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Comment author: Grothor 02 February 2017 07:57:58PM 1 point [-]

When this sum hit the mainstream interwebz a while back, we had some discussion about it in the physics department where I work. The consensus was that it was misrepresented as a spooky non-intuitive fact about adding numbers, when really it's closer to a particular notation for assigning a finite value to a diverging sum that happens to be useful in physics*. Some of us were annoyed, because it feels like it's reinforcing this idea that math is impossibly opaque, a notion that we have to deal with on a regular basis when trying to teach physics to undergraduates.

Also, FWIW, I don't recall seeing this presented in my QFT class, but then again, I only took one semester.

*I think you're actually characterizing a it a little differently and a little more precisely, as a way of actually evaluating the sum, while subtracting off a term of order infinity, in a way that allows for certain kinds of manipulations that happen to be useful in physics.

Comment author: shev 02 February 2017 08:51:33PM *  0 points [-]

Yeah, that's the exact same conclusion I'm pushing here. That and "you should feel equipped to come to this conclusion even if you're not an expert." I know.. several people, and have seen more online (including in this comment section) who seem okay with "yeah, it's negative one twelfth, isn't that crazy?" and I think that's really not ok.

My friend who's in a physics grad program promised me that it does eventually show up in QFT, and apparently also in nonlinear dynamics. Good enough for me, for now.

Comment author: phl43 02 February 2017 04:18:56AM 0 points [-]

I now understand that people on LW don't like to talk about politics here, and like I said I don't really care about this particular incident, nor do I want to argue that you should change the customs around here. But I want to point out that, as far as the claim I was attacking in my post was concerned, I don't think I was assuming anything controversial to show that it was not supported by the evidence.

I'm guessing that's not really what you meant when you said that "[I] wrote in a style that assumed a lot of opinions are held by [my] readers, without justification", but just in case it was, I wanted to make that clear. It matters to me because, although I have a natural tendency to write in a polemical style on political issues, I usually try to give rational and evidence-based arguments in favor of my views, and I think it was also true of the post we are talking about.

Comment author: shev 02 February 2017 04:58:15AM *  9 points [-]

The assumed opinions I'm talking about are not the substance of your argument; they're things like "I think that most of these reactions are not only stupid, but they also show that American liberals inhabit a parallel universe", and what is implied in the use of phrases like 'completely hysterical', 'ridiculous', 'nonsensical', 'proposterous', 'deranged', 'which any moron could have done', 'basically a religion', 'disconnected from reality', 'save the pillar of their faith', etc. You're clearly not interested in discussion of your condemnation of liberals, and certainly not rational discussion. You take it as an obvious fact that they are all stupid, deranged morons.

So when you write "I’m also under no delusion that my post is going to have any effect on most of those who weren’t already convinced", I think you are confused. People who don't already agree with you won't be convinced because you obviously disdain them and are writing with obviously massive bias against them. Not because their opinions are "basically a religion, which no amount of evidence can possibly undermine."

I think your post would be much stronger if you just removed all your liberal-bashing entirely, quoted an example of someone saying hate crimes had gone up since trump's election, and then did the research. I'm totally opposed to polemics because I think they have no good results. Especially the kind that is entirely pandering to one side and giving the finger to the other. (I also think you're wildly incorrect about your understanding of liberals, as revealed by some of your weird stereotypes, but this is not the place to try to convince you otherwise.) But I guess if that's the way people write in a certain community and you're writing for that community, you may as well join in. I prefer to categorically avoid communities that communicate like that - I've never found anything like rational discussion in one.

I also think such obvious bias makes your writing weaker even for people on your side. It's hard to take writing seriously that is clearly motivated by such an agenda and is clearly trying to get you to rally with it in your contempt for a common enemy.

