Comment by komponisto2 on [deleted post] 2010-09-20T01:16:28.014Z

While obviously the legacy of history always remains a social force to some extent, it's open to question exactly how potent that force is. Clearly it's less potent than it used to be -- but acknowledging this is frowned upon in some circles because it sounds like a concession to the enemy.

(By the way, as this comment demonstrates, it is possible to access accounts automatically created from the importation of Overcoming Bias posts into Less Wrong. One simply uses the password reset function, checks the appropriate e-mail address, and follows the instructions in the message that is automatically sent there. A duplicate account such as "komponisto2" apparently results from a different email address being used to create the LW account "komponisto" from that associated with the OB comments from "komponisto". Had the same e-mail address been used, old comments such as the grandparent would have been added to the new LW account when the importation took place. Let this be noted by anyone who commented on OB and has not yet created an account on LW.)

Comment by komponisto2 on 31 Laws of Fun · 2009-01-26T20:27:58.000Z · score: 9 (8 votes) · LW · GW

consider Christian Heaven: singing hymns doesn't sound like loads of endless fun

Unless, perhaps, you happen to enjoy music...

(Seriously -- suppose you got to compose your own hymns.)

A general comment: I am tempted to question the wisdom of tying Fun Theory so closely to the aesthetics of storytelling, by discussing the two in such proximity. As we all know, there's not necessarily any correlation between the worlds we would want to live in and the worlds we like to read about. I'm not just talking about Dystopian stories either. I love watching House, but sure as hell would never want to actually be any of the characters on that show. Shakespeare's Romeo and Juliet is a delight to read despite being (paradoxically) a depressing tragedy. Etc.

Now there is a connection, to be sure, in that aesthetics itself (in the context of any art form, including but not limited to storytelling) is effectively a miniature, special case of Fun Theory. But this connection is more abstract, and has little to do with how closely settings and plots match up with eudaimonic scenarios. (Inhabitants of Eutopia themselves may enjoy tragic stories and the like.)

Comment by komponisto2 on Prolegomena to a Theory of Fun · 2008-12-18T21:40:45.000Z · score: 1 (1 votes) · LW · GW

TGGP, I'm not going to argue the point that there has been moral progress. It isn't the topic of this post.

Phil Goetz:

Everybody says that not taking the land from the Native Americans would have been the right thing to do; but nobody wants to give it back.

The whole point of my original comment was to refute this very inference. Arguing that taking land from the Native Americans was wrong is not the same as arguing that it should be "given back" now (whatever that would mean). Nor is it the same as wishing we lived in a world where it never happened.

What it means is wishing we lived in a world where the Europeans had our moral values -- and thus also in all probability our science and technology -- centuries ago. Before committing misdeeds against Native Americans.

Also, an argument that the actual colonization of America was "wrong" is not the same as an argument that America should never have been turned into a civilization. Surely there are ways to accomplish this without imposing so much disutility on the existing inhabitants*. Likewise for creating nice worlds with ems and AIs.

*There lies the implicit moral principle, in case you didn't notice.

Comment by komponisto2 on Prolegomena to a Theory of Fun · 2008-12-18T12:35:11.000Z · score: 0 (2 votes) · LW · GW

Michael, I take the point about outliers -- but claims like the one I made are inherently statistical in nature.

Furthermore, it is worth noting that (1) pre-WWI Germany would indeed have to be considered one of the more morally enlightened societies of the time; and (2) the Nazi regime ultimately proved no help to the cause of German scientific and cultural advancement -- and that's putting it way too mildly.

So perhaps this episode, rather than undermining the proposed correlation, merely illustrates the point that even advanced civilizations remain vulnerable to the occasional total disaster.

Comment by komponisto2 on Prolegomena to a Theory of Fun · 2008-12-18T07:25:49.000Z · score: 2 (2 votes) · LW · GW

TGGP, I'm afraid you've committed the moral analogue of replying to some truth claim with a statement of the form: "As a non-X-ist, I don't find the notion of truth to be meaningful".

By "moral progress" I simply mean the sense in which Western civilization is nicer today than it used to be. E.g. we don't keep slaves, burn live cats, etc. (If you have any doubts about whether such progress has occurred, you underestimate the nastiness of previous eras.) In particular, please note that I am not invoking any sort of fancy ontology, so let's not get derailed that way.

As for why we should expect moral progress to correlate with other kinds: well, maybe for arbitrary minds we shouldn't. But we humans keep trying to become both smarter and nicer, so it shouldn't be surprising that we succeed in both dimensions more and more over time.

Comment by komponisto2 on Prolegomena to a Theory of Fun · 2008-12-18T04:14:32.000Z · score: 2 (5 votes) · LW · GW

Slightly tangential, but I think this needs addressing:

What is the moral argument for not colonizing America?

Literally interpreted, that's a meaningless question. We can't change history by moral argument. What we can do is point to past deeds and say, "let's not do things like that anymore".

If European civilization circa 1500 had been morally advanced enough to say, "let's not trample upon the rights of other peoples", chances are they would already have been significantly more advanced in other ways too. Moral progress takes work, just like technological and intellectual progress. Indeed we should expect some correlation among these modes of progress, should we not? And isn't that largely what we find?

By critiquing the errors of the past, we may hope to speed up our own progress on all fronts. This is (or should be) the point of labeling the colonization of America (in the way it happened) as "wrong".

Comment by komponisto2 on You Only Live Twice · 2008-12-12T21:04:05.000Z · score: 10 (10 votes) · LW · GW

Eliezer, although you and Robin agree on the general principle, Robin has signed up with Alcor, while you have signed up with CI. (Despite the fact that you say you could afford Alcor also.) How much of a disagreement is this, and what does it reflect?

More generally, how should one rationally approach this decision?

Comment by komponisto2 on Thanksgiving Prayer · 2008-11-29T20:25:39.000Z · score: 0 (0 votes) · LW · GW


Komponisto: that definition includes human beings

No it doesn't. I said controlling the weather, not affecting it or influencing it.

Comment by komponisto2 on Thanksgiving Prayer · 2008-11-29T11:16:11.000Z · score: 1 (1 votes) · LW · GW

Unknown, how about this:

God: a conscious entity capable of controlling the weather.

(At least, I propose these as necessary attributes of a deity.)

Under this definition, I'm pretty sure Eliezer is an atheist. On the other hand, do you dare assert that a typical theist doesn't believe their god could make it rain tomorrow?

Comment by komponisto2 on Lawful Creativity · 2008-11-10T08:11:34.000Z · score: 3 (3 votes) · LW · GW

To all defending Modern Art: Please point to at least one item available online which exemplifies that which you think I'm ignoring or missing.

Funny -- I didn't actually read the post as an attack on Modern Art. The point seemed to be that, appearances to the contrary, Modern Artists are in fact trying to hit a narrow target, albeit not the one you might at first think. It is presumably this attempted optimization that makes Modern Art (to the extent such a thing does in fact exist) a worthwhile or interesting activity to those who practice it.

Comment by komponisto2 on My Bayesian Enlightenment · 2008-10-06T07:24:13.000Z · score: 3 (3 votes) · LW · GW

Larry D'Anna on Jaynes:

I found the first two chapters of PT:TLOS to be absolutely, wretchedly awful. It's full of technical mistakes, crazy mischaracterizations of other people's opinions, hidden assumptions and skipped steps (that he tries to justify with handwaving nonsense), and even a discussion of Godel's theorems that mixes meta levels and completly misses the point.

Not to mention the totally unnecessary and irrelevant screeds against mainstream pure mathematics in general, which can only serve to alienate potential converts in that discipline (they sure alienated the hell out of me).

Comment by komponisto2 on My Bayesian Enlightenment · 2008-10-05T20:08:25.000Z · score: 3 (3 votes) · LW · GW

Also do we really want to assign a prior probability of 0 that the mathematician is a liar! :)

That's not the point I was making.

I'm not attacking unrealistic idealization. I'm willing to stipulate that the mathematician tells the truth. What I'm questioning is the "naturalness" of Eliezer's interpretation. The interpretation that I find "common-sensical" would be the following:

Let A = both boys, B = at least one boy. The prior P(B) is 3/4, while P(A) = 1/4. The mathematician's statement instructs us to find P(A|B), which by Bayes is equal to 1/3.

Under Eliezer's interpretation, however, the question is to find P(A|C), where C = the mathematician says at least one boy (as opposed to saying at least one girl).

So if anyone is attacking the premises of the question, it is Eliezer, by introducing the quantity P(C) (which strikes me as contrived) and assigning it a value less than 1.

Comment by komponisto2 on My Bayesian Enlightenment · 2008-10-05T18:18:02.000Z · score: 0 (0 votes) · LW · GW

No, wait -- my question stands!

Do we really want to assign a prior of 0 to the mathematician saying "I have two children, one boy and one girl"?

Comment by komponisto2 on My Bayesian Enlightenment · 2008-10-05T18:11:23.000Z · score: 0 (0 votes) · LW · GW

Never mind -- missed the "If" clause. (Sorry!)

Comment by komponisto2 on My Bayesian Enlightenment · 2008-10-05T18:07:02.000Z · score: 0 (0 votes) · LW · GW

If the mathematician has one boy and one girl, then my prior probability for her saying 'at least one of them is a boy' is 1/2 and my prior probability for her saying 'at least one of them is a girl' is 1/2

Why isn't it 3/4 for both? Why are these scenarios mutually exclusive?

Comment by komponisto2 on The Level Above Mine · 2008-09-27T19:33:00.000Z · score: 1 (1 votes) · LW · GW

Lara, I don't think they value it "for its own sake" as opposed to as a means to an end; rather, they see it as a necessary condition for achieving their ends, and are worried they don't have what it takes. Nothing but an anxiety trip.

And of course, there's also the ego thing -- when people build superiority over others into their self-image. This is counterproductive, of course. When someone else demonstrates that they're "smarter" than you by offering unexpected insight, you don't fatalistically wallow in jealous misery; you listen to the content of what they say, in the hope of becoming as smart as they are.

Eliezer of all people ought to realize this (actually I suspect he does).

FWIW, I've met both Eliezer and John Conway, and have spent approximately the same total amount of time with both of them (on the order of 10 hours). I don't know which of them is smarter. Yet I suspect neither is too far above my own level for me to be able to e.g. benefit from listening to a conversation between them.

Comment by komponisto2 on How Many LHC Failures Is Too Many? · 2008-09-21T00:29:13.000Z · score: 1 (3 votes) · LW · GW

At the risk of asking the obvious:

Does the fact that no one has yet succeeded in constructing transhuman AI imply that doing so would necessarily wipe out humanity?

Comment by komponisto2 on Rationality Quotes 13 · 2008-09-04T00:05:36.000Z · score: 0 (1 votes) · LW · GW

Robin, the underlying point of the soldier quote (and others like it) is that the liberal society we enjoy comes at a (military) cost. Freedom, as the saying goes, isn't free. If we really want freedom of speech and the like, we had better be prepared to enforce it (ironic though that may seem).

Comment by komponisto2 on Mirrors and Paintings · 2008-08-24T01:07:18.000Z · score: 3 (3 votes) · LW · GW

Eliezer, while I think that Caledonian (and perhaps also Richard Hollerith) has apparently missed the whole point of a number of your posts (in particular the recent ones on Löb's theorem, etc), I'm not sure why you are so concerned about people being "fooled". These are comments, which happen to be clearly labeled as not being authored by you. Would anyone really assume that a particular commenter, be it Caledonian or anyone else, has necessarily summarized your views accurately?

Furthermore, for every one such "misrepresentative" comment, there are undoubtedly several lurkers suffering from an honest misunderstanding similar to the one being articulated (whether in good faith or not) by the commenter. It may be worthwhile to simply correct these misunderstandings as often as possible, even at the risk of repetition. These are, after all, subtle points, and it may take time (and reinforcement) for people to understand them.

Comment by komponisto2 on Dumb Deplaning · 2008-08-19T03:36:44.000Z · score: 1 (1 votes) · LW · GW

The flipside of this is the inanity of Southwest Airlines employees with respect to boarding the plane:

As is well known, Southwest doesn't have assigned seats, so the choice of seating is determined by boarding order, with earlier people getting more choices. People want to avoid middle seats, so the natural tendency of later boarders on crowded flights is to keep walking as far as necessary toward the back of the cabin in the hope of finding and empty aisle or window seat. For some inexplicable reason, however, Southwest flight attendants and gate managers actively discourage this, wanting people instead to take the first middle seat they find. The all-too-predictable result is a traffic jam in the aisle and the jetway, as the line continually stops to wait for the leading person to stow their luggage and take their seat.

