Rafael Harth

• Rafael Harth 15 Feb 2021 19:56 UTC

  2 points

  in reply to: just_browsing’s comment on: Ra­fael Harth’s Shortform

  Here is a construction of $(\dots ,1,1,1,\dots )$: We have that $1+x+x^2+\dots$ is the inverse of $1-x$. Moreover, $\frac{1}{x}+\frac{1}{x^2}+\frac{1}{x^3}+\dots$is the inverse of $x-1$. [...]

  Yeah, that’s conclusive. Well done! I guess you can’t divide by zero after all ;)

  I think the main mistake I’ve made here is to assume that inverses are unique without questioning it, which of course doesn’t make sense at all if I don’t yet know that the structure is a field.

  My hunch is that any bidirectional sum of integer powers of x which we can actually construct is “artificially complicated” and it can be rewritten as a one-directional sum of integer powers of x. So, this would mean that your number system is what you get when you take the union of Laurent series going in the positive and negative directions, where bidirectional coordinate representations are far from unique. Would be delighted to hear a justification of this or a counterexample.

  So, I guess one possibility is that, if we let $\left[x\right]$ be the equivalence class of all elements that are $=x$ in this structure, the resulting set of classes is isomorphic to the Laurent numbers. But another possibility could be that it all collapses into a single class—right? At least I don’t yet see a reason why that can’t be the case (though I haven’t given it much thought). You’ve just proven that some elements equal zero, perhaps it’s possible to prove it for all elements.

• Rafael Harth 14 Feb 2021 8:31 UTC

  2 points

  in reply to: just_browsing’s comment on: Ra­fael Harth’s Shortform

  You’ve understood correctly minus one important detail:

  The structure you describe (where we want elements and their inverses to have finite support)

  Not elements and their inverses! Elements or their inverses. I’ve shown the example of $1+\frac{1}{x}$ to demonstrate that you quickly get infinite inverses, and you’ve come up with an abstract argument why finite inverses won’t cut it:

  To show that nothing else works, let $P\left(x\right)$ and $Q\left(x\right)$ be any two nonzero sums of finitely many integer powers of $x$ (so like $\frac{1}{x}+1-x^2$). Then, the leading term (product of the highest power terms of $P$ and $Q$) will be some nonzero thing. But also, the smallest term (product of the lower power terms of $P$ and $Q$) will be some nonzero thing. Moreover, we can’t get either of these to cancel out. So, the product can never be equal to $1$. (Unless both are monomials.)

  In particular, your example of $x+\frac{1}{x}$ has the inverse $x-x^3+x^5-x^7\cdots$. Perhaps a better way to describe this set is ‘all you can build in finitely many steps using addition, inverse, and multiplication, starting from only elements with finite support’. Perhaps you can construct infinite-but-periodical elements with infinite-but-periodical inverses; if so, those would be in the field as well (if it’s a field).

  If you can construct $(\cdots 1,1,1,1\cdots )$, it would not be field. But constructing this may be impossible.

  I’m currently completely unsure if the resulting structure is a field. If you get a bunch of finite elements, take their infinite-but-periodical inverse, and multiply those inverses, the resulting number has again a finite inverse due to the argument I’ve shown in the previous comment. But if you use addition on one of them, things may go wrong.

  A larger structure to take would be formal Laurent series in $x$. These are sums of finitely many negative powers of x and arbitrarily many positive powers of $x$. This set is closed under multiplicative inverses.

  Thanks; this is quite similar—although not identical.

• Rafael Harth 11 Feb 2021 17:27 UTC

  4 points

  on: Ra­fael Harth’s Shortform

  Edit: this structure is not a field as proved by just_browsing.

  Here is a wacky idea I’ve had forever.

  There are a bunch of areas in math where you get expressions of the form $\frac{0}{0}$ and they resolve to some number, but it’s not always the same number. I’ve heard some people say that $\frac{0}{0}$ “can be any number”. Can we formalize this? The formalism would have to include $4\cdot 0$ as something different than $3\cdot 0$, so that if you divide the first by 0, you get 4, but the second gets 3.

