/Lights2indep.gif" height="100" width="133" /></a></div>
Let's say these lights are statistically independent. This means that knowing the state of one doesn't tell you anything about the other. In this case, to identify the state of the system requires two bits of information—that is, two yes/no questions, one for the first light and one for the second. We can depict this situation with a diagram like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWgZ3uqU0XnuRcRqxqfhh8ospYPMHq_9nsodv4UZbp9pqM-bvNhULXbB_8AFUxRSa_7C_5PZJk-X7xWvWtSQLcVvav_IPI0p1gpLwpj8gKbBnSfPP8-K7BrG7TXSVPLNgp4Pm3KZOyM4EM/s1600/VennIndep.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgWgZ3uqU0XnuRcRqxqfhh8ospYPMHq_9nsodv4UZbp9pqM-bvNhULXbB_8AFUxRSa_7C_5PZJk-X7xWvWtSQLcVvav_IPI0p1gpLwpj8gKbBnSfPP8-K7BrG7TXSVPLNgp4Pm3KZOyM4EM/s1600/VennIndep.png" height="96" width="200" /></a></div>
The circles are drawn separately, since information describing one of them tells us nothing about what the other is doing. We could say that each of these bits applies at "scale one", since each describes only a single light bulb. <br />
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Here are two lights that behave in a completely different fashion:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiE8WTAKxUYzWtqARp_RJiYFxDZFX55_Dkq4yWc-RFRGtBViL4VitjYv0toYqUF1l1tmCe38edRLageiqfoW4mfEGj2nSguNkY5z9BGVV7DeDV1q_sWwpyU141DGtXqE3cj0vg5scBXj4d/s1600/Lights2dep.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjiE8WTAKxUYzWtqARp_RJiYFxDZFX55_Dkq4yWc-RFRGtBViL4VitjYv0toYqUF1l1tmCe38edRLageiqfoW4mfEGj2nSguNkY5z9BGVV7DeDV1q_sWwpyU141DGtXqE3cj0vg5scBXj4d/s1600/Lights2dep.gif" height="100" width="133" /></a></div>
Note that the two light bulbs are always either both on or both off. Thus, even though there are two components, the system can still be described by a single bit of information—a single yes/no question. The answer to this question (e.g. "are they on?") applies to both bulbs at once. The "information diagram" for this system looks like two completely overlapping circles:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJ3RojxrjUn0mMob9WURekE3SzrHT3soBp1VvYjVyVtw0A7bhef7tjtU6E4T77U1a-lfboOA_IZr0IvleSjCOGKgW3lEHU5W8mNI1zMUO44usMgFaUC60hyphenhyphen_9UxT3GAcngsQjE-A0uCvld/s1600/Venn2dep.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhJ3RojxrjUn0mMob9WURekE3SzrHT3soBp1VvYjVyVtw0A7bhef7tjtU6E4T77U1a-lfboOA_IZr0IvleSjCOGKgW3lEHU5W8mNI1zMUO44usMgFaUC60hyphenhyphen_9UxT3GAcngsQjE-A0uCvld/s1600/Venn2dep.png" height="100" width="104" /></a></div>
We could say that the one bit of information describing this system applies at "scale two", since it describes two light bulbs at once.<br />
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A more interesting case occurs between these two extremes:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8Vv-p_S7fIjKkKxN9Y75iL9rUIQyMSZpZ1I8oc2ksQIenuDGFpWYi62UA3sNSjSmKvfSArBKy0AL8DzWiEvdOcWwnu_jbLcMYUYB1DWNk5f8Bo932EDA1xYKFaYd90uIDn8uQn7ZqD3ex/s1600/Lights2partdep.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8Vv-p_S7fIjKkKxN9Y75iL9rUIQyMSZpZ1I8oc2ksQIenuDGFpWYi62UA3sNSjSmKvfSArBKy0AL8DzWiEvdOcWwnu_jbLcMYUYB1DWNk5f8Bo932EDA1xYKFaYd90uIDn8uQn7ZqD3ex/s1600/Lights2partdep.gif" height="100" width="133" /></a></div>
It's hard to see it, but I've animated these bulbs to be in the same state 3/4 of the time, and the opposite state 1/4 of the time. If I told you the state of the first bulb, you wouldn't completely know the state of the second, but you could make an educated guess. Specifically, if I told you the first bulb is ON, you could guess that the second is ON too, and you'd be right 75% of the time. So there is <i>information overlap</i>: Information about the first bulb gives <i>partial</i> information about the second. In fact, we can use <a href="http://en.wikipedia.org/wiki/Information_theory#Mutual_information_.28transinformation.29" target="_blank">Shannon's formulas</a> to actually calculate how much overlap there is: approximately 0.19 bits. So if you know the state of the first bulb (1 bit), then you also know 0.19 bits about the second bulb—not enough to know its state with certainty, but enough to make a guess that is 75% accurate. The overlapping information can be depicted like this:<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_E971SAbePthqY-qoUYQ3jzp86-oRvVhwcZV9Qfv7-VTO_hE2BtYrmq3sMTvuGSt2lOncbYFkmPETVI8QGcyJghtLRUzyVOW0jYezZy-BiVehl-ozrj4ZRLOQPGrC8roZO2Zx6T-eTbk/s1600/Venn2partdep.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjK_E971SAbePthqY-qoUYQ3jzp86-oRvVhwcZV9Qfv7-VTO_hE2BtYrmq3sMTvuGSt2lOncbYFkmPETVI8QGcyJghtLRUzyVOW0jYezZy-BiVehl-ozrj4ZRLOQPGrC8roZO2Zx6T-eTbk/s1600/Venn2partdep.png" height="100" /></a></div>
As you can see, 0.19 bits of information apply to both light bulbs at once (scale two), while the remaining 0.81+0.81=1.62 bits apply only to a single bulb (scale one).<br />
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In principle, these "information diagrams" (we call them<i> dependency diagrams</i>) exist for any system. Highly ordered systems, like system <b>A</b> above, have lots of overlapping, large-scale information. Highly disordered systems like <b>B</b> have mostly small-scale, non-overlapping information. The systems that are most interesting to complex-systems researchers, like the starlings in example <b>C</b>, have lots of partial overlaps, with information distributed over a wide range of scales. <br />
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And that's the basic premise of our theory of structure. The structure of a system is captured in the overlaps of information describing different components, and the way information is distributed across scales. While we take these concepts quite a bit further in our paper, the central idea is right here in these blinking lights. <br />
<br />
Thanks for reading!</div>
Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com8tag:blogger.com,1999:blog-8398797088391606752.post-68269480878890982012014-08-17T10:47:00.000-07:002014-10-26T18:37:51.061-07:00The time the cops pulled their guns on me<div dir="ltr" style="text-align: left;" trbidi="on">
This post is not about science.<br />
<br />
I'm writing this because the <a href="http://www.nytimes.com/interactive/2014/08/12/us/13police-shooting-of-black-teenager-michael-brown.html?hp&action=click&pgtype=Homepage&module=first-column-region&region=top-news&WT.nav=top-news&_r=0#/#time348_10373" target="_blank">horrific news</a> out of Ferguson, Missouri—the <a href="http://www.theroot.com/articles/culture/2014/08/new_witness_gives_her_account_of_michael_brown_shooting.html" target="_blank">killing of an unarmed man</a> and the subsequent assault on the <a href="http://www.nytimes.com/2014/08/14/us/missouri-teenager-and-officer-scuffled-before-shooting-chief-says.html" target="_blank">populace</a> and <a href="http://www.washingtonpost.com/politics/in-ferguson-washington-post-reporter-wesley-lowery-gives-account-of-his-arrest/2014/08/13/0fe25c0e-2359-11e4-86ca-6f03cbd15c1a_story.html" target="_blank">media</a>—has been bringing back memories an experience I had with the police ten years ago in Chicago.<br />
<br />
I should be clear about why I'm choosing to share this. It's not because I think my own problems are particularly deserving of attention in comparison to the violence done to Michael Brown, Eric Garner, and other recent victims of police violence. In fact, what I experienced was relatively tame in comparison. But that's kind of the point. This incident instantly brought my white privilege into sharp focus, in a way that has stuck with me ever since. Issues like racial profiling can be somewhat abstract for white people. I hope my story can open a new entry point into these issues for those who rarely experience them directly.<br />
<br />
After college, I joined <a href="http://plektix.fieldofscience.com/2008/06/wsj-teach-for-america-proves-that.html" target="_blank">Teach for America</a>. I was assigned to a high school on the West side of Chicago, where I taught math and coached the chess team. The school and the surrounding neighborhood were nearly 100% black. (Yep, Chicago is segregated.) It was also a rough neighborhood in the sense that drug dealers and prostitutes operated openly within a block of the high school, and students talked about gang warfare the way those at other schools might gossip about the Homecoming dance. I was not a great teacher in that environment, but I felt a strong bond with the students—especially with those on the chess team, who would squeeze into my tiny Civic every month or so to face off against other teams, often from much more affluent suburban schools.<br />
<br />
One Saturday, we got back to the West side around 10pm, and I decided to give each of the team members a ride home. After I dropped the last student off, I got back into the car to head home. But as I tried to start out, there was another car right next to me, blocking me into my parking space. And the driver was looking at me.<br />
<br />
I didn't know what they wanted. Maybe they wanted my parking spot. To try to get out of their way, I pulled forward a bit. But they moved in parallel, blocking me in again. We repeated this dance two or three times. They motioned to me to roll down my window. But seeing as I had no idea who they were, I thought this was probably a bad idea and kept my window shut.<br />
<br />
Then the driver and passenger got out, walked in front of my car, pulled guns out, and pointed them at me.<br />
<br />
As a child, I frequently had nightmares in which "bad guys" would shoot me with guns. I started to feel like I had slid into one of those nightmares. It didn't feel like reality—it felt like a dream that was happening to me. I thought maybe I was mistakenly mixed up in a criminal conspiracy, and they were going to kidnap me or worse.<br />
<br />
They shouted "PUT THE FUCKING CAR IN PARK!" I complied. Then one of them yanked open my car door and put his gun to my head (literally, it was touching my temple). He shouted "TAKE YOUR FUCKING SEATBELT OFF", which I did as well as I could given how much I was shaking. He then pulled me out, put me in handcuffs, and bent me over the trunk of their car.<br />
<br />
It was at this point that I realized I was probably dealing with the police, rather than some criminal organization. I told them I didn't know they were police. One of them responded "Who else would be going the wrong way down a motherfucking one way street?"<br />
<br />
Ummm, I guess this chain of logic might have occurred to me if I wasn't scared shitless by the fact that strangers were blocking me in and pointing guns at me. <br />
<br />
The other one, who still had his gun to my head, said "We don't want to hurt you, we just want to know your source!" I had no idea what they were talking about. I told them that I was a math teacher at the local high school. His response was "Oh yeah? Well how long have you been doing heroin?" They continued to interrogate me and searched my pockets as I told them about the chess team, the tournament, and the student I had just dropped off. <br />
<br />
After a minute or so, it became clear to them that I was not, in fact, a heroin user. It was remarkable how quickly I shifted in their view from "junkie" to "white do-gooder". Within sixty seconds, their tone of voice changed, they took me out of cuffs, and their started explaining why they had taken the approach that they did.<br />
<br />
Their explanation went like this: The corner where I had dropped of this student was a well-known herion point. White people are so rare in this neighborhood that those who are around after dark are usually there for the drugs. Transactions often occur in the buyer's car, with the buyer driving the dealer around the block as the deal is made. So I fit the profile of a heroin buyer. When I failed to stop for them, they escalated by getting out and drawing guns. When I continued to creep my car forward towards them (unintentionally, since I had no idea what I was doing at that point), they felt they had to escalate further my opening the door and putting a gun to my head.<br />
<br />
It almost makes sense, except that <i>they never identified themselves as cops.</i> They were in an unmarked car and never bothered to show me a badge. Because they read me as a heroin junkie, they assumed I would be familiar with the routine of being pulled over by an unmarked car. Just to emphasize the point: <i>They were quicker to pull their guns on me than to show me any kind of police identification.</i><br />
<br />
The next week, I told the chess team what happened during practice. I'll never forget what one of them said to me next: "Mr. Allen, I'm sorry you had to go through that, but you know what that makes you? A <i>black man</i>. We go through that shit every day." He then told me about a time the cops made him strip to his underwear and stand outside in the middle of winter for hours, cuffed to a police car, before they released him without charge. All of my students had stories. They all had stories of the cops treating them as if their time, their dignity, and even their lives were worthless.<br />
<br />
I did end up filing a complaint with the Chicago Police Department, but I was unable to ID the officers. I had (and still have) a clear mental picture of one of them, but none of the photos they showed me matched him. So the case was dropped.<br />
<br />
What do I take from this experience? For one thing, some very real anxiety. It still haunts me sometimes when I'm trying to sleep, and I was shaking when typing this out. But I also try to accept it as an alternate-reality window into something I would never have otherwise experienced. For a brief moment in time, the usual dynamics were reversed: I was profiled for being a white person in an all-black neighborhood. Because of the color of my skin and the block I was on, the cops read me as a criminal and treated me like one. But only for about a minute. Once they realized I was not a junkie, my white privilege reasserted itself and suddenly they were there to <i>serve</i> rather than threaten me. <br />
<br />
As a white person with financial and educational privilege to boot, I can be reasonably certain that I will not experience such an incident again, unless I choose to return to a situation like urban teaching in which the usual rules become twisted. But imagine (and I'm talking to white folks here) if you had no choice. Imagine if you could never tell whether the cops—the people who are supposed to protect you—would arbitrarily read you as a criminal and decide to <i>threaten your life</i> before even explaining who they are or what they want. Imagine how that might change your concept of safety, the way you present yourself outside, or even your plans for any given evening. That is the reality that my chess team described to me. It is the reality that underlies the headline-grabbing incidents like Michael Brown, Eric Garner, or Trayvon Martin. It is the reality that millions of people live every day.</div>
Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com4tag:blogger.com,1999:blog-8398797088391606752.post-72447818505118321622014-04-07T19:33:00.000-07:002014-04-08T06:18:21.619-07:00Brian Arthur's vision of Complexity Economics<div dir="ltr" style="text-align: left;" trbidi="on">
My friend <a href="http://www.dariaroithmayr.com/" target="_blank">Daria Roithmayr</a> alerted me to a <a href="http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CCsQFjAA&url=http%3A%2F%2Ftuvalu.santafe.edu%2F~wbarthur%2FPapers%2FComp.Econ.SFI.pdf&ei=60pDU_SsOZK_sQTmg4CYDw&usg=AFQjCNEryzaX6pfQo87B4DnGhtPeQc9ZWA&sig2=S55wcoM5LC9NZZKaX3ZE-Q&bvm=bv.64367178,d.cWc&cad=rja" target="_blank">working paper </a>of <a href="http://tuvalu.santafe.edu/~wbarthur/" target="_blank">Brian Arthur</a> laying out a vision for a new approach to studying economics. Brian Arthur is one of the pioneers of complex systems thought, and has devoted his life to understanding what <i>really </i>happens in our economy, and why this behavior is so different from what classical economics predicts.<br />
<br />
Classical economics is a theory based on the concept of equilibrium. Equilibrium, in economics, is a state in which everyone is doing the best thing they could possibly do, relative to what everyone else is doing. And since everyone is doing the best possible thing, no one has incentive to change. So everything stays the same. Forever.<br />
<br />
Okay, that doesn't sound much like our actual economy. So why is the equilibrium concept so central to economics? The answer is that equilibria can be <i>calculated. </i>If you make certain simplifying assumptions about how economic actors behave, you can prove that exactly one equlibrium exists, and you can calculate exactly what every actor is doing in this equilibrium. This allows economics to make predictions. <br />
<br />
These predictions are useful in explaining many broad phenomena—for example, the relationship between supply, demand, and price. But they exclude any possibility of movement or change, and therefore exclude what is really interesting (and lucrative!) about the economy. Arthur explains it this way:<br />
<blockquote class="tr_bq">
We could similarly say that in an ocean under the undeniable force of gravity an approximately equilibrium sea level has first-order validity. And this is certainly true. But, as with markets, in the ocean the interesting things happen
not at the equilibrium sea level which is seldom realized, they happen on the surface where ever-present disturbances cause further disturbances. That, after all, is where the boats are. </blockquote>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg68yAXu_eHU8KTpwV7MQB4D8Y6k8r0msLRecfWFYg1qvpUinOPWSVlNqdVRJX78ZrQotRoIyAGF1c_fTF3RAdteBBqdhDvJIwrngbBgG8x2tLNcmvBL0YDBUmvNVRPICE1S4QXfrrMtm8X/s1600/Slide1.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg68yAXu_eHU8KTpwV7MQB4D8Y6k8r0msLRecfWFYg1qvpUinOPWSVlNqdVRJX78ZrQotRoIyAGF1c_fTF3RAdteBBqdhDvJIwrngbBgG8x2tLNcmvBL0YDBUmvNVRPICE1S4QXfrrMtm8X/s1600/Slide1.jpg" height="200" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.youtube.com/watch?v=avaSdC0QOUM" target="_blank">T-Pain</a> understands the need for nonequilibrium theories.</td></tr>
</tbody></table>
<br />
<br />
The vision of economics that Arthur lays out is based not on equilibrium, but on <i>computation:</i><br />
<blockquote class="tr_bq">
A better way forward is to observe that in the economy, current circumstances form the conditions that will determine what comes next. The economy is a system whose elements are constantly updating their behavior based on the present situation.
