We humans are an egotistical bunch. We'd like to think that we are capable of anything, that our minds are infinite, and that there is no limit to our potential ingenuity.
Nevertheless we are, by any measure, creatures of finite complexity. Our bodies and our brains contain a finite number of cells, we live a finite amount of time, and at any given time there are a finite number of things we are physically and mentally capable of doing.
Since our complexity is finite, we should be able to quantify it somehow. As we discussed last time, there are different ways of quantifying complexity. We could look at ourselves as a system of cells and chemicals, and ask how many pages it would take to write a complete description of how a human is composed of these parts. Alternatively, we could look at ourselves as active beings and ask how many potential actions we could take at any given instant. Or how many actions we actually take (on average) over the course of a lifetime. Yaneer Bar-Yam has suggested this example: You could record a digital movie of a person from birth until death, store this movie in a digital file, and calculate the size of this file in gigabytes. I don't know if any of these computations has ever been tried, but each would give you an approximate number which quantifies just how finite we are.
Scary, huh? At least I find it so.
This may seem like just an interesting excercise, but it has important consquences due to the following fundamental rule:
To illustrate this rule, suppose you are trying to manage a group of people; say, a family, business, class, or club. You might wish to control the actions of all of them, to make sure they don't act against your wishes. However, the group is more complex than you are because there are more of them then there are of you. The only way to control them completely would be to reduce the complexity of the group; for example, you could chain them to a wall and thereby limit their potential actions.
Nevertheless we are, by any measure, creatures of finite complexity. Our bodies and our brains contain a finite number of cells, we live a finite amount of time, and at any given time there are a finite number of things we are physically and mentally capable of doing.
Since our complexity is finite, we should be able to quantify it somehow. As we discussed last time, there are different ways of quantifying complexity. We could look at ourselves as a system of cells and chemicals, and ask how many pages it would take to write a complete description of how a human is composed of these parts. Alternatively, we could look at ourselves as active beings and ask how many potential actions we could take at any given instant. Or how many actions we actually take (on average) over the course of a lifetime. Yaneer Bar-Yam has suggested this example: You could record a digital movie of a person from birth until death, store this movie in a digital file, and calculate the size of this file in gigabytes. I don't know if any of these computations has ever been tried, but each would give you an approximate number which quantifies just how finite we are.
Scary, huh? At least I find it so.
This may seem like just an interesting excercise, but it has important consquences due to the following fundamental rule:
You can't control a system that is more complex than yourself.The reason for this is simple: If a system is more complex than you, it has more possible actions than you have potential responses. So it will eventually present you with a situation for which you have no response.
To illustrate this rule, suppose you are trying to manage a group of people; say, a family, business, class, or club. You might wish to control the actions of all of them, to make sure they don't act against your wishes. However, the group is more complex than you are because there are more of them then there are of you. The only way to control them completely would be to reduce the complexity of the group; for example, you could chain them to a wall and thereby limit their potential actions.
If you wish to organize a group without such restrictive measures, your best option is to put incentives and disincentives in place to promote the actions you wish. Then step back and let the group evolve as a system. If you designed your incentives correctly, the group should evolve into a system with the properties you desire. If not, the incentives should be changed. But no matter how you set up the system, you will not be in control of it. The group and its members will be making their own decisions, and different groups will evolve differently under the same set of incentives. This is the nature of the game.
Tune in next week, when we find that this discussion has massively political implications!
About the complexity of a human body, a good way to determine the simplest way to describe a human body is to look at the mechanism created by the greatest creative force in existence, evolution. The human genome is relatively small, for a description of a complex sentient being 32 billion base pairs is pretty small*, yet describes the human body completely enough to make a human.
ReplyDelete*http://nature.ca/genome/03/a/03a_11a_e.cfm
Let's see. A ninety-minute movie can be compressed in DivX format and stored on a CD, so to get an order-of-magnitude figure, let's say that it takes a gigabyte to store an hour of video. That makes 24 gigabytes per day, and 24 * 365 = 8,760 gigabytes per year (if you record sleep too). Assume a full-fledged human lifespan is eighty years, and you get 700,000 gigabytes, or the better part of a petabyte, to represent a human life.
