Tom_McCabe2

Karma: 439

Tom_McCabe2 May 21, 2008, 10:32 PM
5 points
on: Einstein’s Speed
“IIRC, Einstein wasn’t the first to try to develop a curvature theory of gravity. Riemann himself apparently tried. And, IIRC, Einstein was one of Riemann’s students. Einstein brought to the table the whole thing about having to deal with spacetime rather than space.”

Riemann died in 1866, Einstein was born in 1879. Riemann was a mathematician: he developed the math of differential geometry, among a great deal of other things, so a lot of stuff is named after him. Einstein applied Riemann’s geometry to the physical universe. So far as I know, none of the early non-Euclidean geometry people thought that their geometries might be applicable in reality. The first theorems of hyperbolic geometry were produced in an attempt to create a contradiction and so prove Euclid’s fifth postulate.

“I disagree strongly with the suggestion Einstein was a proponent of MWI. In fact, the overemphasis on deduction (defined here as induction from few au priors) caused him to waste the remaining ²⁄₃ of his life attempting to disprove quantum phenomena, no?”

I have to find an actual physicist to discuss this with, but there appears to be nothing wrong with Einstein’s quest for a unified theory; he simply didn’t have the prerequisite information of QM at the time (Feynman, Dyson, etc. didn’t develop renormalization until the 1940s). MWI wasn’t proposed until several years after Einstein’s death.

“A willingness to reconsider his assumptions, an openness to new explanations, and an abiding belief that hypotheses should always be tested against the data—and discarded if they were found wanting.”

Plenty of scientists have these, and many of them make significant discoveries in their fields. But what was it about Einstein that let him discover, not one, but two of the fundamental theories of physics?

Tom_McCabe2 May 18, 2008, 6:59 PM
3 points
on: Changing the Definition of Science
“Science tolerates errors, Bayescraft does not. Nobel laureate Robert Aumann, who first proved that Bayesians with the same priors cannot agree to disagree, is a believing Orthodox Jew.”

I think there’s a larger problem here. You can obviously make a great deal of progress by working with existing bodies of knowledge, but when some fundamental assumption breaks down, you start making nonsensical predictions if you can’t get rid of that assumption gracefully. Aumann learned Science, and Science worked extremely well when applied to probability theory, but because Aumann didn’t ask “what is the general principle underlying Science, if you move into an environment without a long history of scientific thought?”, he didn’t derive principles which could also be applied to religion, and so he remained Jewish. The same thing, I dare say, will probably happen to Bayescraft if it’s ever popularized. Bayescraft will work better than Science, across a larger variety of situations. But no textbook could possibly cover every situation- at some point, the rules of Bayescraft will break down, at least from the reader’s perspective (you list an example at http://lesswrong.com/lw/nc/newcombs_problem_and_regret_of_rationality/). If you don’t have a deeper motivation or system underlying Bayescraft, you won’t be able to regenerate the algorithms and work around the error. It’s Feynman’s cargo cult science, applied to Science itself.

Tom_McCabe2 May 18, 2008, 4:59 AM
3 points
on: Do Scientists Already Know This Stuff?
“I figure that anyone who wants to paint me as a lunatic already has more than enough source material to misquote. Let them paint and be damned!”

The problem isn’t individual nutcases wanting to paint you as a lunatic; their cause would be better served by SitS or other Singularity-related material. It’s that people who haven’t heard your ideas before- the largest audience numerically, if you publish this in book form- might classify you as a lunatic and then ignore the rest of your work. Einstein, when writing about SR, did not go on about how the classical physicists were making a bunch of stupid mistakes and how his methods were superior to anything Newton ever developed. You have, of course, made far more extreme statements elsewhere (by mainstream standards), but the overall proportion of such material should scale polynomially with the number of readers who reject you as a crackpot.

Tom_McCabe2 May 17, 2008, 10:39 PM
2 points
on: Do Scientists Already Know This Stuff?
“This is insanity. Does no one know what they’re teaching?”