To state this in another way, formally, we can say that the economy is an ongoing computation—a vast, distributed,
massively parallel, stochastic one. Viewed this way, the economy becomes a system that evolves procedurally in a series
of events; it becomes algorithmic.</blockquote>
The part of this essay that was most challenging to me personally was where he talks about the limitations of mathematics:<br />
<br />
<blockquote class="tr_bq">
...the reader may be wondering how the study of such computer-based worlds can qualify as economics, or what relationship this might have to doing theory. My answer is that theory does not consist of mathematics. Mathematics is a technique, a tool, albeit a sophisticated one. Theory is something different. Theory lies in the discovery, understanding, and
explaining of phenomena present in the world. Mathematics facilitates this—enormously—but then so does computation. Naturally, there is a difference. Working with equations allows us to follow an argument step by step and reveals conditions a solution must adhere to, whereas computation does not. But computation—and this more than compensates—allows us to see phenomena that equilibrium mathematics does not. It allows us to rerun results under different conditions, exploring when structures appear and don’t appear, isolating underlying mechanisms, and simplifying again and again to extract the bones of a phenomenon. Computation in other words is an aid to thought, and it joins earlier aids in economics—algebra, calculus, statistics, topology, stochastic processes—each of which was resisted in its time.</blockquote>
He later explains the limitations of mathematics with an analogy to biology:
<br />
<blockquote>
Even now, 150 years after Darwin’s Origin, no one has succeeded in reducing to an equation-based system the process by which novel species are created, form ecologies, and bring into being whole eras dominated by characteristic species. The reason is that the evolutionary process is based on mechanisms that work in steps and trigger each other, and
it continually defines new categories—new species. Equations do well with changes in number or quantities within given
categories, but poorly with the appearance of new categories themselves. Yet we must admit that evolution’s central mechanisms are deeply understood and form a coherent group of general propositions that match real world observations, so these understandings indeed constitute theory. Biology then is theoretical but not mathematical; it is process-
based, not quantity-based. In a word it is procedural. By this token, a detailed economic theory of formation and
change would also be procedural. It would seek to understand deeply the mechanisms that drive formation in the economy and not necessarily seek to reduce these to equations. </blockquote>
Or, as <a href="http://stuartkauffman.com/" target="_blank">Stuart Kauffman</a> asked me when I told him about my mathematical biology research, "Can any of your equations predict rabbits fucking?"</div>
Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com1tag:blogger.com,1999:blog-8398797088391606752.post-17220602053381693872014-01-20T18:08:00.000-08:002014-01-20T19:07:38.714-08:00How natural processes can create meaning<div dir="ltr" style="text-align: left;" trbidi="on">
The project of science is largely about asking <i>why</i> things happen. We seek causal explanations: Why do planets follow elliptical orbits? Why does water become solid in cold temperatures?<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAtWsZmxmqKva9mv066x-EEPjeYtLhIYrJn2exCJiwnrSjL4G2q11bYNT9EWwL2NMNiUA_gX6y5dm5Ot9_CvNB3hcEhi6auABV0_gpB6MyaNXwfC97Tf4XwcEcd8F17Gp8F4Oy5L5SsmNH/s1600/because-science.american-apparel-unisex-fitted-tee.black.w760h760.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAtWsZmxmqKva9mv066x-EEPjeYtLhIYrJn2exCJiwnrSjL4G2q11bYNT9EWwL2NMNiUA_gX6y5dm5Ot9_CvNB3hcEhi6auABV0_gpB6MyaNXwfC97Tf4XwcEcd8F17Gp8F4Oy5L5SsmNH/s1600/because-science.american-apparel-unisex-fitted-tee.black.w760h760.jpg" height="320" width="320" /></a></div>
<br />
Historically, this project has been largely <i>reductionist</i> in its approach. That is, scientists have generally taken the view that phenomena can be explained in terms of smaller components. We can understand how molecules behave by looking at their atoms; we can understand how atoms behave by looking at subatomic particles, etc. This program has been extremely productive: we can explain <a href="http://en.wikipedia.org/wiki/Tide" target="_blank">why oceans have tides</a> and <a href="http://en.wikipedia.org/wiki/Prism" target="_blank">why prisms make rainbows</a>. Because of this success, some people believe that science will eventually be able to explain everything this way. They argue that, if we can just understand matter at its tiniest level—quarks or whatever else is smaller than them—explanations for everything else will follow as a matter of course.<br />
<br />
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjncPeFCjyKJQUbEDpBsbHagi4rWipLKyb1QaGPbLy_rk1iq_7XFjY8xeL6sWRS9RVtpuigyVremJxf8Ab5kAIR1JiybbsSNaTNVGQIExTpCC6SQPnJWf9aGexStb0vFksNNoOViUImNzc5/s1600/Duck_of_Vaucanson.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjncPeFCjyKJQUbEDpBsbHagi4rWipLKyb1QaGPbLy_rk1iq_7XFjY8xeL6sWRS9RVtpuigyVremJxf8Ab5kAIR1JiybbsSNaTNVGQIExTpCC6SQPnJWf9aGexStb0vFksNNoOViUImNzc5/s1600/Duck_of_Vaucanson.jpg" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A postulated interior of the <a href="http://en.wikipedia.org/wiki/Digesting_Duck" target="_blank">Duck of Vaucanson</a> (1738-1739) by an American observer. SOURCE: Wikimedia Commons</td></tr>
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I encounter this extreme view not so much in academic papers, but moreso in casual conversations among people who want to ground their arguments in science. It seems to be a common "move" to argue that some concept is meaningless or illusory, because it can ultimately be reduced to the level of atoms, genes, or some other constituent entity. Jerry Coyne, for example, argues in a <a href="http://www.edge.org/response-detail/25381" target="_blank">recent essay </a>that free will does not exist, because our brains are composed of atoms that must obey the laws of physics.<br />
<br />
I argue that this extreme reductionism does not make for convincing arguments, on two grounds. (I should pause to say that the ideas here are heavily influenced by many other thinkers—<a href="http://en.wikipedia.org/wiki/Stuart_Kauffman" target="_blank">Stuart Kauffman</a> in particular.) The first is that understanding the behavior of the parts of a system doesn't necessarily imply an understanding of the behavior of the whole. This is a result of <a href="http://en.wikipedia.org/wiki/Chaos_theory" target="_blank">chaos theory.</a> It can be shown that most systems with many interacting parts are chaotic, meaning that even if one could measure the present behavior of each component to within arbitrary precision, this would not suffice to predict the system's behavior for more than a brief window of time. Any initial inaccuracies in measurement rapidly compound until all predictive power is lost. (This is the famous "<a href="http://en.wikipedia.org/wiki/Butterfly_effect" target="_blank">butterfly effect</a>": the future can be changed by a flap of a butterfly's wings.) Additionally, quantum effects add another source of indeterminacy to any physical system. Thus it is impossible, for example, to predict the advent of <a href="https://www.youtube.com/watch?v=F5FEj9U-CJM" target="_blank">mantis shrimp</a> or David Bowie by starting from the Big Bang and applying the laws of physics. These entities do not <i>contradict</i> the laws of physics, but they're not predicted by them either. (Okay, maybe Bowie contradicts the laws of physics just a little bit.)<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9VKfEnoAHSSgAzJgzvhaD8RBFPiL5NCrgepYyqtJIHDVRRxrl_eU2VmJ2WVWgoQY3tS26jNS2qhA8Wdhfk_c21Bra9f5OY3fJw-sWzJfW04meVr7Rkm-i36AEETc2TIHxX1G1EyO7ndvW/s1600/David-Bowie-stripes2.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9VKfEnoAHSSgAzJgzvhaD8RBFPiL5NCrgepYyqtJIHDVRRxrl_eU2VmJ2WVWgoQY3tS26jNS2qhA8Wdhfk_c21Bra9f5OY3fJw-sWzJfW04meVr7Rkm-i36AEETc2TIHxX1G1EyO7ndvW/s1600/David-Bowie-stripes2.jpg" height="400" width="298" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The laws of physics do not predict this hotness.</td></tr>
</tbody></table>
<br />
The second ground—and the idea I most want to explore here—is the following:<br />
<br />
<div style="text-align: center;">
<i>Natural processes create new reasons for things to happen.</i><br />
<br />
<div style="text-align: left;">
The prime example of this is evolution. Consider, for example, a bacterium swimming up a glucose gradient—perhaps the simplest goal-directed behavior in nature. The bacterium senses more glucose on one of its sides than the other, and swims in the direction of more glucose. What would we say is the <i>reason</i> for this behavior? One could investigate the physics and chemistry of the bacterium and identify mechanisms that cause it to move this way. But this does not explain the apparent agency in the bacterium's movement. The more satisfying explanation appeals to evolution: it moves toward greater sugar concentrations because evolution has provided it this mechanism to find food in order to reproduce.<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOV0c-EeTwVkomSceksH2pj7sph2MEh4fY7mSIt-ogpAGsKKO3ZE_OG-hGmlQpRGUGl21F5L_27sOCtQDCAlXdJtPrdj19DOUDYARJ45f-jd3Ilm4pakxc2phItax8XjVemqGY7CP1xlkU/s1600/find_food.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOV0c-EeTwVkomSceksH2pj7sph2MEh4fY7mSIt-ogpAGsKKO3ZE_OG-hGmlQpRGUGl21F5L_27sOCtQDCAlXdJtPrdj19DOUDYARJ45f-jd3Ilm4pakxc2phItax8XjVemqGY7CP1xlkU/s1600/find_food.gif" height="251" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Simulation of bacteria undergoing biased random walk toward a food source. SOURCE: <a href="http://www.mit.edu/~kardar/teaching/projects/chemotaxis%28AndreaSchmidt%29/finding_food.htm" target="_blank">http://www.mit.edu/~kardar/teaching/projects/chemotaxis%28AndreaSchmidt%29/finding_food.htm</a></td></tr>
</tbody></table>
Notice, however, that this explanation only makes sense on the level of the whole organism. The carbon and other atoms that comprise this bacterium do not act as if they had any goal. Only the bacterium as a whole appears to be goal-oriented. Thus reductionism completely fails to explain the bacterium's behavior. Evolution—a natural and spontaneous process—has created a new reason for something to happen. This reason applies to the whole organism, but not to its parts.<br />
<br />
Once we accept that natural processes create new reasons for things to happen, many new questions arise. For instance, do different kinds of evolutionary processes create different reasons? Yes! It turns out that evolution in spatially dispersed populations can <a href="http://elife.elifesciences.org/content/2/e01169" target="_blank">select for cooperative behaviors</a> that would be disfavored if all individuals were mixed together. So the explanation "it behaves that way in order to help its neighbors" makes sense under some evolutionary conditions but not others.<br />
<br />
We can also ask what other kinds of processes can create new causal explanations. Humans, for instance, engage in many activities that do not seem to be directly related to survival or reproduction; I would argue that this is due to a complex process in which <a href="http://en.wikipedia.org/wiki/Dual_inheritance_theory" target="_blank">our genes co-evolved with our cultures</a>. <br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1wBkBvSx4FIRma48cBlSGmC-yoXVFu2OTUAF-oBOft2KiZoKE-1udQpn0uIRY6Dq4qBCTItCWZXE7_Xbc0Ma4qlOjUJjexUY8AjEAziAtXBUIe7WO5oRelr6BH7Ub1a1gHw1Jlq1Vycbw/s1600/pardonme.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi1wBkBvSx4FIRma48cBlSGmC-yoXVFu2OTUAF-oBOft2KiZoKE-1udQpn0uIRY6Dq4qBCTItCWZXE7_Xbc0Ma4qlOjUJjexUY8AjEAziAtXBUIe7WO5oRelr6BH7Ub1a1gHw1Jlq1Vycbw/s1600/pardonme.gif" height="215" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This man wants a slippery butt, but the individual cells that comprise him do not much care how slippery his butt is. SOURCE: <a href="http://threewordphrase.com/pardonme.htm" target="_blank">Three Word Phrase</a> by Ryan Pequin</td></tr>
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In short, nature can be creative. Not only can it create new objects and life forms, it can also create new <i>meanings</i>, in the sense of reasons for things to happen. These new meanings arise via naturally occurring processes that are consistent with—but not predicted by—the laws of physics. These processes can even generate new, higher-level processes, which then create additional new layers of meaning. If we, as scientists and as humans, want to understand why things happen, we must first understand the multiple, distinct ways that meaning and causality can arise. </div>
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Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com2tag:blogger.com,1999:blog-8398797088391606752.post-42111195514818154532013-12-03T15:02:00.000-08:002013-12-03T15:06:08.085-08:00What's the deal with inclusive fitness theory?<div dir="ltr" style="text-align: left;" trbidi="on">
You may not be aware of it, but there is a battle afoot in the theory of evolution. The fight is over inclusive fitness theory—an approach to studying the evolution of cooperation. I, together with mathematical biologist Martin Nowak and naturalist E. O. Wilson, just published an <a href="http://www.pnas.org/content/early/2013/11/22/1317588110.abstract" target="_blank">article</a> pointing out weaknesses in the theory, and suggesting that it might not tell us much about why cooperation actually evolves. This is my attempt to explain the controversy—and our new paper—to those who may not know anything about it.<br />
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The essential question is, "Why do organisms sometimes help others at a cost to themselves?" Such helping behaviors have been observed from microbes to insects to humans. At first glance, these behaviors may appear to contradict natural selection, since the cost of helping reduces the chances that the behavior is passed on to offspring. <br />
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Theorists have identified a <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3279745/" target="_blank">number of different ways</a> that costly helping can actually be favored by natural selection. One way is if the help is primarily directed toward close relatives. These relatives have a good chance of sharing the "helping" gene, so that help increases the overall prevalence of this gene. This mechanism is called <i>kin selection</i>.<br />
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Inclusive fitness theory is one way of representing the idea of kin selection. Let's say you have some gene that makes you sacrifice your time and energy to help others. This help affects <i>fitness</i>—the number of healthy offspring you produce. ("Healthy" offspring are the ones that will eventually grow up and have offspring of their own.) The first idea is to split fitness into the offspring that you produce on your own, and those which can be attributed to help from others:<br />
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The idea of <i>inclusive</i> fitness is to disregard the offspring that others help you produce, but instead count the ones that <i>you</i> help <i>others</i> produce:<br />
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To determine the overall effect on the helping gene, offspring that you help others produce must be weighted by the probability that they share the helping gene, which can be interpreted as your "relatedness" to them. (For example, help you give to your siblings is weighted by one-half, equal to the probability that you inherited the same parental copy of the helping gene.) Adding up these amounts of help times relatedness gives your <i>inclusive fitness</i>. In some simplified models, it can be shown that natural selection favors organisms that have the highest inclusive fitness. <br />
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At this point you may be asking "Wait, does it really make sense to divide offspring into those produced on one's own versus those produced by help from others?" This is exactly the problem! Aside from the obvious point that no one reproduces without help in sexual species, nature is full of synergistic and nonlinear interactions, so that making clean divisions like this is impossible in most situations. Thus the idea of inclusive fitness theory only works in simplified toy models of reality. <br />
