Monthly Archives: August 2007

Making History Available

Followup toFailing to Learn from History

There is a habit of thought which I call the logical fallacy of generalization from fictional evidence, which deserves a blog post in its own right, one of these days.  Journalists who, for example, talk about the Terminator movies in a report on AI, do not usually treat Terminator as a prophecy or fixed truth.  But the movie is recalled – is available – as if it were an illustrative historical case.  As if the journalist had seen it happen on some other planet, so that it might well happen here.  More on this in Section 6 of this paper.

There is an inverse error to generalizing from fictional evidence: failing to be sufficiently moved by historical evidence.  The trouble with generalizing from fictional evidence is that it is fiction – it never actually happened.  It’s not drawn from the same distribution as this, our real universe; fiction differs from reality in systematic ways.  But history has happened, and should be available.

In our ancestral environment, there were no movies; what you saw with your own eyes was true.  Is it any wonder that fictions we see in lifelike moving pictures have too great an impact on us?  Conversely, things that really happened, we encounter as ink on paper; they happened, but we never saw them happen.  We don’t remember them happening to us.

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We Are Not Unbaised

Comments about Overcoming Bias can be found at these posts by Bryan Caplan, Arnold Kling, and Tyler Cowen.  Several complaints go like this:

Those people claim to be against bias, but someone there supported position P on topic T; wow is that ever biased! 

Just to be completely clear: we do not claim to be unbiased.  People who attend church do not claim to be without sin, and we do not claim to be without bias.  People at church do claim to be trying to overcome sin, and we claim to be trying to overcome bias.  You would be right to think us hypocrites if it seemed we weren’t even trying to overcome bias, but instead just wanted to feel superior by pretending to try. 

Some complain we talk too abstractly, without enough concrete examples.  Others complain we too often take positions on concrete issues, arbitrarily painting those who disagree as "biased."  We will hopefully continue to try to find the right middle ground between these extremes. 

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Failing to Learn from History

Continuation of:  My Wild and Reckless Youth

Once upon a time, in my wild and reckless youth, when I knew not the Way of Bayes, I gave a Mysterious Answer to a mysterious-seeming question.  Many failures occurred in sequence, but one mistake stands out as most critical:  My younger self did not realize that solving a mystery should make it feel less confusing.  I was trying to explain a Mysterious Phenomenon – which to me meant providing a cause for it, fitting it into an integrated model of reality.  Why should this make the phenomenon less Mysterious, when that is its nature?  I was trying to explain the Mysterious Phenomenon, not render it (by some impossible alchemy) into a mundane phenomenon, a phenomenon that wouldn’t even call out for an unusual explanation in the first place.

As a Traditional Rationalist, I knew the historical tales of astrologers and astronomy, of alchemists and chemistry, of vitalists and biology.  But the Mysterious Phenomenon was not like this.  It was something new, something stranger, something more difficult, something that ordinary science had failed to explain for centuries -

- as if stars and matter and life had not been mysteries for hundreds of years and thousands of years, from the dawn of human thought right up until science finally solved them -

We learn about astronomy and chemistry and biology in school, and it seems to us that these matters have always been the proper realm of science, that they have never been mysterious.  When science dares to challenge a new Great Puzzle, the children of that generation are skeptical, for they have never seen science explain something that feels mysterious to them.  Science is only good for explaining scientific subjects, like stars and matter and life.

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Seeking Unbiased Game Host

Alex Tabarrok recently proposed:

A game show, So You Think You Can Be President? … [with] at least three segments.

Coase it Out: Presidential candidates have 12 hours to get a bitterly divorcing couple to divide their assets in a mutually agreeable manner. …

Game Theory: Candidates compete in a game of Diplomacy.   I would also include several ringers …

Spot the Fraud:  … candidates are provided with an economic scenario (mortgage defaults are up, hedge funds are crashing, liquidity is tight).  Three experts propose plans.  The candidate must choose one of the plans.  After the candidate chooses, the true identities of the "experts" are revealed. One is a trucker, another a scuba diver instructor and the last a distinguished economist.

