## Search found 42 matches

- Tue May 01, 2012 4:59 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1049: "Bookshelf"
- Replies:
**867** - Views:
**134746**

### Re: 1049: "Bookshelf"

I've been hurting my head trying to read the last few pages. Might I suggest that those of you interested in ethics debate ethics directly, and not what Rand thought or what Objectivism is? Definitions, especially composite ones, are a nebulous business.

- Thu Jan 19, 2012 4:16 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1005: "SOPA"
- Replies:
**128** - Views:
**67087**

### Re: 1005: "SOPA"

Certainly, userly, we should be doing this sort of thing every time our freedoms are violated against our constitution. Hopefully, we'll remember this come the next time; even if we don't, though, yesterday was a remarkable day for the internet and for the common people of the world as a whole. The ...

- Thu Jan 19, 2012 8:02 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 1005: "SOPA"
- Replies:
**128** - Views:
**67087**

### Re: 1005: "SOPA"

From what I understand, you're not allowed to shut a site down for infringement unless it's your property being infringed. So if "anyone with a grudge" can shut down a site that shares his content, he should explain this, because it's not immediately apparent. In theory, yes. In practice,...

- Mon Oct 31, 2011 7:57 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0971: "Alternative Literature"
- Replies:
**180** - Views:
**39053**

### Re: 0971: "Alternative Literature"

I've been trying to convince my parents about homeopathy for years, they refuse to listen :( ...did you READ the comic before posting it? I'm not one to get all preachy to someone who chooses to use it, for example my friend who has something for anxiousness which is really just all in her head, it...

- Mon Oct 31, 2011 5:51 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0971: "Alternative Literature"
- Replies:
**180** - Views:
**39053**

### 0971: "Alternative Literature"

How has no one posted yet? It's almost 2AM :o http://imgs.xkcd.com/comics/alternative_literature.png Alt text: I just noticed CVS has started stocking homeopathic pills on the same shelves with--and labeled similarly to--their actual medicine. Telling someone who trusts you that you're giving them m...

- Mon Aug 29, 2011 7:12 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0944: "Hurricane Names"
- Replies:
**101** - Views:
**27757**

### Re: 0944: "Hurricane Names"

Still can't give them finite names if they form a continuum over the earth's surface.

- Fri Aug 26, 2011 6:31 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0943: "Empirical"
- Replies:
**80** - Views:
**28110**

### Re: 0943: "Empirical"

scarletmanuka wrote:But how are you going to repeat the experiment, for verifiability? I mean, it could have just been an outlier.

Capability isn't probability - he did it once, so he -can- do it.

- Fri Jul 01, 2011 6:47 pm UTC
- Forum: Mathematics
- Topic: Sequence of Primes modulo N
- Replies:
**13** - Views:
**2063**

### Re: Sequence of Primes modulo N

If they are periodic, the periods would have to be very large, and grow quite rapidly - Dirichlet tells us that any cycle mod p must cycle through all the nonzero residues mod p, so if it's periodic modulo a series of primes p1, p2, p3...pn, then letting x = p1*p2*p3...pn, the period would have to b...

- Fri May 20, 2011 3:32 am UTC
- Forum: Mathematics
- Topic: Volume of a liquid in a barrel
- Replies:
**12** - Views:
**2630**

### Re: Volume of a liquid in a barrel

If it has circular cross-sections and constant thickness of the barrel material itself, by running a tape measure from the bottom of the barrel to the top, then measuring how much down the length of the barrel the measure moves when you retract it one inch along the curve, you should be able to get ...

- Mon May 16, 2011 12:25 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0899: "Number Line"
- Replies:
**355** - Views:
**81721**

### Re: 899: "Number Line"

K^2 wrote:Hm. I was thinking of it more in terms of re-assigning multiplication unit. Defining (Gird-3)*a=a would make new ring isomorphic to integers.

Since that makes Gird-3 a multiplicative identity, wouldn't that just give Gird = 4, since you can only have one mult. identity in a ring?

- Mon May 16, 2011 5:16 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0899: "Number Line"
- Replies:
**355** - Views:
**81721**

### Re: 899: "Number Line"

Oh dear, Randall has reignited the .9999... = 1 debacle.

Protip: they're exactly equal.

Protip: they're exactly equal.

- Wed Apr 27, 2011 4:06 am UTC
- Forum: Mathematics
- Topic: Compound Interest
- Replies:
**14** - Views:
**2331**

### Re: Compound Interest

I suppose one could make the argument that the units in which one measures time would affect it. But yeah, stupid question, since that would in turn change the value of r.

- Wed Apr 27, 2011 4:04 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0891: "Movie Ages"
- Replies:
**158** - Views:
**39794**

### Re: 891: Movie Ages

I could never forget the date of Finding Nemo. It was the only way we could get my (then two-year-old) brother to shut up.

- Tue Apr 26, 2011 2:14 am UTC
- Forum: Mathematics
- Topic: Maths problems to do over spring break
- Replies:
**7** - Views:
**1494**

### Re: Maths problems to do over spring break

3*7 mod 8 is just 5, so you're looking for pairs (x,y) where 5x ~ y (mod , using ~ for congruence. It should be clear, if you've done much modular arithmetic at all, that for any x, there's exactly one congruence class that satisfies that equation.

- Tue Apr 26, 2011 2:06 am UTC
- Forum: Mathematics
- Topic: Fermat's Little Theorem
- Replies:
**2** - Views:
**1057**

### Re: Fermat's Little Theorem

If nothing else, their proof fails because p-1 is not composite for all primes. Not that it's hard to check the p=3 case, but still. Here's the proof my number theory class gave: Suppose p does not divide a - that is, a is nonzero modulo p. Consider the product a*2a*3a...*(p-1)a - that is, take the ...

- Mon Apr 25, 2011 4:18 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0890: "Etymology"
- Replies:
**170** - Views:
**30421**

### Re: 0890: Etymology

I always chalked this sort of thing up to http://tvtropes.org/pmwiki/pmwiki.php/M ... Convention

- Fri Apr 22, 2011 8:19 am UTC
- Forum: Mathematics
- Topic: Help with a non-integer exponent
- Replies:
**7** - Views:
**2195**

### Re: Help with a non-integer exponent

Ah, yeah, good call. @OP, are you looking for approximate numerical solutions or asymptotic behavior as n grows?

- Thu Apr 21, 2011 4:59 pm UTC
- Forum: Mathematics
- Topic: Help with a non-integer exponent
- Replies:
**7** - Views:
**2195**

### Re: Help with a non-integer exponent

Is D rational? If I remember right, a rational base to an irrational power is transcendental (unless f is 0 or 1, but this can be checked easily), so if B and C are algebraic and D is irrational, we have B*f^D is transcendental, so (1-Bf^D)/C is as well, so f^2 would have to be, so f would have to b...

- Sun Apr 17, 2011 4:33 am UTC
- Forum: Mathematics
- Topic: Calculus: Mixed Partials different
- Replies:
**3** - Views:
**825**

### Re: Calculus: Mixed Partials different

In general, they're always equal for well-behaved functions.

http://en.wikipedia.org/wiki/Mixed_part ... f_symmetry

http://en.wikipedia.org/wiki/Mixed_part ... f_symmetry

- Sun Apr 17, 2011 2:56 am UTC
- Forum: Mathematics
- Topic: Assistance with an analytic solution to radical
- Replies:
**15** - Views:
**2316**

### Re: Assistance with an analytic solution to radical

There might very well be no analytic solution known for this - Wolfram claims there's none known for the one below, anyway.

[math]r = \sqrt(1+\sqrt(2+\sqrt(3+\sqrt(4 + ...))))[/math]

http://mathworld.wolfram.com/NestedRadicalConstant.html

[math]r = \sqrt(1+\sqrt(2+\sqrt(3+\sqrt(4 + ...))))[/math]

http://mathworld.wolfram.com/NestedRadicalConstant.html

- Fri Apr 15, 2011 6:50 am UTC
- Forum: Mathematics
- Topic: I don't get the Riemann hypothesis
- Replies:
**16** - Views:
**3179**

### Re: I don't get the Riemann hypothesis

The function's quite messy - I'm quite a few steps ahead of you in terms of classes, but I only loosely understand how it works. To be fair, the fact that the Riemann Hypothesis has remained unproven for so long means that no one fully understands how it works :D The best I can do for you in terms o...