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Nowak and Wilson, together with mathematician Corina Tarnita, made this point forcefully in a 2010 <a href="http://www.nature.com/nature/journal/v466/n7310/full/nature09205.html" target="_blank">Nature</a> <a href="http://ped.fas.harvard.edu/people/faculty/publications_nowak/NowakNature2010.pdf" target="_blank">article</a>. In response, more than 100 authors signed a letter saying that inclusive fitness theory has no limitations, and is as general as natural selection itself. (There were also <a href="http://whyevolutionistrue.wordpress.com/2010/08/30/a-misguided-attack-on-kin-selection/" target="_blank">heated</a> <a href="http://www.myrmecos.net/2010/09/14/whats-the-big-deal-with-nowak-tarnita-and-wilson/" target="_blank">blog</a> <a href="http://www.biasedtransmission.org/2012/04/e-o-wilson-and-inclusive-fitness-theory-two-minute-summary.html" target="_blank">posts</a> and a <a href="https://www.youtube.com/watch?v=zHYsTSmD84w&feature=youtube_gdata_player" target="_blank">talking bear video</a>!) <br />
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What are we to make of this claim that inclusive fitness theory has no limitations at all? This claim turns out to be based on the idea that, however complex the interactions are in nature, one can always use linear regression to split one's offspring into those attributable to oneself versus others.<br />
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Our <a href="http://www.pnas.org/content/early/2013/11/22/1317588110.abstract" target="_blank">new paper</a> shows that this approach is not exactly wrong, but nonsensical. To see why, let's consider a hypothetical helping trait (call it Trait X), and see if this approach can tell us whether and how this trait is selected for. <br />
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Can the this method predict whether Trait X will succeed in evolution? No, because in order to even set up the regression, one must know in advance whether it succeeds not. The whole method is based on retrospectively analyzing known results of natural selection, and so it logically cannot predict anything new.<br />
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Ok, so if we must know in advance whether or not Trait X is favored, can this method at least help us understand why it succeeds or fails? The answer is no again, at least not in general. The reason is that the regression method looks for correlations between having type X as a partner and having high fitness. If there is a positive correlation, this method says that trait X is "altruistic". But as any statistics student knows, correlation does not imply causation. In fact, it is easy to come up with examples where the regression method misidentifies the nature of a trait.<br />
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For example, suppose Trait X is actually a jealous trait—if you have it, it makes you want to find high-fitness individuals and attack them, reducing their fitness as well as your own. A hypothetical example with numbers is illustrated here:<br />
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The greenish numbers are the fitnesses before the attack; while the red numbers indicate the results of the attack. The individual with Trait X (indicated in red) found the highest-fitness individual (5, in this case) and attacked him, reducing each of their fitnesses by one. But since the attacked individual still has fitness 4, there is a positive correlation between having Trait X as your partner and having high fitness. So the regression method calls this "altruism" when it clearly is not. <br />
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In short, the regression method generates a "just-so-story", which is often wrong, for an outcome that is already known. The fact that this method is trumpeted as <a href="http://onlinelibrary.wiley.com/doi/10.1111/j.1420-9101.2011.02236.x/pdf" target="_blank">"the very foundation of social-evolution theory"</a> indicates a weird state of affairs in this corner of biology. My reading is that many researchers fell in love with inclusive fitness theory (which admittedly can be elegant and intuitive when it works), and tried to stretch it to include all of natural selection. Similar problems exist in economics, in that some researchers fall in love with the elegant mathematics of their theories and forget that they may not always apply to the real world.<br />
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I'm not proposing that we replace inclusive fitness theory with some other all-encompassing theory or framework. Rather, I'm suggesting that the method of analysis be tailored to the problem at hand. A <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3279745/" target="_blank">variety of mechanisms</a> can support the evolution of cooperation, and a variety of approaches are needed to understand them. The only truly general theory in evolutionary biology is the theory of evolution itself. <br />
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<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft_id=info%3Apmid%2F24277847&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=Limitations+of+inclusive+fitness.&rft.issn=0027-8424&rft.date=2013&rft.volume=&rft.issue=&rft.spage=&rft.epage=&rft.artnum=&rft.au=Allen+B&rft.au=Nowak+MA&rft.au=Wilson+EO&rfe_dat=bpr3.included=1;bpr3.tags=Biology%2CMathematics%2CEvolutionary+Biology%2C+Applied+Mathematics">Allen B, Nowak MA, & Wilson EO (2013). Limitations of inclusive fitness. <span style="font-style: italic;">Proceedings of the National Academy of Sciences of the United States of America</span> PMID: <a href="http://www.ncbi.nlm.nih.gov/pubmed/24277847" rev="review">24277847</a></span> <br />
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<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Journal+of+evolutionary+biology&rft_id=info%3Apmid%2F21371156&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=The+genetical+theory+of+kin+selection.&rft.issn=1010-061X&rft.date=2011&rft.volume=24&rft.issue=5&rft.spage=1020&rft.epage=43&rft.artnum=&rft.au=Gardner+A&rft.au=West+SA&rft.au=Wild+G&rfe_dat=bpr3.included=1;bpr3.tags=Biology%2CEvolutionary+Biology">Gardner A, West SA, & Wild G (2011). The genetical theory of kin selection. <span style="font-style: italic;">Journal of evolutionary biology, 24</span> (5), 1020-43 PMID: <a href="http://www.ncbi.nlm.nih.gov/pubmed/21371156" rev="review">21371156</a></span> <br />
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<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Nature&rft_id=info%3Apmid%2F20740005&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=The+evolution+of+eusociality.&rft.issn=0028-0836&rft.date=2010&rft.volume=466&rft.issue=7310&rft.spage=1057&rft.epage=62&rft.artnum=&rft.au=Nowak+MA&rft.au=Tarnita+CE&rft.au=Wilson+EO&rfe_dat=bpr3.included=1;bpr3.tags=Biology%2CMathematics%2CEvolutionary+Biology%2C+Applied+Mathematics">Nowak MA, Tarnita CE, & Wilson EO (2010). The evolution of eusociality. <span style="font-style: italic;">Nature, 466</span> (7310), 1057-62 PMID: <a href="http://www.ncbi.nlm.nih.gov/pubmed/20740005" rev="review">20740005</a></span>
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Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com7tag:blogger.com,1999:blog-8398797088391606752.post-28836239102129312872012-04-29T15:54:00.001-07:002012-05-05T20:30:10.474-07:00On math and magic<div style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;">
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I've been on a kick lately of re-reading my old favorite fantasy novels. I started with some of Lloyd Alexander's <a href="http://en.wikipedia.org/wiki/The_Chronicles_of_Prydain">Prydain Chronicles</a>, and am now going back through Ursula K. LeGuin's Earthsea Trilogy. I haven't touched this books—or anything in the fantasy genre—since my early teens, and its been interesting to see how differently I relate to them now.<br />
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<tr><td class="tr-caption" style="text-align: center;">...from another former obsession </td></tr>
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One moment in particular struck me. In LeGuin's <i>A Wizard of Earthsea</i>, there's a scene in which a young apprentice-mage sneaks a look at his master's dusty old spellbooks and becomes transfixed by the ancient runes inside. I realized that the visceral feeling evoked by this passage (and others like it throughout the fantasy genre) is exactly what I felt as a college freshman exploring the math section of my undergraduate science library. I would spend hours at a time browsing dusty old math books, the more arcane the better, trying to decipher their internal logic. Yes, I wanted to learn new math, but I was also hooked on the feeling of being lost in these mysterious tomes. Like the mage's spellbooks, these math books contained strange symbols describing deep and powerful truths, which could only be understood through long, deep study.<br />
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<tr><td class="tr-caption" style="text-align: center;">A sample from a recent <a href="http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CDEQFjAA&url=http%3A%2F%2Fwww.people.fas.harvard.edu%2F%7Eballen%2FGraphMutInPress.pdf&ei=ncSdT4H_M-i16AHckpXmDg&usg=AFQjCNF2wZ4B4r164AUntTDDDlQ47u52BQ&sig2=yKjfWTrdSMeEk0ywe68Frw" target="_blank">article</a> of mine. Doesn't math look cool?</td></tr>
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Reflecting back on these moments highlights how my relationship to mathematics has changed. I was initially drawn to math because of its beauty, elegance, mystery, and because it contained a kind of absolute truth. But after teaching for three years and studying differential geometry for one, I found that abstract beauty and truth were no longer enough to sustain my excitement. I wanted to discover and describe important patterns in the world, not just relationships between abstract constructs. Metaphorically speaking, I wanted to work my magic in the world, not just study it for its own sake. This lead me to study study of complex systems and eventually evolutionary dynamics. Mathematics has lost none of its beauty or mystery for me, but my focus now is on its connection to the world rather than its absolute, self-contained truths. <br />
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This parallels, in some ways, the differences I've noticed in the way I approach these fantasy novels now. As a hyper-imaginative pre-teen, I wanted to lose myself in these fantasy worlds, to blur the lines in my mind between these worlds and my own. Re-reading them now, I have no desire to escape into these worlds. Rather I look for metaphors and themes connecting these worlds to mine. These books (and the genre as a whole) seem obsessed with the idea of power: discovering one's own power, learning about different sources of power, coming to grips with the dangers and limitations of power, avoiding the temptation to use power for evil. As a researcher, a future professor, and simply an adult actor in this world, I have a certain measure of real-world power now that I lacked as a bookish pre-teen. In these books, I'm finding an opportunity to reflect on how to wield that power, and the responsibility that comes with it.<br />
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Perhaps the larger theme is this: I used to think I needed to escape from the world in order to be myself. Now my goal is to connect to the world, as much as possible, while still being deeply, authentically, myself.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com2tag:blogger.com,1999:blog-8398797088391606752.post-72546519624677939082012-04-07T20:26:00.001-07:002012-05-05T20:29:26.711-07:00Can we find meaning in evolution?I'm a mathematician who studies evolution. I'm also a person who thinks about how people can find meaning and purpose in their lives. And so, combining these, I've spent a fair bit of time thinking about what, if anything, evolution can tell us about the meaning and purpose of human life.<br />
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My friend <a href="http://www.patheos.com/blogs/scienceonreligion/author/connorwood/">Connor Wood</a> recently <a href="http://www.patheos.com/blogs/scienceonreligion/2012/03/darwinism-its-true-but-it-aint-pretty/">wrote</a> on this topic. Specifically, he probed the question of why, precisely, many conservative religious traditions find the idea of evolution so objectionable. His argument is encapsulated in this quote:<br />
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I strongly suspect that evolutionary theory makes people so uncomfortable, not because it disagrees with Genesis (lots of things contradict Genesis), but because it presents a vision of a natural world whose “values” are <i>fundamentally</i> opposed to those of our religious cultures.</blockquote>
By "values" (in quotes because evolution is an amoral process), Connor is referring to the often violent struggle to survive and reproduce one's genes, which includes such behavior as <a href="http://en.wikipedia.org/wiki/Infanticide_%28zoology%29#Infanticide_involving_sexual_conflict">infanticide</a> in some mammals and birds. While I agree with Connor's basic argument, I think it's not primarily the violence and struggle that offends some religious sensibilities (the Old Testament and many other religious texts are full of violence) but rather the inherent randomness and lack of ultimate purpose in the process. <br />
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Even though scientists generally don't intend it as such, evolution fills the role of a creation story. Like other creation stories, it explains where we came from and how we got here. But unlike other creation stories, it gives us few clues as to where we're going or what we're supposed to do. In fact, it tells us that we're the product of random events. If this randomness had gone differently, we might not be here at all. I think the randomness and lack of purpose implied by this story is why many people—including some who believe it as a scientific hypothesis—find the idea of evolution disturbing.<br />
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<tr><td class="tr-caption" style="text-align: center;">Where did all this come from?? What does it mean??</td></tr>
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Interestingly, several thinkers have tried to turn this equation around, claiming that evolution can, in fact, satisfy our deepest psychological/spiritual needs. One of these is <a href="http://en.wikipedia.org/wiki/Stuart_Kauffman">Stuart Kauffman</a>, one of the biggest names in complex systems. Kauffman's latest book, <a href="http://www.amazon.com/Reinventing-Sacred-Science-Reason-Religion/dp/0465003001">Reinventing the Sacred</a>, argues that evolution is such a creative and fundamentally unpredictable process that it can provide us with all the divine-like inspiration we need. <br />
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Unfortunately, Kauffman's idea doesn't quite get there for me. It's true that the variety of life is awe-inspiring, with more and more surprises the closer one looks. However, I think that just being awestruck by the beauty and creativity of nature is insufficient: it doesn't satisfy the questions of why we're here or what we should try to do with our lives. <br />
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Another approach is to focus on the potential of evolution to produce cooperation, creativity, and complexity. These aspects of evolution are highlighted in <a href="http://www.amazon.com/SuperCooperators-Altruism-Evolution-Other-Succeed/dp/B005GNKJYI/ref=cm_cr_pr_product_top">Supercooperators</a>, the new book by my boss and mentor Martin Nowak. I think one of the reasons for the past few decades' surge of research into this side of evolution (the "<a href="http://www.nytimes.com/2011/04/10/books/review/book-review-supercooperators-by-martin-a-nowak.html?pagewanted=all">snuggle for existence</a>") is that it changes the story evolution tells about us, allowing us to understand how love, empathy, and compassion are also products of our evolutionary history. <br />
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But I don't find this to be of great philosophical comfort either. First, for every example of the evolution of cooperation, there's a complementary example of evolved selfishness and violence. Second, knowing that my feelings of love and empathy exist because they were successful traits in my ancestors doesn't make me feel better about them. In fact, it makes me feel worse. I want to think of these as fundamental to who I am, not some ploy to reproduce my genes. Every time I try to think about all my love and altruism as being a product of evolution, I become sad and want to stop thinking about it. Perhaps I'm just not thinking about it right, but I imagine others may have this difficulty too.<br />
<br />