  Here is a way to turn this into what may be a field or ring. Each element is a function $f:Z\to R$, where a function of the form $(\cdots 0,4,3,5,1,2,0\cdots )$ reads as $4\cdot 0^2+3\cdot 0+5+\frac{1}{0}+\frac{2}{0^2}$. Addition is component-wise ($3\cdot 0+6\cdot 0=9\cdot 0$; this makes sense), i.e., $(f+g)\left(z\right):=f\left(z\right)+g\left(z\right)$, and multiplication is, well, $\frac{3}{0}\cdot \frac{2}{0}=\frac{6}{0^2}$, so we get the rule

  $$(f\cdot g)\left(z\right)=\sum _{k+\ell =z}f\left(k\right)g\left(\ell \right)$$

  This becomes a problem once elements with infinite support are considered, i.e., functions $f$ that are nonzero at infinitely many values, since then the sum may not converge. But it’s well defined for numbers with finite support. This is all similar to how polynomials are handled formally, except that polynomials only go in one direction (i.e., they’re functions from $N$ rather than $Z$), and that also solves the non-convergence problem. Even if infinite polynomials are allowed, multiplication is well-defined since for any $n\in N$, there are only finitely many pairs of natural numbers $k,\ell$ such that $k+\ell =n$.

  The additively neutral element in this setting is $0:=(\cdots 0,0,0,0,0\cdots )$ and the multiplicatively neutral element is $1:=(\cdots 0,0,1,0,0\cdots )$. Additive inverses are easy; $(-f)\left(z\right)=-f\left(z\right)\forall z\in Z$. The interesting part is multiplicative inverses. Of course, there is no inverse of $0$, so we still can’t divide by the ‘real’ zero. But I believe all elements with finite support do have a multicative inverse (there should be a straight-forward inductive proof for this). Interestingly, those inverses are not finite anymore, but they are periodical. For example, the inverse of $1\cdot 0$ is just $\frac{1}{0}$, but the inverse of $1+1\cdot 0$ is actually

  $$1-1\cdot 0+1\cdot 0^2-1\cdot 0^3+1\cdot 0^4\cdots$$

  I think this becomes a field with well-defined operations if one considers only the elements with finite support and elements with inverses of finite support. (The product of two elements-whose-inverses-have-finite-support should itself have an inverse of finite support because $(fg{)}^{-1}=g^{-1}{f}^{-1}$). I wonder if this structure has been studied somewhere… probably without anyone thinking of the interpretation considered here.

• Rafael Harth 6 Feb 2021 14:29 UTC

  9 points

  on: Open & Wel­come Thread – Fe­bru­ary 2021

  There are a bunch of sequences, like the value learning sequence, that have structured formatting in the sequence overview (the page the link goes to), so something like Headline, a bunch of posts, headline, a bunch of more posts.

  How is this done? When I go into the sequence editor, I only see one text field where I can write something which then appears in front of the list of posts.

• Rafael Harth 29 Jan 2021 20:24 UTC

  13 points

  on: The GameS­top Si­tu­a­tion: Sim­plified

  This post is similar to the one Eliezer Yudkowsky wrote.

• Rafael Harth 26 Jan 2021 19:45 UTC

  2 points

  in reply to: rohinmshah’s comment on: Pre­face to the Se­quence on Fac­tored Cognition

  Cool, thanks.

• Rafael Harth 26 Jan 2021 10:38 UTC

  12 points

  on: Qualia Re­search In­sti­tute: His­tory & 2021 Strategy

  While QRI is only occasionally talked about on LessWrong, I personally continue to think that they’re doing the most exciting research that exists today, provided you take a utilitarian perspective. I’ve donated to Miri in the past, in part because their work seems highly non-replaceable. I still stand by that reason, but it applies even more to QRI. Even if there is only a small chance that formalizing consciousness is both possible and practically feasible, the potential upside seems enormous. Success in formalizing suffering wouldn’t solve AI alignment (for several reasons, one of them being Inner Optimizers), but I imagine it would be extremely helpful. There is nothing approximating a consensus on the related philosophical problems in the community, and positions on those issues seem to have a significant causal influence on what research is being pursued.

  It helps that I share most if not all of the essential philosophical intuitions that motivate QRI’s research. On the other hand, research should be asymmetrical with regard to what’s true. In the world where moral realism is false and suffering isn’t objective or doesn’t have structure, beliefs to the contrary (which many people in the community hold today) could lead to bad alignment-related decisions. In that case, any attempts to quantify suffering would inevitably fail, and that would itself be relevant evidence.

