Field of Science

How much can we know?

Scientific progress is often viewed as an inexorable march toward increasing knowledge. We'll never know everything about the universe, but we've gotten used to the idea that we keep knowing ever more, at an ever-increasing rate.

However, as we discussed some time ago, human beings are creatures of finite complexity. There is only a finite amount we can do, and, more relevant to the present discussion, there is only a finite amount we can know. It's very likely that the human brain holds less pure information than the average hard drive. So while we humans as a collective might be able to increase our knowledge indefinitely, our knowledge as individuals has a definite limit.

What does this limit mean for the study and practice of science? For one thing, it limits the knowledge that a single scientist can apply to a particular problem. A researcher studying a virus can't apply all of science, or all of molecular biology, or all of virology to his study. Even just the scientific knowledge about this particular virus might be too much to fit into this researcher's brain. As scientists, we attack our problems using whatever knowledge we've gained from coursework, reading, and conversations with others--a tiny fraction of the wealth of potentially relevant knowledge out there.

Worse, as the frontier of knowledge keeps expanding, the amount of background knowledge needed to comprehend a single patch of this frontier increases steadily. I started my math career in differential geometry/topology: a beautiful subject, but one that requires years of graduate coursework to understand current research questions even on a superficial level. Since we have finite brainpower, no individual can maintain this kind of expertise in more than a few subjects. So we become specialists, unable to discuss our research with anyone outside our narrowly defined field. Before I switched to complex systems, I was continually frustrated by the isolation that came with specialized research. And I hear this same frustration from many of the other math/science grad students I talk to.

The danger is that science will keep branching into smaller, more arcane, and more isolated subsubdisciplines. This would make interdisciplinary research increasingly difficult, and the prospect of a science career ever more daunting and unappealing for students. And it would not get us any closer to solving some of our biggest problems in science, which lie not at the fringes of some highly specialized discipline, but in the synthesis of results from all branches of science.

What is needed is a sustained push for big-picture thinking. Whereas small-picture science focuses on the complex and the narrowly defined, big-picture sceince seeks the broad and the simple. It combines the many complex discoveries made by small-picture scientists, and distills them into ideas that can fit in a single human's head.

Here's a useful example, stolen from the website and based on this paper:

The above is a diagram of a yeast protein interaction network. It represents the cumulative work of many scientists who investigated whether and how certain proteins interact with each other. A remarkable achievement, certainly.

But the sheer volume of information makes this diagram useless to anyone but a specialist, and probably not very helpful for the specialists either. Trying to draw conclusions from a diagram like this would be like trying to navigate cross country using a map that shows every side street and alley in the US. It's just too much information for one brain to handle.

The authors go on to describe an algorithm that can transform complex networks like this:

into simplified ones like this:

that represent simple, understandable relationships.

I don't mean to belittle the work done by small-picture scientists; without them the big picture thinkers would have nothing to talk about. But I think the scientific establishment is so structured around the small-picturists that big picture thinking often gets squeezed out, which only impedes our understanding of science in general.


  1. i wish you were the moderator for Philosophy Café.
    Actually, how about starting such a thing for complex systems?

  2. I don't think we need to "push" anything at all. The pendulum between analytic and synthetic modes works fine guided by its own invisible hand. I know it does in mathematics and I'm sure it does in the sciences as well.

    Mathematics over the millennia has expanded and contracted many times. A field is split into finer and finer disciplines, which are then related back into a new unifying vision. This happens over and over again with no guidance from well-meaning human meddlers. You just have to have the patience to watch for it, because the cycle turns at a glacial pace.

  3. The simplification of that one diagram reminds me of what I read about Godel's work in GEB...and then makes me think that john armstrong is right. Won't this all become simplified, applied within more broadly-applicable formulae, and then once again get simplified?

  4. John and Mundane, you make a very good point. The cycle of analysis and synthesis has indeed repeated thoughout history, and will no doubt continue.

    I guess my worry is that institutionally, grad students are pushed toward the small-picture end of scientific research, and I don't really see big picture thinking being fostered in coursework or in student-advisor interactions. And I think the institutional focus on the small picutre turns off some potential scientists.

    @Raya-I'd love for there to be a "cafe" type discussion board for complex systems. But I have neither the time nor the expertise to start such a thing any time soon.

  5. Over at the Secret Blogging Seminar, Noah Snyder has kicked off a series on subfactors and planar algebras.

    Not only is this mixing two seemingly-disparate fields on its face, but he's "taking a very indeosyncratic representation theory approach to the topic". This is an interdisciplinary approach to highlight different aspects of the theory than the standard treatments do. And his advisor seems to be backing him on it.

  6. Noah Snyder? I went to math camp with that kid!

  7. I think words like information and knowing have some useful abstract meanings that can become mixed up
    with more practical evaluations. Yes, a hard drive can hold a lot more information in the meaning of data, but that doesn't measure up to knowing. A hard drive could hold a million expert programs while the average human might achieve expertise in maybe 1,000 expert activities such as medical diagnosis. But the hard drive can only achieve behavior, which to me means 'know how to do' of a fragment of the human potential. The problem of AI is that there is no overseer which knows when to execute its expertise as contexts evolve. The human brain has been hardwired over millions of years of evolutionary challenges, some of them random. There is no algorithmic method to discover the rules the brain uses, Minsky, Neat vs. Scuffy, and it is intractable to discover all complex rules which have rules, John Case, COLT. Thus I think the hard drive comparison replaces information as abstract data from the meaningful information which is the basis of a self-aware knowledge; the ability to make decisions, to plan, to prioritize important information even when hard drives become large enough to create more synapses than the human brain.

  8. It's certainly true that the brain can do many important things a hard drive can't do. And I agree that a hard drive doesn't really "know" anything, any more than a sheet of paper does.

    But I still think there is a concrete, physical limit to the amount of raw information our brains can store, and this limit is probably less than can be stored in a hard drive.

    Why does this matter? Suppose there was some scientific discovery out there to be made, but to discover it would require you to hold a million points of data in your head and understand the relationships in that data. Our brains are simply incapable of doing that. Data visualization techniques can help significantly, but even these can't clarify the most complex relationships. Such a discovery would have to be made by a machine learning system, or not at all.


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