I made a handy (oversimplified) chart to summarize what I think evolution can and can't do for us in terms of filling philosophical/spiritual voids:<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1Mx0xcTgxjJavcRKI1QEBPng6qV27sE2-KAhmjX2zjxQRLy0xpmt4YRNt-O0VBaO73gVK5LUNjcYZubRTEBYpwzYSyvHOuHni7Dr_cs7fMCB-3uYZOtOMdhggREEONyosJjYYYOpPkXyC/s1600/EvolutionMeaning.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="160" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1Mx0xcTgxjJavcRKI1QEBPng6qV27sE2-KAhmjX2zjxQRLy0xpmt4YRNt-O0VBaO73gVK5LUNjcYZubRTEBYpwzYSyvHOuHni7Dr_cs7fMCB-3uYZOtOMdhggREEONyosJjYYYOpPkXyC/s320/EvolutionMeaning.jpg" width="320" /></a></div>
In short, my answer is that no, I don't think evolution can provide us with satisfying answers to many of our deepest questions.<br />
<br />
Some atheists/materialists argue that the conversation should end here: There is no larger meaning or purpose to life, and any quest for such is a waste of time. But these questions are a real part of who I am, as real as love or anything else I feel. Doubtless, such searchings are products of evolution themselves. Yet to rationalize them away would be to deny a fundamental part of myself. Besides, if life truly has no purpose, then what would my time be better spent doing? Reproducing my genes? Why should I care about that either, if that's also just another artifact of evolution? <br />
<br />
My approach is to grapple with these questions head on, knowing that there are no easy answers. Evolution—the most credible scientific theory as to how we got here—doesn't tell us where we're going or what to strive for. And yet it has implanted us with a deep need to plumb these questions. One could, I suppose, see this as a cruel joke that our evolutionary history has played on us. But I think these questions are as real and important as anything else we experience in life, and there is fulfillment and self-knowledge to be found in exploring them, even if we strongly suspect that satisfying answers will never be found.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com12tag:blogger.com,1999:blog-8398797088391606752.post-45597666604152808782011-11-27T10:54:00.000-08:002011-11-28T09:17:17.847-08:00The Origins of Inequality<span style="float: right; padding: 5px;"><a href="http://www.researchblogging.org/"><img alt="ResearchBlogging.org" src="http://www.researchblogging.org/public/citation_icons/rb2_large_gray.png" style="border: 0;" /></a></span><br />
Inequality is a national conversation topic now, thanks largely to the efforts of Occupy Wall Street and the broader Occupy movement. Fundamental questions are being asked, such as "Must inequality necessarily be a part of human society?", "<a href="http://news.nationalpost.com/2011/11/25/occupy-wall-street-plagued-by-the-hierarchy-it-seeks-to-destroy/">Are we genetically disposed toward hierarchy or egalitarianism?</a>", and "What would a global egalitarian human society look like?"<br />
<br />
We can gain a bit of perspective on these questions by looking at the evolutionary history of humans and our primate relatives:<br />
<ul><li> Our two closest animal relatives are <a href="http://en.wikipedia.org/wiki/Common_chimpanzee">chimpanzees</a> and <a href="http://en.wikipedia.org/wiki/Bonobo">bonobos</a>. Chimpanzee society is characterized by a strict hierarchy of males, with frequent aggressive conflicts between them to maintain or challenge dominance order. In bonobo society, on the other hand, hierarchies are weak, and conflict resolution is peaceful, often involving sex play. </li>
<li> <a href="http://en.wikipedia.org/wiki/Baboons">Baboon</a> societies in the wild are also characterized by a strict dominance hierarchy, in which higher-ranking males regularly harass lower-ranking ones and commandeer their food or resting spots. There is one <a href="http://www.primates.com/baboons/culture.html">notable exception</a>, however. In 1982, all of the dominant males in a baboon tribe observed by Robert Saplosky were suddenly wiped out by a tuberculosis outbreak, leaving only the lower-ranking males. There followed a marked shift in the culture of the troop: hierarchy remained, but those at the top were much less likely to harass lower-ranking males or steal their food. Moreover, this more relaxed culture was observed in the same tribe two decades later, even after all the males present during the original shift had died or migrated to other tribes (Saplosky and Share 2004).</li>
<li>Modern hunter-gatherer societies, the closest analogue we know of to our distant ancestors, are uniformly characterized by a strong egalitarian ethos, in which resources are shared and those who attempt to hoard them are ostracized (<a href="http://books.google.com/books?hl=en&lr=&id=ljxS8gUlgqgC&oi=fnd&pg=PR11&ots=FtwIcp-M19&sig=897EKy4CPu16aOhcXQt1mBW6qVs#v=onepage&q&f=false">Boehm 2001</a>). On the other hand, the transition to agriculture lead to the advent of unequal social classes, with the lower classes often suffering from malnutrition (<a href="http://virtual.yosemite.cc.ca.us/ottej/PDF/diamond.pdf">Diamond 1987</a>).</li>
</ul><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwJkGbe-wDDN-e71Oou67HhFlAzccykhJ6g1366K0XVOr4uv4IjVkH9_ZYrytoOdhiV1uzr6x2_CgZO7EqhG9sMbz0-uvl34543oJzC7UTyMm_3l4MVTDtEtPQolaT5M3tbF0Ca6qqyAmG/s1600/Primates.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwJkGbe-wDDN-e71Oou67HhFlAzccykhJ6g1366K0XVOr4uv4IjVkH9_ZYrytoOdhiV1uzr6x2_CgZO7EqhG9sMbz0-uvl34543oJzC7UTyMm_3l4MVTDtEtPQolaT5M3tbF0Ca6qqyAmG/s400/Primates.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">From left to right: Chimpanzee, Bonobo, Olive Baboon. Source: <a href="http://pin.primate.wisc.edu/">Primate Info Net</a></td></tr>
</tbody></table><br />
Taken together, these examples suggest that humans aren't inevitably predisposed to either hierarchy or egalitarianism. Rather, we are capable of either mode of society. These examples also suggest that, like the baboons, we might be able to shift from one mode to the other in the wake of a destabilizing catastrophe.<br />
<br />
A mathematician, economist, or theoretical biologist would call this an example of <i>multiple equilibria</i>. The situation might be depicted like this:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGWm0AQCkuRnY1jIqO6e24hZl2pbxy6G9wEg1K6JlJnOjUAiflwFeM6l2cgI8-65h6ZQSlwgU-thsHm3bPOscAn8SIXsf0H11TGFZshZToIWCve1kLXv84IWOoKH_S9rISaL4ujmZqFRw8/s1600/Equilibria.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGWm0AQCkuRnY1jIqO6e24hZl2pbxy6G9wEg1K6JlJnOjUAiflwFeM6l2cgI8-65h6ZQSlwgU-thsHm3bPOscAn8SIXsf0H11TGFZshZToIWCve1kLXv84IWOoKH_S9rISaL4ujmZqFRw8/s400/Equilibria.jpg" width="400" /></a></div><br />
That is, there are two stable configurations of society (really, much more than two, but we're simplifying here): hierarchical and egalitarian. Each equilibrium is stabilized by different mechanisms. In hierarchical societies, those at the top have enough power to squelch any attempt at overthrowing the hierarchy. In egalitarian societies, those who attempt to selfishly amass resources or power are ostracized by the rest of the group. Christopher Boehm discovered these mechanisms for egalitarianim in his <a href="http://books.google.com/books?hl=en&lr=&id=ljxS8gUlgqgC&oi=fnd&pg=PR11&ots=FtwIcp-M19&sig=897EKy4CPu16aOhcXQt1mBW6qVs#v=onepage&q&f=false">survey</a> of modern hunter-gatherer societies<br />
<blockquote>I discovered that their egalitarian political arrangements were quite deliberate. They believed devoutly in maintaining political parity among adults. This belief was so strong that males who turned into selfish bullies, or even tried to boss others around for reasons useful to the group, were treated brutally, as moral deviants. (<a href="http://greatergood.berkeley.edu/article/item/political_primates/">Boehm 2007</a>)<br />
</blockquote>Because of these mechanisms, the two extreme ends of this spectrum are quite stable. Escaping them is very difficult without a demographic catastrophe like the tuberculosis outbreak in baboons, a major technological shift like the development of agriculture, or a "starting over" opportunity like the colonization of a new continent. <br />
<br />
The middle regions of this spectrum, however, are less stable. In these regions, some individuals wield a disproportionate share of power, but not enough to completely suppress the interests of the less-powered classes (the <a href="http://wearethe99percent.tumblr.com/">99%</a>). This leads to persistent power struggles between these classes, in which the balance could ultimately be tipped in either direction.<br />
<br />
The United States has always been an unequal society, but the checks and balances of democracy have thus far kept it from sliding into despotic hierarchy. The balance of power has fluctuated throughout our history, with periods of robber baron-style capitalism alternating with progressivist movements. I'm worried, however, that we're currently sliding toward self-reinforcing inequality, as the moneyed elite increase their influence over politics, which leads to policies that make them richer, which gives them even greater influence over politics, and so on. <br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7dnLJG6GiwVnKb28nv00aqBJ_15GjkDIdjnefwmI-IJNBmzGqoOsF7EtynR3UuUP588MeFoxuvbikFOrhG2e_NmHASEZelVO4MTMqbg_vjMtRFXOV9C17MBT0csaGPrbl8XLzpNCQk64F/s1600/Equilibria2.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="200" width="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj7dnLJG6GiwVnKb28nv00aqBJ_15GjkDIdjnefwmI-IJNBmzGqoOsF7EtynR3UuUP588MeFoxuvbikFOrhG2e_NmHASEZelVO4MTMqbg_vjMtRFXOV9C17MBT0csaGPrbl8XLzpNCQk64F/s400/Equilibria2.jpg" /></a></div><br />
This multiple equilibria model tells us that we may have only a limited window of opportunity to correct this slide. If an equilibrium of extreme inequality is reached, only an enormous catastrophe would be able to undo it. <br />
<span style="display:none">sciseekclaimtoken-4ed3be515c693</span></p><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=PLoS+Biology&rft_id=info%3Adoi%2F10.1371%2Fjournal.pbio.0020106&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=A+Pacific+Culture+among+Wild+Baboons%3A+Its+Emergence+and+Transmission&rft.issn=1544-9173&rft.date=2004&rft.volume=2&rft.issue=4&rft.spage=0&rft.epage=&rft.artnum=http%3A%2F%2Fbiology.plosjournals.org%2Fperlserv%2F%3Frequest%3Dget-document%26doi%3D10.1371%252Fjournal.pbio.0020106&rft.au=Sapolsky%2C+R.&rft.au=Share%2C+L.&rfe_dat=bpr3.included=1;bpr3.tags=Mathematics">Sapolsky, R. and Share, L. (2004). A Pacific Culture among Wild Baboons: Its Emergence and Transmission <span style="font-style: italic;">PLoS Biology, 2</span> (4) DOI: <a href="http://dx.doi.org/10.1371/journal.pbio.0020106" rev="review">10.1371/journal.pbio.0020106</a></span><br />
<p>Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com10tag:blogger.com,1999:blog-8398797088391606752.post-61261414877090682912011-08-02T01:43:00.000-07:002011-08-02T03:52:08.823-07:00Demographic Transitions and the Future of HumanityThis week, the <a href="http://www.fieldofscience.com/">field of science</a> bloggers are addressing the question "<a href="http://labs.fieldofscience.com/2011/07/are-we-doomed.html">Are we doomed?</a>" It's a good question. There is no shortage of evidence that we are, in fact, doomed. But as an incorrigible optimist, my response is a cautious "maybe not?"<br />
<br />
What am I referring to here? In talking to friends concerned about the future of the world, many express a fear that the human population and its economies will continue to grow until they can no longer be sustained by the resources available on the planet. At this point there will be a great "crunch", as billions die and the rest endure a life of scarcity and strife. This fear is not new; it dates back to <a href="http://en.wikipedia.org/wiki/Thomas_Robert_Malthus">Thomas Robert Malthus</a>, who wrote in his 1798 <a href="http://en.wikipedia.org/wiki/Thomas_Robert_Malthus#An_Essay_on_the_Principle_of_Population">"Essay on the Principle of Population"</a> that<br />
<br />
<blockquote>The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world.</blockquote><br />
So the Maltusian prediction is yes, we are doomed. But according to contemporary demographic forecasters, Malthus was, surprisingly, wrong. The human population is not growing without bound. Rather, the growth rate is slowing, so that the total population level is headed for a peak—and relatively soon! A 2001 study entitled "The End of World Population Growth" put the chances at 85% that the human population will peak before 2100. Here's a graph of their projections, with the most likely outcomes shaded darkest:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicJtCf7d2pttJcB8BwtIB4RdP2xaZ9Upazu0fr4n8QdQbY5uwf-btrLkr8J2JW4StKAwXF6-cOAZPLM4x8z3vmUH3ZQgzcRMKNVKyRbyWcPSc12gRgJNH_RDHrovbmTiy5oC9ujsl9-jP5/s1600/PopulationForecast.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="396" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEicJtCf7d2pttJcB8BwtIB4RdP2xaZ9Upazu0fr4n8QdQbY5uwf-btrLkr8J2JW4StKAwXF6-cOAZPLM4x8z3vmUH3ZQgzcRMKNVKyRbyWcPSc12gRgJNH_RDHrovbmTiy5oC9ujsl9-jP5/s640/PopulationForecast.jpg" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The numbers on the right-hand side are probabilities of being <i>less than</i> some number. For example, there is an estimated 14.4% chance that the population will be less than 6 billion in 2100, and an 89.4% chance it will be less than 12 billion. The thick white line is a UN prediction, not part of this study, provided for the sake of comparison.</td></tr>
</tbody></table><br />
This turnaround is remarkable, since the <a href="http://en.wikipedia.org/wiki/World_population">human population</a> has been <a href="http://en.wikipedia.org/wiki/File:Population_curve.svg">growing</a> <a href="http://en.wikipedia.org/wiki/File:World_population_growth_%28lin-log_scale%29.png">exponentially</a>, with few declines, since the beginnings of recorded history. So what's behind this unprecedented reversal?<br />
<br />
It turns out that Malthus didn't know everything about human nature. Population scientists have noticed a surprising, yet robust, pattern in human societies, which they call the <a href="http://en.wikipedia.org/wiki/Demographic_transition">"demographic transition"</a>. This transition occurs in stages, which are linked to economic and social development.<br />
<ol><li> In pre-industrial societies, parents have many children, since the survival of each individual child is uncertain.</li>
<li>As improvements are made to food supply, hygiene, health care, and infrastructure, more children survive. This leads to a period of rapid population growth.</li>
<li>As the society becomes increasingly urbanized, children become less of an asset (for helping with farmwork) and more of an expense (they must be educated in order to participate in the economy). Increasing education also gives women options other than motherhood. Access to and acceptance of contraception increases. As a net result, birth rates fall.</li>
<li>Eventually, birth rates decrease to levels comparable to or even less than the death rate. The population level then stabilizes or even contracts.</li>
</ol>This transition can be seen clearly in the birth and death rates of Sweden:<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDcD_BYvzDhDqC8966ZMhYXBChwoPVCU1RiyL29DkH_I7ZGtU8y1AuWtEdV6Nts2_TTzQp-b038vcQNLJOxO8_OqqQmua6D9M5nlB33V3hTwNwmrMB9lWJs1u7AreDk24CiUUP_ps6pWCE/s1600/sweden.gif" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="408" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDcD_BYvzDhDqC8966ZMhYXBChwoPVCU1RiyL29DkH_I7ZGtU8y1AuWtEdV6Nts2_TTzQp-b038vcQNLJOxO8_OqqQmua6D9M5nlB33V3hTwNwmrMB9lWJs1u7AreDk24CiUUP_ps6pWCE/s640/sweden.gif" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Lines indicate number of births (blue) and deaths (red) per 1000 people per year.</td></tr>
</tbody></table><br />
Note that the death rate in Sweden now exceeds the birth rate. This is <a href="http://en.wikipedia.org/wiki/Sub-replacement_fertility">also true</a> of most European nations, as well as Canada, Russia, Iran, Japan, China, and many other countries. The United States is an exception for now—but the New England states are an exception to the exception! Many more developing countries have declining birth rates, so that their populations are predicted to stabilize within decades. <br />
<br />
The idea of the demographic transition, and its robustness across human societies, gives me hope. Not only because it predicts the end of population growth, but also because it suggests a new paradigm of human existence. A paradigm where <i>quality</i> of life is valued over <i>quantity</i> of life. A paradigm where each individual is cared for, educated, and allowed to dictate the course of his or her own life. A paradigm where the population is stabilized not by coercion, disease, wars or famine (as Malthus predicted) but by the free choices of happy and healthy people.<br />
<br />
