Big Picture Part Two: Understanding

One of a series of quick posts on the six sections of my book The Big PictureCosmos, Understanding, Essence, Complexity, Thinking, Caring.

Chapters in Part Two, Understanding:

  • 9. Learning About the World
  • 10. Updating Our Knowledge
  • 11. Is It Okay to Doubt Everything?
  • 12. Reality Emerges
  • 13. What Exists, and What Is Illusion?
  • 14. Planets of Belief
  • 15. Accepting Uncertainty
  • 16. What Can We Know About the Universe Without Looking at It?
  • 17. Who Am I?
  • 18. Abducting God

If, as a naturalist, you want to seriously engage with people who might not agree with you already, you’re going to have to talk a bit about epistemology — how we know what we know. It’s common for non-naturalists to level the accusation (perhaps sincerely felt) that naturalists simply assume their conclusion, and use methodologies that are not sensitive to the possibility of something outside the natural world.

I don’t agree, so in The Big Picture I spend a decent amount of time talking about how we actually go about the task of understanding the world. In particular, science doesn’t presume naturalism, it concludes that it’s the best explanation for the world we experience. Provisionally, of course — science never “proves” anything in the logical sense, so we should always be open to changing our minds in the face of new evidence. I talk a good deal (maybe too much) about Bayesian reasoning and how to update our beliefs.

As an extremely simple — but usefully illustrative — example of this philosophy in action, I concocted a straw-man example of theory choice:

Simplicity is sometimes easy to gauge, sometimes it is less so. Consider three competing theories. One says that the motion of planets and moons in the Solar System is governed, at least to a pretty good approximation, by Isaac Newton’s theories of gravity and motion. Another says that Newtonian physics doesn’t apply at all, and that instead every celestial body has an angel assigned to it, and these angels guide the planets and moons in their motions through space, along paths that just coincidentally match those that Newton would have predicted.

Most of us would probably think that the first theory is simpler than the second — you get the same predictions out, without needing to invoke vaguely-defined angelic entities. But the third theory is that Newtonian gravity is responsible for the motions of everything in the Solar System except for the Moon, which is guided by an angel, and that angel simply chooses to follow the trajectory that would have been predicted by Newton. It is fairly uncontroversial to say that, whatever your opinion about the first two theories, the third theory is certainly less simple than either of them. It involves all of the machinery of both, without any discernible difference in empirical predictions. We are therefore justified in assigning it a very low prior credence. (This example seems frivolous, but analogous moves become common when we start talking about the progress of biological evolution or the nature of consciousness.)

Some people don’t like the Bayesian emphasis on priors, because they seem subjective rather than objective. And that’s right — they are. It can’t be helped; we have to start somewhere. On the other hand, ideally the likelihoods of making certain observations can be objectively determined. If you have a certain theory about the world, and that theory is precise and well-defined, you can say with confidence what the chances are of observing various bits of data under the assumption that your theory is correct. In realistic circumstances, we are often stuck trying to evaluate theories that aren’t so rigorously defined in the first place. (“Consciousness transcends the physical” is a legitimate proposition, but it’s not sufficiently precise to make quantitative predictions.) Nevertheless, it’s our job to try to make our propositions as well-defined as possible, to the point where we can use them to objectively establish the likelihoods of different observations.

Everyone’s entitled to their own priors, but not to their own likelihoods.

Sadly, as much as we might aspire to be, we humans are not always completely rational. One concept I talk about is that of a “planet of belief” — rather than grounding our beliefs on an unshakeable foundation, we assemble a collection of beliefs that hold together under a mutual epistemological attraction. That’s not a mistake, it’s the best we can do. The secret is not to grow so attached to our planets that we equip them with impregnable defense systems, so that they can never be altered no matter what new things we learn.

Planets of Belief

Here we see some representative components of three plausible planets of belief. Can you figure out what kind of person each might belong to?

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11 Responses to Big Picture Part Two: Understanding

  1. Richard W says:

    Clockwise, from left Aristotle, Carroll and Descartes, but it’s been a long time since I read two of them!

  2. Tim Zajac says:

    Would it be possible that that the planets of beliefs we have are more better conceived as the top of a funnel? So as we transverse to the very tip of the funnel we become more abstract such as mathematics or our the basic assumptions we need to make? (I’m on my break from work so I’m typing this on my phone which is why this is short. I just hope you understand the question. If not, I’ll ellobotate more tomorrow…unless I totally butchered what you’re arguing).

  3. S says:

    Have you considered using (the inverse of) Kolmogorov complexity as a measure of the prior? In your example, Angelic theories will have way more complexity than Newtonian physics. I can’t even begin to imagine how you would program a computer in the angelic scenario.

