Overcoming Bias

Chaotic Inversion

I was recently having a conversation with some friends on the topic of hour-by-hour productivity and willpower maintenance - something I've struggled with my whole life.

I can avoid running away from a hard problem the first time I see it (perseverance on a timescale of seconds), and I can stick to the same problem for years; but to keep working on a timescale of hours is a constant battle for me.  It goes without saying that I've already read reams and reams of advice; and the most help I got from it was realizing that a sizable fraction other creative professionals had the same problem, and couldn't beat it either, no matter how reasonable all the advice sounds.

"What do you do when you can't work?" my friends asked me.  (Conversation probably not accurate, this is a very loose gist.)

And I replied that I usually browse random websites, or watch a short video.

"Well," they said, "if you know you can't work for a while, you should watch a movie or something."

"Unfortunately," I replied, "I have to do something whose time comes in short units, like browsing the Web or watching short videos, because I might become able to work again at any time, and I can't predict when -"

And then I stopped, because I'd just had a revelation.

Beliefs Require Reasons, or: Is the Pope Catholic? Should he be?

In the early days of this blog, I would pick fierce arguments with Robin about the no-disagreement hypothesis.  Lately, however, reflection on things like public reason have brought me toward agreement with Robin, or at least moderated my disagreement.  To see why, it's perhaps useful to take a look at the newspapers...

the pope said the book “explained with great clarity” that “an interreligious dialogue in the strict sense of the word is not possible.” In theological terms, added the pope, “a true dialogue is not possible without putting one’s faith in parentheses.”

What are we to make of a statement like this?

Aiming at the Target

Previously in series:  Belief in Intelligence

Previously, I spoke of that very strange epistemic position one can occupy, wherein you don't know exactly where Kasparov will move on the chessboard, and yet your state of knowledge about the game is very different than if you faced a random move-generator with the same subjective probability distribution - in particular, you expect Kasparov to win.  I have beliefs about where Kasparov wants to steer the future, and beliefs about his power to do so.

Well, and how do I describe this knowledge, exactly?

In the case of chess, there's a simple function that classifies chess positions into wins for black, wins for white, and drawn games.  If I know which side Kasparov is playing, I know the class of chess positions Kasparov is aiming for.  (If I don't know which side Kasparov is playing, I can't predict whether black or white will win - which is not the same as confidently predicting a drawn game.)

More generally, I can describe motivations using a preference ordering. When I consider two potential outcomes, X and Y, I can say that I prefer X to Y; prefer Y to X; or find myself indifferent between them. I would write these relations as X > Y; X < Y; and X ~ Y.

Suppose that you have the ordering A < B ~ C < D ~ E. Then you like B more than A, and C more than A.  {B, C}, belonging to the same class, seem equally desirable to you; you are indifferent between which of {B, C} you receive, though you would rather have either than A, and you would rather have something from the class {D, E} than {B, C}.

When I think you're a powerful intelligence, and I think I know something about your preferences, then I'll predict that you'll steer reality into regions that are higher in your preference ordering.

Belief in Intelligence

Previously in series:  Expected Creative Surprises

Since I am so uncertain of Kasparov's moves, what is the empirical content of my belief that "Kasparov is a highly intelligent chess player"?  What real-world experience does my belief tell me to anticipate?  Is it a cleverly masked form of total ignorance?

To sharpen the dilemma, suppose Kasparov plays against some mere chess grandmaster Mr. G, who's not in the running for world champion.  My own ability is far too low to distinguish between these levels of chess skill.  When I try to guess Kasparov's move, or Mr. G's next move, all I can do is try to guess "the best chess move" using my own meager knowledge of chess.  Then I would produce exactly the same prediction for Kasparov's move or Mr. G's move in any particular chess position.  So what is the empirical content of my belief that "Kasparov is a better chess player than Mr. G"?

Expected Creative Surprises

Imagine that I'm playing chess against a smarter opponent.  If I could predict exactly where my opponent would move on each turn, I would automatically be at least as good a chess player as my opponent.  I could just ask myself where my opponent would move, if they were in my shoes; and then make the same move myself.  (In fact, to predict my opponent's exact moves, I would need to be superhuman - I would need to predict my opponent's exact mental processes, including their limitations and their errors.  It would become a problem of psychology, rather than chess.)

So predicting an exact move is not possible, but neither is it true that I have no information about my opponent's moves.

Personally, I am a very weak chess player - I play an average of maybe two games per year.  But even if I'm playing against former world champion Garry Kasparov, there are certain things I can predict about his next move.  When the game starts, I can guess that the move P-K4 is more likely than P-KN4.  I can guess that if Kasparov has a move which would allow me to checkmate him on my next move, that Kasparov will not make that move.

Much less reliably, I can guess that Kasparov will not make a move that exposes his queen to my capture - but here, I could be greatly surprised; there could be a rationale for a queen sacrifice which I have not seen.

And finally, of course, I can guess that Kasparov will win the game...

Dark Side Epistemology

Followup to:  Entangled Truths, Contagious Lies

If you once tell a lie, the truth is ever after your enemy.

I have previously spoken of the notion that, the truth being entangled, lies are contagious.  If you pick up a pebble from the driveway, and tell a geologist that you found it on a beach - well, do you know what a geologist knows about rocks?  I don't.  But I can suspect that a water-worn pebble wouldn't look like a droplet of frozen lava from a volcanic eruption.  Do you know where the pebble in your driveway really came from?  Things bear the marks of their places in a lawful universe; in that web, a lie is out of place.

What sounds like an arbitrary truth to one mind - one that could easily be replaced by a plausible lie - might be nailed down by a dozen linkages to the eyes of greater knowledge.  To a creationist, the idea that life was shaped by "intelligent design" instead of "natural selection" might sound like a sports team to cheer for.  To a biologist, plausibly arguing that an organism was intelligently designed would require lying about almost every facet of the organism.  To plausibly argue that "humans" were intelligently designed, you'd have to lie about the design of the human retina, the architecture of the human brain, the proteins bound together by weak van der Waals forces instead of strong covalent bonds...

Or you could just lie about evolutionary theory, which is the path taken by most creationists.  Instead of lying about the connected nodes in the network, they lie about the general laws governing the links.

And then to cover that up, they lie about the rules of science - like what it means to call something a "theory", or what it means for a scientist to say that they are not absolutely certain.

Entangled Truths, Contagious Lies

"One of your very early philosophers came to the conclusion that a fully competent mind, from a study of one fact or artifact belonging to any given universe, could construct or visualize that universe, from the instant of its creation to its ultimate end..."
        -- First Lensman

"If any one of you will concentrate upon one single fact, or small object, such as a pebble or the seed of a plant or other creature, for as short a period of time as one hundred of your years, you will begin to perceive its truth."
        -- Gray Lensman

I am reasonably sure that a single pebble, taken from a beach of our own Earth, does not specify the continents and countries, politics and people of this Earth.  Other planets in space and time, other Everett branches, would generate the same pebble.  On the other hand, the identity of a single pebble would seem to include our laws of physics.  In that sense the entirety of our Universe - all the Everett branches - would be implied by the pebble.  (If, as seems likely, there are no truly free variables.)

So a single pebble probably does not imply our whole Earth.  But a single pebble implies a very great deal.  From the study of that single pebble you could see the laws of physics and all they imply.  Thinking about those laws of physics, you can see that planets will form, and you can guess that the pebble came from such a planet.  The internal crystals and molecular formations of the pebble formed under gravity, which tells you something about the planet's mass; the mix of elements in the pebble tells you something about the planet's formation.

