More on this book
Community
Kindle Notes & Highlights
Bayes’s Theorem shows that falsification is very strong evidence compared to confirmation, but falsification is still probabilistic in nature; it is not governed by fundamentally different rules from confirmation, as Popper argued.
And that’s Bayes’s Theorem. Rational inference on the left end, physical causality on the right end; an equation with mind on one side and reality on the other. Remember how the scientific method turned out to be a special case of Bayes’s Theorem? If you wanted to put it poetically, you could say that Bayes’s Theorem binds reasoning into the physical universe.
Antoine-Laurent de Lavoisier discovered that breathing (respiration) and fire (combustion) operated on the same principle. It was one of the most startling unifications in the history of science, for it brought together the mundane realm of matter and the sacred realm of life, which humans had divided into separate magisteria.
Newton’s discovery gave rise to the notion of a universal law, one that is the same everywhere and everywhen, with literally zero exceptions.
One of the reasons the ancient Greeks didn’t discover science is that they didn’t realize you could generalize from experiments. The Greek philosophers were interested in “normal” phenomena. If you set up a contrived experiment, you would probably get a “monstrous” result, one that had no implications for how things really worked.
That’s the fundamental difference in mindset. Old School statisticians thought in terms of tools, tricks to throw at particular problems. Bayesians—at least this Bayesian, though I don’t think I’m speaking only for myself—we think in terms of laws. Looking for laws isn’t the same as looking for especially neat and pretty tools. The Second Law of Thermodynamics isn’t an especially neat and pretty refrigerator.
Sometimes you can’t use Bayesian methods literally; often, indeed. But when you can use the exact Bayesian calculation that uses every scrap of available knowledge, you are done. You will never find a statistical method that yields a better answer. You may find a cheap approximation that works excellently nearly all the time, and it will be cheaper, but it will not be more accurate. Not unless the other method uses knowledge, perhaps in the form of disguised prior information, that you are not allowing into the Bayesian calculation; and then when you feed the prior information into the
...more
We aren’t enchanted by Bayesian methods merely because they’re beautiful. The beauty is a side effect. Bayesian theorems are elegant, coherent, optimal, and provably unique because they are laws.
You could look at the Standard Dispute over “If a tree falls in the forest, and no one hears it, does it make a sound?,” and you could do the Traditional Rationalist thing: Observe that the two don’t disagree on any point of anticipated experience, and triumphantly declare the argument pointless. That happens to be correct in this particular case; but, as a question of cognitive science, why did the arguers make that mistake in the first place?
The cognitive algorithms we use are the way the world feels. And these cognitive algorithms may not have a one-to-one correspondence with reality—not even macroscopic reality, to say nothing of the true quarks. There can be things in the mind that cut skew to the world.
I say all this, because it sometimes seems to me that at least 20% of the real-world effectiveness of a skilled rationalist comes from not stopping too early. If you keep asking questions, you’ll get to your destination eventually. If you decide too early that you’ve found an answer, you won’t.
But when you’re really done, you’ll know you’re done. Dissolving the question is an unmistakable feeling—once you experience it, and, having experienced it, resolve not to be fooled again. Those who dream do not know they dream, but when you wake you know you are awake.
So here’s your homework problem: What kind of cognitive algorithm, as felt from the inside, would generate the observed debate about “free will”?
Where the mind cuts against reality’s grain, it generates wrong questions—questions that cannot possibly be answered on their own terms, but only dissolved by understanding the cognitive algorithm that generates the perception of a question.
Where the mind cuts against reality’s grain, it generates wrong questions questions that cannot possibly be answered on their own terms , but only dissolved by understanding the cognitive algorithm that generates the perception of a question.
E. T. Jaynes used the term Mind Projection Fallacy to denote the error of projecting your own mind’s properties into the external world. Jaynes, as a late grand master of the Bayesian Conspiracy, was most concerned with the mistreatment of probabilities as inherent properties of objects, rather than states of partial knowledge in some particular mind. More about this shortly.
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.
The Bayesian says, “Uncertainty exists in the map, not in the territory. In the real world, the coin has either come up heads, or come up tails. Any talk of ‘probability’ must refer to the information that I have about the coin—my state of partial ignorance and partial knowledge—not just the coin itself. Furthermore, I have all sorts of theorems showing that if I don’t treat my partial knowledge a certain way, I’ll make stupid bets. If I’ve got to plan, I’ll plan for a 50/50 state of uncertainty, where I don’t weigh outcomes conditional on heads any more heavily in my mind than outcomes
...more
So that is the Bayesian view of things, and I would now like to point out a couple of classic brainteasers that derive their brain-teasing ability from the tendency to think of probabilities as inherent properties of objects.