    This idea is very similar to Jeffrey’s objective prior btw.

  4. g says:

    S: If you make it not 1/Kcomplexity but 1/2^Kcomplexity and fill in the details appropriately, what you get is “Solomonoff induction”. The probabilities you get out depend on what machine you use to define Kolmogorov complexity, but not too much: if you pick any two machines, the ratio between the probabilities you get is bounded by a (possibly enormous) constant. Compared with any possible computable way of doing empirical induction, this is never worse by more than a (possibly enormous) constant factor.

    Of course, it’s not actually computable, which is a bit of an obstacle to (e.g.) programming it into a computer and immediately getting out a general-purpose (very slow) AI.

  5. Torbjörn Larsson says:

    I have my usual problem of discerning the science under the burden of an unnecessary overgrowth of philosophy. (If something should be ejected on grounds of simplicity, it would be my nearest candidate!)

    But I recognize bayesian induction as a general means of learning. [ ] And I recognize simplicity as a means of avoiding overtraining in learning processes. [ ]

    I wouldn’t be overly concerned. A better way of avoiding overtraining is used by our brains. Thanks to the bayesian mechanism of evolution they avoid overtraining by the use of symbols. [ ]

    Sounds familiar? Using symbolic methods means we can ease the constraint of going for the simplest theory, when necessary. Admittedly in general, because laws ultimately comes from the simplification inherent in symmetries, theories tend to be simple and hence applications complex.

    Note: As interested in astrobiology I recognize abiogenesis not as a belief but a testable hypothesis out of two observations. Early Earth was sterile because it was born hot, and now it isn’t. An abiogenesis event must have occurred along the way. Tests would be along the observation of Russell et al, who identifies ~ 20 Hadean geological traits that modern cells have frozen in under inheritance from our geological ancestor system. (Alkaline hydrothermal vent pH differential and size, available elements used, et cetera.)

  6. Platohagel says:

    Contextuality has some fundamental meaning here then regarding quantum cognition as the identification of developing positions within a philosophical timeline…..?

  7. Pete says:

    The “planet of belief” concept looks very much like the coherentism espoused by philosophers like WVO Quine. I like the idea but it suffers from the fact that any web of beliefs can be made coherent, even if its completely incorrect.

    I don’ think there’s anything wrong with foundationalism, or at least not when we move to a “modest” foundationalism, where the foundational beliefs aren’t taken to be infallible (but very likely to be on the right track). It also makes sense considering so many things we hold near and dear (mathematics, logic, theoretical physics) operate on foundational axioms or equations. There’s also foundherentism, a fusion of the two espoused by philosophers like Susan Haack.

    Interesting discussion all around. Keep it coming!

  8. Vizzini says:

    Let me put it this way. You’ve heard of Carroll, Aristotle, Descartes?

  9. Polonius says:

    Sorry to nitpick, but surely (at least two of) these three “theories” are not theories, but hypotheses? When flat-earth creationists argue that the theory of evolution is “only a theory”, scientists need to be able to argue that, in science, a “theory” isn’t a wild-assed guess: it’s a model that has survived a thorough peer review by people who would love to prove it wrong.

  10. Rhett says:

    One question as I’m listening…. You made the comment that science should not rule out the possibility of the supernatural or of being able to test/detect the supernatural.

    But at that point, should we be able to do that, doesn’t that mean that the detected/tested thing is no longer supernatural?

    In a sense, isn’t it impossible for there to be a supernatural? If Jesus were to return, per your example, that would not be a supernatural event. If we were able to see it, it would be due to photons emitted/reflected off of Jesus. That Jesus would be a natural thing in the real world. For us to be effected by something, it must be part of the natural world. In this case, granting the assumption, it might be a part of the natural world that we had not yet experienced, but it would still be part of the natural world.

    How can there be anything supernatural? Or, even if there was, there is no possible mechanism by which we could experience it.

    So the statement by the NAS is true, the supernatural is outside of the purview of science. Science only works on the natural…

    I was sort of surprised by your take there….


  11. Fred says:

    Sean – I have a suggestion. Before publication, talk to some professional philosophers of science to critique your position and arguments, to validate and improve them. Don’t get me wrong, I personally have no problem with anything you have said. But I also had no problems with anything Stephen Hawking or Lawrence Krauss said in their books, but philosophers blasted them. You are one of my favorite authors, and I’d hate to see it happen to you. My impression is that you have a good working knowledge of philosophy, better than most physicists, but don’t let hubris get the better of you.