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Open thread, August 14 - August 20, 2017

The full answer is: they cannot return if there are only finitely many balls, but they can if there are infinitely many.

Let's first assume that there are finitely many balls. As Thomas pointed out, we can assume that the center of mass is fixed. Let's consider R defined to be the distance from the center of mass to the furthest ball and call that furthest ball B (which ball that is might change over time). R might be decreasing at the start - we might start with B going towards the center of mass. But if R decreased forever then we would know that they never return to their starting location (since R would be different)! So at some point it must become at least as large as it was at the start. At that point either the derivative of R is 0 or it is positive. In either case, R must increase forever onwards - which again shows it can't return to its original starting point. Why is it always increasing from that point onwards? Well, the only way for the ball B to turn around and start heading back towards the center is if there is another ball further away than it to collide with it. But that can't be, since B is the furthest out ball! (Edit: I see now that this is essentially equivalent to cousin_it's argument.)

For infinitely many balls, you can construct a situation where they return to their original position! We're going to put a bunch of balls on a line (you don't even need the whole plane). In the interval [0,1], there'll be two balls with initial velocity heading in towards each other at unit speed, with one ball at the left edge of the interval and one ball at the right. Then do the same thing for each interval [k,k+1]. When you let them go, each pair in each interval will collide and then be heading outwards with unit interval. Then they'll collide at the boundary with the next interval with the ball from the next interval. That sets them back at the starting position. I.e. all balls collide first with their neighbor on one side, then their neighbor on the other side, setting them back to their starting position.

Why election models didn't predict Trump's victory — A primer on how polls and election models work

A cursory glance through Fivethirtyeight's collected poll data shows a survey with over 84,000 voters (CCES/YouGov) giving Clinton a +4 percentage point lead, with 538 adjusting that to +2. Google and SurveyMonkey routinely had surveys of 20,000+ individuals, with one SurveyMonkey one having 70,000 with Clinton +5 (+4 adjusted). There was no clear reason to prefer your poll (whichever that one was) over these. https://projects.fivethirtyeight.com/2016-election-forecast/national-polls/

And it should go without saying that Clinton did end up at +2 nationally.

Triple or nothing paradox

I don't like any of the proposed solutions to that when I glanced through the SEP article on it. They're all insightful but are sidestepping the hypothetical. Here's my take:

Compute the expected utility not of a choice BET/NO_BET but of a decision rule that tells you whether to bet. In this case, the OP proposed the rule "Always BET" which has expected utility of 0 and is bested by the rule "BET only once" which is in turn bested by the rule "BET twice if possible" and so on. The 'paradox' then is that there is a sequence of rules whose expected earnings are diverging to infinity. But then this is similar to the puzzle "Name a number; you get that much wealth." Which number do you name?

(Actually I think the proposed rule is not "Always BET" but "Always make the choice for which maximizes expected utility conditional to choosing NO_BET on the next choice". The fact that this strategy is flawed seems reasonable: you're computing the expectation assuming you choose NO_BET next but don't actually choose NO_BET next. Don't count your eggs before they hatch.)

Open thread, Oct. 24 - Oct. 30, 2016

Vaporising a comet takes significant energy. Heating up a comet to vaporization point takes significant energy. Dissipating the vaporized comet (still the same total mass and momentum as when it was in a solid state) takes significant energy. I really find this simplistic a treatment to be not useful. Still an interesting thought-experiment and a little scary.

How my social skills went from horrible to mediocre

I'm curious why you that I'm not part of your target audience – feel free to elaborate.

I'm not sure we understand each other here, but I'm assuming you want to know why I do not consider myself part of your target audience. I don't have a concrete answer here, it's just that I read this and thought it didn't apply to me. I had some of the same difficulties as you, but not in a way that I feel your advice would have applied or still does apply. I can think of a friend for whom some of your advice would probably apply, though, and imagine you are targeting him and not me.

I might be oblivious, but I don't see where I called myself smarter than the typical LW reader

This is what I take from: " I almost never went to Less Wrong meetups, because I had already thought about most of what people discussed, so that it was more efficient for me to learn on my own." and similar comments. I can see how you would take it as saying that you simply have already thought about that ahead of time and so you're not claiming to be smarter. (I've tried to explain that circumstance to people before myself.) But most people will take that to mean that you think you're too smart for them. Other comments suggest that this "most people" does not transfer to "most LW readers," though, so maybe I'm misplaced. This is also something that I thought could have been left out entirely. If you had to include this I would have suggested mollifying it a bit: make the problem seem to be yourself rather than others. Something like, "I struggled to find common ground to talk about even during LW meetups." This loses some specificity, but I'd play around with that kind of phrasing where you claim the fault is your own.