I fear the public would not respect candidates willing to play such a game; it might tarnish their presidential image.  Worse, I fear our society is too polarized to choose a neutral host to run such a game.  Hosting such games would require many detailed judgment calls, calls which a secretly-partisan host could use to favor one side or the other.   

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My Wild and Reckless Youth

It is said that parents do all the things they tell their children not to do, which is how they know not to do them.

Long ago, in the unthinkably distant past, I was a devoted Traditional Rationalist, conceiving myself skilled according to that kind, yet I knew not the Way of Bayes.  When the young Eliezer was confronted with a mysterious-seeming question, the precepts of Traditional Rationality did not stop him from devising a Mysterious Answer.  It is, by far, the most embarrassing mistake I made in my life, and I still wince to think of it.

What was my mysterious answer to a mysterious question?  This I will not describe, for it would be a long tale and complicated.  I was young, and a mere Traditional Rationalist who knew not the teachings of Tversky and Kahneman.  I knew about Occam’s Razor, but not the conjunction fallacy.  I thought I could get away with thinking complicated thoughts myself, in the literary style of the complicated thoughts I read in science books, not realizing that correct complexity is only possible when every step is pinned down overwhelmingly.  Today, one of the chief pieces of advice I give to aspiring young rationalists is "Do not attempt long chains of reasoning or complicated plans."

Nothing more than this need be said:  Even after I invented my "answer", the phenomenon was still a mystery unto me, and possessed the same quality of wondrous impenetrability that it had at the start.

Make no mistake, that younger Eliezer was not stupid.  All the errors of which the young Eliezer was guilty, are still being made today by respected scientists in respected journals.  It would have taken a subtler skill to protect him, than ever he was taught as a Traditional Rationalist.

Indeed, the young Eliezer diligently and painstakingly followed the injunctions of Traditional Rationality in the course of going astray.

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Kind Right-Handers

Imagine a society like ours, but with a moral norm against ever using a right hand to hurt anyone.  They kill, rape, torture, and so on, but always with their left hand, never with their right.  They are proud to live in a civilized society, and are disgusted by barbaric societies where right-handed harm is common.  Their disgust sometimes makes them war against barbarians, to civilize them.  But even in war they are careful to show their moral superiority by only killing with their left hands.   Are these people as moral as they believe? 

James Miller’s recent post on replacing prison with torture suggested to me this allegory of kind right-handers.  Most of us are apparently very proud of our moral norm against torture, even though we allow ourselves to impose great harms in other ways.  We tend to be disgusted by Muslim torture practices, encouraging us to go to war against such "barbarians."   But I fear such moral norms do more to help us feel superior than to reduce the total amount of harm.

So who wants to start a crusade against right-handed harm?   

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Say Not “Complexity”

Once upon a time…

This is a story from when I first met Marcello, with whom I would later work for a year on AI theory; but at this point I had not yet accepted him as my apprentice.  I knew that he competed at the national level in mathematical and computing olympiads, which sufficed to attract my attention for a closer look; but I didn’t know yet if he could learn to think about AI.

I had asked Marcello to say how he thought an AI might discover how to solve a Rubik’s Cube.  Not in a preprogrammed way, which is trivial, but rather how the AI itself might figure out the laws of the Rubik universe and reason out how to exploit them.  How would an AI invent for itself the concept of an "operator", or "macro", which is the key to solving the Rubik’s Cube?

At some point in this discussion, Marcello said:  "Well, I think the AI needs complexity to do X, and complexity to do Y -"

And I said, "Don’t say ‘complexity’."

Marcello said, "Why not?"

