All of ec429's Comments + Replies

I'm not quite sure how you're defining "causal model" here, but the bit about "get paid to build a factory, which then produces goods, meanwhile you don't consume the goods you were paid" seems causal to me. By not consuming the proceeds of your work, you have caused society to have more capital than otherwise. Heck, the paragraph beginning "But suppose…" is also describing a series of causes and effects, although it glosses over exactly how removing money from circulation drives up the value of money (that&#x... (read more)

I suppose a world without law at all would be one in which people habitually defect on the Prisoner's Dilemma. Even when it's the least 'true' a PD can be and still be a PD (so, iterated, with reputational incentives, all that stuff). There are no Schelling points, and thus no coördination: Nash equilibria and Moloch for all.

The "rule of law", perhaps, is a list of particular properties of the law (collection of Schelling points): that they contain no proper nouns, for example (the same law binds the King), that they do not ... (read more)

One cause might be that some of the underlying drivers of performance (of which IQ is but one) correlate with race. For a non-IQ-related example, if your interview process for a basketball team includes a jumping test, this will have a "disparate impact" because on average blacks jump better than whites. Therefore, even if you can demonstrate that you use the jump test because the regression analysis showed it was a good predictor of performance, the usual suspects will scream "algorithmic bias" and now even if you prove (possibly in ... (read more)

Curiously, from a civilisational perspective it doesn't matter whether you invest the money or just stuff it in your mattress; either way you're creating capital relative to the alternative, which is to spend it now on some form of consumption. (Note that, in this view, charitable giving is a consumption good rather than a capital good. In practice, of course, it's more complicated, because Africans with mosquito nets are more likely to generate endogenous economic growth than Africans with malaria. But to first order, saving African live... (read more)

I don't know if I count as part of the "movement", but I can't agree on these demands, because they all assume that notions such as "public policy" and "government" are valid and legitimate.

Suppose we were to turn them round and write them as negative demands; 5, 6, and 8 all reduce to freedom of contract. 7 is covered by "no crimes, only torts" since the concept of a "victimless tort" is obviously meaningless. 1 and 2 are fundamentally just questions of governance procedure, and become a lot le... (read more)

I think you're misusing the notion of "rule of law", possibly because of the Jewish-upbringing factors you mention. Economist Don Boudreaux would argue, after Hayek, that legislation and law are different things. My version of this, heavily influenced by David D. Friedman, is that law is really a collection of Schelling points, and legislation (the statute book) is one way (of many) in which new Schelling points can be created. This is far more obvious to someone who was brought up under the common-law system — and the US's legal tra... (read more)

most of us probably won't be able to find much of a trunk build that we can agree on

I think you're wrong as a question of fact, but I love the way you've expressed yourself.

It's more like a non-monotonic DVCS; we may all have divergent head states, but almost every commit you have is replicated in millions of other people's thought caches.

Also, I don't think the system needs to be Byzantine fault tolerant; indeed we may do well to leave out authentication and error correction in exchange for a higher raw data rate, relying on Release Early Release Often... (read more)

On the other hand, if you’re Dr. Evil and you’re in your moon base preparing to fire your giant laser at Washington, DC when you get a phone call from Austin “Omega” Powers

So, does this mean ata is going to write an Austin Powers: Superrational Man of Mysterious Answers fanfic?

How exactly are abstract, non-physical objects -- laws of nature, living in their "transcendent aerie" -- supposed to interact with physical stuff? What is the mechanism by which the constraint is applied? Could the laws of nature have been different, so that they forced electrons to attract one another?

I feel I should link to my post The Apparent Reality of Physics right now. To summarise: both the "descriptions" and "rules" views are wrong as they suppose there is something to be described or ruled. The (to me, obvious) dissolution is to state that a Universe is its rules.

There is a further subtlety here. As I discussed in "Syntacticism", in Gödel's theorems number theory is in fact talking about "number theory", and we apply a metatheory to prove that "number theory is "number theory"", and think we've proved that number theory is "number theory". The answer I came to was to conclude that number theory isn't talking about anything (ie. ascription of semantics to mathematics does not reflect any underlying reality), it's just a set of symbols and rules for manipulating sam... (read more)

I don't believe it, but it sounds like it should be testable, and if it hasn't been tested I'd be somewhat interested in doing so. I believe there are standard methods of comparing legibility or readability of two versions of a text (although, IIRC, they tend to show no statistically significant difference between perfect typesetting and text that would make a typographer scream).

You're probably not the only one bothered by the colour scheme, though; historically, every colour scheme I've used on the various iterations of my website has bothered many people. The previous one was bright green on black :S

That's interesting, because I would see a difference. Given the choice, I'd test it on the barren rock. However, I can't justify that, nor am I sure how much benefit I'd have to derive to be willing to blow up Eta Kudzunae.

Agree, and think your changes alter the question I was trying to ask, which is, not whether destroying Xenokudzu Planet would be absolutely unacceptable (as a rule, most things aren't), but whether we'd need a sufficiently good reason.

which has choked out all other life

I think the LCPW for you here is to suppose that this planet is only capable of supporting this xenokudzu, and no other kind of life. (Maybe the xenokudzu is plasma helices, and the 'planet' is actually a sun, and suppose for the sake of argument that that environment can't support sent... (read more)

Well, my source is Dr Bursill-Hall's History of Mathematics lectures at Cambridge; I presume his source is 'the literature'. Sorry I can't give you a better source than that.

Hmm. I do understand that, but I still don't think it's relevant. I don't try to argue that Premise 1 is true (except in a throwaway parenthetical which I am considering retracting), rather I'm arguing that Premise 2 is true, and that consequently Premise 1 implies the conclusion ("transposons have ethical value") which in turn implies various things ranging from the disconcerting to the absurd. In fact I believed Premise 1 (albeit without great examination) until I learned about transposons, and now I doubt it (though I haven't rejected it so... (read more)

My ethics were influenced a nonzero amount by reading Orson Scott Card. More to the point, OSC provided terminology which I felt was both useful and likely to be understood by my audience.

I now think that my use of the word "must" in the above-quoted passage was a mistake.

Your comment is a very good argument against a position - but unfortunately not the position I hold. I may have poorly expressed my meaning; it's not strictly the definition of the English word 'life' that I care about, but rather the exploration of my utility function, and whether my preferences are consistent and coherent, or whether they make an arbitrary distinction between "life with moral status" (people, chimps, and kittens) and "life without moral status" (cockroaches, E. coli, and transposons).

Can you suggest a good way for me to explain this in the article itself?

Sorry to have to tell you this, but Pythagoras of Samos probably didn't even exist. More generally, essentially everything you're likely to have read about the Pythagoreans (except for some of their wacky cultish beliefs about chickens) is false, especially the stuff about irrationals. The Pythagoreans were an orphic cult, who (to the best of our knowledge) had no effect whatsoever on mainstream Greek mathematics or philosophy.

Hmm, infinitary logic looks interesting (I'll read right through it later, but I'm not entirely sure it covers what I'm trying to do). As for Platonism, mathematical realism, and Tegmark, before discussing these things I'd like to check whether you've read http://lesswrong.com/r/discussion/lw/7r9/syntacticism/ setting out my position on the ontological status of mathematics, and http://lesswrong.com/lw/7rj/the_apparent_reality_of_physics/ on my version of Tegmark-like ideas? I'd rather not repeat all that bit by bit in conversation.

The computer program 'holds the belief that' this way-powerful system exists; while it can't implement arbitrary transfinite proofs (because it doesn't have access to hypercomputation), it can still modify its own source code without losing a meta each time: it can prove its new source code will increase utility over its old, without its new source code losing proof-power (as would happen if it only 'believed' PA+n; after n provably-correct rewrites it would only believe PA, and not PA+1. Once you get down to just PA, you have a What The Tortoise Said To ... (read more)

Can you explain more formally what you mean by "proves that it itself exists"?

The fundamental principle of Syntacticism is that the derivations of a formal system are fully determined by the axioms and inference rules of that formal system. By proving that the ordinal kappa is a coherent concept, I prove that PA+kappa is too; thus the derivations of PA+kappa are fully determined and exist-in-Tegmark-space.

Actually it's not PA+kappa that's 'reflectively consistent'; it's an AI which uses PA+kappa as the basis of its trust in mathematics that's... (read more)

Well, I'm not exactly an expert either (though next term at uni I'm taking a course on Logic and Set Theory, which will help), but I'm pretty sure this isn't the same thing as proof-theoretic ordinals.

You see, proofs in formal systems are generally considered to be constrained to have finite length. What I'm trying to talk about here is the construction of metasyntaxes in which, if A1, A2, ... are valid derivations (indexed in a natural and canonical way by the finite ordinals), then Aw is a valid derivation for ordinals w smaller than some given ordinal.... (read more)

I think that's a very good summary indeed, in particular that the "unique non-ambiguous set of derivations" is what imbues the syntax with 'reality'.

Symbols are indeed not defined, but the only means we have of duck-typing symbols is to do so symbolically (a symbol S is an object supporting an equality operator = with other symbols). You mention Lisp; the best mental model of symbols is Lisp gensyms (which, again, are objects supporting only one operator, equality).

conses of conses are indeed a common model of strings, but I'm not sure whether t... (read more)

Now I see why TDT has been causing me unease - you're spot on that the 5-and-10 problem is Löbbish, but what's more important to me is that TDT in general tries to be reflective. Indeed, Eliezer on decision theory seems to be all about reflective consistency, and to me reflective consistency looks a lot like PA+Self.

A possible route to a solution (to the Löb problem Eliezer discusses in "Yudkowsky (2011a)") that I'd like to propose is as follows: we know how to construct P+1, P+2, ... P+w, etc. (forall Q, Q+1 = Q u {forall S, [](Q|-S)|-S}). We ... (read more)

Oh, I'm willing to admit variously infinite numbers of applications of the rules... that's why transfinite induction doesn't bother me in the slightest.

But, my objection to the existence of abstract points is: what's the definition of a point? It's defined by what it does, by duck-typing. For instance, a point in R² is an ordered pair of reals. Now, you could say "an ordered pair (x,y) is the set {x,{x,y}}", but that's silly, that's not what an ordered pair is, it's just a construction that exhibits the required behaviour: namely, a constructo... (read more)

The locus exists, as a mathematical object (it's the string "{x \in R²: |x|=r}", not the set {x \in R² : |x|=r}). The "circle" on the other hand is a collection of points. You can apply syntactic (ie. mathematical) operators to a mathematical object; you can't apply syntactic operators to a collection of points. It is syntactic systems and their productions (ie. mathematical systems and their strings) which exist.

I have also (disappointingly/validatingly) thought of this and then read Tegmark. (It's even more disappointing/validating than that, though, since as well as Tegmark, you appear to have invented Syntacticism. You even have all my arguments, like subverting the simulation hypothesis and talking about 'closure'). However, I have one more thing to add, which may answer the problem of regularity. That one thing is what I call the 'causality manifold': Obviously by simulating a universe we have no causal effect upon it (if we are assuming the mathematical ... (read more)

Yes, it still works, because of the way the subjective probability flow on Tegmark-space works. (Think of it like PageRank, and remember that the s.p. flows from the simulated to the simulator)

It is technically possible that the differences between how much the two Universes simulate each other can, when combined with differences in how much they are simulated by other Universes, can cause the coupling between the two not to be strong enough to override some other couplings, with the result that the s.p. expectation of "giving Omega the $100" is... (read more)

Under my syntacticist cosmology, which is a kind of Tegmarkian/Almondian crossover (with measure flowing along the seemingly 'backward' causal relations), the answer becomes trivially "yes, give Omega the $100" because counterfactual-me exists. In fact, since this-Omega simulates counterfactual-me and counterfactual-Omega simulates this-me, the (backwards) flow of measure ensures that the subjective probabilities of finding myself in real-me and counterfactual-me must be fairly close together; consequently this remains my decision even in the Al... (read more)

Indeed. Circles are merely a map-tool geometers use to understand the underlying territory of Euclidean geometry, which is precisely real vector spaces (which can be studied axiomatically without ever using the word 'circle'). So, circles don't exist, but {x \in R² : |x|=r} does. (Plane geometry is one model of the formal system)

It doesn't seem odd at all, we have an expectation of the calculator, and if it fails to fulfill that expectation then we start to doubt that it is, in fact, what we thought it was (a working calculator).

Except that if you examine the workings of a calculator that does agree with us, you're much much less likely to find a wiring fault (that is, that it's implementing a different algorithm).

if (a) [a reasonable human would agree implements arithmetic] and (b) [which disagrees with us on whether 2+2 equals 4] both hold, then (c) [The human decides she v

I don't understand the meaning of the word "symbols" in the abstract, without a brain to interpret them with and map them onto reality.

Think in terms of LISP gensyms - objects which themselves support only one operation, ==. The only thing we can say about (rg45t) is that it's the same as (rg45t) but not the same as (2qox), whereas we think we know what (forall) means (in the game of set theory) - in fact the only reason (forall) has a meaning is because some of our symbol-manipulating rules mention it.

I think ec429 “sides” with the first intuition, and you tend more towards the second. I just noticed I am confused.

No, I'd say nearer the second - the mathematical expression of the world of P2 "exists" indifferently of us, and has just as much "existence" as we do. Rocks and trees and leptons, and their equivalents in P2-world, however, don't "exist"; only their corresponding 'pieces of math' flowing through the equations can be said to "exist".

What is clear to me is that when we set up a physical system (such as a Von Neumann machine, or a human who has been 'set up' by being educated and then asked a certain question) in a certain way, some part of the future state of that system is (say with 99.999% likelihood) recognizable to us as output (perhaps certain patterns of light resonate with us as "the correct answer")

But note that there are also patterns of light which we would interpret as "the wrong answer". If arithmetic is implementation-dependent, isn't it a bit odd t... (read more)

When you look at the statement 2+2=4 you think some form of "hey, that's true". When I look at the statement, I also think some form of "hey, that's true". We can then talk and both come to our own unique conclusion that the other person agrees with us.

I think your argument involves reflection somewhere. The desk calculator agrees that 2+2=4, and it's not reflective. Putting two pebbles next to two pebbles also agrees.

Look at the discussion under this comment; I maintain that cognitive agents converge, even if their only common con... (read more)

But you don't have to have unlimited resources, you just have to have X large but finite amount of resources, and you don't know how big X is.

Of course, in order to prove that your resources are sufficient to find the proof, without simply going ahead and trying to find the proof, you would need those resources to be unlimited - because you don't know how big X is. But you still know it's finite. "Feasibly computable" is not the same thing as "computable". "In principle" is, in principle, well defined. "In practice&qu... (read more)

It's P(I will find a proof in time t) that is asking for the probability of a definite event. It's not that evaluating this number at large t is so problematic, it's that it doesn't capture what people usually mean by "provable in principle."

Suppose that a proof is a finite sequence of symbols from a finite alphabet (which supposition seems reasonable, at least to me). Suppose that you can determine whether a given sequence constitutes a proof, in finite time (not necessarily bounded). Then construct an ordering on sequences (can be done, it... (read more)

One can certainly compute the digits of pi, so that since (as non-intuitionists insist anyway) either the $n$th digit is even, or it is odd, we must have P($n$th digit is even) > P(axioms) or P($n$ digit is odd) > P(axioms).

I don't think that's valid - even if I know (P=1) that there is a fact-of-the-matter about whether the nth digit is even, if I don't have any information causally determined by whether the nth digit is even then I assign P(even) = P(odd) = ½. If I instead only believe with P=P(axioms) that a fact-of-the-matter exists, then I a... (read more)

I am still arguing with you because I think your misstep poisons more than you have yet realized, not to get on your nerves.

I wasn't suggesting you were trying to get on my nerves. I just think we're talking past each other.

"A proof exists" is a much murkier statement and it is much more difficult to discuss its probability.

As a first approximation, what's wrong with "\lim_{t -> \infty} P(I can find a proof in time t)"?

Also, I don't see why the prior has to be oracular; what's wrong with, say, P(the 3^^^3th decimal digit of p... (read more)

lengthiness is not expected to be the only obstacle to finding a proof

True; stick a ceteris paribus in there somewhere.

You are trying to reason about reality from the point of view of a hypothetical entity that has infinite resources.