• Rafael Harth 26 Jan 2021 9:24 UTC

  2 points

  in reply to: rohinmshah’s comment on: Pre­face to the Se­quence on Fac­tored Cognition

  Re personal opinion: what is your take on the feasibility of human experiments? It seems like your model is compatible with IDA working out even though no-one can ever demonstrate something like ‘solve the hardest exercise in a textbook’ using participants with limited time who haven’t read the book.

• Rafael Harth 26 Jan 2021 9:19 UTC

  4 points

  in reply to: rohinmshah’s comment on: Pre­face to the Se­quence on Fac­tored Cognition

  This is an accurate summary, minus one detail:

  The judge decides the winner by evaluating whether the final statement is true or not.

  “True or not” makes it sound symmetrical, but the choice is between ‘very confident that it’s true’ and ‘anything else’. Something like ’80% confident’ goes into the second category.

  One thing I would like to be added is just that I come out moderately optimistic about Debate. It’s not too difficult for me to imagine the counter-factual world where I think about FC and find reasons to be pessimistic about Debate, so I take the fact that I didn’t as non-zero evidence.

FC fi­nal: Can Fac­tored Cog­ni­tion schemes scale?

Three types of Evidence

• Rafael Harth 17 Jan 2021 10:24 UTC

  LW: 4 AF: 2

  AF

  in reply to: Charlie Steiner’s comment on: Why I’m ex­cited about Debate

  I think the Go example really gets to the heart of why I think Debate doesn’t cut it.

  Your comment is an argument against using Debate to settle moral questions. However, what if Debate is trained on Physics and/​or math questions, with the eventual goal of asking “what is a provably secure alignment proposal?”

• Rafael Harth 17 Jan 2021 10:20 UTC

  2 points

  on: [Er­ror com­mu­ni­cat­ing with LW2 server]

  Before offering an “X is really about Y” signaling explanation, it’s important to falsify the “X is about X” hypothesis first. Once that’s done, signaling explanations require, at minimum:

  1. An action or decision by the receiver that the sender is trying to motivate.

  2. (2.1) An explanation for why the receiver is listening for signals in the first place, and (2.2) why the sender is trying to communicate them.

  3. A language that the sender has reason to think the receiver will understand and believe as the sender intended.

  4. A physical mechanism for sending and receiving the signal.

  (Added numbers for reference.)

  I think 1, 2.1, and 3 are all wrong, in that none of them are required for a signaling hypothesis to be plausible. I believe you’re assuming that signaling is effective and/​or rational, but this is a mistake. Signaling was optimized to be effective in the ancestral environment, so there’s no reason why it should still be effective today. As far as I can tell, it generally is not.

  As an example, consider men wearing solid shoes in the summer despite finding those uncomfortable. There is no action this is trying to motivate, and there is no reason to expect the receiver is listening—in fact, there is often good reason to expect that they are not listening (in many contexts, people really don’t care about your shoes). Nonetheless, I think conformity signaling is the correct explanation for this behavior.

  The pilot example is problematic because in this case, signaling is part of a high-level plan. This is a non-central example. Most of the time, signaling is motivated by evolutionary instincts, like the fear of standing out. In the case of religion, I think this is most of the story. Those instincts can then translate into high-level behavior like going to the church, but it’s not the beginning of the causal chain.

• Rafael Harth 15 Jan 2021 10:11 UTC

  2 points

  on: Pseu­do­ran­dom­ness con­test: prizes, re­sults, and analysis

  Thanks for hosting this contest. The overconfidence thing in particular is a fascinating data point. When I was done with my function that output final probabilities, I deliberately made it way more agnostic, thinking that at least now my estimates are modest—but it turns out that I should have gone quite a bit farther with that adjustment.

  I’m also intrigued by the variety of approaches for analyzing strings. I solely looked at frequency of monotone groups (i.e., how many single 0′s, how many 00′s, how many 000′s, how many 111′s, etc.), and as a result, I have widely different estimates (compared to the winning submissions) on some of the strings where other methods were successful.

• Rafael Harth 12 Jan 2021 8:23 UTC

  3 points

  on: Open & Wel­come Thread—Jan­uary 2021

  Do the newest numbers indicate that the new Covid strand isn’t that bad after all, for whatever reason? If not, why not?

  Edit: Zvi gave a partial answer here.

