## Search found 117 matches

- Fri Feb 17, 2017 2:11 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1799: "Bad Map Projection: Time Zones"
- Replies:
**70** - Views:
**15305**

### Re: 1799: "Bad Map Projection: Time Zones"

Maybe I'm misunderstanding something, but… why is Poland "reaching" to the east? It's in the same time zone as Germany and most of the Western Europe, and they observe DST the same way. I guess it is because Poland and Belorussia share a border, and Randall tries to show that. The same th...

- Mon Jun 24, 2013 6:59 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1229: "Screensaver"
- Replies:
**51** - Views:
**18500**

### Re: 1229:Screensaver

Is this not a case of? repeat newstar.x=random(); newstar.y=random(); until newstar.x<>0 or newstar.y<>0; But wouldn't it be more fun, if we had a live web cam feed from Hubble monitoring Betelgeuze? I mean, if/when it goes supernova, it would be so cool to be the first to see it, right?

- Wed Oct 19, 2011 5:39 am UTC
- Forum: Mathematics
- Topic: A Semantic Survey
- Replies:
**17** - Views:
**2249**

### Re: A Semantic Survey

I would phrase it either as "Not all three are hearts" (meaning the negation of "all three are hearts") or "All three are non-hearts" (where the admittedly contrived word "non-heart" means a card from a suit other than hearts). Don't know, if that would be any...

- Sun Oct 16, 2011 6:34 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0964: "Dorm Poster"
- Replies:
**155** - Views:
**41508**

### Re: 0964: "Dorm Poster"

I totally didn't know that FTFY also stands for "Focused That For Ya"

- Wed Sep 21, 2011 6:08 pm UTC
- Forum: Mathematics
- Topic: Why do "secant" lines and "1/cos" share a name?
- Replies:
**11** - Views:
**5928**

### Re: Why do "secant" lines and "1/cos" share a name?

This thread gives me a reason to bring something up. You know. I never use either sec x or csc x. I always use 1/cos x or 1/sin x. This is the way it was taught to me as an undergrad, and now that I'm teaching first year calculus I won't even mention secant or cosecant to my students. Today I discus...

- Mon Sep 19, 2011 11:56 am UTC
- Forum: Mathematics
- Topic: Rational tangent values [puzzle]
- Replies:
**5** - Views:
**2895**

### Re: Rational tangent values [puzzle]

If \alpha=arctan 2 were a rational multiple of \pi , then z=\cos\alpha+i\sin\alpha=(1+2i)/\sqrt5 would be a root of unity. But the minimal polynomial of z over the rationals is quartic. If the order of the root of unity were equal to n, then the degree of the minimal polynomial is known to ...

- Mon Sep 05, 2011 3:18 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0947: “Investing”
- Replies:
**148** - Views:
**32522**

### Re: 0947: “Investing”

The problem is that a decade is too short a time to show the nature of the asymptotics. If the population of the Earth keeps growing at the rate of 2% per year, in a few dozen millennia the volume of human flesh, if collected together in a single ball, will have a radius growing at the speed of lig...

- Mon Sep 05, 2011 9:22 am UTC
- Forum: Mathematics
- Topic: What does the adjacency matrix of e8 lie group look like?
- Replies:
**9** - Views:
**3083**

### Re: What does the adjacency matrix of e8 lie group look like

Ok. While googling something else I saw this. That is probably the graph you have been talking about. The graph describes an 8-dimensional polytope. Apparently this polytope shares lots of symmetries with the E 8 root system. I'm afraid I am not familiar with the notation they use, so I don't know t...

- Mon Sep 05, 2011 4:37 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0947: “Investing”
- Replies:
**148** - Views:
**32522**

### Re: 0947: “Investing”

The problem is that a decade is too short a time to show the nature of the asymptotics. If the population of the Earth keeps growing at the rate of 2% per year, in a few dozen millennia the volume of human flesh, if collected together in a single ball, will have a radius growing at the speed of ligh...

- Fri Sep 02, 2011 6:23 pm UTC
- Forum: Mathematics
- Topic: What does the adjacency matrix of e8 lie group look like?
- Replies:
**9** - Views:
**3083**

### Re: What does the adjacency matrix of e8 lie group look like

@scratch123 This post reminded me that I really need to learn more group theory before I try to understand lie groups. Do you think you could describe this in terms of graph theory? I know much more graph theory than group theory and I am having trouble understanding the difference between the 2. L...

- Fri Sep 02, 2011 6:45 am UTC
- Forum: Mathematics
- Topic: What does the adjacency matrix of e8 lie group look like?
- Replies:
**9** - Views:
**3083**

### Re: What does the adjacency matrix of e8 lie group look like

@scratch123 The 248 dimensions come from the 240 roots (each adds one dimension), and 8 dimensions of the maximal toral subalgebra (of the Lie algebra). That 8 = rank of the root system = dimension of the space the root system resides in. A number of identifications and a little bit of Lie theory ar...

- Wed Aug 31, 2011 12:01 pm UTC
- Forum: Mathematics
- Topic: What does the adjacency matrix of e8 lie group look like?
- Replies:
**9** - Views:
**3083**

### Re: What does the adjacency matrix of e8 lie group look like

Hmm. Exactly which adjacency matrix do you want to see? I'm troubled by the term "Lie group" in your question. Can't be related to the Cayley graph (like Sagekilla seemed to suggest), because the Lie group has continuum cardinality. Can't be related to the lattice (countably infinite). I'm...

- Sat Aug 13, 2011 8:41 pm UTC
- Forum: Mathematics
- Topic: The Tau Manifesto
- Replies:
**165** - Views:
**43399**

### Re: The Tau Manifesto

antonfire wrote:I think you mean pi/180.Jyrki wrote:Pi/2 it is!!!!

LOL. Even a good idea can be overdone?

- Sat Aug 13, 2011 3:55 pm UTC
- Forum: Mathematics
- Topic: The Tau Manifesto
- Replies:
**165** - Views:
**43399**

### Re: The Tau Manifesto

I see it mostly as a way of making trig make sense to people who are just learning it. I took pi to be the same as 180 degrees for the longest time, and then what do I find out? Degrees are stupid and shouldn't even be taught in the first place. Why not have 1 tau = 1 turn? Everything just clicks t...

- Wed Jul 06, 2011 1:34 pm UTC
- Forum: Mathematics
- Topic: Research adviser question.
- Replies:
**17** - Views:
**2504**

### Re: Research adviser question.

2 years possibly includes multiple rejections from some journals before being published imo... No. Two years for the usual cycle. Review, accept with minor revisions, revise, wait, get galley proofs, wait some more. I guess it depends heavily on the field. [Edit]Removed a passage were I was being a...

- Wed Jul 06, 2011 5:05 am UTC
- Forum: Mathematics
- Topic: Research adviser question.
- Replies:
**17** - Views:
**2504**

### Re: Research adviser question.

:) In the olden days (90s just called) all reputable journals had a backlog of close to one year. The most prestigeous ones had 2-3 years, but, alas, yours truly had nothing to do with those. While I'm at it, and my inner grumpy old man hasn't had enough coffee, I need to get something off my chest....

- Fri Jun 17, 2011 7:53 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0913: "Core"
- Replies:
**95** - Views:
**20486**

### Re: 0913: "Core"

So is he worried about a core dump?

- Wed Jun 15, 2011 4:56 am UTC
- Forum: Mathematics
- Topic: Counting Subspaces
- Replies:
**4** - Views:
**1300**

### Re: Counting Subspaces

Sounds correct to me. In calculations like this it sometimes helps to use duality. Here you are tallying 2-dimensional subspaces of a 3D-space. Let (,) be a non-degenerate bilinear pairing on the 3-dimensional subspace. For example the usual dot product will do nicely. Then w.r.t to that pairing a 2...

- Sun Jun 12, 2011 6:22 am UTC
- Forum: Mathematics
- Topic: PhD in hand
- Replies:
**43** - Views:
**5825**

### Re: PhD in hand

Congrats and welcome to the club!

- Thu Jun 09, 2011 11:47 am UTC
- Forum: Mathematics
- Topic: Determinant calculation
- Replies:
**2** - Views:
**785**

### Re: Determinant calculation

I don't see a better form either. Mark this one solved.