Not so; I am reasoning about reality in terms of what it is theoretically possible we might conclude with finite resources. It is just that enumerating the collection of things it is theoretically possible we might conclude with finite resources requires infinite resources (and may not be possible even then). Fortunat... (read more)

Paul Almond

To Minds, Substrate, Measure and Value Part 2: Extra Information About Substrate Dependence I make his Objection 9 and am not satisfied with his answer to it. I believe there is a directed graph (possibly cyclic) of mathematical structures containing simulations of other mathematical structures (where the causal relation proceeds from the simulated to the simulator), and I suspect that if we treat this graph as a Markov chain and find its invariant distribution, that this might then give us a statistical measure of the probability of being i... (read more)

But then, how do you determine whether information exists-in-the-universe at all? Does the number 2 exist-in-the-universe? (I can pick up 2 pebbles, so I'm guessing 'yes'.) Does the number 3^^^3 exist-in-the-universe? Does the number N = total count of particles in the universe exist-in-the-universe? (I'm guessing 'yes', because it's represented by the universe.) Does N+1 exist-in-the-universe? (After all, I can consider {particles in the universe} union {{particles in the universe}}, with cardinality N+1) If you allow encodings other than unary, le... (read more)

I am aware it can be very small. The only sense in which I claimed otherwise was by a poor choice of wording. The use I made of the claim that "Agents implementing the same deduction rules and starting from the same axioms tend to converge on the same set of theorems" was to argue for the proposition that there is a fact-of-the-matter about which theorems are provable in a given system. You accept that my finding a proof causes you to update P(you can find a proof) upwards by a strictly positive amount - from which I infer that you accept that... (read more)

Your conclusion on truth is a physical state in your mind, generated by physical processes. The existence of a metaphysical truth is not required for you to come to that conclusion.

I think a meta- has gone missing here: I can't be certain that others tend to reach the same truth (rather than funny hats), and I can't be certain that 2+2=4. I can't even be certain that there is a fact-of-the-matter about whether 2+2=4. But it seems damned likely, given Occamian priors, that there is a fact-of-the-matter about whether 2+2=4 (and, inasmuch as a reflective... (read more)

A positive but minuscule amount.

Right - but if there were no 'fact-of-the-matter' as to whether a proof exists, why should it be non-zero at all?

we find it hard to taboo words that are truly about the fundamentals of our universe, such as 'causality' or 'reality' or 'existence' or 'subjective experience'.

I tabooed "exist", above, by what I think it means. You think 'existence' is fundamental, but you've not given me enough of a definition for me to understand your arguments that use it as an untabooable word.

words like 'mathematical equations'

I'd say that (or rather 'mathematics') is just 'the orderly manipulations of symbols'. Or, as I prefer to phrase it, 'symbol games'.

'corr

But why should feasibility matter? Sure, the more steps it takes to prove a proposition, the less likely you are to be able to find a proof. But saying that things are true only by virtue of their proof being feasible... is disturbing, to say the least. If we build a faster computer, do some propositions suddenly become true, because we now have the computing power to prove them?

Me saying I have a proof of a theorem should cause you to update P(you can find a proof) upwards. (If it doesn't, I'd be very surprised.) Consequently, there is something comm... (read more)

Ok, now taboo your uses of "reality" and "preexisted" in the above comment, because I can't conceive of meanings of those words in which your comment makes sense.

Surely can't be exactly what you mean, as exists(our Univese) and ¬exists(everything else) seems coherent if rather unlikely

I would dispute this, on the grounds that my deductions in formal systems come from somewhere that has a causal relation to my brain - the formal system causes me to be more likely to deduce the things which are valid deductions than the things that aren't. So, if I 'exist', I maintain that the formal systems have to 'exist' too, unless you're happy with 'existing' things being causally influenced by 'non-existing' things - in whi... (read more)

So if you've ever read Probability Theory, by E.T. Jaynes

I haven't; I probably should.

the position that, in order to make sense when applied to the real world, infinite things have to behave like limits of finite things.

Is this "limits" in the sense of analysis (epsi-delta limits), or is it "limit points" (like ω)? If the former, then that position involves not believing that arithmetic makes sense when applied to the real world. If the latter, then the position doesn't seem different from what most mathematicians believe, beca... (read more)