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The Function of Prizes

My aunt’s husband, Field Medal winner Atle Selberg, died a few weeks ago.  The Washington Post:

The Fields Medal was awarded to Dr. Selberg for his work on proving a challenging theory about the distribution of prime numbers. For years, mathematicians had believed that it could be proved only by the laborious application of ponderous techniques. In 1949, Dr. Selberg and another celebrated mathematician, Paul Erdos, achieved a proof through techniques of startling simplicity.  Each, it was reported, was to report on his own contribution in the same issue of the same mathematics journal. Because of what has been described as a misunderstanding that led to hurt feelings, Dr. Selberg published first.  His Fields Medal, recognizing him for a variety of accomplishments, followed.

The usual story about such independent discoveries is that they both deserve recognition.  And this makes sense if the point of such prizes is to identify and validate genius.  But if we awarded prizes instead to create incentives for discovery, we should reward neither discoverer.  After all, the marginal contribution to progress of each simultaneous independent discovery is near zero – without that discovery progress would have been nearly the same, since the other sources were available.   

Yes, independent replications can aid progress in experiments and data analysis.  But much less so for math, and few think later replications deserve anywhere near the same reward – so why should simultaneous replications get more?  Yes, rewarding both might reduce their risk in seeking the reward, but we already accept an awful lot of risk in such situations.  The slight additional risk from rewarding only substantial marginal contributions would create important incentives for researchers to coordinate on their research topics. 

Independent simultaneous discovery is a waste, not a triumph.  The fact that we seem to feel otherwise is to me further evidence that academia’s main local function is to validate impressive people.  Relative to the main goals of most participants, research progress is only a side effect. 

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Positive Bias: Look Into the Dark

I am teaching a class, and I write upon the blackboard three numbers:  2-4-6.  "I am thinking of a rule," I say, "which governs sequences of three numbers.  The sequence 2-4-6, as it so happens, obeys this rule.  Each of you will find, on your desk, a pile of index cards.  Write down a sequence of three numbers on a card, and I’ll mark it "Yes" for fits the rule, or "No" for not fitting the rule.  Then you can write down another set of three numbers and ask whether it fits again, and so on.  When you’re confident that you know the rule, write down the rule on a card.  You can test as many triplets as you like."

Here’s the record of one student’s guesses:

4, 6, 2              No
4, 6, 8              Yes
10, 12, 14         Yes

At this point the student wrote down his guess at the rule.  What do you think the rule is?  Would you have wanted to test another triplet, and if so, what would it be?  Take a moment to think before continuing.

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Is Overcoming Bias Important?

Arnold Kling says he "does not buy this argument" of mine:

If you have a cause, then other people probably disagree with you …  When other people disagree with you, they are usually more right than you think they are. … Before you go and attach yourself to this cause, shouldn’t you try to reduce the chances that you are wrong? Ergo, shouldn’t you work on trying to overcome bias?

Tyler Cowen riffs:

[Such] views are tautologically true and they simply boil down to saying that any complaint can be expressed as a concern about error of some kind or another.  … draw an analogy with statistics.  Biased estimators are one problem but not the only problem.  There is also insufficient data, lazy researchers, inefficient estimators, and so on.  Then I don’t see why we should be justified in holding a strong preference for overcoming bias, relative to other ends.

We have never claimed bias is the only problem.  But to let Arnold and Tyler more clearly identify where they disagree, let me outline an argument for the importance of overcoming bias:

  1. Our beliefs have many errors, i.e., deviations from truth.
  2. Reducing error is important goal, for which we are willing to pay substantial costs.
  3. The causes of our errors can be seen as ranging from context specific to general trends.
  4. We in fact have many identifiable stable general error trends, in addition to legion context specific causes.
  5. By reflecting on error causes, we can seek ways to adjust our pattens of thought and social institutions to reduce error.
  6. For a substantial fraction of error causes, we can in fact find feasible adjustments. 
  7. It is often more cost-effective to seek and implement adjustments for general trends, than for context specific errors.

Together these points suggest we should be willing to pay substantial costs to reflect on and seek adjustments for general error trends.  Our being here suggests we draw a similar conclusion.  It seems a confident proposer bias to suggest we claim more.

Added: Bryan Caplan weighs in.

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