ReplyDeleteGood point, sami! The genome can certainly be thought of as a way to describe a human, and is useful in comparing our complexity to that of other biological entities.
ReplyDeleteThe human genome project estimates that a single genome takes about 3 gigabytes to store, much less than the digital video file.
I remember reading somewhere that the human genome is smaller than the Microsoft Word, though that seems a bit suspicious if it's 3GB
ReplyDeleteIt probably depends on the version of Word.
ReplyDeleteI'd also like to add that the genome describes what a human IS, whereas the video file describes what a human DOES. Very different.
If genome size is your measure of complexity, don't forget the humble onion. They've got almost five times as much DNA as we do. The marbled African lungfish beats even that.
ReplyDeleteIt might be better to describe the genome as specifying "how humans are made" rather than "what humans are". Consider that we have far more cells in our body (roughly one hundred trillion) or even in our brain (call it 100 billion in round figures) than we have bases in our genome. The DNA doesn't code for Cartesian coordinates of cells, but rather patterns of growth and development which lead to the eventual form of the human body.
I wonder if Kolmogorov-Sinai entropy, which measures the "rate of entropy increase" during a process, could be applied to biological development?
Blake: I think genome size isn't useful as a complexity measure, but as a complexity bound. There's a lot of wasted space in any given genome.
ReplyDeleteTo say that a human genome is 3GB really means that a human can (biologically) be described in less than 3GB.
This is what happens when you start talking about complexity: the questions just keep multiplying!
ReplyDelete1. Thanks Blake for pointing that out! I suppose I could argue that the generating process for humans is so different from that of onions or lungfish that the numbers are not comparable. And John is correct that most of the space in a genome seems to be wasted. Still, we shouldn't completely discount the possibility that there is a deep reason for these organisms having more DNA than us.
2. Blake is also correct that DNA is more of a generating algorithm for humans than a description of what humans actually are. But generating algorithms are often taken as measures of complexity; this is the basis of Kolmogorov complexity.
Consider the number pi. Most of us think of it as a richly complex number, but it can be generated from a simple computer program. Does that make it simple? You decide!
3. Kolmogorov-Sinai entropy does measure the rate of (global) entropy increase in a system. However, a longer genome has lower physical entropy than a shorter one, so the process of genome lengthening involves a (local) decrease in entropy. Longer DNA strands appear more complex because the complexity has "scaled up" from the level of atoms to the level of molecules. Sill, I won't discount the possibility that KS entropy could tell us something meaningful here.
The interplay of complexity and scale will definitely be discussed in a future post.
@blake
ReplyDeleteIt might be better to describe the genome
as specifying "how humans are made"
rather than "what humans are".
I didn't think of that, which is a very good point. I think though, that I have a pretty good analogy. While a bitmap of a high resolution circle would describe exactly what the image of that circle is, an svg would result in the exact same image but would be more compact. In the discussion so far the bitmap would be the raster image and the genome would be the vector image.
Samineru:
ReplyDeleteI like that analogy. Still, we should remember that the "algorithms" of biological development are horribly messy — hacks on top of kludges on top of billion-year-old mutational accidents. For a comparison of Drosophila morphogenesis and computer code, see this essay by PZ Myers.
Ben:
I wasn't thinking so much about the change in DNA complexity over evolutionary time, but rather about whether we could quantify the change in complexity during embryo development: if you abstract the heck out of a zygote, you might be able to treat it as a dynamical system to which KS entropy is applicable.
About the phrase:
ReplyDelete"You can't control a system that is more complex than yourself."
What is the theorie about 2 systems working together?
If you work together with someone else, I think you would be more complex then 2 individuals. Is there a relation between the number of controllers working together, and the amount of individual, equally complex people/things they can control?
billions of chemical reactions occured your body with out even knowing it.they are building and breaking then casscading like waterfalls then start to regroup in cycle. very complex.the only notion you can come up is there God.
ReplyDelete