It should be obvious that, regardless of how crowded the flight is, boarding efficiency is maximized by having each passenger go as far to the back of the cabin as possible, to allow the line to keep moving forward. Is this goal somehow less important than that of teaching people not to vainly expect aisle or window seats?

Comment by komponisto2 on The Bedrock of Morality: Arbitrary? · 2008-08-15T02:24:12.000Z · score: 0 (0 votes) · LW · GW

Clarification: in the first paragraph of the above comment, when I wrote "The whole point of 'morality' is..." what I meant was "The whole point of non-relativist 'morality' is...".

Comment by komponisto2 on The Bedrock of Morality: Arbitrary? · 2008-08-15T02:13:13.000Z · score: 7 (7 votes) · LW · GW

I'm really having trouble understanding how this isn't tantamount to moral relativism -- or indeed moral nihilism. The whole point of "morality" is that it's supposed to provide a way of arbitrating between beings, or groups, with different interests -- such as ourselves and Pebblesorters. Once you give up on that idea, you're reduced, as in this post, to the tribalist position of arguing that we humans should pursue our own interests, and the Pebblesorters be damned. When a conflict arises (as it inevitably will), the winner will then be whoever has the bigger guns, or builds AI first.

Mind you, I don't disagree that this is the situation in which we in fact find ourselves. But we should be honest about the implications. The concept of "morality" is entirely population-specific: when groups of individuals with common interests come into contact, "morality" is the label they give to their common interests. So for us humans, "morality" is art, music, science, compassion, etc. in short, all the things that we humans (as opposed to Pebblesorters) like. This is what I understand Eliezer to be arguing. But if this is your position, you may as well come out and admit that you're a moral relativist, because this is the position that the people who are scared of moral relativism are in fact scared of. What they dread is a world in which Dennis could go on saying that Dennis-morality is what really matters, the rest of us disagree, war breaks out, Dennis kills us all, eats the whole pie, and is not spanked by any cosmic force. But this is indeed the world we live in.

Comment by komponisto2 on Hiroshima Day · 2008-08-07T05:35:27.000Z · score: 0 (2 votes) · LW · GW

The Second World War, as a whole, was probably the most catastrophic event in humanity's recorded history. The world was pretty much screwed as soon as it started -- indeed, probably as soon as Hitler acquired control of Germany.

For the purpose of saving humanity in the future, it may not be most effective to focus our attention on particular decisions (even apparently large ones) made during the course of the war (indeed, near the end of it); we risk missing the forest for the trees.

Comment by komponisto2 on No Logical Positivist I · 2008-08-04T06:58:28.000Z · score: 12 (12 votes) · LW · GW

Eliezer, you're definitely setting up a straw man here. Of course it's not just you -- pretty much everybody suffers from this particular misunderstanding of logical positivism.

"Untestable" does not mean "untestable by humans using current technology". What it means is untestable, period -- even by (say) a hypothetical being with godlike powers. This is what distinguishes a chocolate cake in the sun from "post-colonial alienation". If a chocolate cake spontaneously formed in the Sun, there would be physical consequences. These consequences would necessarily be detectable to sufficiently advanced beings. We need only imagine a Laplacian calculator, for example.

The feasibility of performing the verification is utterly beside the point, because we're only interested in the meaning of the statement.

Contrast this with "post-colonial alienation". The problem there is not that we lack some technological gadget. Rather, the problem is that no being, not even a god or a Laplacian demon, could verify the statement. In the case of a chocolate cake, you simply present God with a list of ingredients, and tell him/her to look for them in the Sun; but what do you tell God to look for in the works of Shakespeare in order to determine whether there is "post-colonial alienation"?

So this is not a counterexample to logical positivism at all. In fact, you yourself already gave the positivist's reply to this criticism in "Belief in the Implied Invsible". The point is, you're allowed in logical positivism to use the full apparatus of mathematics and logic (and that includes probability theory!) in formulating theories (hence the name logical positivism); verificationism is not a constraint on mathematics.