- Fri Apr 15, 2011 6:07 am UTC
- Forum: Mathematics
- Topic: Random Integer
- Replies:
**18** - Views:
**2828**

### Re: Random Integer

It actually is sort of a cardinality thing. You can't ever have a uniform, countably additive distribution on a countable set - the probability of getting each element would have to be a number that, when added to itself countably many times, gives you 1. Of course, no such number exists. It makes ...

- Wed Apr 13, 2011 3:15 pm UTC
- Forum: Mathematics
- Topic: Random Integer
- Replies:
**18** - Views:
**2828**

### Re: Random Integer

That example would work on [0,1], too. Removing any finite set from an infinite one will never get you down to a finite set, but clearly probability on [0,1] (or (0,1)) is well-defined. The issue as I understand it isn't the size of the set, it's that the integers are discrete.

- Wed Apr 13, 2011 5:53 am UTC
- Forum: Mathematics
- Topic: Beautiful mathematical pictures (large images!)
- Replies:
**10** - Views:
**3239**

### Re: Beautiful mathematical pictures (large images!)

Wow, some of those are fascinating - why are there very few 'almost real' algebraics? @squareroot - I was actually thinking more of something like, say, Minecraft. Take a border of the mandelbrot set, and wind it around block by block to create some freaky, freaky terrain. Also, the last picture in ...

- Tue Apr 12, 2011 11:53 pm UTC
- Forum: Mathematics
- Topic: Beautiful mathematical pictures (large images!)
- Replies:
**10** - Views:
**3239**

### Re: Beautiful mathematical pictures (large images!)

Has anyone ever worked on using fractals for procedural generation of, say, terrain? Things like the Mandelbrot set where you see new structures at any zoom seem like interesting candidates.

- Tue Apr 12, 2011 8:08 pm UTC
- Forum: Mathematics
- Topic: Beautiful mathematical pictures (large images!)
- Replies:
**10** - Views:
**3239**

### Beautiful mathematical pictures (large images!)

We all know there's a thousand beautiful proofs out there - but what about literal visual beauty of fractals and the like? To get things started, I present this visualization of the algebraic numbers (via http://en.wikipedia.org/wiki/Algebraic_number) - the size of the dot indicates the size of the ...

- Tue Apr 12, 2011 7:18 pm UTC
- Forum: Mathematics
- Topic: The Facebook Problem
- Replies:
**6** - Views:
**1787**

### Re: The Facebook Problem

Someone get this to Randall to create a pretty picture, stat.

- Tue Apr 12, 2011 7:16 pm UTC
- Forum: Mathematics
- Topic: |i|
- Replies:
**34** - Views:
**5856**

### Re: |i|

I'm not 100% sure, but I seem to remember that for all the proofs where we had to let ||z|| -> infinity we generally did something with considering an arbitrary point on or outside a circle of radius R, and then let R approach infinity. Or something along those lines. "outside a circle of radi...

- Tue Apr 12, 2011 7:14 pm UTC
- Forum: Mathematics
- Topic: Table Seating Problem
- Replies:
**7** - Views:
**2622**

### Re: Table Seating Problem

Yeah, the p-1 case is straightforward, but obviously that doesn't cover all composites.

- Tue Apr 12, 2011 9:35 am UTC
- Forum: Mathematics
- Topic: Substitution
- Replies:
**18** - Views:
**2731**

### Re: Substitution

I find that when teaching the basics of substitution it's best to stick to funny random things that can't be misconstrued. For example when you're working with f(x) = x^2, you could say f(mickey mouse) = (mickey mouse)^2, and draw a picture of mickey mouse. This usually makes people laugh and for s...

- Tue Apr 12, 2011 9:33 am UTC
- Forum: Mathematics
- Topic: Assistance with an analytic solution to radical
- Replies:
**15** - Views:
**2316**

### Re: Assistance with an analytic solution to radical

Yeah, I figured that out in the intervening hours :P I wonder if maybe multiplying it by, say, 2 might help. Then we replace each 2^n term in the radical with 2^(2^n + n), and double the value of the whole radical. So we have 2r = 2*\sqrt(1+\sqrt(2+\sqrt(4+\sqrt(8 + ...)))...

