Search found 42 matches

by Cranica
Tue May 01, 2012 4:59 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1049: "Bookshelf"
Replies: 867
Views: 120230

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.
by Cranica
Thu Jan 19, 2012 4:16 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1005: "SOPA"
Replies: 128
Views: 63626

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 ...
by Cranica
Thu Jan 19, 2012 8:02 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1005: "SOPA"
Replies: 128
Views: 63626

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,...
by Cranica
Mon Oct 31, 2011 7:57 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0971: "Alternative Literature"
Replies: 180
Views: 34839

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...
by Cranica
Mon Oct 31, 2011 5:51 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0971: "Alternative Literature"
Replies: 180
Views: 34839

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...
by Cranica
Mon Aug 29, 2011 7:12 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0944: "Hurricane Names"
Replies: 101
Views: 24426

Re: 0944: "Hurricane Names"

Still can't give them finite names if they form a continuum over the earth's surface.
by Cranica
Fri Aug 26, 2011 6:31 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0943: "Empirical"
Replies: 80
Views: 25490

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.
by Cranica
Fri Jul 01, 2011 6:47 pm UTC
Forum: Mathematics
Topic: Sequence of Primes modulo N
Replies: 13
Views: 1874

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...
by Cranica
Fri May 20, 2011 3:32 am UTC
Forum: Mathematics
Topic: Volume of a liquid in a barrel
Replies: 12
Views: 2450

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 ...
by Cranica
Mon May 16, 2011 12:25 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0899: "Number Line"
Replies: 355
Views: 76392

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?
by Cranica
Mon May 16, 2011 5:16 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0899: "Number Line"
Replies: 355
Views: 76392

Re: 899: "Number Line"

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

Protip: they're exactly equal.
by Cranica
Wed Apr 27, 2011 4:06 am UTC
Forum: Mathematics
Topic: Compound Interest
Replies: 14
Views: 2173

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.
by Cranica
Wed Apr 27, 2011 4:04 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0891: "Movie Ages"
Replies: 158
Views: 34944

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.
by Cranica
Tue Apr 26, 2011 2:14 am UTC
Forum: Mathematics
Topic: Maths problems to do over spring break
Replies: 7
Views: 1358

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 8), 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.
by Cranica
Tue Apr 26, 2011 2:06 am UTC
Forum: Mathematics
Topic: Fermat's Little Theorem
Replies: 2
Views: 1025

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 ...
by Cranica
Mon Apr 25, 2011 4:18 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0890: "Etymology"
Replies: 170
Views: 26206

Re: 0890: Etymology

I always chalked this sort of thing up to http://tvtropes.org/pmwiki/pmwiki.php/M ... Convention
by Cranica
Fri Apr 22, 2011 8:19 am UTC
Forum: Mathematics
Topic: Help with a non-integer exponent
Replies: 7
Views: 2050

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?
by Cranica
Thu Apr 21, 2011 4:59 pm UTC
Forum: Mathematics
Topic: Help with a non-integer exponent
Replies: 7
Views: 2050

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...
by Cranica
Sun Apr 17, 2011 4:33 am UTC
Forum: Mathematics
Topic: Calculus: Mixed Partials different
Replies: 3
Views: 766

Re: Calculus: Mixed Partials different

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

http://en.wikipedia.org/wiki/Mixed_part ... f_symmetry
by Cranica
Sun Apr 17, 2011 2:56 am UTC
Forum: Mathematics
Topic: Assistance with an analytic solution to radical
Replies: 15
Views: 2078

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
by Cranica
Fri Apr 15, 2011 6:50 am UTC
Forum: Mathematics
Topic: I don't get the Riemann hypothesis
Replies: 16
Views: 2981

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...
by Cranica
Fri Apr 15, 2011 6:07 am UTC
Forum: Mathematics
Topic: Random Integer
Replies: 18
Views: 2449

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 ...
by Cranica
Wed Apr 13, 2011 3:15 pm UTC
Forum: Mathematics
Topic: Random Integer
Replies: 18
Views: 2449

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.
by Cranica
Wed Apr 13, 2011 5:53 am UTC
Forum: Mathematics
Topic: Beautiful mathematical pictures (large images!)
Replies: 10
Views: 3031

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 ...
by Cranica
Tue Apr 12, 2011 11:53 pm UTC
Forum: Mathematics
Topic: Beautiful mathematical pictures (large images!)
Replies: 10
Views: 3031

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.
by Cranica
Tue Apr 12, 2011 8:08 pm UTC
Forum: Mathematics
Topic: Beautiful mathematical pictures (large images!)
Replies: 10
Views: 3031

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 ...
by Cranica
Tue Apr 12, 2011 7:18 pm UTC
Forum: Mathematics
Topic: The Facebook Problem
Replies: 6
Views: 1722

Re: The Facebook Problem

Someone get this to Randall to create a pretty picture, stat.
by Cranica
Tue Apr 12, 2011 7:16 pm UTC
Forum: Mathematics
Topic: |i|
Replies: 34
Views: 4757

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...
by Cranica
Tue Apr 12, 2011 7:14 pm UTC
Forum: Mathematics
Topic: Table Seating Problem
Replies: 7
Views: 2460

Re: Table Seating Problem

Yeah, the p-1 case is straightforward, but obviously that doesn't cover all composites.
by Cranica
Tue Apr 12, 2011 9:35 am UTC
Forum: Mathematics
Topic: Substitution
Replies: 18
Views: 2315

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...
by Cranica
Tue Apr 12, 2011 9:33 am UTC
Forum: Mathematics
Topic: Assistance with an analytic solution to radical
Replies: 15
Views: 2078

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 + ...)))...
by Cranica
Tue Apr 12, 2011 7:42 am UTC
Forum: Mathematics
Topic: The Facebook Problem
Replies: 6
Views: 1722

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.
by Cranica
Tue Apr 12, 2011 7:40 am UTC
Forum: Mathematics
Topic: Substitution
Replies: 18
Views: 2315

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...
by Cranica
Tue Apr 12, 2011 7:31 am UTC
Forum: Mathematics
Topic: Assistance with an analytic solution to radical
Replies: 15
Views: 2078

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.
by Cranica
Tue Apr 12, 2011 7:29 am UTC
Forum: Mathematics
Topic: |i|
Replies: 34
Views: 4757

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...
by Cranica
Tue Apr 12, 2011 7:21 am UTC
Forum: Mathematics
Topic: Table Seating Problem
Replies: 7
Views: 2460

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...
by Cranica
Mon Apr 11, 2011 4:01 pm UTC
Forum: Mathematics
Topic: Assistance with an analytic solution to radical
Replies: 15
Views: 2078

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?
by Cranica
Mon Apr 11, 2011 6:18 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0884: "Rogers St."
Replies: 241
Views: 64629

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
by Cranica
Mon Apr 11, 2011 6:12 am UTC
Forum: Individual XKCD Comic Threads
Topic: 0710: "Collatz Conjecture"
Replies: 278
Views: 65464

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...
by Cranica
Mon Apr 11, 2011 3:34 am UTC
Forum: Mathematics
Topic: Solo study - where to go from here?
Replies: 7
Views: 1056

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...

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