Archive for January, 2012

Understanding the Mind

Why don’t we understand psychology? We have highly developed knowledge of almost everything we can observe, other than people. The light of science has been shone into every corner of the observable world, but for some reason it has not penetrated the realm of the mind to any significant extent. Why not?

A lack of curiosity is not the reason. There is little we are more curious about than ourselves.

Maybe the reason is that introspection is hard. We have high-fidelity sense organs to tell us about the outside world. Though we can see our own thoughts, we cannot see them with the kind of clarity that we can see the outside world. Our thoughts are shadowy and fleeting unto us.

And yet, we have very solid knowledge of the subatomic world, despite the most paltry means of observing it. Our introspective powers, even if they are dim, should be enough for a determined investigator to make progress.

Recognizing that introspection hasn’t gotten us to a general theory of psychology, psychology has now turned towards behavioral and neuroscientific methods. But these don’t seem to be working either. We still don’t have anything even remotely resembling a general theory of psychology. The question remains, why?

I think the reason is that people are complicated. The chains of causality which go into a “simple” human behavior are infathomably massive. They resist analysis.

With the most paltry means of observation, physicists were able to figure out the rules governing subatomic particles, because the rules governing subatomic particles are fundamentally simple. We haven’t been able to do the same with people, because the rules governing people are fundamentally complicated. Maybe an approximately correct theory of psychology would involve terabytes of equations.

How does one approach such a problem? My final answer is, I don’t know. I don’t have much experience with solving impossibly difficult problems.

I do think that I know some things about how to study psychology. In particular, I think I know that experimental psychology is not the best way to make progress on this problem.

Psychology, like many other fields, suffers from “science envy.” It wants to be like the physical sciences. But it shoots itself in the foot by trying to do this. What works for studying atoms, molecules, etc., doesn’t work for studying the mind.

In the physical sciences, the problem is one of studying fairly simple phenomena to the point of exhausting everything there is to know about them, and formulating fully precise and general theories of how they work. The methods of physical science work well for doing this.

In psychology, the problem is one of trying to learn more about an almost intractably complicated phenomenon. The nature of the task is that fully precise and general theories are basically out of the question. Our knowledge will always be vague and tentative, and full of exceptions. And, because we are studying people, our knowledge will always be influenced by our own biases.

In academia there are strong norms against saying things that are vague, things that are tentative, things that have exceptions, and things that are biased. I think that these norms are not helpful for psychology. In psychology, when we refuse to say things that aren’t perfect, we end up saying nothing interesting.

How does one treat an intractably difficult problem? Not by waiting until one’s thoughts are perfect before sharing them. Not by holding others’ thoughts to high standards of correctness. Not by trying prematurely to fit the data into a generalized and rigid framework. Rather, one floats all kinds of hypotheses, without taking any hypothesis too seriously, and remaining radically open-minded.

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The Mind and the Brain

If the mind is not the brain, then we need to say that there is an additional thing out there, which is the mind. It will be a very mysterious thing.

That thing needs to interact with the brain somehow. We know, from experimental psychology, that many psychological functions are functions of the brain — the brain is implicated in memory, learning, sensory and motor functions, executive functions, language, etc.

So we need to say that the mind and the brain bear some sort of relationship to each other, and both contribute in their own ways to psychological functioning.

It makes sense to me to say that the brain serves functions which are more “mechanical,” lower-level, than the functions served by the mind. The mind, then, would serve higher-level functions. Under this view, we would say things such as these:

* My brain is the thing that computes sums, but my mind is the thing that enjoys doing math.
* When I compose music in my head, my temporal lobes contain a representation of the music, but my mind is the thing that is performing the creative act of composition.
* When I feel pain, there is a chain of signaling proceeding from my peripheral neurons, and eventually into my brain, but that which feels the pain qualia is my mind.

These examples give a rough idea of the sort of division of functions I am hypothesizing. I can make the idea more concrete with a metaphor.

Imagine that my body is a giant robot, like the robots in Gundam Wing, and my mind is the pilot of this robot. The brain is the set of instruments, in the cockpit, with which the pilot interacts with the world.

