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49
New Improved Lottery
People are still suggesting that the lottery is not a waste of hope, but a service which enables purchase of fantasy—“daydreaming about becoming a millionaire for much less money than daydreaming about hollywood stars in movies.” One commenter wrote: “There is a big difference between zero chance of becoming wealthy, and epsilon. Buying a ticket allows your dream of riches to bridge that gap.”
Actually, one of the points I was trying to make is that between zero chance of becoming wealthy, and epsilon chance, there is an order-of-epsilon difference. If you doubt this, let epsilon equal one over googolplex.
Anyway, if we pretend that the lottery sells epsilon hope, this suggests a design for a New Improved Lottery. The New Improved Lottery pays out every five years on average, at a random time—determined, say, by the decay of a not-very-radioactive element. You buy in once, for a single dollar, and get not just a few days of epsilon chance of becoming rich, but a few years of epsilon. Not only that, your wealth could strike at any time! At any minute, the phone could ring to inform you that you, yes, you are a millionaire!
Think of how much better this would be than an ordinary lottery drawing, which only takes place at defined times, a few times per week. Let’s say the boss comes in and demands you rework a proposal, or restock inventory, or something similarly annoying. Instead of getting to work, you could turn to the phone and stare, hoping for that call—because there would be epsilon chance that, at that exact moment, you yes you would be awarded the Grand Prize! And even if it doesn’t happen this minute, why, there’s no need to be disappointed—it might happen the next minute!
Think of how many more fantasies this New Improved Lottery would enable. You could shop at the store, adding expensive items to your shopping cart—if your cellphone doesn’t ring with news of a lottery win, you could always put the items back, right?
Maybe the New Improved Lottery could even show a constantly fluctuating probability distribution over the likelihood of a win occurring, and the likelihood of particular numbers being selected, with the overall expectation working out to the aforesaid Poisson distribution. Think of how much fun that would be! Oh, goodness, right this minute the chance of a win occurring is nearly ten times higher than usual! And look, the number 42 that I selected for the Mega Ball has nearly twice the usual chance of winning! You could feed it to a display on people’s cellphones, so they could just flip open the cellphone and see their chances of winning. Think of how exciting that would be! Much more exciting than trying to balance your checkbook! Much more exciting than doing your homework! This new dream would be so much tastier that it would compete with, not only hopes of going to technical school, but even hopes of getting home from work early. People could just stay glued to the screen all day long, why, they wouldn’t need to dream about anything else!
Yep, offering people tempting daydreams that will not actually happen sure is a valuable service, all right. People are willing to pay; it must be valuable. The alternative is that consumers are making mistakes, and we all know that can’t happen.
And yet current governments, with their vile monopoly on lotteries, don’t offer this simple and obvious service. Why? Because they want to overcharge people. They want them to spend money every week. They want them to spend a hundred dollars for the thrill of believing their chance of winning is a hundred times as large, instead of being able to stare at a cellphone screen waiting for the likelihood to spike. So if you believe that the lottery is a service, it is clearly an enormously overpriced service—charged to the poorest members of society—and it is your solemn duty as a citizen to demand the New Improved Lottery instead.
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50
But There’s Still a Chance, Right?
Years ago, I was speaking to someone when he casually remarked that he didn’t believe in evolution. And I said, “This is not the nineteenth century. When Darwin first proposed evolution, it might have been reasonable to doubt it. But this is the twenty-first century. We can read the genes. Humans and chimpanzees have 98% shared DNA. We know humans and chimps are related. It’s over.”
He said, “Maybe the DNA is just similar by coincidence.”
I said, “The odds of that are something like two to the power of seven hundred and fifty million to one.”
He said, “But there’s still a chance, right?”
Now, there’s a number of reasons my past self cannot claim a strict moral victory in this conversation. One reason is that I have no memory of whence I pulled that 2750,000,000 figure, though it’s probably the right meta-order of magnitude. The other reason is that my past self didn’t apply the concept of a calibrated confidence. Of all the times over the history of humanity that a human being has calculated odds of 2750,000,000:1 against something, they have undoubtedly been wrong more often than once in 2750,000,000 times. E.g. the shared genes estimate was revised to 95%, not 98%—and that may even apply only to the 30,000 known genes and not the entire genome, in which case it’s the wrong meta-order of magnitude.
But I think the other guy’s reply is still pretty funny.
I don’t recall what I said in further response—probably something like “No”—but I remember this occasion because it brought me several insights into the laws of thought as seen by the unenlightened ones.
It first occurred to me that human intuitions were making a qualitative distinction between “No chance” and “A very tiny chance, but worth keeping track of.” You can see this in the Overcoming Bias lottery debate, where someone said, “There’s a big difference between zero chance of winning and epsilon chance of winning,” and I replied, “No, there’s an order-of-epsilon difference; if you doubt this, let epsilon equal one over googolplex.”