Comment by komponisto2 on The Comedy of Behaviorism · 2008-08-03T21:00:11.000Z · score: 1 (1 votes) · LW · GW

(Correction: "Tom Tyler" above is a typo for "Tim Tyler")

Comment by komponisto2 on The Comedy of Behaviorism · 2008-08-03T20:56:59.000Z · score: 0 (0 votes) · LW · GW

Tom Tyler: The point [Watson] was making was that that stuff isn't real, it's all actually down to physiology

Eliezer: Tim, that wouldn't argue against Freud.

It's hard to see how any philosophy of mind (whether physicalist, dualist, or idealist) could directly argue against Freud, whose important claims were about psychology itself, not what psychology reduces to.

Comment by komponisto2 on The Comedy of Behaviorism · 2008-08-03T06:39:32.000Z · score: 2 (2 votes) · LW · GW

Eliezer, it's particularly important to make a distinction, as the SEP and Wikipedia articles do to an extent, between "behaviorism" as a methodological stance in the field of psychology (of which Skinner was an advocate), and "(logical) behaviorism" as a position in the philosophy of mind associated with the logical positivists such as Carnap.

Carnap's thesis, as expressed in his 1932/33 article "Psychology in Physical Language", was simply that psychology could (ultimately) be reduced to physics -- a proposition I presume you accept, but which used to be controversial, and still is in some quarters. Because neuroscience was not as advanced in the 1930s as it is now, the examples that Carnap gave of "translations" (e.g. "Mr. A is excited" translates into various propositions about his physical behavior, such as jumping up and down yelling, high blood pressure, etc.) have mislead some later readers (such as Hilary Putnam) into thinking that Carnap was saying mental states just consist of observed macroscopic behavior. In truth, however, there is nothing in Carnap's article to suggest that the "behavior" of which mental states are alleged to consist excludes the microscopic behavior of neurons.

Comment by komponisto2 on Detached Lever Fallacy · 2008-08-01T06:55:07.000Z · score: 1 (1 votes) · LW · GW

Growing human brains are wired to learn syntactic language - even when syntax doesn't exist in the original language, the conditional response to the words in the environment is a syntactic language with those words.

This, under the name "universal grammar", is the insight that Noam Chomsky is famous for.

At the risk of revealing my identity, I recall getting into an argument about this with Michael Vassar at the NYC meetup back in March (I think it was). If memory serves, we were talking at cross-purposes: I was trying to make the case that the discipline of theoretical ("Chomskian") linguistics, whose aim is to describe the cognitive input-response system that goes by the name of the "human language faculty", teaches us not to regard individual languages such as English or French as Platonic entities, but rather merely as ad-hoc labels for certain classes of utterances. Vassar, it seemed (and he's of course welcome to correct me if I'm misremembering), took me to be arguing for the Platonicity of some more abstract notion of "human language".

Comment by komponisto2 on Fake Norms, or "Truth" vs. Truth · 2008-07-23T06:45:59.000Z · score: 2 (2 votes) · LW · GW

A felony conviction within 10 years is usually admissible on the question of credibility if the perpetrator takes the stand.

Does this apply only when the perpetrator lied about the felony conviction (which would be directly relevant to credibility), or just in general (on the theory that people with felony convictions are Bad and thus likely to be dishonest)?

Comment by komponisto2 on The Gift We Give To Tomorrow · 2008-07-18T06:02:00.000Z · score: 1 (3 votes) · LW · GW

The book How Music Really Works has some decent ideas about the evolution of music.

On the contrary. That is exactly the sort of rubbish that gives evolutionary psychology such a bad name.

The idea that something like music -- an extremely high-level byproduct of human cognition -- could be explained directly as an evolutionary adaptation is absurd enough. (Imagine trying to give a Darwinian account of why chess pieces move in the way they do.) The invocation of sexual selection -- the process that explains the peacock's fancy tail -- borders on the ludicrous. Sexual selection is only a candidate explanation in cases of marked sexual dimorphism -- a significant phenotypic difference between males and females, as in the peacock. The fact (if true) that professional musicians statistically tend to be males doesn't come anywhere close to cutting it.