• Rafael Harth 11 Jan 2021 18:17 UTC

  10 points

  on: In Defense of Twit­ter’s De­ci­sion to Ban Trump

  I happen to agree with your conclusion, but I don’t think you’re addressing what EY said. He tweeted the following:

  What America needs now, to heal, is for the left and the right to be on entirely different social networks. Still with the ability to subtweet alleged screencaps from the Other network of Others being outrageous, of course! But with no ability for Others to clarify or respond.

  My Translation: I’m worried that banning Trump from twitter will increase polarization because it will make the two tribes more segregated than they were before. This is not that similar to your #7, and otherwise missing from the list entirely.

  I also think #8 is unlikely. It doesn’t strike me as plausible that the Capitol incident provided any rational person with significant evidence on which to update their view of Trump. On the other hand, public opinion appears to have shifted significantly. A financial motive seems likely here, especially for Zukerberg.

• Rafael Harth 6 Jan 2021 23:32 UTC

  2 points

  in reply to: Dentin’s comment on: Grokking illusionism

  Comparing consciousness to plastic surgery seems to me to be a false analogy. If you have your model of particles bouncing around, then plastic surgery is a label you can put on a particular class of sequences of particles doing things. If you didn’t have the name, there wouldn’t be anything to explain, the particles can still do the same thing. Consciousness/​subjective experience describes something that is fundamentally non-material. It may or may not be cause by particles doing things, but it’s not itself made of particles.

  If your response to this is that there is no such thing as subjective experience—which is what I thought your position was, and what I understand strong illusionism to be—then this is exactly what I mean when I say consciousness isn’t real. By ‘consciousness’, I’m exclusively referring to the qualitatively different thing called subjective experience. This thing either exists or doesn’t exist. I’m not talking about the process that makes people move their fingers to type things about consciousness.

  I apologize for not tabooing ‘real’, but I don’t have a model of how ‘is consciousness real’ can be anything but a well-defined question whose answer is either ‘yes’ or ‘no’. The ‘as real as X’ framing doesn’t make any sense to me. it seems like trying to apply a spectrum to a binary question.

• Rafael Harth 6 Jan 2021 17:23 UTC

  5 points

  in reply to: Dentin’s comment on: Grokking illusionism

  Apologies, I communicated poorly. ImE, discussions about consciousness are particularly prone to misunderstandings. Let me rephrase my comment.

  1. Many (most?) people believe that consciousness is an emergent phenomenon but also a real thing.

  2. My assumption from reading your first comment was that you believe #1 is close to impossible. I agree with that.

  3. I took your first comment (in particular this paragraph)...

  Because ultimately, down at the floor, it’s all just particles and forces and extremely well understood probabilities. There’s no fundamental primitive for ‘consciousness’ or ‘experience’, any more than there’s a fundamental primitive for ‘green’ or ‘traffic’ or ‘hatred’. Those particles and forces down at the floor are the territory; everything else is a label.

  … as saying that #2 implies illusionism must be true. I’m saying this is not the case because you can instead stipulate that consciousness is a primitive. If every particle is conscious, you don’t have the problem of getting real consciousness out of nothing. (You do have the problem of why your experience appears unified, but that seems much less impossible.)

  Or to say the same thing differently, my impression/​worry is that people accept that ‘consciousness isn’t real’ primarily because they think the only alternative is ‘consciousness is real and emerges from unconscious matter’, when in fact you can have a coherent world view that disputes both claims.

• Rafael Harth 6 Jan 2021 15:48 UTC

  2 points

  in reply to: Rudi C’s comment on: Grokking illusionism

  That’s fair. However, if you share the intuition that consciousness being emergent is extremely implausible, then going from there directly to illusionsism means only comparing it to the (for you) weakest alternative. And that seems like the relevant step for people in this thread other than you.

• Rafael Harth 6 Jan 2021 15:14 UTC

  3 points

  in reply to: Dentin’s comment on: Grokking illusionism

  There’s no fundamental primitive for ‘consciousness’

  I’m not sure if this is the case, but I’m worried that people subscribe to illusionism because they only compare it to the weakest possible alternative, which (I would say) is consciousness being an emergent phenomenon. If you just assume that there’s no primitive for consciousness, I would agree that the argument for illusionism is extremely strong since [unconscious matter spontaneously spawning consciousness] is extremely implausible.

  However, you can also just dispute the claim and assume consciousness is a primitive, which gets around the hard problem. That leaves the question ‘why is consciousness a primitive’, which doesn’t seem particularly more mysterious than ‘why is matter a primitive’.