The problem is that probability theory sometimes lets us calculate a chance which is, indeed, too tiny to be worth the mental space to keep track of it—but by that time, you’ve already calculated it. People mix up the map with the territory, so that on a gut level, tracking a symbolically described probability feels like “a chance worth keeping track of,” even if the referent of the symbolic description is a number so tiny that if it was a dust speck, you couldn’t see it. We can use words to describe numbers that small, but not feelings—a feeling that small doesn’t exist, doesn’t fire enough neurons or release enough neurotransmitters to be felt. This is why people buy lottery tickets—no one can feel the smallness of a probability that small.
But what I found even more fascinating was the qualitative distinction between “certain” and “uncertain” arguments, where if an argument is not certain, you’re allowed to ignore it. Like, if the likelihood is zero, then you have to give up the belief, but if the likelihood is one over googol, you’re allowed to keep it.
Now it’s a free country and no one should put you in jail for illegal reasoning, but if you’re going to ignore an argument that says the likelihood is one over googol, why not also ignore an argument that says the likelihood is zero? I mean, as long as you’re ignoring the evidence anyway, why is it so much worse to ignore certain evidence than uncertain evidence?
I have often found, in life, that I have learned from other people’s nicely blatant bad examples, duly generalized to more subtle cases. In this case, the flip lesson is that, if you can’t ignore a likelihood of one over googol because you want to, you can’t ignore a likelihood of 0.9 because you want to. It’s all the same slippery cliff.
Consider his example if you ever you find yourself thinking, “But you can’t prove me wrong.” If you’re going to ignore a probabilistic counterargument, why not ignore a proof, too?
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51
The Fallacy of Gray
The Sophisticate: “The world isn’t black and white. No one does pure good or pure bad. It’s all gray. Therefore, no one is better than anyone else.”
The Zetet: “Knowing only gray, you conclude that all grays are the same shade. You mock the simpl
icity of the two-color view, yet you replace it with a one-color view . . .”
—Marc Stiegler, David’s Sling1
I don’t know if the Sophisticate’s mistake has an official name, but I call it the Fallacy of Gray. We saw it manifested in the previous essay—the one who believed that odds of two to the power of seven hundred and fifty millon to one, against, meant “there was still a chance.” All probabilities, to him, were simply “uncertain” and that meant he was licensed to ignore them if he pleased.
“The Moon is made of green cheese” and “the Sun is made of mostly hydrogen and helium” are both uncertainties, but they are not the same uncertainty.
Everything is shades of gray, but there are shades of gray so light as to be very nearly white, and shades of gray so dark as to be very nearly black. Or even if not, we can still compare shades, and say “it is darker” or “it is lighter.”
Years ago, one of the strange little formative moments in my career as a rationalist was reading this paragraph from Player of Games by Iain M. Banks, especially the sentence in bold:2
A guilty system recognizes no innocents. As with any power apparatus which thinks everybody’s either for it or against it, we’re against it. You would be too, if you thought about it. The very way you think places you amongst its enemies. This might not be your fault, because every society imposes some of its values on those raised within it, but the point is that some societies try to maximize that effect, and some try to minimize it. You come from one of the latter and you’re being asked to explain yourself to one of the former. Prevarication will be more difficult than you might imagine; neutrality is probably impossible. You cannot choose not to have the politics you do; they are not some separate set of entities somehow detachable from the rest of your being; they are a function of your existence. I know that and they know that; you had better accept it.
Now, don’t write angry comments saying that, if societies impose fewer of their values, then each succeeding generation has more work to start over from scratch. That’s not what I got out of the paragraph.
What I got out of the paragraph was something which seems so obvious in retrospect that I could have conceivably picked it up in a hundred places; but something about that one paragraph made it click for me.
It was the whole notion of the Quantitative Way applied to life-problems like moral judgments and the quest for personal self-improvement. That, even if you couldn’t switch something from on to off, you could still tend to increase it or decrease it.
Is this too obvious to be worth mentioning? I say it is not too obvious, for many bloggers have said of Overcoming Bias: “It is impossible, no one can completely eliminate bias.” I don’t care if the one is a professional economist, it is clear that they have not yet grokked the Quantitative Way as it applies to everyday life and matters like personal self-improvement. That which I cannot eliminate may be well worth reducing.
Or consider this exchange between Robin Hanson and Tyler Cowen. Robin Hanson said that he preferred to put at least 75% weight on the prescriptions of economic theory versus his intuitions: “I try to mostly just straightforwardly apply economic theory, adding little personal or cultural judgment.” Tyler Cowen replied:
In my view there is no such thing as “straightforwardly applying economic theory” . . . theories are always applied through our personal and cultural filters and there is no other way it can be.
