Okay, so I'm reading this book topics in algebra by herstein. he says finite groups which are not trivial do exist. What does that mean trivial in this context?
@KyleKanos what do you mean they work closely together?
@StanShunpike In the probability, the denominator is needed for normalization purposes. If we choose the overall state and the constituent states to all be normalized, the denominator becomes 1 and we can omit it. It is still "there", but just equal to 1.
this is freakin amazing. dont understand this. use ipad. updated os recently. it seems to support a very large set of keyboard icons somehow! & they seem to work in chat! 😵 ← can you guys see that? (cant believe it wild dont know how it works)
@0celo7 Right, I get the idea that the denominator has to be one so we can in effect not have to write it. I just don't get why we have the numerator and the denominator in the first place. What do the two quantities have to do with each other?
Presumably the top is the probability of ending up in xi
there were some more comments by chat regulars earlier on the topic of older mathematicians. an interesting essay cited. zhangs (recent) case is a counterpoint.
inf thinking of maybe writing a blog on the "youth vs science" topic. saw a very good essay on the topic once (would be miracle to find it again but might try some google jujitsu). it basically proposed that accomplishments in life match a sort of bell curve with most productive in midlife. "naturally". anyway you might find this interesting.
@Danu Were you the one I was talking to about the music and Mazzola? Have you read any of his Topos of Music yet? When you do let me know! I can't understand it at all and want to know if it's any use for making music
if you asked me, hardy seemed at times almost to suffer from depression... his writing comes off like that at times. anyway his remark re ramanujan is self-effacing. ramanujan was brilliant but so was hardy. its one of the greatest math collaborations of all time.
not sure if hardy ever rated other mathematicans as you say. have not heard that. wonder if you can cite it. other mathematicians might not rate him so low. not really sure the rating game is helpful to anyone anyway.
I think many people have one or two big insights to share. When they reveal them may depend on circumstances. Not many (but some) have many great ideas. After Einstein's Miraculous Year, he had another big win with GR, but not so much after that. He never really assimilated QM, and struggled with several tries at a unified field theory, which never worked out.
← finding a zillion articles surveying age vs scientific productivity etc, amazing blog topic... & think found the one looking for! the google jujitsu is still strong :)
(thx) ofc the fields medals are another factor in scientific ageism.
awarded only under 40. that was not at the exact request of Fields, but was a choice by the prize committee in interpreting his wishes honoring "young" mathematicians.
@SabreTooth 1) you didn't understand the meaning of my words. 2) I don't ask people in what they believe, so, your beliefs are your business. 3) In this site participate all the nations of the world, of all the possible religions, and everyone has to be fully respected. If you consider smart to throw in the face of people that you defy their beliefs, don't mix me.
J (thx for ref) you write the basic story of einsteins life as viewed "by the establishment". however, how would einstein view his own life? he was an iconoclast until the end. sometimes it paid off with recognition, other times (later) it meant decades of isolation & "wandering in the wilderness"
If I've been offered to be a coauthor on a paper -- one which my institute knows nothing about, and is not through a prof of my institute or collaboration of the same sort -- am I allowed to, and should I still put my affiliation as that institute and use that email ID?
@ChrisWhite That's why I made that meta! I'm much more consistent about offering the new users help now because I can simply link them to a detailed HOWTO :D
actually (that reminds me) there is a modern pseudonymous mathematican half-crank involved in the rating game himself. he had some very lively commentary on the last fields medal awards. etc. its a troll-like blog. check it out for fun/ laughs. actually all the hardcore math geeks here might get a kick out of it & find some goofy stuff. stop timothy gowers by "sowa"
@ManishEarth Ah. That's an interesting question. I think you should just put the university at which you study. I am 99% sure that's the proper thing to do.
(Servo's written in Rust, which is probably the least functional functional programming language, but the most functional amongst non-functional programming languages, depending on how you label it :P)
I've also heard that Rust backed off on some of its nicer originally planned concurrency features because the devs want to make sure it can be used for kernels (a.k.a. small runtime). Any comments there?
@StanShunpike I was just doing laundry - people were talking about it in the elevator, people were walking by arguing about it, some guys were arguing from a window.
@NeuroFuzzy Lol I said what's up to my friend from Jamaica and that was the first thing he asked me about. Demanded an answer. I said blue/black. He said gtfoh.
user54412
7:46 AM
@ManishEarth Your affiliation is like your address, but "Department of All Knowledge, University of Awesomeness" looks better than "Generic Street, Some City," and it's where you'd want related correspondence addressed anyway.
As has been shown in this paper, pointed out by Matthew in the comments, the expression found is indeed correct and can be understood from a holographic point of view. I now reproduce the argument from relevant section (number 5) of the paper:
It seems unusual from the gravitational point of ...
Note the messages at the beginning and end of the answer
Although @DavidZ did tell me later on I should not necessarily have made it a 'community wiki' because the points would've been rightfully mine. However, this gives a solution that you may like: Use community wiki, so nobody gets the points ;)
@Sofia This doesn't really help: I did this one the one I just linked, and the commenter simply didn't reply. Often, people will not be active anymore
@StanShunpike Yes, one just needs to realize that $\mathrm{d}^n x$< which physicists usually write, is a tensor density and not a tensor, I think, and basically $\mathrm{d}^n x \sqrt{g}$ where $g=\text{det}g_{\mu\nu}$ does the job
@StanShunpike Susskind is one of the giants of modern theoretical physics, with a lifetime of achievements behind him. I'm not sure Motl agrees with some of his views on the landscape and anthropic principle, but I would guess both respect the other.
@StanShunpike The only thing I would say about Susskind, and here you need to remember that my opinion is worth only as much (or less) than you pay for it ...
@JohnRennie hmmm...at first I thought that was a joke. I actually was skeptical at first but I like 't Hooft and he seemed to be a proponent too if I rememeber correctly
I mean it sounds philosophical but what in string theory isn't purely theoretical at the moment? Both math and philosophy have in common that neither is concrete so it didn't seem implauible when I looked at the rest of sorts of things string theory seems to want to propose
@StanShunpike For those of us who ask "why" the anthropic principle is repellant because it tells us there is no answer to the question "why". But I have to concede that the AP currently appears to be the only sensible answer to lots of questions.
@JohnRennie I will need to read more about it to decide for myself. I take it the version of the AP your refer to is the one discussed between Susskind and Smolin?
@StanShunpike I'm not sure what was discussed between Susskind and Smolin. I'm using term anthropic principle in a general sense to refer to all such arguments.
@ChrisWhite I don't think so. I think it's never the answer to 'why', but it does allow one to tell approx. what the value is, and that it cannot be different by the AP
Wher physicists argue about philosophy it's usually related to trying to explain initial conditions. Philosophy creeps in because there is no good physically motivated explanation.
user54412
@JohnRennie I agree mostly, but I feel things get dicey when one starts asking really fundamental questions.
@ChrisWhite Agreed, and I'm not endorsing the practice. My own view is that these discussions are great in the bar late at night, but not so great when they appear on the Arxiv.
Also, I think there's a pretty good answer to be found re the annoying dress color question: Give it to a computer and have it tell you what color it is. lol
user54412
I'm probably still bitter about never having gotten a straight answer as to why inflation is necessary or even desirable. It always comes down to some sort of "initial conditions" argument that I find completely bogus.
As has been shown in this paper, pointed out by Matthew in the comments, the expression found is indeed correct and can be understood from a holographic point of view. I now reproduce the argument from relevant section (number 5) of the paper:
It seems unusual from the gravitational point of ...
