How confident are you in the Atomic Theory of Matter?

It is more likely that I have misread the question completely — that it is actually about the smell of blue cheese, the color of dinosaur feathers, or some other thing — than that atomic theory is false.

Indeed, it is more likely that I have hallucinated Less Wrong than that atomic theory is false.

Because if atomic theory is false, then none of chemistry, electronics, etc. make any sense.

Therefore, so far as I am capable of caring, atomic theory is certain; I can go into solipsistic crisis on less evidence than I can seriously doubt it.

At least +40 dB. “Next Thursday I will not meet a funeral procession on my way home from the bus stop” is somewhere between +35 dB and +40 dB (given that such a thing has happened to me exactly once that I remember of), and I'm more confident that ordinary matter is made of atoms than that.

It occurs to me that there are several entirely different types of things which would indicate "Atomic Theory may be Wrong."

1: You look into an Electron Microscope, expecting to see Atoms. You see Infinitely divisible Swiss Cheese spelled out into the shape of the word "Nope."

2: You use an ultra accurate scale, expecting to weigh something at 1.255000001. It weighs 1.255000002. Because the integral weight of the subatoms, subsubatoms, subsubsubatoms etc, causes your measurement to be off.

3: I am inexplicably transported to "Fantasia." Atomic theory doesn't work here because Fantasia is constructed from strange matter, namely infinitely divisible magicons, but it does still work on Earth, which is in fact still made of ordinary matter.

4: I am in the middle of looking into a Microscope which is broadcasting onto a TV. everyone is suprised to note that at 12:00 noon exactly, the Atoms suddely appeared to be more divisible than they were before.

5: Omega shows up and I am informed that I am in a simulation which does not actually use real world physics. Instead, it uses simplified physics.

Ergo, if Atomic Theory is invalid, it brings up the question of how it is invalid:

Does it work on everything except this thing? Does it approximately work on everything, but doesn't exactly work? Does it work on everything in a particular area, but not in other areas? Does it work at some times and not at others? Does it only work because it is the rules of the simulation?

This is important, because for instance, If there's a 1% chance that I'm in a Omega simulation, and a 1% chance that an Omega simulation is not being run using the real worlds physics, then even if I was 100% confident that Atomic Physics described my simulation (which I shouldn't be), my confidence that the Atomic theory correctly describes the real world shouldn't exceed 99.99%, if I've been doing the math correctly.

So I feel like the answer is, my number doesn't describe anything without some kind of shared context between me and the person.

Please elucidate the purpose of this question.

Welp - it seems that I definitely managed to phrase my question poorly. So I'll try again:

By 'atomic theory', I'm referring to the century-plus-old theory that ordinary stuff, like trees and pencils and animals, are made out of something like particles, rather than matter being a 'stuff' that you can just keep on dividing into smaller and smaller pieces. I'm referring to the theory that's the foundation of chemistry.

Put yet another way: "Do you think that 'H2O' is a meaningful description of water?"

For many of the obvious ways to pose the question, atomic theory is already false - multiparticle states are the real building blocks, and you can do pretty unusual things with them if you try hard enough. I think the most sensible thing to ask about is sudden failure of properties that we normally ascribe to atomic theory, like ratios working in chemical reactions or quantum mechanics predicting NMR spectra. In which case, I'd need said failures to replicate to be as good as the supporting evidence, or propose a simple-ish mechanism, like "we're in a simulation and it's just changed." Taking that as my lowest standard, I'd be satisfied with a standard star-blinking pattern, or maybe a pi-message, the usual sort of thing, with null probability with an exponent somewhere in the -25 range.

1-epsilon. It is more likely that the atomic description of the universe is generally accurate (although it does break down at the subatomic level) than that I am answering a question about it.

99.99998754%.

Actually, I don't know. The number above has been determined by both my credence in the atomic theory and the shape of my keyboard, anchoring and perhaps many other biases; the biases could have driven the number far away from its true value. But I dislike dodging questions about probability and believe that disagreements would be easier to resolve if people shared their probabilities when asked, so I provide an answer which is as good as I can make it.

I believe that there is a useful reformulation of similar questions: how many bits of evidence against the atomic theory would make you to doubt the theory on the level of approximately 50% confidence? People are much better at evaluationg the strength of their beliefs when they are an about that level, so this question could be in principle settled experimentally. Of course, people aren't ideal Bayesians and the persuasive power of evidence would depend on the way it is presented, perhaps a sufficiently clever demagogue can talk me out of my belief in the atomic theory without any evidence at all, so the approach has its limits. But it still seems that "how much evidence would it take to change my opinion" is an easier question to tackle directly than "what's the probability that I am right". Unfortunately, I can't answer that for the case of the atomic theory without some hard thinking, and I am lazy to think about it hard just now.

The idea of assigning a probability to such a thing might be, I think, what Nassim Nicholas Taleb calls the "Ludic fallacy" (see http://en.wikipedia.org/wiki/Ludic_fallacy). Alternatively, as I see it, to do such a thing, we need to start with some sort of paradigm by which we know how to set probabilities and do something useful with them. Poker is a good example, and not coincidentally, "Ludic" is from the Latin ludus, meaning "play, game, sport, pastime." It is no accident that so many introductory examples in statistics are about things like coin tossing.

Can we start by asking "Of all the universes I've known, in how many of them does the Atomic Theory apply?" Maybe this is frequentist, and Bayes will offer some plausible approach, but does anyone have a clue how to attack it that way?

Taleb can seem like a curmudgeonish contrarian at times, but at other times he seems to me at least like he's onto some deep ideas. I need to read and think a lot more before I can possibly make up my mind, but at least feel very motivated to do just that.

How confident are you in the existence of cats?

This is a colossal waste of time.

I'm still not sure how I'm supposed to interpret this question. If you're asking whether I think "matter is made up of atoms" is an extremely useful working hypothesis for many many scientific purposes, then the answer is obviously "yes" with probability that only negligibly differs from 1. (ETA: Don't ask me how negligibly different, because I couldn't tell you. I am not enough of an ideal Bayesian that I can meaningfully attach probabilities with many significant digits to my beliefs.)

If you're asking whether the fundamental structure of matter is in fact discrete, I would assign that a probability of about 0.3. Quantum field theory is sometimes interpreted as a particle theory, but this seems wrong to me. It is best interpreted as telling us that the basic constituents of nature are continuous field configurations (or, to be more precise, linear superpositions of field configurations).

Particle number is not fixed in any workable relativistic quantum field theory. This strongly suggests that particles are emergent rather than fundamental. If you suppose that a a particle cannot be located at two disjoint regions in a single space-like hyperplane, then any relativistic quantum theory of a fixed number of particles predicts a zero probability of finding a particle anywhere (see here for the proof). So the only consistent particle QFT is one where there are no particles!

There's also the fact that an observer accelerating uniformly in a Minkowski vacuum will see a thermal bath of particles (the Unruh effect). If one can bring particles in or out of existence simply by a change of reference frame, then they shouldn't be part of one's fundamental ontology.

Of course QFT itself is in all probability not the right fundamental theory, so matter may still turn out to have discrete constituents.

Querying my expectations I find that my expectations of reality aren't at all related to verbal statements like "The Atomic Theory of Matter" even if my verbal centers want to endorse it strongly.

I currently believe that the atomic theory of matter is a descriptive, predictive theory relating to the sorts of objects physicists have categorized and the sorts of tools that exist.

Asking "How confident are you that there are discrete units" feels like asking "how confident are you that jumping on one goomba's head in mario gives you 100 points" (or whatever, it has been a while.)

The answer is, if you upload the code for the game and hack it then the question of points stops being relevant.

So the translation of what my expectations is is that I believe that "elementary particles" are indivisible insofar as the theory of elementary particles treats them as particles. But if everything is probability distributions further down, then I don't even know what it means to say that something is indivisible. Does it mean that the distribution emerges from an indecomposable, finite-dimensional representation? In that case these distributions will have an atomic theory, but I don't think that will actually be true, and it may be better at a smaller scale to switch analogies to something where the previous idea of atomic theory no longer makes any sense at all.

I guess that puts me at about -10 decibans; I don't see an a priori reason that probability distributions should be atomic, and I can imagine them being fundamental. And if they aren't, that adds to the probability of our formalisms being overturned over and over again.

Q: How confident are you in Newton's law of universal gravitation?

A: Depends on the conditions.

Main evidence: Universal belief (including experts), coherence of theory, directly testable implications that I deal with on a day-to-day basis (fuel cells), lots more directly testable predictions (brownian motion, all the rest of chemistry, thermodynamics, solid and fluid mechanics...)

Let's put it this way, if I encountered the kind of evidence that would be required to cast it into doubt, I'd have to revise my belief in pretty much everything. Cartesian demon level.

Maybe 15 bits? Mostly metauncertainty.

EDIT: I feel profoundly unqualified as a mere human to be tossing around that kind of certainty, but I'm going to leave it.

for 'The Epicurean Truth' namely that matter works on simple computable rules and everything actually perceptible to humans is emergent: Certainty with an epsilon-sized crack (connected to sudden doubt of everything whatsoever)

For what you actually asked about: I'd say its almost the same, maybe over a hundred decibans.