Yes, but you can try to minimize that effect, or you can do things that are bound to increase it. And if you try to minimize it, then in many cases I don’t think it’s unreasonable to call the output “straightforward”—even in economics.
“Everyone is imperfect.” Mohandas Gandhi was imperfect and Joseph Stalin was imperfect, but they were not the same shade of imperfection. “Everyone is imperfect” is an excellent example of replacing a two-color view with a one-color view. If you say, “No one is perfect, but some people are less imperfect than others,” you may not gain applause; but for those who strive to do better, you have held out hope. No one is perfectly imperfect, after all.
(Whenever someone says to me, “Perfectionism is bad for you,” I reply: “I think it’s okay to be imperfect, but not so imperfect that other people notice.”)
Likewise the folly of those who say, “Every scientific paradigm imposes some of its assumptions on how it interprets experiments,” and then act like they’d proven science to occupy the same level with witchdoctoring. Every worldview imposes some of its structure on its observations, but the point is that there are worldviews which try to minimize that imposition, and worldviews which glory in it. There is no white, but there are shades of gray that are far lighter than others, and it is folly to treat them as if they were all on the same level.
If the Moon has orbited the Earth these past few billion years, if you have seen it in the sky these last years, and you expect to see it in its appointed place and phase tomorrow, then that is not a certainty. And if you expect an invisible dragon to heal your daughter of cancer, that too is not a certainty. But they are rather different degrees of uncertainty—this business of expecting things to happen yet again in the same way you have previously predicted to twelve decimal places, versus expecting something to happen that violates the order previously observed. Calling them both “faith” seems a little too un-narrow.
It’s a most peculiar psychology—this business of “Science is based on faith too, so there!” Typically this is said by people who claim that faith is a good thing. Then why do they say “Science is based on faith too!” in that angry-triumphal tone, rather than as a compliment? And a rather dangerous compliment to give, one would think, from their perspective. If science is based on “faith,” then science is of the same kind as religion—directly comparable. If science is a religion, it is the religion that heals the sick and reveals the secrets of the stars. It would make sense to say, “The priests of science can blatantly, publicly, verifiably walk on the Moon as a faith-based miracle, and your priests’ faith can’t do the same.” Are you sure you wish to go there, oh faithist? Perhaps, on further reflection, you would prefer to retract this whole business of “Science is a religion too!”
There’s a strange dynamic here: You try to purify your shade of gray, and you get it to a point where it’s pretty light-toned, and someone stands up and says in a deeply offended tone, “But it’s not white! It’s gray!” It’s one thing when someone says, “This isn’t as light as you think, because of specific problems X, Y, and Z.” It’s a different matter when someone says angrily “It’s not white! It’s gray!” without pointing out any specific dark spots.
In this case, I begin to suspect psychology that is more imperfect than usual—that someone may have made a devil’s bargain with their own mistakes, and now refuses to hear of any possibility of improvement. When someone finds an excuse not to try to do better, they often refuse to concede that anyone else can try to do better, and every mode of improvement is thereafter their enemy, and every claim that it is possible to move forward is an offense against them. And so they say in one breath proudly, “I’m glad to be gray,” and in the next breath angrily, “And you’re gray too!”
If there is no black and white, there is yet lighter and darker, and not all grays are the same.
G2 points us to Asimov’s “The Relativity of Wrong”:3
When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.
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1. Marc Stiegler, David’s Sling (Baen, 1988).
2. Iain Banks, The Player of Games (Orbit, 1989).
3. Isaac Asimov, The Relativity of Wrong (Oxford University Press, 1989).
52
Absolute Authority
The one comes to you and loftily says: “Science doesn’t really know anything. All you have are theorie
s—you can’t know for certain that you’re right. You scientists changed your minds about how gravity works—who’s to say that tomorrow you won’t change your minds about evolution?”
Behold the abyssal cultural gap. If you think you can cross it in a few sentences, you are bound to be sorely disappointed.
In the world of the unenlightened ones, there is authority and un-authority. What can be trusted, can be trusted; what cannot be trusted, you may as well throw away. There are good sources of information and bad sources of information. If scientists have changed their stories ever in their history, then science cannot be a true Authority, and can never again be trusted—like a witness caught in a contradiction, or like an employee found stealing from the till.
Plus, the one takes for granted that a proponent of an idea is expected to defend it against every possible counterargument and confess nothing. All claims are discounted accordingly. If even the proponent of science admits that science is less than perfect, why, it must be pretty much worthless.
When someone has lived their life accustomed to certainty, you can’t just say to them, “Science is probabilistic, just like all other knowledge.” They will accept the first half of the statement as a confession of guilt; and dismiss the second half as a flailing attempt to accuse everyone else to avoid judgment.
You have admitted you are not trustworthy—so begone, Science, and trouble us no more!
Rationality- From AI to Zombies Page 22