Comment by komponisto2 on The Gift We Give To Tomorrow · 2008-07-18T02:36:47.000Z · score: 1 (1 votes) · LW · GW

Douglas Knight:

I've heard that isn't true in tonal languages

Where did you hear that?

It's false. "Tone" as a lexical property of words (as in "tonal languages") is a specific technical concept that is not to be confused with "intonation", which is an essentially universal phenomenon of human speech.

Comment by komponisto2 on 2 of 10, not 3 total · 2008-07-04T05:52:32.000Z · score: 0 (0 votes) · LW · GW

I second Davis: current commenting system fine except for pagination limit and link problems (using both Firefox and IE in my case).

Comment by komponisto2 on [deleted post] 2008-06-28T17:52:41.000Z

In an ideal world, this would be a reasonable comment. In the real world, with the history of male oppression of women that comes with it, there is an asymmetry that means these things are not equivalent.

Shouldn't we be trying to move our "real world" in the direction of an "ideal world"?

I sometimes get the impression that contemporary sex/race-oppression consciousness is analogous to the Jewish Yom Kippur ritual as Eliezer described it, in which the point is confessing sins, not trying to avoid them and keeping track of how well one has done. Just as it would be a violation for a participant in the ceremony to say e.g. "Actually, I'm happy to report that I didn't steal anything this year, so I'm going to leave that part out, thank you", so too is it something of a faux pas for a member of contemporary Western polite society to fail to treat the historical oppression of women and minorities as if it were a currently potent social force in his/her own culture.

Comment by komponisto2 on The Design Space of Minds-In-General · 2008-06-25T18:54:07.000Z · score: 3 (3 votes) · LW · GW

Caledonian, Sapir-Whorf becomes trivial to abolish once you regard language in the correct way: as an evolved tool for inducing thoughts in others' minds, rather than a sort of Platonic structure in terms of which thought is necessarily organized.

Phil, I don't see how the argument is obviously incorrect. Why can't two works of literature from different cultures be as different from each other as Hamlet is from a restaurant menu?

Comment by komponisto2 on Against Devil's Advocacy · 2008-06-09T18:27:16.000Z · score: 0 (0 votes) · LW · GW

Don't you mean Michael Ruse?

Comment by komponisto2 on Why Quantum? · 2008-06-04T20:24:03.000Z · score: 2 (2 votes) · LW · GW

Why does the area under a curve equal the antiderivative?

The rate of area-accumulation is given by the height of the curve, i.e. the value of the function. You can see this easily with constant functions: a horizontal line 2 units above the horizontal axis accumulates area underneath at a rate of 2 square units per unit of length.

At least that's how I like to think about it.

Comment by komponisto2 on Why Quantum? · 2008-06-04T20:02:55.000Z · score: 1 (1 votes) · LW · GW

As one who understood linear operators (as mathematics) for years without having a clue what they might have to do with atoms and quarks (and never seeing this spelled out in writing anywhere), I can relate to Eliezer's sentiments.

Out of curiosity, Eliezer, what should the calculus textbooks have said?

Comment by komponisto2 on The Rhythm of Disagreement · 2008-06-02T00:11:17.000Z · score: 1 (1 votes) · LW · GW

Whoa, said I to myself, Steven Pinker is a mysterian?

Well, he had already said as much in How the Mind Works. And also in this conversation with Robert Wright.

Comment by komponisto2 on Mach's Principle: Anti-Epiphenomenal Physics · 2008-05-24T08:44:41.000Z · score: 7 (7 votes) · LW · GW

Sure, what I just said is logically impossible


Here's an analogy: Suppose you thought you lived on the unit interval [0,1] in the real line. Then experiments showed that whenever you got to 1, you were magically whisked away back to 0. So a clever mathematical physicist, well versed in topology, comes along and says, "Hey! Why don't we just identify 0 and 1 as the same point? That way, we can say that we're living on a circle, instead of a line segment".

Suddenly, a whole new research program emerges. If we're living on a circle, what's its radius? Is it even a circle at all, or mightn't it be an ellipse? Or something even more exotic? Is there an "extra dimension", i.e. an underlying 2-dimensional plane in which the circle (or whatever) is embedded? And so forth.