- Wed Jun 08, 2011 6:27 am UTC
- Forum: Mathematics
- Topic: Show us your articles! Or what's your Erdos number?
- Replies:
**185** - Views:
**266741**

### Re: Show us your articles! Or what's your Erdos number?

My Erdös number is 3. Just in case somebody is building stats on this

- Tue Jun 07, 2011 5:33 am UTC
- Forum: Mathematics
- Topic: Too easy of an undergrad?
- Replies:
**20** - Views:
**3049**

### Re: Too easy of an undergrad?

For instance, in my linear algebra class, we never mentioned isomorphisms unlike in this thread: http://forums.xkcd.com/viewtopic.php?f=17&t=71107 Am I just being paranoid, or should I be able to solve this topic by now? As a poster in that thread let me give a few words, too. The solution base...

- Thu Jun 02, 2011 5:38 pm UTC
- Forum: Mathematics
- Topic: Proof that there are at least 5 regular polyhedra?
- Replies:
**11** - Views:
**3013**

### Re: Proof that there are at least 5 regular polyhedra?

I don't know if it helps you much, but since you have Coxeter's book at hand here is a possibility. If you believe in the classification of finite groups generated by reflections (these are often also called Coxeter groups, and are probably covered in his book), then you get a sort of uniform constr...

- Sat May 21, 2011 8:09 am UTC
- Forum: Mathematics
- Topic: alternative mathematics
- Replies:
**128** - Views:
**14547**

### Re: alternative mathematics

Agree. Alternative math looks like something written by a squirrel on LSD, so either explain your point or shut up. Getting the first thread locked up was supposed to be a hint.

- Thu May 19, 2011 7:00 pm UTC
- Forum: Mathematics
- Topic: Lie algebra representations
- Replies:
**2** - Views:
**818**

### Re: Lie algebra representations

In my somewhat, but not too distant youth I think I was fully conversant with Humphreys' GTM series Lie algebra text. Category O I'm much less familiar with, but let's try anyway. I'm fairly sure that you have left out something. The claim does not hold for all the simple roots \alpha_i , unless the...

- Mon May 16, 2011 7:36 pm UTC
- Forum: Mathematics
- Topic: Uncountably Many Zeroes
- Replies:
**38** - Views:
**4029**

### Re: Uncountably Many Zeroes

In this case start with a function that is identically zero on the interval [0,1]. Instead of removing the middle third, replace it by a hump, so that the function is still continuous but non-zero on that middle third interval. Repeat on the other thirds, and in the limit you get a function that sa...

- Sun May 15, 2011 5:43 pm UTC
- Forum: Mathematics
- Topic: Bee Problem
- Replies:
**2** - Views:
**1010**

### Re: Bee Problem

It seems to me that the answer to your question is the constant term of the two variable rational generating function P_n(x,y)=\left(xy+x+y+\frac1y+\frac1x+\frac1{xy}\right)^n. This is arrived at in the following way. Use a basis {u,v} of two unit vectors with a 120 degree angle in b...

- Sat May 14, 2011 8:07 pm UTC
- Forum: Mathematics
- Topic: Linear Algebra: Basis of Eigenvectors
- Replies:
**4** - Views:
**2427**

### Re: Linear Algebra: Basis of Eigenvectors

This proof still doesn't quite seem suited for my students considering they know nothing about roots of unity yet, but it's something to fall back on at least. That is a problem. To `convince' your students you can do this construction in the cases k=2 and k=4, where they will be familiar with the ...

- Sat May 14, 2011 1:27 pm UTC
- Forum: Mathematics
- Topic: Linear Algebra: Basis of Eigenvectors
- Replies:
**4** - Views:
**2427**

### Re: Linear Algebra: Basis of Eigenvectors

Agree with your claim. It is true for isomorphisms from C n to C n . Two points: 1) If pressed to prove this quickly, I would cop out, and put f in its Jordan canonical form, and show that if the off-diagonal part is not all-zeros, then the off-diagonal part won't vanish for any power of f either. 2...

- Thu Apr 28, 2011 6:32 pm UTC
- Forum: Mathematics
- Topic: Übernions
- Replies:
**3** - Views:
**1371**

### Re: Übernions

What's nice about quaternions and octonions (and real/complex numbers) is they are Division algebras . I am a little bit disturbed by that Wikipedia article. When I was in graduate school anything called an 'algebra' was automatically assumed to be a ring, i.e. both associative and to have a multip...

- Tue Apr 26, 2011 12:14 pm UTC
- Forum: Mathematics
- Topic: Jordan Normal Form
- Replies:
**7** - Views:
**1867**

### Re: Jordan Normal Form

@OP: Surely somewhere in your lecture notes/textbook there is an example showing what to do, when the characteristic polynomial has a multiple root, but there aren't enough linearly independent eigenvectors? That piece of the theory seems to have hit you full force.