As for the paradox, there isn’t one. The appearance of paradox comes from thinking that the probabilities must be properties of the cards themselves. The ace I’m holding has to be either hearts or spades; but that doesn’t mean that your knowledge about my cards must be the same as if you knew I was holding hearts, or knew I was holding spades.
That’s what happens when you start thinking as if probabilities are in things, rather than probabilities being states of partial information about things.
Probabilities express uncertainty, and it is only agents who can be uncertain. A blank map does not correspond to a blank territory. Ignorance is in the mind.
Similarly, the notion of truth is quite different from the notion of reality. Saying “true” compares a belief to reality. Reality itself does not need to be compared to any beliefs in order to be real. Remember this the next time someone claims that nothing is true.
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.”
Surprise exists in the map, not in the territory. There are no surprising facts, only models that are surprised by facts. Likewise for facts called such nasty names as “bizarre,” “incredible,” “unbelievable,” “unexpected,” “strange,” “anomalous,” or “weird.” When you find yourself tempted by such labels, it may be wise to check if the alleged fact is really factual. But if the fact checks out, then the problem isn’t the fact—it’s you.
(I strongly suspect that a major part of science’s PR problem in the population at large is people who instinctively believe that if knowledge is given away for free, it cannot be important. If you had to undergo a fearsome initiation ritual to be told the truth about evolution, maybe people would be more satisfied with the answer.)
And really the situation is even worse than this, because in the Standard Model of physics (discovered by bastards who spoiled the puzzle for everyone else) the universe is spatially infinite, inflationarily branching, and branching via decoherence, which is at least three different ways that Reality is exponentially or infinitely large.
The conventional theory for explaining this is “psychological reactance,” social-psychology-speak for “When you tell people they can’t do something, they’ll just try even harder.” The fundamental instincts involved appear to be preservation of status and preservation of options. We resist dominance, when any human agency tries to restrict our freedom. And when options seem to be in danger of disappearing, even from natural causes, we try to leap on the option before it’s gone.
As Cialdini remarks, a chief sign of this malfunction is that you dream of possessing something, rather than using it. (Timothy Ferriss offers similar advice on planning your life: ask which ongoing experiences would make you happy, rather than which possessions or status-changes.)
The light came on when I realized that I was looking at a trick of Dark Side Epistemology—if you make something private, that shields it from criticism. You can say, “You can’t criticize me, because this is my private, inner experience that you can never access to question it.” But the price of shielding yourself from criticism is that you are cast into solitude—the solitude that William James admired as the core of religious experience, as if loneliness were a good thing. Such relics of Dark Side Epistemology are key to understanding the many ways that religion twists the experience of
...more
Now, I know what you’re going to say: “But science is surrounded by fearsome initiation rituals! Plus it’s inherently difficult to learn! Why doesn’t that count?” Because the public thinks that science is freely available, that’s why. If you’re allowed to learn, it must not be important enough to learn.
People seem to have holes in their minds for Esoteric Knowledge, Deep Secrets, the Hidden Truth. And I’m not even criticizing this psychology! There are deep secret esoteric hidden truths, like quantum mechanics or Bayes-structure. We’ve just gotten into the habit of presenting the Hidden Truth in a very unsatisfying way, wrapped up in false mundanity.
In reality, of course, the levels are bound together even tighter than that—bound together by the tightest possible binding: physical identity. You can see this: You can see that saying (1) “hand” or (2) “fingers and thumb and palm,” does not refer to different things, but different points of view.
Alcmaeon of Croton, a Pythagorean of the fifth century BCE, put his finger on the brain as the seat of intelligence, because he’d traced the optic nerve from the eye to the brain. Still, with the amount of evidence he had, it was only a guess.
The reductionist thesis (as I formulate it) is that human minds, for reasons of efficiency, use a multi-level map in which we separately think about things like “atoms” and “quarks,” “hands” and “fingers,” or “heat” and “kinetic energy.” Reality itself, on the other hand, is single-level in the sense that it does not seem to contain atoms as separate, additional, causally efficacious entities over and above quarks.
Our map, then, is very much unlike the territory; our maps are multi-level, the territory is single-level. Since the representation is so incredibly unlike the referent, in what sense can a belief like “I am wearing socks” be called true, when in reality itself, there are only quarks?
Just: There are patterns that exist in reality where we see “hands,” and these patterns have something in common, but they are not fundamental.
Though it is a bit unnerving to contemplate that every single concept and belief in your brain, including these meta-concepts about how your brain works and why you can form accurate beliefs, are perched orders and orders of magnitude above reality . . .
By far the best definition I’ve ever heard of the supernatural is Richard Carrier’s: A “supernatural” explanation appeals to ontologically basic mental things, mental entities that cannot be reduced to nonmental entities.
I previously defined the reductionist thesis as follows: human minds create multi-level models of reality in which high-level patterns and low-level patterns are separately and explicitly represented. A physicist knows Newton’s equation for gravity, Einstein’s equation for gravity, and the derivation of the former as a low-speed approximation of the latter. But these three separate mental representations are only a convenience of human cognition. It is not that reality itself has an Einstein equation that governs at high speeds, a Newton equation that governs at low speeds, and a “bridging
...more
Besides, as a Bayesian, I don’t believe in phenomena that are inherently confusing. Confusion exists in our models of the world, not in the world itself. If a subject is widely known as confusing, not just difficult . . . you shouldn’t leave it at that. It doesn’t satisfice; it is not an okay place to be. Maybe you can fix the problem, maybe you can’t; but you shouldn’t be happy to leave students confused.
I have argued elsewhere that the imprimatur of science should be associated with general laws, rather than particular events, because it is the general laws that, in principle, anyone can go out and test for themselves. I assure you that I happen to be wearing white socks right now as I type this. So you are probably rationally justified in believing that this is a historical fact. But it is not the specially strong kind of statement that we canonize as a provisional belief of science, because there is no experiment that you can do for yourself to determine the truth of it; you are stuck with
...more
If you take all this literally, it becomes the consciousness-causes-collapse interpretation of quantum mechanics. These days, just about nobody will confess to actually believing in the consciousness-causes-collapse interpretation of quantum mechanics— But the physics textbooks are still written this way! People say they don’t believe it, but they talk as if knowledge is responsible for removing incompatible “probability” amplitudes.
Once upon a time, the notion of the scientific method—updating beliefs based on experimental evidence—was a philosophical notion. But it was not championed by professional philosophers. It was the real-world power of science that showed that scientific epistemology was good epistemology, not a prior consensus of philosophers.
Today, this philosophy of belief-updating is beginning to be reduced to calculation—statistics, Bayesian probability theory.
The only reason why many-worlds is not universally acknowledged as a direct prediction of physics which requires magic to violate, is that a contingent accident of our Earth’s scientific history gave an entrenched academic position to a phlogiston-like theory that had an unobservable faster-than-light magical “collapse” devouring all other worlds. And many academic physicists do not have a mathematical grasp of Occam’s Razor, which is the usual method for ridding physics of invisible angels. So when they encounter many-worlds and it conflicts with their (undermined) intuition that only one
...more
So let me state then, very clearly, on behalf of any and all physicists out there who dare not say it themselves: Many-worlds wins outright given our current state of evidence. There is no more reason to postulate a single Earth, than there is to postulate that two colliding top quarks would decay in a way that violates Conservation of Energy. It takes more than an unknown fundamental law; it takes magic. The debate should already be over. It should have been over fifty years ago. The state of evidence is too lopsided to justify further argument. There is no balance in this issue. There is no
...more
As long as most scientists can manage to accept definite, unmistakable, unambiguous experimental evidence, science can progress. It may happen too slowly—it may take longer than it should—you may have to wait for a generation of elders to die out—but eventually, the ratchet of knowledge clicks forward another notch. Year by year, decade by decade, the wheel turns forward. It’s enough to support a civilization. So that’s all that Science really asks of you—the ability to accept reality when you’re beat over the head with it. It’s not much, but it’s enough to sustain a scientific culture.
And this is not easily reconciled with Bayesianism’s notion of an exactly right probability estimate, one with no flex or room for whims, that exists both before and after the experiment. Bayesianism doesn’t match well with the ancient and traditional reason for Science—the distrust of grand schemas, the presumption that people aren’t rational enough to get things right without definite and unmistakable experimental evidence. If we were all perfect Bayesians, we wouldn’t need a social process of science.
Sir Roger Penrose—a world-class physicist—still thinks that consciousness is caused by quantum gravity. I expect that no one ever warned him against mysterious answers to mysterious questions—only told him his hypotheses needed to be falsifiable and have empirical consequences. Just like Eliezer18.
I did not generalize the concept of “mysterious answers to mysterious questions,” in that many words, until I was writing a Bayesian analysis of what distinguishes technical, nontechnical and semitechnical scientific explanations. Now, the final output of that analysis can be phrased nontechnically in terms of four danger signs:
