Overcoming Bias

Science Isn't Strict Enough

Followup to:  When Science Can't Help

Once upon a time, a younger Eliezer had a stupid theory.  Eliezer₁₈ was careful to follow the precepts of Traditional Rationality that he had been taught; he made sure his stupid theory had experimental consequences.  Eliezer₁₈ professed, in accordance with the virtues of a scientist he had been taught, that he wished to test his stupid theory.

This was all that was required to be virtuous, according to what Eliezer₁₈  had been taught was virtue in the way of science.

It was not even remotely the order of effort that would have been required to get it right.

The traditional ideals of Science too readily give out gold stars. Negative experimental results are also knowledge, so everyone who plays gets an award.  So long as you can think of some kind of experiment that tests your theory, and you do the experiment, and you accept the results, you've played by the rules; you're a good scientist.

You didn't necessarily get it right, but you're a nice science-abiding citizen.

The Dilemma: Science or Bayes?

Followup to:  If Many-Worlds Had Come First, The Failures of Eld Science

"Eli: You are writing a lot about physics recently.  Why?"
        -- Shane Legg (and several other people)

"In light of your QM explanation, which to me sounds perfectly logical, it seems obvious and normal that many worlds is overwhelmingly likely. It just seems almost too good to be true that I now get what plenty of genius quantum physicists still can't. [...] Sure I can explain all that away, and I still think you're right, I'm just suspicious of myself for believing the first believable explanation I met."
        -- Recovering irrationalist

RI, you've got no idea how glad I was to see you post that comment.

Of course I had more than just one reason for spending all that time posting about quantum physics.  I like having lots of hidden motives, it's the closest I can ethically get to being a supervillain.

But to give an example of a purpose I could only accomplish by discussing quantum physics...

In physics, you can get absolutely clear-cut issues.  Not in the sense that the issues are trivial to explain.  But if you try to apply Bayes to healthcare, or economics, you may not be able to formally lay out what is the simplest hypothesis, or what the evidence supports.  But when I say "macroscopic decoherence is simpler than collapse" it is actually strict simplicity; you could write the two hypotheses out as computer programs and count the lines of code. Nor is the evidence itself in dispute.

I wanted a very clear example - Bayes says "zig", this is a zag - when it came time to break your allegiance to Science.

Decoherence is Falsifiable and Testable

Continuation of:  Decoherence is Simple

The words "falsifiable" and "testable" are sometimes used interchangeably, which imprecision is the price of speaking in English.  There are two different probability-theoretic qualities I wish to discuss here, and I will refer to one as "falsifiable" and the other as "testable" because it seems like the best fit.

As for the math, it begins, as so many things do, with:

This is Bayes's Theorem.  I own at least two distinct items of clothing printed with this theorem, so it must be important.

Decoherence is Simple

(An epistle to the physicists.)

When I was but a little lad, my father, a Ph.D. physicist, warned me sternly against meddling in the affairs of physicists; he said that it was hopeless to try to comprehend physics without the formal math. Period.  No escape clauses.  But I had read in Feynman's popular books that if you really understood physics, you ought to be able to explain it to a nonphysicist.  I believed Feynman instead of my father, because Feynman had won the Nobel Prize and my father had not.

It was not until later - when I was reading the Feynman Lectures, in fact - that I realized that my father had given me the simple and honest truth.  No math = no physics.

By vocation I am a Bayesian, not a physicist.  Yet although I was raised not to meddle in the affairs of physicists, my hand has been forced by the occasional gross misuse of three terms:  Simple, falsifiable, and testable.

The foregoing introduction is so that you don't laugh, and say, "Of course I know what those words mean!"  There is math here.

Belief in the Implied Invisible

Followup to:  The Generalized Anti-Zombie Principle

One generalized lesson not to learn from the Anti-Zombie Argument is, "Anything you can't see doesn't exist."

It's tempting to conclude the general rule.  It would make the Anti-Zombie Argument much simpler, on future occasions, if we could take this as a premise.  But unfortunately that's just not Bayesian.