* The occipital lobe is a video display.
* The temporal lobe is a sound system.
* The motor cortex is a control panel, with joysticks, buttons, etc.
* The frontal lobe is a sort of digital assistant, which automatically performs various helpful tasks. Among other things, it has a pocket calculator, a calendar, and software that gives me important reminders from time to time.
* The brain also has a filesystem which stores all of my memories.

This crude analogy is intended to illustrate the sort of relationship that the mind and the brain might bear to each other. A finished theory would give precise descriptions of the respective functions of the mind and the brain; but I do not have that information.

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Mysterious Words

Bob and Elaine are scientists who live in a two-dimensional world called Finlandia. The people of Finlandia have a culture much like our own, including elaborately developed physics and mathematics. All of their physics and mathematics are in two dimensions. Everything they experience is in two dimensions.

One day, Bob has a vision of a three-dimensional sphere. He tries to explain his revelation to Elaine.

Bob: “I saw something grand and marvelous! Something unlike anything I’ve ever seen before!”
Elaine: “What was it?”
Bob: “Uh… It was this amazing thing! The most profound revelation I’ve ever had!”
Elaine: “Cool, but what was it?”
Bob: “It’s hard to explain. I think it might have been like the thing discussed in that old sacred text, ‘The Revelations of Thoth.’ I’m thinking of the passage that goes, ‘…and it shall be a form beyond form, a substance beyond substance, outside the world, without the limits of corporeal existence, and all men shall wonder at it.'”
Elaine: “But modern science has thoroughly falsified the Revelations of Thoth. Only the uneducated and superstitious believe in that any more. Are you slipping out of common sense, Bob?”
Bob: “Look, I know it doesn’t fit with science, but I saw it! It was right there in front of my eyes!”
Elaine: “Well, I’d like to see it for myself. Do you know how I can do that?”
Bob: “No, I have no idea. The vision just came to me.”
Elaine: “That’s no good. Well if I can’t see it for myself, can you at least explain clearly what you saw?”
Bob: “Yeah, the Revelations of Thoth explains it perfectly clearly.”
Elaine: “Hmm, well I don’t really understand it. I’m not sure that what Thoth is saying even makes logical sense. Can you try to explain it more clearly?”
Bob: “Sure, let me give it a try.”
[thinks for a few moments]
Bob: “I guess I saw outside space. I transcended space.”
Elaine: “What would that mean?”
Bob: “Uhh, there was this thing. It was like a circle, but it wasn’t anything like an ordinary circle. It was a super-circle.”
Elaine: “What is a super-circle? I mean, I know what a circle is, but what was ‘super’ about this circle?”
Bob: “It was outside space.”
Elaine: “That sounds like nonsense.”
Bob: “I’m telling you, it was outside space!”
Elaine: “What would that even mean?”
Bob: “Hmm, this isn’t working. I need to think more, and then I’ll get back to you.”
[the next day]
Bob: “OK, maybe now I can explain. So we have a circle, of radius r. Except that the circle is also every size smaller than r, and it repeats itself infinitely in super-space, without ever becoming more than one thing.”
Elaine: “Well that’s starting to look more like an explanation. But it’s full of contradictions and undefined terms. How could a circle be more than one size? How could something be repeated infinitely while only being one thing? And what the heck is super-space? You’re not even using your terms consistently. Before you said that thing was outside space; now you say that it’s in super-space. Which is it? And what would either of those even mean?”
Bob: “Well they really mean the same thing, you see. But you have a good point. I’m really bothered by my inability to explain this thing clearly. Let me try again and get back to you.”
[the next day]
Bob: “OK, I’ve got it now. Imagine a point, which expands to become a circle, and then shrinks back down to a point. Except this process is timeless. It is in every state at once, in an eternal state of superposition.”
Elaine: “Hmm… Here’s the thing, Bob. Your explanations sound sensible and scientific on the surface, but if you look more closely, they don’t really make sense. Like, what you said has a formal, mathematical flavor to it, but it can’t actually correspond to a coherent idea. What would it mean for a process to be timeless? How could a circle be more than one radius at once? And what do you mean by ‘superposition?’ I mean, I know what that word normally means in the context of physics, but you’ve appropriated it in a way that doesn’t make sense. I’m starting to lose faith in you, Bob. I think you’re just spouting pseudoscientific nonsense.”
Bob: “Huh! [storms off angrily]”
[a few days later]
Bob: “Elaine, I think I figured out why I can’t explain the super-circle to you. It’s beyond math, beyond physics, beyond language, even beyond thought. We can’t understand it with the intellect. It breaks logic. That’s why it can’t be explained in language. The only way to understand it is through direct experience. Anybody who hasn’t had a vision of a super-circle can’t make sense of discourse about it.”
Elaine: “…I don’t know what to say to that. I think you’ve lost it.”

Bob was not the first person to have a vision of a sphere. The person who wrote the Revelations of Thoth had also had such a vision; as had many Finlandian mystics. Even some Finlandian mathematicians had had visions of three-dimensional objects, but they generally kept the visions to themselves, for fear of being thought insane. So occasionally conversations like the one between Bob and Elaine would happen; but the concept of three-dimensional objects never gained wide acceptance in the scientific community.

This was true until several hundred years after Bob lived, when a mathematician laid down the theoretical framework which could generalize to arbitrary numbers of dimensions. This was harder for Finlandians to think of than it was for us, because they only had two data points from which to notice the pattern of N dimensions, whereas we had three.

Initially there was a great deal of controversy about the theory of higher dimensions. But it eventually became accepted, because it helped to resolve some obscure problems in physics and higher mathematics.

A lot of people regarded the theory of higher dimensions as nothing more than a meaningless formal device. Of course, the mathematician who formulated the theory was working from his direct experience of higher dimensions; and other mathematicians had such experiences, or intuited the possibility of such experiences. So there was an ongoing debate between the higher-dimensional formalists, and the higher-dimensional realists.

Why was Bob unable to speak clearly about spheres? I think the basic reason was that they were outside of “consensus reality.” Since there was no analogy to spheres in ordinary Finlandian experience, there was not even adequate language to talk about them.

At first Bob simply spoke in vast, empty superlatives: “super,” “transcendent,” etc. When pushed to make his ideas more logically precise, he ended up with things that half made sense, but were full of undefined terms and logical contradictions. It is understandable that he finally concluded that spheres were indescribable and ineffable, beyond the limits of thought.

Bob and Elaine’s dialogue is intended as an allegory about mysticism. Bob’s discourse is very similar to mystical discourse about God, the Tao, Brahman, etc.

“Tao” is a word much like “super-circle.” We know that we mean something by it, but we don’t know exactly what. “Tao” is a placeholder for “this mysterious thing that we have some vague ideas about but don’t understand well enough to talk about clearly.”

The further analogy between the Tao and the super-circle is that both of them refer to things which only some people experience. Somebody sees a sphere and then goes around talking about it, making no sense to the people who haven’t seen a sphere. That is also how it is for the Tao.

The person who has experienced the Tao thinks, rightly, that they will not make sense to anybody who has not experienced the Tao. But there is an additional level on which they don’t make sense even to themselves.

Nobody has a firm grasp on the Tao, in the way that we have a firm grasp on, say, trigonometry. The Tao is something that is mysterious unto us. So when we talk about the Tao, we are talking about something of which we have a very shaky understanding.

Philosophy is full of mysterious words like this. “Mind,” “consciousness,” “qualia,” “idea,” “existence,” “a priori,” “truth,” “probability,” “property,” “should,” etc. We know that we mean something by these words; but we don’t know exactly what.

Philosophy is almost exclusively a discipline of thinking about things that are mysterious unto us. This can account for many facts about philosophy. It can account for its lack of rigor, relative to math and science; for the lack of consensus among philosophers; for the way that problems go unsolved for thousands of years. These are all things that we would expect to see in a discipline of thinking about mysterious questions.

I do not think that an idea’s being mysterious, vague, or speculative is reason to refrain from talking about it. Surely there is use in talking about consciousness, thoughts, ethics — and yes, the Tao — even though we don’t really know what any of these things are.

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Running Mean Estimates

Here is some statistical theory. I thought it up because it is applicable to an aspect of my AI project. I don’t know much statistics; it seems likely that I’m groping towards something that already exists. But here it is.

Suppose that we have a black box which outputs a series of numbers between zero and one. We don’t know how it works, and we want to determine the mean value of its output.

One way we could do this would be to record a series of outputs, and take their mean. This works if the black box’s behavior is regular; that is, the mean will be the same in the distant future as it is right now. But what if the trends of the black box’s output gradually change over time, so that the mean will be different in the future?

An analogous case would be the mean income of a U.S. citizen. This is a mean which changes over time. How do we deal with this sort of case?

One solution would be to re-calculate the mean periodically, taking a new sample every so often and calculating its mean. This is how we produce statistics about mean income.

But we could also compute the mean dynamically. Returning to our black box, we could come up with a scheme by which every time the black box outputs a number, it adjusts our estimate of the mean slightly. This solution is more elegant in the case of an AI which wants to dynamically monitor the trends in its own internal data structures.

In the case of the black box, how do we compute a running estimate of the mean?

Suppose we imitate the conventional way of estimating the mean. We can do this by keeping track of the number of numbers we have observed (the sample size), and a running sum of all of the numbers we have observed. Every time a new number comes down the pipe, we add one to the sample size, add the number to the running sum, and re-compute the mean as the running sum over the sample size.

The problem with this method is that, as time goes by, each number will have a progressively smaller impact on the estimate of the mean. It doesn’t capture the idea that the mean is changing over time, which demands that we put more weight on recent samples than on samples in the distant past.

Let us consider another method. Suppose we keep a running mean (m). Let p = 0.5 be its initial estimate, before we have observed any numbers. Furthermore, we have a number (w, for “weight”) which says how much impact every sample has on the running mean. w is analogous to the sample size. For instance, w = .05 is analogous to a sample size of 20 (1/.05 = 20).

Every time we observe a new number (n), we say m’ = (1 – w) * m + w * n. m’ is the new mean, and m is the old mean.

Let t be the number of numbers we have observed since we started our running estimate, and n1, n2, …, nt be those numbers. Then we can say that, at any time, m = p * (1 – w)^t + n1 * w(1 – w)^(t-1) + n2 * w(1 – w)^(t-2) + … + nt * w(1 – w)^(t-t).

Suppose that w is set to a value analogous to a statistically significant sample size. Then, if the real mean doesn’t change over time, this method of estimating the mean will always keep the estimate near the real mean; m will never change significantly.

But this method will capture fluctuations in the real mean, keeping the estimate near the real mean as the real mean changes. It will do so more in a more fine-grained fashion with larger values of w, or a more coarse-grained fashion with smaller values of w.

The biggest questions for this method are: how do we choose a value for p (the initial estimate of the mean), and how do we choose a value for w (the amount of impact each new number has on our mean estimate, which determines the coarseness with which we follow fluctuations in the mean)?

These are two very difficult questions. The first question is a basic problem of Bayesian statistics: how do we choose our prior probabilities? The second question I haven’t seen before, but it also seems fairly enigmatic.

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Further Work on Music AI

I do not intend to make any more blog posts on music AI. Further work will occur in the design document, of which the current draft can be found here:

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That which is neither lawful nor random

What does it mean for something to behave lawfully?

Roughly, we ought to be able to discover some mathematics which correctly predict the thing’s behavior.

An example of something with lawful behavior is the position over time of a rock dropped from the top of a building. If the rock has mass m, and its initial position is i, then its position at time t is p = i + 0.5G * t^2.

It is clear that pretty much and for the most part, physical things have lawful behavior.

What does it mean for something to behave randomly?

Roughly, it has no discernible pattern in its behavior. It has an even probability distribution over all possible outcomes. An example of something with random behavior is a toss of a fair six-sided die.

Some things have behavior which involves a mixture of lawfulness and randomness. For instance, suppose we toss the six-sided die several times, producing a series of numbers d1, d2, d3, …, and then define a function f(n) whose value is the square of d1 + d2 + … + dn. f(n)’s behavior involves a mixture of lawfulness and randomness.

Could there be a kind of behavior which is neither lawful nor random, nor a mixture of the two? What would that look like?

Such a thing would have behavior which was not evenly distributed over all possible outcomes. But it would also have the property that we could not discover any mathematics which would correctly predict its behavior.

Can we imagine an example of this? Well, let’s suppose that we have a black box, which constantly outputs a string of ones and zeroes. It can read our thoughts, and so it knows everything that we think about it.

The black box’s output always follows some rule. But, every time we figure out what the rule is, it changes the rule.

Suppose that we discover that the black box changes the rule according to some meta-rule. Then it would have to be the case that, when we figure out the meta-rule, the meta-rule changes.

We would need to say the same thing about any meta-meta-rule, meta-meta-meta-rule, etc.

So this black either has an infinite series of rules, or at some point the series of rules stops. Let us return to the simple case where there is no meta-rule.

In this case, there is simply a Creative Void which can come up with arbitrary mathematical rules. The rules of the black box look like this:

1. Output ones and zeroes according to the current rule.
2. If the humans have figured out the rule, ask the Void for a new rule.

So we can imagine our black box in two ways. It could have an infinitely complex rule set; or, it could have a finitely complex rule set, and a Creative Void which changes the rules sometimes.

It is an important point that we could not distinguish empirically between these two cases.

Whether or not such a box could exist in our universe, we can imagine, in thought experiment, what it would be like to interact with such a box. We have the simple empirical observation that this box never does what we expect it to.

We have clarified the idea of something whose behavior is neither lawful nor random. Let us call it “magical.”

The black box in the thought experiment is magical. But is there anything magical in our universe? It is possible that humans are such a thing. What observations would make us think this?

Suppose we that construct a mathematical model of human psychology which correctly predicts everybody’s behavior in every case we have observed so far. Then we tell somebody, “our model predicts that you will do x.” Out of sheer capriciousness, they decide to do y instead. If humans are magical, then we would expect that this could happen.

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The Hammer and Nails Bias

A lot of thinkers seem to fall into the bias described by the aphorism, “when all you have is a hammer, everything looks like a nail.”

Consider Freud. Freud noticed, correctly, that a lot of psychological problems revolve around sexuality; and he erred by trying to say that all, or nearly all, psychological problems have to do with sexuality.

Adler did something similar. He correctly noticed that a lot of psychological problems revolve around self-esteem, and he erred by trying to say that all psychological problems revolve around self-esteem.

Now consider Wittgenstein. Wittgenstein correctly noticed that a lot of philosophical problems are due to confusions over language, and can be dissolved by pointing out and correcting the confusion implicit in the posing of the problem. He erred by saying that every philosophical problem can be resolved in this fashion. (In the Blue Book, for instance, he gives a quite unsatisfactory attempt to resolve the mind-body problem by saying that it is a confusion over language.)

Further, I think that the Western intellectual culture as a whole has fallen into the hammer-and-nails bias with respect to science. We correctly noticed that a lot of questions can be answered through the scientific method; and we erroneously decided that the scientific method should be how we answer all questions. We failed to notice its inadequacy in the areas where it is inadequate, such as psychology.

I also fell into this bias for a while with the Ra material, trying to solve every problem using the tools it provides. I have seen some of my friends do the same thing with the Ra material.

So it seems to be quite common for us to find really shiny hammers and then distort our perceptions into a world of nails. But the world is complicated enough that we need more than one tool in our toolkits.

Another thing we can notice about this bias is that it seems to occur more frequently when one is the inventor of the hammer. Freud, Adler, and Wittgenstein were all the inventors of their hammers, and all of them tried to turn everything into a nail. So it seems like one is especially vulnerable to this bias with ideas of one’s own invention.

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