I doubt any systematic study has been done on the difference in curricula between MIT and Generic State U., even though it would be much easier, and MIT has 78 affiliated Nobel laureates while State U. probably has zero. You can argue from first principles (http://www.paulgraham.com/colleges.html) or experimental data (http://www.csis.gvsu.edu/~mcguire/worth_college_leagues.html) that elite colleges are selecting Nobel Prize winners rather than creating them, but I don’t know how accurate this is. If we could make MIT and Caltech replicas pop up all over the country, it would be well worth the time and effort.

Tom_McCabe2 May 15, 2008, 8:13 PM
1 point
on: When Science Can’t Help
“If scientific reasoning is merely Bayesian,”

Scientific reasoning is an imperfect approximation of Bayesian reasoning. Using your geometric analogy, science is the process of sketching a circle, while Bayesian reasoning is a compass.

“It seems to me that it is easy to represent strict standards of evidence within looser ones, but not vice versa.”

If you already understand the strict standard, it’s usually easy to understand the looser standard, but not vice-versa. Physicists would have a much easier time writing literature papers than literary theorists would writing physics papers.

“The frequency of ‘Bayesian reasoners’ mistaking data for evidence on this site should serve as example enough.”

Data, assuming it’s not totally random, is always evidence for some theory. Of course, not all data is evidence for every theory.

Tom_McCabe2 May 13, 2008, 10:28 PM
5 points
on: The Dilemma: Science or Bayes?
“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.”

Your work on FAI is still pretty supervillain-esque to most SL0 and SL1 people. You are, essentially, talking about a human-engineered end to all of civilization.

“I wanted to present you with a nice, sharp dilemma between rejecting the scientific method, or embracing insanity. Why? I’ll give you a hint: It’s not just because I’m evil. If you would guess my motives here, think beyond the first obvious answer.”

The obvious answer is that the scientific method is simply an imperfect approximation of ideal rationality, and it was developed before Bayes’ Theorem was even proposed, so we should expect it to have some errors. So far as I know, it was never even defined mathematically. I haven’t thought of any non-obvious answers yet.

“I don’t believe you. I don’t believe most scientists would make such huge mistakes.”

It took thirty years between the original publication of Maxwell’s laws (1865) and Einstein’s discovery of their inconsistency with classical mechanics (~1895). It took another ten years before he published (1905). In the meantime, so far as I know, nobody else realized the fundamental incompatibility of the two main theories of classical physics.

Tom_McCabe2 May 12, 2008, 9:05 PM
3 points
on: The Failures of Eld Science
This. Is. Awesome. If you weren’t busy with FAI, you could make a fortune selling this stuff to universities.

Tom_McCabe2 May 5, 2008, 8:47 PM
2 points
on: Spooky Action at a Distance: The No-Communication Theorem
“The idea that density matrices summarize locally invariant entanglement information is certainly helpful, but I still don’t know how to start with a density matrix and visualize some physical situation, nor can I take your proof and extract back out an argument that would complete the demonstration in this blog post. I confess this is strictly a defect of my own education, but...”

From what I understand (which is admittedly not much; I could well be wrong), a density matrix is the thingy that describes the probability distribution of the quantum system over all possible states. Suppose that you have a set of quantum states A1...An. The density matrix is a way of describing a system that, say, has a 75% chance of being in A1 and a 25% chance of being in A2, or a 33% chance of being in A1 or A2 or A4, or whatever. You can then plug the density matrix into the standard quantum equations, but everything you get back will have one extra dimension, to account for the fact that the system you are discussing is described by a distribution rather than a pure quantum state.

The gist of Scott Aaronson’s proof is (again, if I understand correctly): Suppose that you have two quantum systems, A and B. List the Cartesian product over all possible states of A and B (A1B1, A2B1, A3B1, etc., etc.). Use a density matrix to describe a probability distribution over these states (10% chance of A1B1, 5% chance of A1B2, whatever). Suppose that you are physically located at system A, and you fiddle with the density matrix using some operator Q. Using some mathematical property of Q which I don’t really understand, you can show that, after Q has been applied, another person’s observations at B will be the same as their earlier observations at B (ie, the density matrix after Q acts the same as it did before Q, so long as you only consider B).