Comment author: shev 02 February 2017 03:20:14AM *  2 points [-]

It's true that politics is generally discouraged around here. But, also -- I'm the person who commented negatively on your post, and I want to point out that it wasn't going to be well-received, even if politics was okay here. You wrote in a style that assumed a lot of opinions are held by your readers, without justification, and that tends to alienate anyone who disagrees with you. Moreover, you write about those opinions as if they are not just true but obviously true, which tends to additionally infuriate anyone who disagrees with you. So I think your post's style was a specific example of the kind of 'mind-killing' that should be avoided.

I appreciate exhaustive research of any kind, and the body of your post was good for that. But the style of the frame around it made it clear that you had extremely low opinions of a large group of people and wanted to show it, and.. well, I personally don't think you should write that way ever, but especially not for this forum.

Comment author: Thomas 30 January 2017 01:32:06PM *  0 points [-]

Perhaps, but it follows.

It happens also at the Game of Life by Conway, at the game of chess and at many related games, as well as in real life geography.

Comment author: shev 31 January 2017 11:44:44AM *  3 points [-]

It doesn't count in the discussions of coloring graphs, such as in the four color map theorem, and that's the kind of math this is most similar to. So you really need to specify.

Comment author: morganism 30 January 2017 11:52:38PM *  2 points [-]

If there is no anti-gravity force, then how can an galactic scale empty section be "pushing" us toward the Great Attractors....

"Discovery of the “Dipole Repeller” confirms that both attraction and repulsion are at play in our extragalactic neighborhood"


Some decent visualizations linked, and an original one on Utube from a French team is one of the coolest large scale animations i've ever seen...

Edit: and there it is, linked at bottom of viz page! http://irfu.cea.fr/cosmography

Comment author: shev 31 January 2017 11:35:47AM *  2 points [-]

Are you just wondering what 'pushing' means in this context? Or speculating about the existence of anti-gravity?

I'm pretty sure that this is just interpreting as region of low density as 'pushing' because it 'pulls less' than a region of average density would.

This is similar to how electron 'holes' in a metal's atomic lattice can be treated as positive particles.

Comment author: madhatter 27 January 2017 12:42:03AM 1 point [-]

I'm not surprised. But I also don't see much utility from this study; most people already believe that coffee helps them focus.

Comment author: shev 27 January 2017 06:27:14AM 2 points [-]

Don't you think there's some value of doing a more controlled study of it?

Comment author: Davidmanheim 23 January 2017 08:47:15PM 0 points [-]

You left out a possibility; true dependent on something outside your realm of knowledge. In this case, it's true for real numbers, but false for surreal numbers.

Comment author: shev 24 January 2017 12:44:14AM 0 points [-]

No, because it's not a possibility that when you thought you were doing math in the reals this whole time, you were actually doing math in the surreals. Using a system other than the normal one would need to be stated explicitly.

Comment author: whpearson 22 January 2017 11:37:21PM 0 points [-]

Well. We should probably distinguish between what rationality is about and what LW/rationalist communities are about.

Rationalists aren't about rationality? Back in 2007 I don't think there was a split. Maybe we need to rename rationalists if "rationality is winning" is entrenched.

LWperson: I'm a rationalist, I really care about AIrisk.

PersonWhohasReadSomeRationalityStuff: So you will lie to get whatever you want, why should I think AIrisk is as important as you say and give you money?

LWPerson: Sigh...

Rationality-the-mental-art is, I think, about "making optimal plays" at whatever you're doing, which leads to winning (I prefer the former because it avoids the problem where you might only win probabilistically, which may mean you never actually win).

I consider every mental or computational action a "play" because it uses energy and can have a material impact on someones goals. So being more precise in your thinking or modelling is also a 'play' even before you make a play in the actual game.

Evolution doesn't really apply. If some species could choose the way they want to evolve rationally over millions of years I expect they would clobber the competition at any goal they seek to achieve. Evolution is a big probabilistic lottery with no individuals playing it.

I think you missed my point about evolution.