I live my life under the assumption that it is correct, and I do not make allowances in my strategic thinking that it may be false. As for how hard it would be to convince me I was wrong, I am currently sufficiently invested in the atomic theory of matter that I can't think, off-hand, what such evidence would look like. But I presume (hope) that a well-stated falsifiable experiment which showed matter as a continuum would convince me to become curious.

Somewhere between 0 decibans and 50 decibans, depending on the question you are actually trying to ask. If you're asking "Is there some way to interpret QM equations without invoking the concept of atoms," I'd give that about 50/50, because I don't actually know QM and I could see that going either way. If your question is instead "How confident are you that you will continue to make observations consistent with atomic theory for the rest of your life," I'm quite confident that I won't see anything obviously falsifying the existence of, say, hydrogen.

For the "'H2O is a meaningful description of water" question, the same problem comes up: most of the scenarios in which it's not are scenarios in which this was a trick question, because this pattern-matches really strongly as a trick question. My estimate of the probability that I missed something rarely drops below 10% when communicating through asynchronous text with another human.

Since you're trying to put numbers on something which many of us regard as being certainly true, I'll take the liberty of slightly rephrasing your question.

How much confidence do I place in the scientific theory that ordinary matter is not infinitely divisible? In other words, that it is not true that no matter how small an amount of water I have, I can make a smaller amount by dividing it?

I am (informally) quite certain that water is not infinitely subdivisible. I don't think it's that useful an activity for me to try to put numbers on it, though. The problem is that in many of the more plausible scenarios I can think of where I'm mistaken about this, I'm also barking mad, and my numerical ability seems as likely to be affected by that as my ability to reason about atomic theory. I would need to be in the too crazy to know I'm crazy category - and probably in the physics crank with many imaginary friends category as well. Even then I don't see myself as being in a known kind of madness to be that wrong.

The problem here is that I can reach no useful conclusions on the assumption that I am that much mistaken. The main remaining uncertainty is whether my logical mind is fundamentally broken in a way I can neither detect nor fix. It's not easy to estimate the likelihood of that, and it's essentially the same likelihood for a whole suite of apparently obvious things. I neglect even to estimate this number as I can't do anything useful with it.

To not avoid the question, I say 99.9999%. And while saying this, I also note that I am not really good at estimating probabilities with this preciseness.

By the way, you should make a poll. With options e.g. "less than 99%", "99%", "99.9%" ... "99.9999999%", "more than "99.9999999%", "1".

I'm a little confused by this question. In my experience, atomic theory always refers to atoms. I think you're really asking whether quarks and such are divisible. I'm confident that there is no substructure to elementary particles, but I won't give a number.

"All the results of atomic theory are down to random chance, and it's a useless model" [~0%]

"Atomic theory is the absolute best possible model for reality, and handles all edge cases ideally" [~0%]

I'd say 40 decibans is my minimum credence for ANY major established theory, simply due to the possibility of procedural error or unknown factors in any attempted disproof. i.e. I would assume that there's been at LEAST 10,000 erroneous results that purported to disprove the theory.

Alternately, if we assume there are at least a million scientists, and they average 1 test of the theory each, that gives us ~60 decibans.

If we take a common behavior that most of the world has done at least once, that gives us ~90 decibans

How much confidence do you place in the scientific theory that ordinary matter is made of discrete units, or 'atoms', as opposed to being infinitely divisible?

Per Korzybski, I'd say that whatever you say matter is, it is not. Modeling matter as coming in discrete configurations works quite well, though we've seen that there are exceptions where the discrete configurations can be reconfigured if properly physically perturbed. I wouldn't be surprised if there are tons more stable configurations than we've seen or created so far, and even some that no longer model well as "discrete".

How much confidence do you place in the scientific theory that ordinary matter is made of discrete units, or 'atoms', as opposed to being infinitely divisible?

Atoms are divisble. It possible to believe that matter is made of atoms and matter is infinitely divisible.

A reasonably accurate rewording is: "Do you believe 'H2O' is a meaningful description of water?".

What the heck does meaningful mean? While we are at seeking meaning: "What's the meaning of life?" I don't think that the word makes specific predictions that would allow you to put a confidence rating on the claim being true.

It's very important to mentally distinguish different classes of statements. If you start giving claims that make no predictions confidence levels you mess up your way of thinking precisely about the world.

The map is not the territory. Asking for the confidence in the belief that the map is the territory is wrong on a fundamental level.