Tom_McCabe2 Apr 19, 2008, 2:51 PM
3 points
on: Identity Isn’t In Specific Atoms
“If you furthermore had any thoughts about a particular “helium atom” being a factor in a subspace of an amplitude distribution that happens to factorize that way,”

If a helium atom is just an accidential, temporary factorization of an amplitude distribution, then why does it keep appearing over and over again when we look at the universe? If you throw a thousand electrons together, let them interact, zap them with laser radiation, etc., etc., at the end of the day you will still see a bunch of electrons with 511 keV rest mass and −1 charge. Why does the universe so carefully conserve these particular bundles of amplitude, with only one exception that I am aware of (annihilation by positrons), while other bundles of amplitude never exist at all (eg., a particle with 360 keV rest mass, or a particle with ⁷⁄₂ charge).

Tom_McCabe2 Apr 17, 2008, 3:58 AM
0 points
on: The Quantum Arena
“I was simply trying to figure out that if so, what’s the “actual reality”?”

There is none, at least not in those terms. There is no “actual positional configuration space”, any more than there’s an “actual inertial reference frame” or “actual coordinate system”; they are all equivalent in the experimental world. Feel free to use whichever one you like.

“I’d thought the Hilbert space was uncountably dimensional because the number of functions of a real line is uncountable.”

The number of functions of the real line is actually strictly greater than beth-one uncountability (by Cantor’s theorem).

“I’d thought the Hilbert space was uncountably dimensional because the number of functions of a real line is uncountable.”

The category of Hilbert spaces includes spaces of both finite and infinite dimension, so it presumably includes both countable and uncountable infinities.

Tom_McCabe2 Apr 16, 2008, 5:11 PM
0 points
on: The Quantum Arena
Psy-Kosh: I haven’t done the math out myself, but others have shown that all the predictions of QED are self-consistent under special relativity. You can change all the non-Lorentz-invariant numbers (eg, absolute position, absolute velocity) by moving to a different reference frame, but all the actual predictions are Lorentz-invariant.

Tom_McCabe2 Apr 15, 2008, 1:39 AM
0 points
on: Can You Prove Two Particles Are Identical?
“What does “the universe is a lie” mean technically? Otherwise, I think I understand.”

I believe Eli’s referring to the usual “Matrix” scenario, where nothing we see actually exists, and it’s all an illusion carefully created by the deliberate manipulation of our neurons.

Tom_McCabe2 Apr 12, 2008, 10:37 PM
2 points
0
on: Where Philosophy Meets Science
“Just as, once upon a time, it was easier to imagine Thor throwing lightning bolts, than to imagine Maxwell’s Equations—even though Maxwell’s Equations can be described by a computer program vastly smaller than the program for an intelligent agent like Thor.”

Hmmm… perhaps we could define a “relative Kolmogorov complexity”, K[X], where the K[X] of Y is the size of the smallest .diff file that alters program X to make it output Y and then halt. K(Maxwell) < K(Thor), but it seems quite likely that KHuman > KHuman.

Tom_McCabe2 Apr 10, 2008, 4:02 AM
1 point
on: Quantum Explanations
My apologies for the earlier formatting error. Basically, objects on one level of organization (fundamental particles) should only interact in any significant sense with objects on the same level, not with mental representations of fundamental particles or macroscopic blocks of matter. There are exceptions to this (eg, an errant lepton causes quantum physicists to jump for joy), but they require some sort of complex mechanism (in the Kolmogorov sense) to carry information into a different organizational level.

Tom_McCabe2 Apr 10, 2008, 3:57 AM
1 point
on: Quantum Explanations
“The fun part, of course, will be to see how you handle mixed states, where the “map” and the “territory” get scrambled together into a non-uniquely-decomposable linear-algebraic soup...”

I am not a professional quantum physicist, but the suggestion that our thoughts about a quantum process somehow influence the outcome of that process seems to me to be patently absurd. Our thoughts are not somehow separated from the rest of reality; they are made up of the same quarks and leptons that we study in QM experiments. At no point are these quarks and leptons aware of the higher levels of organization within the brain. If there is an interaction between you and the QM experiment, it will be on the level of → , not → .