Of course, there are still major obstacles to overcome before we can live sustainably on this planet. Even as our population stabilizes, irreparable damage to our environment continues. Global consensus remains elusive on challenges such as climate change, deforestation, and biodiversity loss. And conflict, inequality, and oppression squander much of our global human potential.<br />
<br />
But the existence of the demographic transition suggests a goal for humanity:<i> </i><br />
<br />
<i>We must facilitate and manage the demographic transition across human societies, in an environmentally sustainable way.</i><br />
<br />
If we achieve this goal, we will be on our way toward a healthy and happy, indefinitely sustainable human population. So maybe, just maybe, we are not, in fact, doomed.<br />
<br />
<a href="http://twitter.com/#!/search?q=%23SciDoom">#SciDoom</a>Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com4tag:blogger.com,1999:blog-8398797088391606752.post-45837257008730486452011-04-25T08:56:00.000-07:002011-04-25T08:57:50.127-07:00Freedom and the Public Goods<span style="float: right; padding: 5px;"><a href="http://www.researchblogging.org/"><img alt="ResearchBlogging.org" src="http://www.researchblogging.org/public/citation_icons/rb2_large_gray.png" style="border: 0;" /></a></span> <br />
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<a href="http://plektix.fieldofscience.com/2011/03/peanut-allergies-and-future-of.html">Last post</a>, I used the example of a <a href="http://www.huffingtonpost.com/2011/03/24/edgewater-peanut-allergy-protests_n_840319.html">protest against peanut allergy-related procedures</a> to explore how the American conception of "rights" may be changing. In particular, I suggested that ideas of common or collective good were being displaced by an increasingly narrow and selfish definition of individual liberty.<br />
<br />
A few friends pointed out that I may have unfairly maligned libertarians, anarchists, and others wary of government power. These people aren't necessarily opposed to volunteerism or helping others; they just don't want to be <i>coerced</i> into doing so (or have their money taken for these purposes). <br />
<br />
This is a fair point. However, it doesn't make me feel much better about the "leave me alone" political philosophy. I don't think this philosophy will ever be up to solving our common challenges. To illustrate why, I'd like to bring in a concept from game theory.<br />
<br />
The <a href="http://en.wikipedia.org/wiki/Public_goods_game">Public Goods Game</a> represents situations in which there is a common resource ("public good") that benefits all members of a group. The public good might be a clean kitchen, a functioning electrical grid, or a healthy environment. This good cannot be maintained without contributions from some group members. Contributions can be in the form of <i>doing</i> something (washing dishes, working in the community garden, donating to NPR) or <i>not doing</i> something (not littering in a public park, not overfishing a lake).<br />
<br />
The dilemma is this: everyone benefits from the public good, but contributions are voluntary. The public goods game has no built-in incentive to contribute, beyond the desire to make things better for everyone. So "free-riders" can benefit from others' contributions without contributing anything themselves. <br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7bhz1suD1USbjCn-53gtOF5bE25E-58GXBVlU9oRrnRzMlz-YIl1y1eERmczWYZv4HRhQPazZrnEWh6MFMAMEAeN3Rk9Z60FnIqRJqUuCrE1EVKb2voJJtj_odJOJqjl04-b9gsSOuVt7/s1600/Slide1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7bhz1suD1USbjCn-53gtOF5bE25E-58GXBVlU9oRrnRzMlz-YIl1y1eERmczWYZv4HRhQPazZrnEWh6MFMAMEAeN3Rk9Z60FnIqRJqUuCrE1EVKb2voJJtj_odJOJqjl04-b9gsSOuVt7/s320/Slide1.png" width="320" /></a></div><br />
Both theory and experiment predict that cooperation cannot be sustained in such a game. A typical experimental result looks like this:<br />
<br />
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" style="margin-left: auto; margin-right: auto;" width="312" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Horizontal axis is time (number of game rounds) SOURCE: Fehr and Gaechter (2000)</td><td class="tr-caption" style="text-align: center;"><br />
</td><td class="tr-caption" style="text-align: center;"><br />
</td></tr>
</tbody></table></div><br />
Contributions decline over time to virtually nothing. This is not because the participants are inherently selfish. Indeed, at the start of the game, many people are inclined to contribute. However, they realize at some point that others are exploiting their generosity. Not wanting the benefits of their hard work to reward those who don't contribute, people eventually stop contributing altogether. This unfortunate outcome has a name: the <a href="http://en.wikipedia.org/wiki/Tragedy_of_the_commons">Tragedy of the Commons</a>. <br />
<br />
Economists and social scientists have identified a few mechanisms that can reverse this tragedy. If the participants know each other, and also interact in settings aside from the game, then concern for one's reputation can motivate people to contribute (Milinski et al. 2002, Rand et al. 2009). This helps explain why co-ops can be successful: everyone knows each other. They can reward or punish others based on their contributions to cooking, cleaning, and other tasks. <br />
<br />
But what about global challenges like climate change, environmental conservation, and sustainable use of resources? These involve billions of players across the globe, and there are strong financial incentives to exploit the public good for individual gain. Furthermore, it can be difficult to trace problems like pollution or overfishing to the individuals or companies responsible. How these large-scale challenges be solved?<br />
<br />
Research has identified only one answer. If the game is too large and complex for <i>individual</i> interactions to maintain cooperation, the solution is for the participants to invest in <i>institutions</i> (Gureck et al., 2006; Sigmund et al., 2010). These institutions must have the power to investigate the actions of individuals, and reward or punish them based on their contributions. In other words, a <a href="http://en.wikipedia.org/wiki/Social_contract">social contract</a> is needed, together with institutions to enforce it.<br />
<br />
Of course, powerful institutions have inherent potential for corruption and abuse. This is what worries libertarians and anarchists. I share that concern. But the solution, in my view, is to build in democratic checks, so that these institutions are as responsive as possible to the people they serve.<br />
<br />
It's hardly a perfect solution. Institutions can become entangled with those they should regulate. Democratic checks can be co-opted. <br />
<br />
But to solve the largest problems that face humanity, we can't count on good will and personal responsibility alone.<br />
<br />
<u>References: </u><br />
<br />
<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=American+Economic+Review&rft_id=info%3A%2F&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=Cooperation+and+Punishment+in+Public+Goods+Experiments&rft.issn=&rft.date=2000&rft.volume=90&rft.issue=4&rft.spage=&rft.epage=&rft.artnum=http%3A%2F%2Fwww.jstor.org%2Fstable%2F117319&rft.au=Ernst+Fehr&rft.au=Simon+Gaechter&rfe_dat=bpr3.included=1;bpr3.tags=Social+Science%2CEconomics">Ernst Fehr, & Simon Gaechter (2000). Cooperation and Punishment in Public Goods Experiments <span style="font-style: italic;">American Economic Review, 90</span> (4)</span> <br />
<br />
<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Science&rft_id=info%3Adoi%2F10.1126%2Fscience.1123633&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=The+Competitive+Advantage+of+Sanctioning+Institutions&rft.issn=0036-8075&rft.date=2006&rft.volume=312&rft.issue=5770&rft.spage=108&rft.epage=111&rft.artnum=http%3A%2F%2Fwww.sciencemag.org%2Fcgi%2Fdoi%2F10.1126%2Fscience.1123633&rft.au=%C3%96zg%C3%BCr+G%C3%BCrerk&rft.au=Bernd+Irlenbusch&rft.au=Bettina+Rockenbach&rfe_dat=bpr3.included=1;bpr3.tags=Social+Science">Özgür Gürerk, Bernd Irlenbusch, & Bettina Rockenbach (2006). The Competitive Advantage of Sanctioning Institutions <span style="font-style: italic;">Science, 312</span> (5770), 108-111 DOI: <a href="http://dx.doi.org/10.1126/science.1123633" rev="review">10.1126/science.1123633</a></span> <br />
<br />
<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Nature&rft_id=info%3Adoi%2F10.1038%2F415424a&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=Reputation+helps+solve+the+%E2%80%98tragedy+of+the+commons%E2%80%99&rft.issn=00280836&rft.date=2002&rft.volume=415&rft.issue=6870&rft.spage=424&rft.epage=426&rft.artnum=http%3A%2F%2Fwww.nature.com%2Fdoifinder%2F10.1038%2F415424a&rft.au=Milinski%2C+M.&rft.au=Semmann%2C+D.&rft.au=Krambeck%2C+H.&rfe_dat=bpr3.included=1;bpr3.tags=Biology%2CSocial+Science%2CEconomics%2C+Evolutionary+Biology">Milinski, M., Semmann, D., & Krambeck, H. (2002). Reputation helps solve the ‘tragedy of the commons’ <span style="font-style: italic;">Nature, 415</span> (6870), 424-426 DOI: <a href="http://dx.doi.org/10.1038/415424a" rev="review">10.1038/415424a</a></span><br />
<br />
<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Science&rft_id=info%3Adoi%2F10.1126%2Fscience.1177418&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=Positive+Interactions+Promote+Public+Cooperation&rft.issn=0036-8075&rft.date=2009&rft.volume=325&rft.issue=5945&rft.spage=1272&rft.epage=1275&rft.artnum=http%3A%2F%2Fwww.sciencemag.org%2Fcgi%2Fdoi%2F10.1126%2Fscience.1177418&rft.au=Rand%2C+D.&rft.au=Dreber%2C+A.&rft.au=Ellingsen%2C+T.&rft.au=Fudenberg%2C+D.&rft.au=Nowak%2C+M.&rfe_dat=bpr3.included=1;bpr3.tags=Social+Science%2CEconomics">Rand, D., Dreber, A., Ellingsen, T., Fudenberg, D., & Nowak, M. (2009). Positive Interactions Promote Public Cooperation <span style="font-style: italic;">Science, 325</span> (5945), 1272-1275 DOI: <a href="http://dx.doi.org/10.1126/science.1177418" rev="review">10.1126/science.1177418</a></span><br />
<br />
<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.jtitle=Nature&rft_id=info%3Adoi%2F10.1038%2Fnature09203&rfr_id=info%3Asid%2Fresearchblogging.org&rft.atitle=Social+learning+promotes+institutions+for+governing+the+commons&rft.issn=0028-0836&rft.date=2010&rft.volume=466&rft.issue=7308&rft.spage=861&rft.epage=863&rft.artnum=http%3A%2F%2Fwww.nature.com%2Fdoifinder%2F10.1038%2Fnature09203&rft.au=Sigmund%2C+K.&rft.au=De+Silva%2C+H.&rft.au=Traulsen%2C+A.&rft.au=Hauert%2C+C.&rfe_dat=bpr3.included=1;bpr3.tags=Biology%2CSocial+Science%2CEconomics%2C+Evolutionary+Biology">Sigmund, K., De Silva, H., Traulsen, A., & Hauert, C. (2010). Social learning promotes institutions for governing the commons <span style="font-style: italic;">Nature, 466</span> (7308), 861-863 DOI: <a href="http://dx.doi.org/10.1038/nature09203" rev="review">10.1038/nature09203</a></span>Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com5tag:blogger.com,1999:blog-8398797088391606752.post-92047576384627070712011-03-26T08:43:00.000-07:002011-03-26T08:43:52.294-07:00Peanut Allergies and the Future of DemocracyParents are <a href="http://amfix.blogs.cnn.com/2011/03/24/parents-picket-girl-with-peanut-allergy-ask-her-to-withdraw-from-school/">picketing</a> a school in Edgewater, Florida because of restrictions the school put in place to protect a child with a peanut allergy (thanks to my <a href="http://anaphylacticgourmet.com/2011/03/26/parents-picket-girl-with-peanut-allergy-ask-her-to-withdraw-from-school-%E2%80%93-american-morning-cnn-com-blogs/">sister</a> for alerting me):<br />
<br />
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<br />
To summarize: a number of parents apparently feel that common-sense measures such as regular hand-washing (which the school is legally required to enforce by the Americans with Disabilities Act) are too onerous to bear. They are demanding that instead this child be removed from the school.<br />
<br />
What's going on here? First of all, the claim that these procedures are taking away from educational time is ridiculous. A child with even a moderate behavior problem will waste far more instructional time than these hand-washing procedures ever could. But disruptive students aren't targeted for picketing by parents. Then there's the distraction created by the protesters themselves, which I'm sure is seeping into the classroom.<br />
<br />
So it's not about educational time. What <i>is</i> it about then? I can't read these parents' minds, but there are disturbing clues in the language that some of them are using. "They're trying to take away all our rights," says one parent, while a sign reads:<br />
<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizujbZDjhyA5MIc-ex8s8afSQ_BKhOf10ENPEQYG0TmDyiYjjG0qHsviybTMa5cvw2GSMpLE5rTvFGjvw1IlYREG81k0OTYUekc_7j2KOHbzdpdEJnZDxDqv3opyBTqogqzI-P18nCXN6R/s1600/Screen+shot+2011-03-26+at+10.21.24+AM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="191" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizujbZDjhyA5MIc-ex8s8afSQ_BKhOf10ENPEQYG0TmDyiYjjG0qHsviybTMa5cvw2GSMpLE5rTvFGjvw1IlYREG81k0OTYUekc_7j2KOHbzdpdEJnZDxDqv3opyBTqogqzI-P18nCXN6R/s320/Screen+shot+2011-03-26+at+10.21.24+AM.png" width="320" /></a></div><br />
To which rights are they referring, exactly? The Right of Sullied Hands? The Rights of the Unwashed Masses?<br />
<br />
This picture is so disturbing because the methods and language of democratic civil rights movements are being used to sacrifice the educational rights of one child so that others can be spared a few minor inconveniences. In this way, these protests are part of a larger, unsettling pattern. The past few years (or perhaps decades?) have seen a subtle shift in the way that terms such as "rights", "justice" and "democracy" are invoked in the US. More and more, these terms are being used to defend <i>indvidual</i>, rather than <i>collective</i> interests, and these individual interests are defined in increasingly narrow and selfish ways. <br />
<br />
Mark Lilla, in a <a href="http://www.nybooks.com/articles/archives/2010/may/27/tea-party-jacobins/?pagination=false">New York Review of Books article</a>, sums this up brilliantly:<br />
<br />
<blockquote>Many Americans, a vocal and varied segment of the public at large, have now convinced themselves that educated elites—politicians, bureaucrats, reporters, but also doctors, scientists, even schoolteachers—are controlling our lives. And they want them to stop. They say they are tired of being told what counts as news or what they should think about global warming; tired of being told what their children should be taught, how much of their paychecks they get to keep, whether to insure themselves, which medicines they can have, where they can build their homes, which guns they can buy, when they have to wear seatbelts and helmets, whether they can talk on the phone while driving, which foods they can eat, how much soda they can drink… the list is long. But it is not a list of political grievances in the conventional sense.<br />
<br />
Historically, populist movements use the rhetoric of class solidarity to seize political power so that “the people” can exercise it for their common benefit. American populist rhetoric does something altogether different today. It fires up emotions by appealing to individual opinion, individual autonomy, and individual choice, all in the service of neutralizing, not using, political power. It gives voice to those who feel they are being bullied, but this voice has only one, Garbo-like thing to say: I want to be left alone.<br />
<br />
A new strain of populism is metastasizing before our eyes, nourished by the same libertarian impulses that have unsettled American society for half a century now. Anarchistic like the Sixties, selfish like the Eighties, contradicting neither, it is estranged, aimless, and as juvenile as our new century. It appeals to petulant individuals convinced that they can do everything themselves if they are only left alone, and that others are conspiring to keep them from doing just that. This is the one threat that will bring Americans into the streets.<br />
<br />
Welcome to the politics of the libertarian mob. </blockquote><br />
This all makes me wonder about the future of democracy, and human society more generally. While young people in the Middle East are are staging revolts to overthrow decades of repression and corruption, the Tea Party and Republican Party more generally are attacking the very notion of collective action for the common good. (See <a href="http://www.theonion.com/articles/republicans-vote-to-repeal-obamabacked-bill-that-w,19025/">"Republicans Vote To Repeal Obama-Backed Bill That Would Destroy Asteroid Headed For Earth"</a> for a satirical example.) <br />
<br />
Unsettlingly, the one recent US protest movement on <i>behalf</i> of collective action---the <a href="http://www.presstv.ir/usdetail/171074.html">showdown</a> over collective bargaining rights in Wisconsin---has apparently failed. The result is a further weakening of unions, themselves one of the few institutional standard-bearers of the idea that we can achieve more together than apart.<br />
<br />
The history of humanity, and indeed of life itself, is a story of <a href="http://en.wikipedia.org/wiki/The_Major_Transitions_in_Evolution">transitions from the individual to the collective, from lower to higher levels of organization</a>. This can, of course, be taken too far, as it was in the case of <a href="http://plektix.fieldofscience.com/2008/02/on-communism.html">Communism</a>. But happens in the other extreme, of radical individualism and resistance to all forms of organization? Are we headed for an evolutionary regression?<br />
<br />
I don't know the answers to these questions, and I don't think they are simple. But since this trend appears to have enormous momentum, it's worth thinking about where it might lead.<br />
<br />
(Many of the ideas in this post actually come from my partner <a href="http://drawmedy.wordpress.com/">Anna</a>. Yay collective action!)Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com8tag:blogger.com,1999:blog-8398797088391606752.post-46566228007277712332010-12-05T21:30:00.000-08:002010-12-05T18:42:55.613-08:00Game theory and Obama's mistakeLike many of my fellow lefties, I'm disillusioned with current US politics. In my view, we have a president who pursued an admirable, ambitious agenda for two years, but failed to win sufficient public support for his initiatives, and wasted too much time searching for nonexistent common ground. Now, with midterm elections lost, our president <a href="http://www.nytimes.com/2010/12/03/opinion/03krugman.html?_r=1&src=me&ref=homepage">seems ready to abdicate all decision making power</a> to the Republicans, whose ideas (in my judgment, as well as in Obama's) will actively make our country worse. <br />
<br />
The problem, as I see it, can be illuminated with a bit of game theory. Consider a two-party government, and suppose each party has three possible strategies:<br />
<ul><li> Ideological (<b>I</b>): Fight for initiatives that are consistent with the party's core beliefs, regardless of how popular or achievable these initiatives are.</li>
<li> Pragmatic (<b>P</b>): Work toward compromise and incremental accomplishments, in the view that "mixed bag" policies are better than stalemate.</li>
<li> Cynical (<b>C</b>): Prioritize winning elections and humiliating political opponents over helping the country and upholding core beliefs.</li>
</ul><br />
Either side can choose any of the three strategies, giving us nine possible outcomes. Of course, when it comes to the needs of the country as a whole, some outcomes are better than others. The following matrix illustrates (in my judgment) how desirable each outcome is for the country's citizens, on a scale of 0 (horrible) to 9 (awesome).<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFa-jtqfjfC0KAOW9YzTHzwkvGDiFqBOSLl_H2PU_-kWKe9mrHitUxv2b0hEYTmYtXqtC0A0-R8HZiGkPnYH6clvf3asL1h2gOCzgpS1KhaXouHHdyJ1N4NnceOOaDPOE_oyEICtIO-fUO/s1600/game1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFa-jtqfjfC0KAOW9YzTHzwkvGDiFqBOSLl_H2PU_-kWKe9mrHitUxv2b0hEYTmYtXqtC0A0-R8HZiGkPnYH6clvf3asL1h2gOCzgpS1KhaXouHHdyJ1N4NnceOOaDPOE_oyEICtIO-fUO/s1600/game1.png" /></a></div>The zeros—the worst possible outcomes—occur when cynics are allowed to set the agenda. A battle of ideologues vs. cynics isn't much better, but at least the ideologues can stop the worst of the cynics' games. Ideologues vs. ideologues is mostly a stalemate, but the ideologies may overlap enough to allow for cooperation on some fronts.<br />
<br />
If both parties are pragmatic, the country gets a solid 7. If one is pragmatic and one is ideological, the outcome depends on how successful the ideology is for the country, hence the wide range of possible values (3-9).<br />
<br />
However, politicians aren't only concerned with the needs of the country. They also want to maintain and expand their power. We must therefore also consider how the choices of the parties affect their own success or failure. <br />
<br />
This depends in part on how the country as a whole is doing. Let's say times are tough right now: unemployment, wars, etc. Then here's (again, in my own judgment) how the various outcomes will affect the party currently in power:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE9qj_OpiVIa2il2rwd3FLtbthuDBhHXGK74VD-q6UvxEUucpps5_EJI3AxWpEVjnsxTRH2wbBmrRrG5GVNRonHvoYA0IRAKjtPx45OYWF2Uh2hF-b0DO8W5dBPTHyJIJ0LuJ38mjTDciG/s1600/game22.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiE9qj_OpiVIa2il2rwd3FLtbthuDBhHXGK74VD-q6UvxEUucpps5_EJI3AxWpEVjnsxTRH2wbBmrRrG5GVNRonHvoYA0IRAKjtPx45OYWF2Uh2hF-b0DO8W5dBPTHyJIJ0LuJ38mjTDciG/s1600/game22.png" /></a></div>As you can see, none of the options are great for the incumbents, because whatever happens, the public will tend to (rightly or wrongly) blame them for the current problems. The best they can do is govern well. However, in a US-like system with a supermajority needed to pass any legislation, progress depends on the cooperation of both parties. With a pragmatic opposition, the incumbents can accomplish what needs to be done, obtaining 6's. However, a cynical opposition can play the "stick in the mud" strategy and prevent the government from accomplishing anything. This is bad for the incumbents, because nothing will improve and they will still take the blame.<br />
<br />
Here's how it looks for the opposition:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirLQmmSiy10FMCqnUFyUaWtKBmJOqCJ474HWSJHiGG2Bo2FK6IPQKG4veKHgbaa_q5cNDq8EFtAWOQ_hE2QA75KZ7EMRl0I4zpbPJax4LJw15MD4jGSbpci_jKKnjpU22qeNjqryrRcDWc/s1600/game3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEirLQmmSiy10FMCqnUFyUaWtKBmJOqCJ474HWSJHiGG2Bo2FK6IPQKG4veKHgbaa_q5cNDq8EFtAWOQ_hE2QA75KZ7EMRl0I4zpbPJax4LJw15MD4jGSbpci_jKKnjpU22qeNjqryrRcDWc/s1600/game3.png" /></a></div>As you can see, the cynical strategy is highly effective for the opposition party. They can stop the wheels of government and, assuming things stay bad, they are virtually guaranteed to win the next election. In game theory terms, <b>C</b> is a <i>Nash equilibrium strategy</i>: <b>C </b>is the best choice no matter what the incumbents do. Of course, "best" here means best for the party, not the country. <br />
<br />
In my reading of events, the Republican leadership has decided that <b>C</b> is the way to go. This strategy is examplified by Senate leader Mitch McConnell's <a href="http://voices.washingtonpost.com/ezra-klein/2010/11/motivated_skepticism_draft.html">statement</a> that "the single most important thing we want to achieve is for President Obama to be a one-term president." There are elements within the Republican party who are more on ideological side, but I see nothing but cynicism from <a href="http://www.politico.com/news/stories/1210/45860.html">Boehner</a> and McConnell.<br />
<br />
Let's say I'm right. Then the Democrats are stuck with these options for their own fortunes:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDkKYqSzwmdYpTs5Bbl4XD1fALdTz9uCGqV6oAteY-HENxi5_BLNSOw4h-WScgcullPByMcHN0HwjBmzeV6nTpIDr8X9JYQcsd45FTaB8dH_6J2SW_nuh96DM5rnB-1ea2bBEP1aTew51A/s1600/game2a.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDkKYqSzwmdYpTs5Bbl4XD1fALdTz9uCGqV6oAteY-HENxi5_BLNSOw4h-WScgcullPByMcHN0HwjBmzeV6nTpIDr8X9JYQcsd45FTaB8dH_6J2SW_nuh96DM5rnB-1ea2bBEP1aTew51A/s1600/game2a.png" /></a></div>and these payoffs for the country:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXPshO1suhtEfgZiNohxLyHqQh2ER1NbzyFubk6k5DTJbCHrs8Y4pVzHfAZT3YRlK2l-j3T_y1_qen4cWGVwW_ja7lE1JBXn-ZQtpjdLlgMnrlrbfKNb85HF7Ot1__lGGGDkph6kyf7bn2/s1600/game1a.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXPshO1suhtEfgZiNohxLyHqQh2ER1NbzyFubk6k5DTJbCHrs8Y4pVzHfAZT3YRlK2l-j3T_y1_qen4cWGVwW_ja7lE1JBXn-ZQtpjdLlgMnrlrbfKNb85HF7Ot1__lGGGDkph6kyf7bn2/s1600/game1a.png" /></a></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDkKYqSzwmdYpTs5Bbl4XD1fALdTz9uCGqV6oAteY-HENxi5_BLNSOw4h-WScgcullPByMcHN0HwjBmzeV6nTpIDr8X9JYQcsd45FTaB8dH_6J2SW_nuh96DM5rnB-1ea2bBEP1aTew51A/s1600/game2a.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><br />
</a></div>Given these options, the worst possible choice for the incumbent party is <b>P</b>. It's bad for the party because it sets them up to be manipulated by the cynics. It's also bad for the country, because it hands the initiative to those who would sacrifice the country's interests for their own gain.<br />
<br />
But, unfathomably, <b>P</b> is <a href="http://www.nytimes.com/2010/11/15/opinion/15krugman.html">exactly what Obama is choosing</a>. This is apparent from his <a href="http://www.portfolio.com/views/blogs/capital/2010/11/03/humbled-obama-offers-compromise/">statements</a> such as<br />
<blockquote>Can Democrats and Republicans sit down together and come up with a list of solutions to common problems? I think that we will be able to. I’m doing a whole lot of reflecting, and I think there’s going to be some areas where we need to do a better job.</blockquote>We see it also from his <a href="http://www.nytimes.com/2010/11/15/opinion/15krugman.html">willingness to accept tax cuts on the wealthiest one percent of earners</a>.<br />
<br />
The take-away message from our game theory model is this: There are times when it's good to compromise. If the other side is being pragmatic, or even ideological, compromise can be good for both the country and the party. <i>But</i> <i>there's no point to playing </i><b>P</b><i> if your opponent is playing </i><b>C</b>! The correct response to <b>C</b> is <b>I</b>: counter cynicism by fighting for your core beliefs. Even if the cynics foil your policies, you can thwart their bad ideas and invigorate your supporters. <br />
<br />
Some democrats (e.g. <a href="http://www.youtube.com/watch?v=H5OtB298fHY">Bernie Sanders</a>) have grasped the logic of this situation. But unfortunately, our president isn't yet among them.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com10tag:blogger.com,1999:blog-8398797088391606752.post-9056907677601922312010-10-24T19:53:00.000-07:002010-10-24T19:55:44.753-07:00The Prisoner's Dilemma on Saturday Morning Breakfast CerealFound on <a href="http://www.smbc-comics.com/">Saturday Morning Breakfast Cereal</a>, via <a href="http://theastronomist.fieldofscience.com/">The Astronomist</a>, the cleanest illustration I've seen anywhere of the <a href="http://plektix.fieldofscience.com/2008/03/prisoners-dilemma.html">Prisoner's Dilemma</a>:<br />
<a href="http://www.smbc-comics.com/index.php?db=comics&id=1899"><br />
<img src="http://www.smbc-comics.com/comics/20100605.gif"></a><br />
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The comic ends with a (brief) survey of attempts to convince people to act altruistically rather than selfishly. For me, the more interesting question is how to transform the <a href="http://plektix.fieldofscience.com/2008/11/evolution-of-cooperation.html">structure of social interactions</a>, so that altruism is the right choice for individuals as well as for the whole group.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com0tag:blogger.com,1999:blog-8398797088391606752.post-23206000010276920282010-10-18T08:25:00.000-07:002010-10-18T10:23:44.969-07:00Don't wait for supermanThis weekend I saw "Waiting for Superman" a documentary directed by Davis Guggenheim of <a href="http://www.imdb.com/title/tt0497116/">Inconvenient Truth</a> fame. It's ostensibly about how great teachers are the key to saving our education system. But what struck me, over and over, was its complete lack of understanding of or regard for what teaching actually entails.<br />
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There are many, many problems with this movie, and I will not discuss them all. A <a href="http://www.notwaitingforsuperman.org/NewsAndReviews/20101016-TeacherKenDailyKos">website</a> has been set up to debunk it, and on the Daily Kos a classroom teacher <a href="http://www.dailykos.com/storyonly/2010/10/16/910716/-This-teacher-reacts-to-seeing-Waiting-for-Superman">provides</a> something of a point-counterpoint. (I should add that I do not necessarily endorse everything said on these sites.) I focus my critique on the movie's conception of teaching, because that's the aspect which clashes most directly with my three years' experience as an urban public school teacher.<br />
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My first two years were at the now-defunct Austin Community Academy in Chicago. As an incoming math teacher, I had the good fortune of being mentored by math department chair Steve McIlrath, one of the most amazing and inspiring educators I know. On the day I was hired, he told me was "This may be the most difficult job in America. Every teacher who works here is a hero."<br />
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I didn't quite believe him then, but after the first month I knew exactly what he meant. The teachers at Austin were not all amazing educators (especially not me). They were not always flawless in their classroom management or sophisticated in their pedagogy. Personally, I was horrible at classroom management and cringed at my own pedagogy. But just the action of coming in every day to face the students---who were facing their own enormous life challenges---and putting in the effort to manage, engage, and educate them was herioc.<br />
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I don't have space to describe how incredibly difficult it is just to be a struggling teacher at these schools, let alone a successful one. If you haven't been there, you don't understand. You can, however, educate yourself through memoirs such as <a href="http://books.google.com/books?id=kL1CaVuov2gC&printsec=frontcover&dq=in+the+deep+heart%27s+core&source=bl&ots=naynEoW9oe&sig=MVtZNQBTsuidFIdoxZtzTYtIs9E&hl=en&ei=aZG7TL7wNYT68Ab0ieGlDg&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCcQ6AEwAg#v=onepage&q&f=false">In the Deep Heart's Core</a>, <a href="http://books.google.com/books?id=DyLYRAAACAAJ&dq=reluctant+disciplinarian&hl=en&ei=1pK7TNbdOMP-8Aa4ycTiDw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCwQ6AEwAA">Reluctant Disciplinarian</a>, <a href="http://books.google.com/books?id=7QQlAQAAIAAJ">Chasing Hellhounds</a>, or (ironically enough) Guggenheim's first film <a href="http://www.imdb.com/title/tt0295260/">The First Year</a>.<br />
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Waiting for Superman (WfS) at times acknowledges that teaching is difficult, and that teachers are a "national treasure". But it includes zero interviews with current classroom teachers, and promotes an absurd notion of what teaching is actually about. In one telling moment, a cartoon depicts teachers opening up students' brains and pouring "knowledge" in from a carton. This, we are told, is the way education is supposed to work. Except that now all kinds of standards and regulations have been instituted by various bureaucracies. This multitude of regulations confuses the teacher, who then spills her precious "knowledge" onto the floor. <br />
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If this is your picture of teaching, then we can't even begin to talk about education reform. It's not an oversimplification, it's just plain wrong. <i>Educating</i> students---getting them to absorb and engage with new ideas---is what makes teaching hard. This is especially difficult in urban districts where it can be difficult to get students to show up to class, let alone sit politely and receive your teachings. There is no magic carton. Even if there were, students are not mere knowledge repositories but active, thinking beings, and they should be taught as such. Sure, I was operating under many layers of regulation, but these were largely irrelevant to me. What mattered in that room were me, my students, and how I was going to teach them.<br />
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WfS's main suggestion for improving our schools is to remove tenure protections so that deadbeat teachers can be fired. These deadbeats are definitely out there. One of them occupied the room right next to Steve's. His idea of music education was to let his students listen to the radio, all day, for the entire year. People like him are criminals. It's deplorable that union contracts prevent the firing of such teachers. I absolutely agree that blanket tenure should be abolished, though there should still be mechanisms to protect teachers from the whims of vindictive principals.<br />
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But WfS seems to suggest that removing tenure is the magic bullet needed to fix our education system. This assumes that for every deadbeat fired, there is an excellent teacher waiting in the wings to be hired. That's not the case. As <a href="http://en.wikipedia.org/wiki/Geoffrey_Canada">Geoffrey Canada</a> acknowledges during the movie, every excellent teacher starts out as a struggling teacher like I was. These struggling teachers must be thoroughly trained and mentored before and during their first year. All teachers must be given manageable class sizes and courseloads, as well as time to collaborate with their colleagues. They must be given excellent textbooks and other classroom resources. They must be well-compensated so that quality talent is attracted. Schools must be better integrated with social services so that students are healthy and in class every day. Teachers' unions have an important role to play in advocating for teachers' rights and quality of life.<br />
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All these reforms are necessary so that struggling teachers can become successful rather than leave the profession (as half do within their first five years). But WfS suggests none of these. Instead, it asserts that all we need is to make teachers more accountable. Trust me, I was already trying as hard as I could. More threats hanging over my head would not have improved my teaching. <br />
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Worse, the movie promotes the dangerous idea that we can fix public schools without investing in them. It claims we "tried" spending money and it didn't work, so now we should try something else. This is horrible logic. All of the above reforms require money, along with a good plan for using it. I'm terribly afraid that for years to come, conservatives will cite this movie in their crusade against government spending. Meanwhile, our public schools will continue to languish underfunded.<br />
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In short, WfS promotes an absurdly simplistic view of teaching, in which teachers are either good or bad. As soon as we fire the bad ones, we will have only good teachers and top-quality education. This ignores the reality for the vast majority of teachers who are trying but struggling. These teachers are performing one of the the most important and difficult jobs in the country. They need to be supported, and their jobs made more manageable, in order for them to succeed. <br />
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I could go on about WfS's other flaws: its bizarre use of pop-culture references (<a href="http://www.imdb.com/title/tt0332379/">School of Rock</a>??), its incomprehensible reverence for No Child Left Behind, its use of schoolchildren as emotionally manipulative props, etc. But I'll end with this thought: in the closing credits, we see the text "The problem is complex. But the solution is simple."<br />
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Take it from a complex systems theorist: this is rarely the case in any context, and it's certainly false when it comes to education reform.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com2tag:blogger.com,1999:blog-8398797088391606752.post-85277452186129607102010-08-30T15:30:00.000-07:002010-08-30T12:46:22.067-07:00Inside the Mathematician's StudioOne of the aims of this blog is to give the general public a sense of what we applied mathematicians and other non-laboratory scientists actually do with our time. An <a href="http://plektix.fieldofscience.com/2010/02/idea-of-applied-mathematics.html">earlier post</a> addressed the <i>content</i> of what we do: the development and analysis of models. This post, on the other hand, will focus on <i>process</i>. Specifically, my process: how I actually <i>do</i> math. This post is a joint project with my partner Anna, whose <a href="http://drawmedy.wordpress.com/2010/08/30/at-work/">beautiful sequence of illustrated text</a> about the nature of the creative process appears on her site <a href="http://drawmedy.wordpress.com/">drawmedy</a>.<br />
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Of course, there are many aspects of what I do. Activities such as reading through the literature, meeting with collaborators, and writing up results, don't require much explanation. I focus here on the parts of my job that makes me feel most like a mathematician: coming up with new ideas and developing them into mathematical arguments. <br />
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It starts with a problem. Most often I'm trying to prove some result of the form "In this model, under these conditions, this kind of behavior can arise". Sometimes these questions can be addressed using textbook-style sequences of steps, or even using programs like Mathematica. But such straightforward solutions don't interest me as a mathematician, and I like to leave this kind of work to other people. What really makes me come alive are the questions for which new mathematical approaches must be conceived.<br />
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This is an inherently creative process. There is no way of knowing at the outset what the solution may look like, or even whether a solution will be found. All you start with is your toolbox of mathematical techniques, and some hunches about which tools might work if applied correctly.<br />
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From this starting point, it's a process of trying approaches, failing, trying other approaches, asking questions, re-framing the problem, working out simple examples, and trying to make connections between different areas of my knowledge. This process plays out in pencil scratchings on my bound notebooks, two pages of which I've reproduced here:<br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqw8frGqI3xFRnw7pWuzpjPWWRg26dqYlRbNcWwq5xHW4mCQbPBAOkiQzlT1LHR67wndIrRcgjT37zNqumyNuMiao_Mip7Bf9hUQ_2hpJFVnZH3gIzkjjSHOFx3rB1EPr5r9MUTVxE3QpR/s1600/bennotebook.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqw8frGqI3xFRnw7pWuzpjPWWRg26dqYlRbNcWwq5xHW4mCQbPBAOkiQzlT1LHR67wndIrRcgjT37zNqumyNuMiao_Mip7Bf9hUQ_2hpJFVnZH3gIzkjjSHOFx3rB1EPr5r9MUTVxE3QpR/s640/bennotebook.jpeg" width="457" /></a></div><div class="separator" style="clear: both; text-align: center;"></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBkH5Nz2kAphAUPRC42iHu2DYxT9oyBoMcw67qG_yrUfStbGs_to0YgE4iupLRMWJLc_cXQoqN7IOzkhPL5_vKZs-BwrbjfgAFBaoUykE2CeQoTefctgfWvqlNN9WQKtKNDgWaqWbioP3N/s1600/bennotebook2.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhBkH5Nz2kAphAUPRC42iHu2DYxT9oyBoMcw67qG_yrUfStbGs_to0YgE4iupLRMWJLc_cXQoqN7IOzkhPL5_vKZs-BwrbjfgAFBaoUykE2CeQoTefctgfWvqlNN9WQKtKNDgWaqWbioP3N/s640/bennotebook2.jpeg" width="458" /></a></div><br />
These two (non-consecutive) pages show some of my musings on <a href="http://plektix.fieldofscience.com/2008/03/prisoners-dilemma.html">Prisoner's Dilemma</a> games played on networks. On the first page I'm mainly working through some visual examples. You can also see some of the general questions these examples inspired. ("Maybe this is all about...")<br />
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The first half of the second page shows me asking questions (indicated by the <u>Q:</u>) and formulating hypotheses about how different models might be connected. I typically jot down my thoughts in real time as they occur to me, so that it almost feels like journalling. I tend to write in complete sentences, but sometimes a thought will end mid-sentence as something else occurs to me. I'll also go back and write in the margins (e.g. the circled questions at the top right of the second page) if I have an idea that connects to something I wrote earlier. <br />
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The second half of the second page shows some calculations as I test one of the hypotheses generated above. Note the circled line with the words "NOT TRUE" to the right. Mistakes and retractions are ubiquitous in my notebooks (as they probably are in the scratchwork of most mathematicians).<br />
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My favorite position for such notebook-scribblings is reclining in a couch or comfy chair, as Anna deftly illustrates:<span id="goog_1289534347"></span><span id="goog_1289534348"></span><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghUAXI8SNVaqKSJXMi5ycS-mhwzykfawp3IaHyfYdUOWbqXgwPGo7SARXo3Md4aukhbNkWLCEywJLywYm0jrm-UfqlsApVIaYlnYiUKddr1xr-ZYJflqym0wF2adp6TCe_de7i0F3mCkJ8/s1600/benatwork.jpg.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEghUAXI8SNVaqKSJXMi5ycS-mhwzykfawp3IaHyfYdUOWbqXgwPGo7SARXo3Md4aukhbNkWLCEywJLywYm0jrm-UfqlsApVIaYlnYiUKddr1xr-ZYJflqym0wF2adp6TCe_de7i0F3mCkJ8/s320/benatwork.jpg.jpeg" /></a></div><br />
I tend to get antsy when sitting upright for too long. In fact, I'm a big fan of changing scene in general. If I'm stuck in one room with no good ideas, I'm liable to go searching for another room to work in. Perhaps this helps me get a new perspective on what I'm doing, or maybe it just stops frustration from building up.<br />
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I should add that many of my best ideas actually come in the shower, or jogging, or in other situations where my brain has the time and space to chart its own course. Other mathematicians I've spoken to share this experience. If you've been focusing on a single problem for long enough, it can seep into your subconscious, which may continue to generate ideas even when you're doing other things. Back in college (when I was a pure mathematician) I even got to the point of solving homework problems in my sleep, though the sleep was not exactly what you'd call "restful".<br />
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I'll end with a call to other science bloggers and writers. The <a href="http://www.theparisreview.com/index.php">Paris Review</a>, since the 1950's, has conducted a <a href="http://www.theparisreview.com/literature.php">series of interviews</a> with world's preeminent writers on their process: how they generate their ideas and shape them into finished pieces of writing. Collectively, these interviews have helped shape public perception of writing as an occupation, and illustrated the variety of methods that writers employ. In this age where science is increasingly misunderstood and distorted in the public eye, I think it would be powerful to have a similar series of documents illustrating the daily processes of scientists. So I'd encourage any science bloggers/writers reading this to consider expressing your own personal "scientific method" to the general public, and pass the word along!Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com5tag:blogger.com,1999:blog-8398797088391606752.post-91191385818597336492010-08-25T20:48:00.000-07:002010-08-25T20:51:03.032-07:00Eusociality and a blow to kin selectionA new paper hit the internet today. "<a href="http://www.nature.com/nature/journal/v466/n7310/full/nature09205.html">The Evolution of Eusociality</a>" by Martin Nowak, Corina Tarnita, and E.O. Wilson re-frames an old evolutionary question and strikes a blow in an increasingly heated debate.<br />
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Eusociality is when individual organisms act as a collective reproducing unit. The best-known examples are ants and honeybees, but recently discovered examples include certain beetles, shrimp, and mole rats. Typically all reproduction is done by a single queen, and the rest of the colony exists only to support and protect the queen. Eusociality represents the highest degree of social organization found in nature. <br />
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The evolutionary origins of eusociality are something of a puzzle. To transition to eusociality, individuals must give up their own reproductive potential to support that of the queen. This is the ultimate sacrifice, as far as evolution is concerned. If evolution favors those who produce the most offspring, how can it select for actually <i>giving up</i> the chance to reproduce?<br />
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The classical answer to this question is kin selection: the idea that cooperative acts can occur between close relatives. Dawkins explained this using the concept of "selfish genes" that promote cooperation with others who have the same gene. One proponent, J.B.S. Haldane, famously said he would jump into a river to save two brothers, or eight cousins.<br />
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Ants and honeybees, the two oldest-known examples of eusocial animals, have a special genetic structure in which siblings share 3/4 of their genes, as compared to 1/2 in most sexual reproducers. It seemed reasonable that these close genetic relationships made possible such large-scale organization and extreme altruism.<br />
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However, as more eusocial species were discovered, including mammals, this association fell apart. There no longer appears to be any significant relationship between eusociality and relatedness of siblings.<br />
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Nowak, Tarnita, and Wilson provide a new model which focuses on the competition between reproductive units, which can be individual or collective. But perhaps more importantly, they thoroughly deconstruct the mathematics underlying kin selection theory.<br />
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The big debate in evolutionary theory right now is between those who believe all cooperation can be explained by kin selection (in its more mathematical guise of <a href="http://en.wikipedia.org/wiki/Inclusive_fitness">inclusive fitness theory</a>), and those who believe that the more standard natural selection concept has more explanatory power. This debate has become increasingly heated in recent years. <br />
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Backed by rigorous mathematics, the authors argue that <br />
<blockquote>Inclusive fitness theory is not a simplification over the standard approach. It is an alternative accounting method, but one that works only in a very limited domain. Whenever inclusive fitness does work, the results are identical to those of the standard approach. Inclusive fitness theory is an unnecessary detour, which does not provide additional insight or information.</blockquote><br />
The import of this argument might not be apparent to those not immersed in the field, but this paper could be a turning point in how the evolution of cooperation is understood. Social behavior cannot all be reduced to selfish genes. There are in fact <a href="http://plektix.fieldofscience.com/2008/11/evolution-of-cooperation.html">many mechanisms</a> allowing cooperation to evolve. Understanding these mechanisms will continue to be a fascinating question in evolutionary theory.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com2tag:blogger.com,1999:blog-8398797088391606752.post-91047056435986303762010-08-24T15:02:00.000-07:002010-08-24T15:04:40.213-07:00Is a new mode of evolution emerging?Evolutionary theorist <a href="http://www.susanblackmore.co.uk/index.htm">Susan Blackmore</a> argues in the <a href="http://opinionator.blogs.nytimes.com/2010/08/22/the-third-replicator/">New York Times</a> (and <a href="http://www.newscientist.com/article/mg20327191.500-evolutions-third-replicator-genes-memes-and-now-what.html">elsewhere</a>) that a new form of evolution is emerging, based on the replication of digital information.<br />
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This would be the third mode of evolution that we humans are aware of. The first is, obviously, the biological evolution of life. Organisms grow according to DNA blueprints, then produce offspring from copies of these blueprints, perhaps with some variations. Competition between variant copies drives the evolution of life as we know it. <br />
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The second mode of evolution is cultural. Ideas spread from person to person, and through this process, whole cultures evolve. Richard Dawkins coined the term "<a href="http://en.wikipedia.org/wiki/Meme">meme</a>" for the units of cultural evolution (i.e. the ideas that "replicate" themselves in people's minds), analagously to genes in biological evolution. Blackmore is a strong <a href="http://www.susanblackmore.co.uk/memetics/">proponent</a> of the meme concept, but there is much debate over the utility of this idea in explaining cultural evolution. In any case, it is clear that there are major differences between how biological and cultural evolution work. Understanding and quantifying these differences is a major project for evolutionary theory, and I hope some day to contribute to this effort.<br />
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Blackmore calls her proposed third mode of evolution "technological", but "digital" might be a more precise term. Every day, millions of files (encoded in binary) are copied from one location to another. Some files are even programmed to copy themselves. But copying isn't always perfect, and sometimes copies differ slightly from the originals. If these variant copies compete for the ability to reproduce, might we witness a whole new form of evolution in which the "organisms" (which Blackmore calls "<a href="http://www.susanblackmore.co.uk/memetics/temes.htm">temes</a>") are purely digital?<br />