Your version of rationality sounds a lot like fitness in evolution. We don't not what it is but it is whatever it is that survives (wins). So if we look at evolution and the goal is survival, lots of creatures manage to survive while not having great modelling capability. This is because modelling is hard and expensive.

Fitness is also not a shared art. Ants telling birds how to be "fit" would not be a productive conversation.

I've run out of time again. I shall try and respond to the rest of your post later.

Comment author: shev 23 January 2017 01:20:46AM 1 point [-]

You had written

"I really want a group of people that I can trust to be truth seeking and also truth saying. LW had an emphasis for that and rationalists seem to be slipping away from it with "rationality is about winning"."

And I'm saying that LW is about rationality, and rationality is how you optimally do things, and truth-seeking is a side effect. And the truth-seeking stuff in the rationality community that you like is because "a community about rationality" is naturally compelled to participate in truth-seeking, because it's useful and interesting to rationalists. But truth-seeking isn't inherently what rationality is.

Rationality is conceptually related to fitness. That is, "making optimal plays" should be equivalent to maximizing fitness within one's physical parameters. More rational creatures are going to be more fit than less rational ones, assuming no other tradeoffs.

It's irrelevant that creatures survive without being rational. Evolution is a statistical phenomenon and has nothing to do with it. If they were more rational, they'd survive better. Hence rationality is related to fitness with all physical variables kept the same. If it cost them resources to be more rational, maybe they wouldn't survive better, but that wouldn't be keeping the physical variables the same so it's not interesting to point that out.

If you took any organism on earth and replaced its brain with a perfectly rational circuit that used exactly the same resources, it would, I imagine, clobber other organisms of its type in 'fitness' by so incredibly much that it would dominate its carbon-brained equivalent to the point of extinction in two generations or less.

I didn't know what "shared art" meant in the initial post, and I still don't.

Comment author: D_Alex 22 January 2017 09:57:32AM *  3 points [-]

In the "proof" presented, the series 1-1+1... is "shown" to equal to 1/2 by a particular choice of interleaving of the values in the series. But with other methods of interleaving, the sum can be made to "equal" 0, 1 1/3 or indeed AFAICT any rational number between 0 and 1.

So... why is the particular interleaving that gives 1/2 as the answer "correct"?

Comment author: shev 22 January 2017 10:10:23AM *  2 points [-]

Interleaving isn't really the right way of getting consistent results for summations. Formal methods like Cesaro Summation are the better way of doing things, and give the result 1/2 for that series. There's a pretty good overview on this wiki article about summing 1-2+3-4.. .

Comment author: CronoDAS 22 January 2017 05:31:29AM 1 point [-]

I actually know a bit about summing series, so I recognize the proof as completely bogus but the actual sum as probably correct, for a certain sense of "sum". You can make a divergent series add up to anything at all by grouping and rearranging terms. On the other hand, there actually are techniques for finding the sum of a convergent series that sometimes don't give nonsensical answers when you try to use them to find the "sum" of a divergent series, and in this sense the sum of 1 + 2 + 3 + etc. actually can be said to equal -1/12.

Comment author: shev 22 January 2017 06:16:38AM *  2 points [-]

I know about Cesaro and Abel summation and vaguely understand analytic continuation and regularization techniques for deriving results from divergent series. And.. I strongly disagree with that last sentence. As, well, explained with this post, I think statements like "1+2+3+...=-1/12" are criminally deceptive.

Valid statements that eliminate the confusion are things like "1+2+3...=-1/12+O(infinity)", or "analytic_continuation(1+2+3+)=-1/12", or "1#2#3=-1/12", where # is a different operation that implies "addition with analytic continuation", or "1+2+3 # -1/12", where # is like = but implies analytic continuation. Or, for other series, "1-2+3-4... #1/4" where # means "equality with Abel summation".

The massive abuse of notation in "1+2+3..=-1/12" combined with mathematicians telling the public "oh yeah isn't that crazy but it's totally true" basically amounts to gaslighting everyone about what arithmetic does and should be strongly discouraged.

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