Tom_McCabe2 Apr 7, 2008, 2:59 AM
17 points
0
on: GAZP vs. GLUT
“Otherwise even a GLUT would be conscious, right?”

I have to admit that this sounds crazy, and that I don’t really understand what’s going on. But it looks like it’s logically necessary that lookup tables can be conscious. As far as we know, the Universe, and everything in it, can be simulated on a giant Turing machine. What is a Turing machine, if not a lookup table? Granted, most Turing machines use a much smaller set of symbols than a GLUT- base 5 or base 10 instead of base 10^10^50- but how would that change a system from being “non-conscious” to being “conscious”? And while a Turing machine has a state register, this can be simulated by just using N lookup tables instead of one lookup table. It seems like we have to believe that 1), the mathematical structure of a UTM relative to a giant lookup table, which is very minimal indeed, is the key element required for consciousness, or 2), the Universe is not Turing-computable, or 3), consciousness does not exist.

Tom_McCabe2 Apr 5, 2008, 11:32 PM
5 points
0
on: The Generalized Anti-Zombie Principle
“But you see the importance of the question, “How far can you generalize the Anti-Zombie Argument and have it still be valid?”″

Hmmm… I can see three different possible generalizations:

1). Any Turing-equivalent device which implements the same algorithms that you do is you, in every ethical and philosophical sense of the word. 2). There are no mysterious “properties” in the universe which can exist or not exist independently of what the quarks and leptons are doing. 3). Physics, and all the larger-scale mental structures based on physics, are topologically continuous (no large-scale effects for arbitrarily small causes).

Tom_McCabe2 Mar 31, 2008, 4:23 AM
6 points
on: Angry Atoms
(Sorry about the double comment, but several responses were posted while I was typing.)

“It’s one thing to say that any implementation of an algorithm (or mind) has some physical basis, which is pretty obviously true and hence not very interesting, but if those implementations have nothing physical in common, then your reduction hasn’t actually accomplished very much.”

The reduction of a software system is just as difficult as the reduction of a physical system, and perhaps even more so. I believe there’s a theorem which states that the problem of producing a Turing machine which will give output Y for input X is uncomputable in the general case.

“That suggests that the algorithm itself is not a physical thing, but something else.”

Algorithms are made from math; math was originally abstracted from physical matter in exactly the way that you describe. You can implement “two” on completely different physical systems- two apples, two computers, two Space Shuttles, and so on.

“Your conjecture seems to be that the Problem of Chess requires intelligence.”

It’s just an example of how complex behaviors can arise from simple parts that don’t exhibit the behaviors themselves. Chess-playing, although not equivalent to general intelligence, does require several complex behaviors which are also used by general intelligence.

“I also don’t see how you can claim that understanding utility functions helps you understand the brain. Do you think that such functions are explicitly represented in the brain?”

Utility functions are general enough to apply to any optimization process which can state a clear preference over outcomes.

Tom_McCabe2 Mar 31, 2008, 4:04 AM
7 points
on: Angry Atoms
“But materialism isn’t that easy. It’s not as cheap as saying, “Anger is made out of atoms—there, now I’m done.”″

If materialism required a detailed understanding of every solved problem in science, none of us could ever be materialists, at least not with human brains. How many times do you have to learn the same lesson (“complex systems can be built from simple parts which don’t share the defining properties of the larger system”)? Hopefully, after a few iterations, you’ll start imagining unseen layers of complexity, rather than phlogiston and elan vital.

Tom_McCabe2 Mar 28, 2008, 11:24 PM
20 points
1
on: Initiation Ceremony
“If I were asked that question, I’d ask for some pencil and paper because I’m mediocre at mental arithmetic.”

I probably would have gotten the answer, but it wouldn’t have occurred to me to say that the initial information was wrong. It’s part of an initiation ritual for a mathematical cult; why would anyone bother checking to see if the actual numbers are correct? Saying “I do not, in fact, believe the information given is correct” feels like saying “The air around me contains oxygen”.