Suppose I transmit a photon out toward infinity, not aimed at any stars, or any galaxies, pointing it toward one of the great voids between superclusters.  Based on standard physics, in other words, I don't expect this photon to intercept anything on its way out.  The photon is moving at light speed, so I can't chase after it and capture it again.

If the expansion of the universe is accelerating, as current cosmology holds, there will come a future point where I don't expect to be able to interact with the photon even in principle - a future time beyond which I don't expect the photon's future light cone to intercept my world-line.  Even if an alien species captured the photon and rushed back to tell us, they couldn't travel fast enough to make up for the accelerating expansion of the universe.

Should I believe that, in the moment where I can no longer interact with it even in principle, the photon disappears?

No.

It would violate Conservation of Energy.  And the second law of thermodynamics.  And just about every other law of physics.  And probably the Three Laws of Robotics.  It would imply the photon knows I care about it and knows exactly when to disappear.

It's a silly idea.

But if you can believe in the continued existence of photons that have become experimentally undetectable to you, why doesn't this imply a general license to believe in the invisible?

(If you want to think about this question on your own, do so before the jump...)

Initiation Ceremony

    The torches that lit the narrow stairwell burned intensely and in the wrong color, flame like melting gold or shattered suns.
    192... 193...
    Brennan's sandals clicked softly on the stone steps, snicking in sequence, like dominos very slowly falling.
    227... 228...
    Half a circle ahead of him, a trailing fringe of dark cloth whispered down the stairs, the robed figure itself staying just out of sight.
    239... 240...
    Not much longer, Brennan predicted to himself, and his guess was accurate:
    Sixteen times sixteen steps was the number, and they stood before the portal of glass.
    The great curved gate had been wrought with cunning, humor, and close attention to indices of refraction: it warped light, bent it, folded it, and generally abused it, so that there were hints of what was on the other side (stronger light sources, dark walls) but no possible way of seeing through - unless, of course, you had the key: the counter-door, thick for thin and thin for thick, in which case the two would cancel out.
    From the robed figure beside Brennan, two hands emerged, gloved in reflective cloth to conceal skin's color.  Fingers like slim mirrors grasped the handles of the warped gate - handles that Brennan had not guessed; in all that distortion, shapes could only be anticipated, not seen.
    "Do you want to know?" whispered the guide; a whisper nearly as loud as an ordinary voice, but not revealing the slightest hint of gender.
    Brennan paused.  The answer to the question seemed suspiciously, indeed extraordinarily obvious, even for ritual.

Qualitatively Confused

Followup to:  Probability is in the Mind, The Quotation is not the Referent

I suggest that a primary cause of confusion about the distinction between "belief", "truth", and "reality" is qualitative thinking about beliefs.

Consider the archetypal postmodernist attempt to be clever:

"The Sun goes around the Earth" is true for Hunga Huntergatherer, but "The Earth goes around the Sun" is true for Amara Astronomer!  Different societies have different truths!

No, different societies have different beliefs.  Belief is of a different type than truth; it's like comparing apples and probabilities.

Ah, but there's no difference between the way you use the word 'belief' and the way you use the word 'truth'!  Whether you say, "I believe 'snow is white'", or you say, "'Snow is white' is true", you're expressing exactly the same opinion.

No, these sentences mean quite different things, which is how I can conceive of the possibility that my beliefs are false.

Oh, you claim to conceive it, but you never believe it.  As Wittgenstein said, "If there were a verb meaning 'to believe falsely', it would not have any significant first person, present indicative."

And that's what I mean by putting my finger on qualitative reasoning as the source of the problem.  The dichotomy between belief and disbelief, being binary, is confusingly similar to the dichotomy between truth and untruth.

Probability is in the Mind

Followup to:  The Mind Projection Fallacy

Yesterday I spoke of the Mind Projection Fallacy, giving the example of the alien monster who carries off a girl in a torn dress for intended ravishing - a mistake which I imputed to the artist's tendency to think that a woman's sexiness is a property of the woman herself, woman.sexiness, rather than something that exists in the mind of an observer, and probably wouldn't exist in an alien mind.