(Technically, you could have asked some of these questions under the old paradigm. E.g.: is our line segment really a line, or is it curved? But you wouldn't necessarily have thought to do so! )

Comment by komponisto2 on Feynman Paths · 2008-04-17T18:01:13.000Z · score: 1 (1 votes) · LW · GW

Since Scott Aaronson has chimed in, it is worth pointing to this discussion on his blog in which Greg Kuperberg explains the Hilbert space issues from the previous thread.

Comment by komponisto2 on The Quantum Arena · 2008-04-17T06:54:39.000Z · score: 1 (1 votes) · LW · GW

a function of a real space has uncountable degrees of freedom

Right -- that's exactly the misunderstanding I was addressing in my earlier comment.

An arbitrary function does indeed have uncountable degrees of freedom, but in that context you're notconsidering it as an element of a Hilbert space. (Those degrees of freedom do not correspond to basis vectors.)

Comment by komponisto2 on The Quantum Arena · 2008-04-17T06:33:46.000Z · score: 0 (0 votes) · LW · GW

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

mitchell porter: But the Hilbert space of a quantum field, naively, ought to have uncountable dimension, because there are continuum-many degrees of freedom.

Given any cardinal number, there exists a Hilbert space with that orthogonal dimension. Note, however, that even if the dimension is uncountable, individual elements are still given by linear combinations with countably many terms. In other words, only countably many dimensions are used "at one time" in specifying an element.

Thus, a Hilbert space formalism cannot accommodate "uncountably many degrees of freedom" in the sense people mean here. Which is okay, because I don't think that's what you need anyway.

Comment by komponisto2 on The Quantum Arena · 2008-04-16T21:41:07.000Z · score: 0 (0 votes) · LW · GW


I'd say that I was assuming the continuum hypothesis, except that I'm an infinite set atheist.

Not that again! Let's not mix up the map and the territory. You may not think there are any infinite sets out there in the territory, but mathematics is about the map -- or, rather, mapmaking in general. So it's a category error to jump from the conviction that the "real world" contains only finitely many things to Kroneckerian skepticism about mathematical objects.

For what it's worth, the cardinality of the set of reals is 2^aleph_0. The continuum hypothesis is precisely the statement that this is equal to aleph_1. So yeah, you're definitely assuming it.

Comment by komponisto2 on The Quantum Arena · 2008-04-16T21:31:48.000Z · score: 0 (0 votes) · LW · GW

I'd thought the Hilbert space was uncountably dimensional because the number of functions of a real line is uncountable

Well, the number of points in a Hilbert space of dimension 2 is uncountable, and yet the space has dimension 2!

I suspect the source of the confusion here is that you're trying to think of the values of a function as its "coordinates". But this is wrong: the "coordinates" are the coefficients of a Fourier series expansion of the function.

The confusion is understandable, given that the two concepts coincide in the finite-dimensional case. You should think of a point in C^2, say (3,7), as a function from the two-element set {1,2} into the complex numbers C (in this case we have f(0) = 3 and f(1)=7). You can then write every such function uniquely as the sum of two "basis" functions: one that sends 1 to 1 and 2 to 0 (call this b_1), and one that sends 1 to 0 and 2 to 1 (call this b_2). Thus f = 3b_1 + 7b_2, i.e. (3,7) = 3(1,0) + 7(0,1).

In the case of functions on the real line, however, the "basis" functions cannot be functions that send one number to 1 and the rest to 0, because in order to represent an arbitrary function, you would need to add uncountably many such things together, which is not a defined operation (or, more technically, is only defined when all but countably many of the summands are zero).

Fortunately, however, if we're talking about the space of square-integrable functions (and that was what we wanted anyway, wasn't it?), we do have a countable orthogonal basis available, as was discovered by Fourier.

(Technical note: Actually, the space of square-integrable functions on (an interval of) the real line doesn't consist of well-defined functions per se, but only of equivalence classes of functions that agree everywhere except on a set of measure zero. See measure theory, Lebesgue integration, L^p space, etc.)