- Wed Apr 20, 2011 10:30 am UTC
- Forum: Mathematics
- Topic: WTF measureable sets.
- Replies:
**4** - Views:
**1751**

### Re: WTF measureable sets.

So we get something like |(G x H)\(U x V)| = |G\U x H| \cup |G x H\V| < e1*e2=e. Exactly how did you get that |G\U x H| would be small? For all we know H could be a huge set. It might have, like, infinite measure. So even if G\U has a very small outer measure, the product set (G\U) x H might not?

- Mon Apr 18, 2011 10:23 am UTC
- Forum: Mathematics
- Topic: Guess numbers by knowing their sum and product
- Replies:
**11** - Views:
**1836**

### Re: Guess numbers by knowing their sum and product

Well. Without any extraneous information we obviously need 4 questions. If the numbers are a,b,c,d, then knowing these numbers is equivalent to knowing the polynomial (x-a)(x-b)(x-c)(x-d)=x^4-s_1x^3+s_2x^2-s_3x+s_4, where the coefficients are the basic symmetric polyn...

- Fri Apr 15, 2011 1:40 pm UTC
- Forum: Mathematics
- Topic: Economics: Integrated cost?
- Replies:
**9** - Views:
**1447**

### Re: Economics: Integrated cost?

But please answer the question posed by MartianInvader! What are your units? Assume that the x-axis is "quantity" measured in "widgets". Then the marginal cost is measured in units "dollars/widget", the total cost is measured in "dollars". So the IC (the area ...

- Thu Apr 14, 2011 1:50 pm UTC
- Forum: Mathematics
- Topic: Reconstructing a signal from its discrete fourier transform
- Replies:
**7** - Views:
**4536**

### Re: Reconstructing a signal from its discrete fourier transf

I managed to reproduce your figures with Mathematica. I think that the following is the root source of your problem. Your sampling window does not span an integer multiple of the wavelength! You may think that it covers exactly 10 periods of the signal with 20 samples from each period. But if you lo...

- Tue Apr 12, 2011 12:50 pm UTC
- Forum: Mathematics
- Topic: Reconstructing a signal from its discrete fourier transform
- Replies:
**7** - Views:
**4536**

### Re: Reconstructing a signal from its discrete fourier transf

Without knowing exactly what kind of a DFT you did it is hard to tell, what went wrong. Is the sign of the phase wrong? Is the phase off by an integer multiple of Pi/2? A combination of the two? The real part of the complex exponential is the cosine wave as opposed to the sine wave. Does your phase ...

- Tue Apr 12, 2011 4:14 am UTC
- Forum: Mathematics
- Topic: Math discovered or invented?
- Replies:
**110** - Views:
**16909**

### Re: Math discovered or invented?

My question to you all is, what do you consider mathematics? Ah. The age old question popped up again! No matter how hard you try, the most concise answer to that question ever given is "Mathematics is what mathematicians do". And, no. Don't start complaining about a circular definition, ...

- Thu Apr 07, 2011 4:09 pm UTC
- Forum: Mathematics
- Topic: Would this ever end? (infinities)
- Replies:
**6** - Views:
**1132**

### Re: Would this ever end? (infinities)

I'm feeling grumpy, so... Since this is a program I say that it is certain to terminate. After all, the integer range is finite. If it's 16-bit integers, then after 32767 we loop down to -32768. Therefore the program gets a fresh chance to hit zero after about every 65536/9 iterations. With 32-bit i...

- Mon Apr 04, 2011 9:13 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0881: "Probability"
- Replies:
**326** - Views:
**104282**

### Re: 0881: "Probability"

The solid line is the survival/non relapse percentage by time. The dashed line is likely a histogram of relapses/deaths by time since being considered "clear" of the initial cancer. This is probably right. My first thought was that the dashed line is a bell curve drawn on top (as in "...

- Mon Mar 28, 2011 11:08 am UTC
- Forum: Mathematics
- Topic: Finite group extensions
- Replies:
**37** - Views:
**3776**

### Re: Finite group extensions

I will say it again: in *group theory*, it is my way round. In topology, for example, it is the other. There isn't a single group theory text or group theorist that would ever put it the other way round. I hate to use proof by authority, but I know many of the world's group theorists, and they will...