@rob: Oh, yeah. My first week on the site I managed to pick up a bounty of 500. I think I was in the top 5 that week - I've never been that high since.
That notation question reminds me of a question I had sometime back. Before the days of the radian measure, did people "know" that the derivative of sin x is cos x, and in what form would they have written it?
(Just a sanity check for the dates: For instance, the radian measure was introduced by a Roger Cotes in 1714. Certainly Newton and Leibniz lived before that I guess.)
@SrivatsanNarayanan Check out the quote from Newton's Principia near the bottom of this page.
If I'm following the statement correctly, he appears to define the trig functions in terms of the arcs they subtend on the circle rather than via the angles.
@SrivatsanNarayanan My understand of the Principia is that Newton tried to present all he knew of the calculus geometrically. So (while I haven't read it) I imagine he had ways of viewing basic results on calculus that are quite different than the ways we normally think about them.
Building off on that, a book I'm reading right now (Needham's Visual Complex Analysis) argues that viewing some of the basic calculus results from a more geometric perspective causes them to make more sense. He gives (in the preface) the example of the derivative of tangent.
Of course, Needham is arguing for the geometric viewpoint for complex analysis as well - that's the entire purpose of his book.
Quoting from the book: It should be observed that the Geometria curvilinea is opened by a long declaration about the lack of rigor and elegance of the methods followed by those "men of recent times" who have abandoned the geometrical methods of the Ancients.
@Jonas: You're right, of course. But I think the point system is one of the genius ideas of the stack exchange network (IMO) - in the way that it partially motivates so many of us to keep coming back to offer our expertise to complete strangers.
@JonasTeuwen Are you talking about the Needham book? I think so - although I'm far from an expert in complex analysis.
@AsafKaragila No, I wasn't drunk. A friend had convinced me that it would be good exercise to run up the Fine Tower stairs several times. I made it up three times before my visit to the bathroom.
@MikeSpivey I never puked from exercises. I puked from being drunk, once from smoking a hookah (with just tobacco, nothing suspicious), from other stuff... never from sports.
Some of my more serious running friends tell me that sometimes they run for a while, stop, throw up, and then keep running. The stairs thing is the only time that's happened to me.
@robjohn It was the higher floors that I remember being so dusty.
@SrivatsanNarayanan: A lot of the focus of the movie is not so much the mathematics as it is Nash's struggle with mental illness. And Russell Crowe does do a good job as Nash.
@MikeSpivey In the movie Nash is taking atypical antipsychotics while in real life Nash stopped taking any medication. If I understood correctly, they have added it so that people don't get the idea of stopping their medication and be more like Nash...
Hmm, is that so? I only know one person in The Netherlands that does PDO. But then again, I only know one doing wavelets.
@SrivatsanNarayanan The name? Atypical antipsychotics are called atypical because they have a different side-effect profile of the "typical" antipsychotics, they are in general more modern, that's why I suppose.
My friend--mildly fanatic about LoTR--once kept Sauron's eye as his gmail status picture. Apparently, one of his woman friends misidentified it as a convex lens against a random background, which left him angry for several weeks.
@Srivatsan: I haven't entered an email-address in my user profile, so my Gravatar depends on my IP, which, in turn, depends on my provider who likes to change it on a daily basis.
@robjohn You can just get up to 200 points from upvotes. If there were downvotes, they get compensated by votes that wouldn't count otherwise. (hope that's clear enough)
Some months ago I left a comment on this thread on MO regarding dual spaces and the axiom of choice.
I only wrote the countable/finite case properly, but I had a proof generalizing it to higher cardinalities. Now I can't find it and I am stuck restoring the proof...
And there's this huge "Asaf claims that ..." in the question, and the OP asked me for a preprint...
So I figured this is something nice to do in order to get myself back into work. I'll sit to write the proof (at least for this specific case) as an answer there.
For this answer, currently it works only for invertible matrices, but for a general matrix, I guess it's a trivial fix because one can always perturb the given matrix a bit to make it noninvertible. (One only needs det to be continuous.)
There are two possibilities I can think of: 1. sin^2(x) = 1/4 could be 150° as well as 30°, but the other angle of 45° knocks that out (I should have said that ). 2. someone mentioned it was a question of the day or something like that, and maybe the downvoter felt I spoiled something.
Just before the room was starting to get active, I was pretty much the most active user in the room on a daily basis. Apparently if the 'real' owner isn't around for long enough the most active user gets throned.
So I talk a lot...
Is this enough reason to give me ownership on the chatroom? Is this ownership going to last until manual removal or something else?