Comment by komponisto2 on The Quantum Arena · 2008-04-16T15:15:46.000Z · score: 0 (0 votes) · LW · GW

I have the same questions for Eliezer as Jadagul and Toby Ord, namely:

  • Why would the space of amplitude distributions have uncountable dimension? Unless I've misunderstood, it sounds like it would be something like L^2, which is separable (has countable orthogonal dimension). (Of course, maybe by "dimension" you just meant the cardinality of a Hamel basis, in which case you're right -- there's no Hilbert space with Hamel dimension aleph_0. However, "dimension" in the context of Hilbert spaces nearly always refers to orthogonal dimension.)

  • Assuming you really did mean uncountable, how do you know aleph_1 is the right cardinality, rather than, say, 2^aleph_0? Are you assuming the continuum hypothesis?

Comment by komponisto2 on Where Philosophy Meets Science · 2008-04-13T04:09:10.000Z · score: 0 (0 votes) · LW · GW

suggest that, like ethics,

Link to SIAI blog here broken (404 Not Found).

Comment by komponisto2 on The Generalized Anti-Zombie Principle · 2008-04-06T21:46:38.000Z · score: 1 (1 votes) · LW · GW

Michael Vassar:

The classical disproof of positivism is that it is self-contradictory. "Only the empirical can be true", but that statement is not empirical.

I have always been mystified at how this glib dismissal has been taken as some kind of definitive refutation. To the contrary, it should be perfectly obvious that a meta-statement like () a statement is nonsense unless it describes an empirically observable phenomenon is not meant to be self-referential. What () does is to lay down a rule of discourse (not meta-discourse). Its purpose is to banish invisible dragons from the discussion.

You cannot appeal to the "legitimacy" of sentences like (*) in order to argue on behalf of your favorite invisible dragon. But this is exactly what is going on in exchanges like the following: A: "The concept of consciousness is meaningless because it has no empirical consequences." B" "Silly amateur! Don't you know that logical positivism has been refuted?"

Comment by komponisto2 on Hand vs. Fingers · 2008-03-31T01:19:00.000Z · score: 1 (1 votes) · LW · GW

We can play "maybe"s all day long, but it doesn't seem very helpful unless you can actually show that a mistake has been made.

Richard, the burden of proof is on you. You are in effect making the claim that a certain problem ("reduce consciousness to physics") is impossible to solve. But why should we believe that? When all is said and done, you appear to be saying, "because it seems that way". This is where Eliezer comes in.

Comment by komponisto2 on Initiation Ceremony · 2008-03-29T18:31:46.000Z · score: 0 (0 votes) · LW · GW

In a traditional school environment, grades are the de facto student motivator

Motivator of what? The point is that whatever behavior it is that grades in school serve to motivate, it is not learning per se. Indeed, grades are more often than not a motivator against learning. To quote Eliezer (emphasis added):

"[S]tudents aren't allowed to be confused; if they started saying, 'Wait, do I really understand this? Maybe I'd better spend a few days looking up related papers, or consult another textbook,' they'd fail all the courses they took that quarter." (Two More Things to Unlearn from School.)

This is where the autodidact has a distinct advantage, because he/she doesn't have to "worry" about "failing courses", and thus doesn't have to actively resist this kind of pressure against learning. By contrast, if a traditional school student is interested in learning, he/she has to be willing to neglect "assigned tasks" and incur the expected social consequences. It is in this sense that I claim it is (or at least can be) easier to stay motivated outside the school system than inside.

Comment by komponisto2 on Initiation Ceremony · 2008-03-29T16:28:12.000Z · score: 7 (7 votes) · LW · GW

Any commited autodidacts want to share how their autodidactism makes them feel compared to traditional schooled learners? I'm beginning to suspect that maybe it takes a certain element of belief in the superiority of one's methods to make autodidactism work

First, "traditional school learning" is itself inherently problematic. Consequently, "belief in the superiority of one's [own] methods" is not hard to acquire.

Second, all actual learning is necessarily autodidactic anyway, because where it takes place is in your own mind, not in your interactions with others.

So yes, in order to learn, you have to be "arrogant" enough to believe that you actually can. That is, you have to have the confidence that you personally can fully appreciate the insights of "authority figures" like Issac Newton. Unfortunately, social pressures seem to discourage such "presumption" in favor of deference to authority.