Another example would be something like describing yourself as "The guy who has deep insights but who doesn't get anything done, because he he's socially dysfunctional so nobody listens to him". This is a pretty big humble brag. If I wanted to say that to a typical person I might have said, "The guy who doesn't get anything done, no matter what insight he has, because he's socially dysfunctional so nobody listens to him." It's more cautious and definitely doesn't claim "deep insight" which is a phrase I'd reserve for describing someone else. You leave it up to the reader exactly how insightful you are implying yourself to be. It also changes the focus to your difficulty rather than the strength (which is demoted to an aside). I'm no writer though, so take this specific suggestion with a grain of salt.

Similarly for claims about deep insights from machine learning. Make the focus the difficulty you faced, not the deep insight you had. Maybe say, "I struggled even more after picking up machine learning jargon and modes of thought which I couldn't well articulate, even to my close friends."

Others have pointed out that you're also very humble throughout. I agree with them, too, and admire your ability to spell out your own failings. But people read "humble brag" mixed statements as primarily bragging. To you, it might seem really really significant that you were struggling, but that's not the focus people will read.

For the doctor analogy, I agree that that's what you're trying to say and I think you partly succeeded at that on one level. But on the other level, people will be turned off when you express expertise in areas where you do not have an obvious qualification. A doctor has a diploma to point to, and people are okay with that. A self-proclaimed student of medicine who had spent 15 years learning privately would be treated quite differently form the doctor. It's not a fair world! Had you been more specific I also might not have taken it like that, instead it seemed to be a blanket statement, like how an adult might say that all conversation with a child is tedious since the child just hasn't had any exposure to interesting ideas. Regardless of how factually true that is, the child could feel slighted.

This is all my take. Lumifer's response seems reasonable, too.

What would I have eliminated to make it shorter? It's a matter of taste, I suppose. I might have removed most of the part about how you grew up. I felt it could be summarized in a few sentences. But looking over this a second time, I think I may have clumped a lot of the things I thought came off as "arrogant" under the tag of "needs to be removed" and then interpreted that to mean that the article was too long. I'm sure it could be tightened up, but other than that growing up section there doesn't seem to be anything major. So take that complaint of mine lightly.

Ugh, I need to take my own advice and not write so much. Easier said than done.

How my social skills went from horrible to mediocre

For example, if a student tells me that I'm the worst teacher he or she has ever had, it makes me feel bad because I feel like I'm not contributing value, but I'm not at all upset with the student: my attitude is that the student is conveying valuable information to me, and that I should be appreciative.

I'm tempted to take that as a Crocker's rule invocation. But I have realized that you wrote this for people-like-you, that is, after all, pretty much its explicit purpose. As such, I'm not sure I have an criticism that I can't definitively think is helpful.

Nonetheless, I want to point out two general things about this will make this hard post to read for most people. First is the length, and even in this you note that you spend too much time explaining something that you've worked on. I think the length was partially unnecessary and not just a reflection of me not being your target audience (I assume). The second is that you come across as exceedingly arrogant. I think you are attempting to explain your background so that we understand the situation. But you explicitly call yourself smarter than the typical reader of the site that you are posting this on. Ouch! But again, perhaps this is just a reflection of you having a very narrow target audience and for them this could read like a "ah, finally someone gets it!"

I hope that you take this to be useful, particularly for when you write for a wider audience. For what its worth, my mental post it note has you labelled as a user that I should pay attention to. I say that since I kind of suspect that you already know everything I just mentioned and aren't bad at overcoming these in other situations, but thought this worth saying explicitly given the context of trying to improve.

Harry Potter and the Methods of Rationality discussion thread, February 2015, chapter 104

We've gotten much less senses of doom with this encounter with Quirrell than any in the past as far as I can tell. Only Sprout's magic caused apprehension, Q not at all.

Was Quirrell in control of the sense of doom all along? Has something changed?

I'm the new moderator

I've been around for more than a couple years and had no idea there was a difference between Main and Promoted. I guess I check "new" for Main by using the side bar on the landing page but didn't pick up on the distinction.

2015 Repository Reruns - Boring Advice Repository

I've been using Mint for a while and, honestly, I'm very unimpressed. You click on the "Trends" tab and what does it show you? A pie chart! Because that's obviously how you analyze your trends...

Actually I just went back there for the first time in a while and it's not as bad as I remembered if you're willing to muck around a bit. It does seem to hide the useful things under a few clicks and force you to do comparisons manually through filtering out certain categories instead of showing you them all at once, things like that. But it's still a lot better than going through a number of accounts. Also, you can type for suggestions when classifying things which is something I had missed before and was a major complaint, having to wander through their list looking for something. Still, though, I'd be open to suggestions for alternatives.

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