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One reason this idea is compelling to me is it follows a pattern of <a href="http://plektix.fieldofscience.com/2010/03/symbolic-representation-is-key-to-major.html">symbolic representations driving changes in the evolutionary process</a>. Biological evolution took off with the advent of DNA/RNA encoding, in which the characteristics of an organism were recorded in an easy-to-copy format. Written language isn't necessary for cultural evolution, but it sure helps. It is much easier to copy the blueprints for, say, a motorcycle, and build new motorcycles from the copied blueprints, than it is to build a new motorcycle by observing an existing one. Symbolic languages facilitate the copying process which is essential for evolution. <br />
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Binary is one of the most powerful symbolic languages ever, with the potential to encode almost anything. Binary is also extremely easy (for computers) to copy. It is therefore quite appealing to think that the copying of binary files could form the basis of a new evolutionary process. The <a href="http://en.wikipedia.org/wiki/Artificial_life">artificial life</a> community has been experimenting with this idea for several decades, and I am far too ignorant to comment on their successes and challenges.<br />
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I will say that, so far, I can't see much evidence of Blackmore's teme-based evolution happening outside of simulations. The closest parallel seems to be computer viruses, which can copy themselves from computer to computer and sometimes mutate along the way. But these viruses are all designed by humans, and I don't know of any that have evolved novel functionality on their own. Viral videos and other internet memes also rely on the copying of digital information. But the decision to copy such memes is made by humans, so this falls within the domain of cultural evolution. <br />
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Will we, in the future, see pieces of code that replicate themselves across the internet, compete with each other, and evolve toward increasing complexity? And if so, will we be able to harness this process for good? Or will it be a mere nuisance, like weeds or spam-bots? I'm not yet convinced that this will happen, but these are important questions to ask.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com4tag:blogger.com,1999:blog-8398797088391606752.post-17595727351786844222010-07-29T07:23:00.000-07:002010-08-30T13:07:09.229-07:00Update on Game-Based High SchoolI <a href="http://plektix.fieldofscience.com/2009/06/middlehigh-school-that-teaches-complex.html">wrote</a> a while back on a high school that uses games as its primary pedagogical tool. NPR's All Things Considered has a new <a href="http://www.npr.org/templates/story/story.php?storyId=128081896&sc=emaf">report</a> on the school. Excerpt:<br />
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<blockquote>"In math, we're traveling around the world," says sixth-grader Rocco Rose, a student at Quest to Learn and a citizen of Creepytown — an imaginary city where his class learns math and English. The students play travel agents, convert currencies, keep blogs about their travel experiences and budget trips.<br />
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Creepytown is structured like a video game that has jumped out of the computer. During their 10-week "missions," students learn to adapt and improvise.<br />
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"The second trimester, Creepytown went broke," Salen says. "They had ... an economic crisis. So the kids worked to figure out ... what had gone wrong. And then they proposed the design of a theme park to bring revenue in."<br />
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<b>Systems Thinking</b><br />
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Salen says playing with complex dynamic systems gives kids opportunities to learn.<br />
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Students "learn how to solve problems, how to communicate, how to use data, how to begin to predict things that might be coming down the line," she says.<br />
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They also learn something called systems thinking, which Salen says is one of the cornerstones of 21st century literacy. It helps you understand how the behavior of a derivatives trader in Hong Kong affects housing prices in Florida. When a system becomes sufficiently complex, Salen says, you start to get outcomes that are hard to foresee.<br />
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"Suddenly you begin to get what's called emergent behavior, and in emergent behavior, that system, the elements in it, begin to relate to one another in ways that can be unpredictable," she says.</blockquote><br />
Hell yeah! If we can give the next generation early experience with complex systems and unintended consequences, there may be hope for the future yet.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com0tag:blogger.com,1999:blog-8398797088391606752.post-41661536793409125722010-07-23T12:36:00.000-07:002010-07-23T12:36:19.384-07:00Big Bang Big BoomEvolution-inspired animated street art, and one of the most amazing works of art I've seen in any medium:<br />
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<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/sMoKcsN8wM8&hl=en_US&fs=1"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/sMoKcsN8wM8&hl=en_US&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com0tag:blogger.com,1999:blog-8398797088391606752.post-23400783098978707562010-06-02T20:03:00.000-07:002010-06-02T20:03:31.668-07:00Quantum Reality and the Measurement ParadoxI may be primarily an evolutionary theorist nowadays, but I have many interests, and this summer is proving to be a good time to explore some areas not directly connected to my need to publish. Lately I've been doing some reading on quantum mechanics, and what it tells us about reality.<br />
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QM is astonishing in both its mathematical elegance and its fundamental counter-intuitiveness. Unfortunately, I think many (including mathematicians) are discouraged from learning about quantum because it is typically presented assuming a deep knowledge of classical mechanics. But in my view, QM isn't just a theory about physics. It's a theory about reality and truth, and many of its implications can be understood with no knowledge of physics at all.<br />
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The essential feature of quantum reality, and what makes it different from the way we naturally think, is the <i>superposition principle</i>. It says that if <i>A</i> and <i>B</i> are two possible states of something (a photon, a cat, the whole world...), these states can be added to get another possible state, <i>A</i>+<i>B</i>. For example, if a light switch can exist in ON and OFF positions, there must also be a possible state ON+OFF. Subtraction works too: the state ON-OFF must is a valid state as well. To my mathematician friends: we are moving from the <i>set</i> of possibilities {ON, OFF} to the two-dimensional <i>vector space</i> generated by the basis vectors ON and OFF. <br />
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It's important to delineate what is <i>not</i> happening here. ON+OFF does not mean that the switch is stuck somewhere between on and off. It also does not mean that it might be either on or off and we just don't know which. ON+OFF is a fully-determined state which is neither ON nor OFF, but a superposition of the two.<br />
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Of course, no one has ever observed a light switch being ON+OFF. Something happens when we observe these superimposed states, such that we can only ever see the "classical" states ON or OFF. <br />
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In the standard (a.k.a. Copenhagen) interpretation of quantum mechanics, when a superimposed state is observed, it "collapses" into one of the classically observable states. In the case of ON+OFF, whenever we look at the switch, it collapses into either an ON or and OFF state, with equal probability. But <i>until</i> we look at it, in remains in the state ON+OFF, which has unique properties making it distinct from either the ON or OFF state. <br />
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This interpretation poses a host of logical difficulties. What exactly constitutes an "observation", and how would a light switch "know" that it is being observed and should therefore jump into an observable state? Many of the best minds in physics believe that observation has something to do with consciousness, but this raises several obvious questions: How is consciousness is defined? What gives it this unique power to induce jumps in physical states?<br />
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I've recently come across a new interpretation, proposed in 1997 by Cerf and Adami. They suggest that superimposed states do not collapse when observed, but rather the observer becomes entangled with the observed, forming a larger superimposed state. <br />
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To illustrate this, let's turn to Schrodinger's cat paradox. An atom is prepared in a superposition of two states: one in which the atom will emit a photon and one in which it won't. This atom is placed in a box with a cat and an apparatus which will release poisonous gas if the photon is emitted (the details of the setup are unimportant). According to the Copenhagen interpretation, the system exists in the superimposed state<br />
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(EMIT and DEAD_CAT)+(NOT_EMIT and ALIVE_CAT)<br />
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until such point as the box is opened by a conscious observer, whereupon the system "collapses" and the cat becomes either just alive or just dead. (This raises some questions of whether cats count as conscious, but such objections only deepen the underlying paradox).<br />
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In the Cerf and Adami interpretation, there is no collapse, only entanglement. When we observe the contents of the box, we ourselves become entangled with this system. We become part of the resulting superimposed state:<br />
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(EMIT and DEAD_CAT and WE_SEE_DEAD_CAT) <br />
+ (NOT_EMIT and ALIVE_CAT and WE_SEE_ALIVE_CAT)<br />
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Of course, we still only see the cat as being either dead or alive, not both. But according to Cerf and Adami, this is only because the state EMIT+NOT_EMIT of the atom is unobservable to us. Of the full superimposed state, we can only see the parts pertaining to the cat and to the observer. Observing only part of the system, it <i>appears</i> to us that the cat is either alive or dead. Anyone else observing the cat would see it to be in the same state that we do, but this is only because the second observer is just as entangled as we are. The cat is still superimposed between alive and dead, and if we could see the whole system, we'd realize that we ourselves are superimposed between seeing it alive and seeing it dead. <br />
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From a mathematical point of view, Cerf and Adami's proposal neatly resolves the paradox of observation and state collapse. However, it raises far more troubling questions of its own, which the authors do not begin to explore. <br />
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Think of a decision you made today. It's not unreasonable to think that there are quantum processes in our brain whose outcomes affect our decisions (this view is advanced by my friend <a href="http://www.informationphilosopher.com/about/">Bob Doyle</a>). Let's say that there was a certain quantum state in your brain whose collapse into one of two states (in the Copenhagen interpretation) tilted your decision one way or the other.<br />
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If this is true, then in Cerf and Adami's interpretation, we actually exist in a superposition of realities: one in which your decision went one way and one in which it went the other. You can only see one of these realities, and everyone you've encountered since has become entangled with you and therefore sees the same reality that you do. But the alternate reality is playing itself out, <a href="http://www.imdb.com/title/tt0120148/">Sliding Doors</a>-style, superimposed on top of our own.<br />
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Furthermore, due to <a href="http://www.dailymotion.com/video/x273ti_quantum-double-electrons-pattern-in_family">quantum interference</a>, any actions taken in this reality can affect any of the superimposed other realities. And conversely, anything your alternate-reality twin does in his or her reality can affect the reality you and I see.<br />
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I tend to believe Cerf and Adami's idea, because millenia of physics research have shown us that the mathematically elegant solution is usually the right one. But this means our universe is weirder than we can possibly imagine.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com13tag:blogger.com,1999:blog-8398797088391606752.post-74675447462594079312010-05-13T14:33:00.000-07:002010-05-13T15:38:06.873-07:00The Future of Evolutionary Theory?Well... it's been quite a month. This April I (a) successfully defended my PhD thesis, and (b) won a Templeton Foundation fellowship to work with Martin Nowak at Harvard for two years. For those who don't know him, Nowak is one of the world's top researchers in abstract evolutionary theory. Working with him will be a tremendous challenge and opportunity.<br /><br />So how to respond to this challenge? My vision for the next two years is to begin laying out a new mathematical approach to the study of evolution. Allow me to explain.<br /><br />Currently, the field of evolutionary theory revolves around the study of models. As I <a href="http://plektix.fieldofscience.com/2010/02/idea-of-applied-mathematics.html">discussed</a> a few posts ago, a model takes a real-world situation and reduces it to those features that are considered essential. The model can then be analyzed mathematically, and hopefully the results tell you something useful about the original real-world problem. <br /><br />Models are powerful tools for understanding the world, but they have a fundamental limitation: they always depend crucially on the particular simplifying assumptions made at the model's inception. A different set of simplifying assumptions might yield completely different conclusions, and it's often unclear which model is more relevant to the natural world.<br /><br />This problem is ubiquitous in mathematical biology: a paper might devote pages and pages of mathematical analysis to understanding one particular model, but if that model were changed just slightly, all that analysis would suddenly be invalid. The question in my mind is always "What insight do we gain from our mathematics?" All the technical derivation in the world is of limited value unless it can help us reach broader conclusions.<br /><br />My vision is to shift the focus of evolutionary research from models to theories. A theory, like a model, rests on certain fundamental assumptions, but in the case of a theory these assumptions are so broad as to apply to any system in question. For example, a theory might specify "Individuals interact, reproduce, and die in some manner", whereas a model would have to specify the particular manner in which this occurs. So a single theory can encompass many (even infinitely many) models. It's like the difference between saying "3+4=4+3" versus "x+y=y+x for any real numbers x and y". Moving from models to theories is a leap forward in abstraction, generality, and power.<br /><br />Shifting to theories also changes the kinds of conclusions you can reach. Models produce predictions: specific outcomes that would occur if reality indeed conformed to the assumptions of the model. Theories produce theorems: general statements that apply to any system of the type in question. A theorem won't tell you exactly what will happen, but it can characterize of the space of possibilities. And that's what I think is needed in evolutionary theory: a general understanding of what can or cannot result from evolution, and how this depends on the certain features of an evolutionary process. <br /><br />So that's my research agenda in a nutshell. I'm extremely excited to see where this leads, and I'm looking forward to sharing more in the future.Ben Allenhttp://www.blogger.com/profile/15594823641514744644noreply@blogger.com4