- Tue Apr 12, 2011 7:42 am UTC
- Forum: Mathematics
- Topic: The Facebook Problem
- Replies:
**6** - Views:
**1787**

### Re: The Facebook Problem

So what's the distribution of the sizes of closed groups? I'd imagine they'd tail off roughly exponentially, with larger and larger closed groups becoming steadily less likely. Would be interesting to write some sort of a crawler that tries to find closed groups with public profiles if any exist.

- Tue Apr 12, 2011 7:40 am UTC
- Forum: Mathematics
- Topic: Substitution
- Replies:
**18** - Views:
**2731**

### Re: Substitution

To address the OP's case specifically - I think your problem here is not an issue with the idea of equality so much as with the idea of a variable. If you say "let x=2", I don't think she understands what you mean - your best bet is probably something like "this thing here has a value...

- Tue Apr 12, 2011 7:31 am UTC
- Forum: Mathematics
- Topic: Assistance with an analytic solution to radical
- Replies:
**15** - Views:
**2316**

### Re: Assistance with an analytic solution to radical

Okay, that makes sense. I just didn't see an obvious setup for the convergence of the second radical.

I showed this to a professor earlier and I'm fairly sure it derailed him for the rest of the day - he at least said he'd seen it before, but didn't remember how it was done.

I showed this to a professor earlier and I'm fairly sure it derailed him for the rest of the day - he at least said he'd seen it before, but didn't remember how it was done.

- Tue Apr 12, 2011 7:29 am UTC
- Forum: Mathematics
- Topic: |i|
- Replies:
**34** - Views:
**5856**

### Re: |i|

^For an intuitive notion of "size" that does not match "modulus," consider the 1-norm |z| = Re(z) + Im(z). This isn't any better than just taking the magnitude, though - it's not even a partial order, since |a+bi| = |b+ai| but a+bi != b+ai How so? I distinctively remember a bunc...

- Tue Apr 12, 2011 7:21 am UTC
- Forum: Mathematics
- Topic: Table Seating Problem
- Replies:
**7** - Views:
**2622**

### Re: Table Seating Problem

For n prime, as noted above, arithmetic progressions like the following work to produce a minimal arrangement in (n-1)/2 seatings: 1,2,3...n [note that since the table is circular, n borders 1 here] 1,3,5...n-1 1,4,7...n-2 ... 1,((n-1)/2)+1,n,...(n+1)/2 A pairing between members a and b occurs on th...

- Mon Apr 11, 2011 4:01 pm UTC
- Forum: Mathematics
- Topic: Assistance with an analytic solution to radical
- Replies:
**15** - Views:
**2316**

### Re: Assistance with an analytic solution to radical

I don't know too much about convergence, but how does the second statement in the OP imply that the radical does in fact converge?

- Mon Apr 11, 2011 6:18 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0884: "Rogers St."
- Replies:
**241** - Views:
**71849**

### Re: 0884: "Rogers St."

mric wrote:Does the name 'Mister Rogers' have a particular reference? It seems like a slightly dull but perfectly adequate porn name to me.

I'm going to assume this is a troll and answer anyway.

http://tvtropes.org/pmwiki/pmwiki.php/Main/Ptitledl68mjvj

- Mon Apr 11, 2011 6:12 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0710: "Collatz Conjecture"
- Replies:
**278** - Views:
**71839**

### Re: 0710: "Collatz Conjecture"

What if you could prove that all numbers eventually converge to an integer of the form \frac{2^n - 1}{3} ? All such integers are odd from my experience, meaning the 3n+1 algorithm is applied, leaving a power of 2, which converges to 1. Your experience is correct (2^n - 1 is always odd, and so is (2...

- Mon Apr 11, 2011 3:34 am UTC
- Forum: Mathematics
- Topic: Solo study - where to go from here?
- Replies:
**7** - Views:
**1145**

### Re: Solo study - where to go from here?

Thanks for the suggestions - you weren't kidding about graph theory being relatively obscure, the results for 'firefighter problem' on wikipedia included the International Association of Black Professional Firefighters and Rescue Me . To the complex analysis post - I'm actually not a huge fan of Cal...