The term "Mind Projection Fallacy" was coined by the late great Bayesian Master, E. T. Jaynes, as part of his long and hard-fought battle against the accursèd frequentists.  Jaynes was of the opinion that probabilities were in the mind, not in the environment - that probabilities express ignorance, states of partial information; and if I am ignorant of a phenomenon, that is a fact about my state of mind, not a fact about the phenomenon.

I cannot do justice to this ancient war in a few words - but the classic example of the argument runs thus:

You have a coin.
The coin is biased.
You don't know which way it's biased or how much it's biased.  Someone just told you, "The coin is biased" and that's all they said.
This is all the information you have, and the only information you have.

You draw the coin forth, flip it, and slap it down.

Now - before you remove your hand and look at the result - are you willing to say that you assign a 0.5 probability to the coin having come up heads?

Mind Projection Fallacy

Followup to:  How an Algorithm Feels From Inside

In the dawn days of science fiction, alien invaders would occasionally kidnap a girl in a torn dress and carry her off for intended ravishing, as lovingly depicted on many ancient magazine covers.  Oddly enough, the aliens never go after men in torn shirts.

Would a non-humanoid alien, with a different evolutionary history and evolutionary psychology, sexually desire a human female?  It seems rather unlikely.  To put it mildly.

People don't make mistakes like that by deliberately reasoning:  "All possible minds are likely to be wired pretty much the same way, therefore a bug-eyed monster will find human females attractive."  Probably the artist did not even think to ask whether an alien perceives human females as attractive.  Instead, a human female in a torn dress is sexy - inherently so, as an intrinsic property.

They who went astray did not think about the alien's evolutionary history; they focused on the woman's torn dress.  If the dress were not torn, the woman would be less sexy; the alien monster doesn't enter into it.

37 Ways That Words Can Be Wrong

Followup to:  Just about every post in February, and some in March

Some reader is bound to declare that a better title for this post would be "37 Ways That You Can Use Words Unwisely", or "37 Ways That Suboptimal Use Of Categories Can Have Negative Side Effects On Your Cognition".

But one of the primary lessons of this gigantic list is that saying "There's no way my choice of X can be 'wrong'" is nearly always an error in practice, whatever the theory.  You can always be wrong.  Even when it's theoretically impossible to be wrong, you can still be wrong.  There is never a Get-Out-Of-Jail-Free card for anything you do.  That's life.

Besides, I can define the word "wrong" to mean anything I like - it's not like a word can be wrong.

Personally, I think it quite justified to use the word "wrong" when:

1. A word fails to connect to reality in the first place.  Is Socrates a framster?  Yes or no?  (The Parable of the Dagger.)
   
   
2. Your argument, if it worked, could coerce reality to go a different way by choosing a different word definition.  Socrates is a human, and humans, by definition, are mortal.  So if you defined humans to not be mortal, would Socrates live forever?  (The Parable of Hemlock.)
   
   
3. You try to establish any sort of empirical proposition as being true "by definition".  Socrates is a human, and humans, by definition, are mortal.  So is it a logical truth if we empirically predict that Socrates should keel over if he drinks hemlock?  It seems like there are logically possible, non-self-contradictory worlds where Socrates doesn't keel over - where he's immune to hemlock by a quirk of biochemistry, say.  Logical truths are true in all possible worlds, and so never tell you which possible world you live in - and anything you can establish "by definition" is a logical truth.  (The Parable of Hemlock.)
   
   
4. You unconsciously slap the conventional label on something, without actually using the verbal definition you just gave.  You know perfectly well that Bob is "human", even though, on your definition, you can never call Bob "human" without first observing him to be mortal.  (The Parable of Hemlock.)
   
   
5. The act of labeling something with a word, disguises a challengable inductive inference you are making. If the last 11 egg-shaped objects drawn have been blue, and the last 8 cubes drawn have been red, it is a matter of induction to say this rule will hold in the future.  But if you call the blue eggs "bleggs" and the red cubes "rubes", you may reach into the barrel, feel an egg shape, and think "Oh, a blegg."  (Words as Hidden Inferences.)