I am not a geologist, so I don't know to which mysteries geologists are privy.  But I find it very easy to imagine showing a geologist a pebble, and saying, "This pebble came from a beach at Half Moon Bay", and the geologist immediately says, "I'm confused" or even "You liar".  Maybe it's the wrong kind of rock, or the pebble isn't worn enough to be from a beach - I don't know pebbles well enough to guess the linkages and signatures by which I might be caught, which is the point.

Friedman's "Prediction vs. Explanation"

David D. Friedman asks:

We do ten experiments. A scientist observes the results, constructs a theory consistent with them, and uses it to predict the results of the next ten. We do them and the results fit his predictions. A second scientist now constructs a theory consistent with the results of all twenty experiments.

The two theories give different predictions for the next experiment. Which do we believe? Why?

One of the commenters links to Overcoming Bias, but as of 11PM on Sep 28th, David's blog's time, no one has given the exact answer that I would have given.  It's interesting that a question so basic has received so many answers.

Horrible LHC Inconsistency

Followup to: When (Not) To Use Probabilities, How Many LHC Failures Is Too Many?

While trying to answer my own question on "How Many LHC Failures Is Too Many?" I realized that I'm horrendously inconsistent with respect to my stated beliefs about disaster risks from the Large Hadron Collider.

First, I thought that stating a "one-in-a-million" probability for the Large Hadron Collider destroying the world was too high, in the sense that I would much rather run the Large Hadron Collider than press a button with a known 1/1,000,000 probability of destroying the world.

But if you asked me whether I could make one million statements of authority equal to "The Large Hadron Collider will not destroy the world", and be wrong, on average, around once, then I would have to say no.

Unknown pointed out that this turns me into a money pump.  Given a portfolio of a million existential risks to which I had assigned a "less than one in a million probability", I would rather press the button on the fixed-probability device than run a random risk from this portfolio; but would rather take any particular risk in this portfolio than press the button.

Then, I considered the question of how many mysterious failures at the LHC it would take to make me question whether it might destroy the world/universe somehow, and what this revealed about my prior probability.

If the failure probability had a known 50% probability of occurring from natural causes, like a quantum coin or some such... then I suspect that if I actually saw that coin come up heads 20 times in a row, I would feel a strong impulse to bet on it coming up heads the next time around.  (And that's taking into account my uncertainty about whether the anthropic principle really works that way.)

Even having noticed this triple inconsistency, I'm not sure in which direction to resolve it!

(But I still maintain my resolve that the LHC is not worth expending political capital, financial capital, or our time to shut down; compared with using the same capital to worry about superhuman intelligence or nanotechnology.)

Optimization

"However many ways there may be of being alive, it is certain that there are vastly more ways of being dead."
        -- Richard Dawkins

In the coming days, I expect to be asked:  "Ah, but what do you mean by 'intelligence'?"  By way of untangling some of my dependency network for future posts, I here summarize some of my notions of "optimization".

Consider a car; say, a Toyota Corolla.  The Corolla is made up of some number of atoms; say, on the rough order of 10²⁹.  If you consider all possible ways to arrange 10²⁹ atoms, only an infinitesimally tiny fraction of possible configurations would qualify as a car; if you picked one random configuration per Planck interval, many ages of the universe would pass before you hit on a wheeled wagon, let alone an internal combustion engine.

Even restricting our attention to running vehicles, there is an astronomically huge design space of possible vehicles that could be composed of the same atoms as the Corolla, and most of them, from the perspective of a human user, won't work quite as well.  We could take the parts in the Corolla's air conditioner, and mix them up in thousands of possible configurations; nearly all these configurations would result in a vehicle lower in our preference ordering, still recognizable as a car but lacking a working air conditioner.

So there are many more configurations corresponding to nonvehicles, or vehicles lower in our preference ranking, than vehicles ranked greater than or equal to the Corolla.

Similarly with the problem of planning, which also involves hitting tiny targets in a huge search space.  Consider the number of possible legal chess moves versus the number of winning moves.

Which suggests one theoretical way to measure optimization - to quantify the power of a mind or mindlike process: