## Search found 133 matches

Fri Aug 19, 2011 12:55 am UTC
Forum: Logic Puzzles
Topic: Looking for hard and rare logic puzzles
Replies: 60
Views: 20602

### Re: Looking for hard and rare logic puzzles

I am thinking of a function f:ℝ→ℝ. You pick a real number c and I tell you the value of my function for all x except for c. You must guess f(c). What strategy can you use to maximize your probability of being right, and what is that maximal probability? Everyone so far has been somewhat restrained ...
Tue Aug 09, 2011 10:55 pm UTC
Forum: News & Articles
Topic: Tottenham Riots
Replies: 261
Views: 32740

### Re: Tottenham Riots

London has calmed down tonight (touch wood). I went home through Camden, scene of one of last night's riots, and it was *almost* like a normal day - except that half the shops were pre-emptively boarded over and there was a very noticeable police presence. Considerably better than rampaging looters,...
Tue Aug 09, 2011 12:09 am UTC
Forum: News & Articles
Topic: Tottenham Riots
Replies: 261
Views: 32740

### Re: Tottenham Riots

I am in London and reading reports in twitter that the riots are getting closer and closer by the hour. Never thought I would see this!
Wed May 25, 2011 9:42 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 0903: "Extended Mind"
Replies: 666
Views: 185077

### Re: 0903: "Extended Mind"

Like everyone else, I decided to try this out. Thought I'd start with something a bit obscure and mathematical and plumped for Supertask.

The resulting chain:
Sun Sep 12, 2010 9:32 pm UTC
Forum: News & Articles
Topic: Cambridge University at no. 1 in world ranking.
Replies: 48
Views: 5758

### Re: Cambridge University at no. 1 in world ranking.

Mumpy wrote:Also, Cambridge, really? Pfffffffffffffft, not even, they don't even have a physics undergrad course.

Cambridge does have a physics undergrad course - it's called "mathematics"
Thu May 20, 2010 11:01 pm UTC
Forum: Mathematics
Topic: Having trouble understanding Topology
Replies: 6
Views: 2833

### Re: Having trouble understanding Topology

The thing about topology is that the features that make it good are also the features that make it hard to grasp. As the previous posters said, topology lets us talk about things being "close" even when it's impossible to define distance in any sensible way - which is automatically non-int...
Thu Feb 25, 2010 11:05 pm UTC
Forum: Mathematics
Topic: Wrong on the Internet: John Gabriel
Replies: 185
Views: 66316

### Re: Wrong on the Internet: John Gabriel

Those knols were fantastic, the cheese was literally burning me. I particularly enjoyed "go away and study it for a day. Welcome back, did you get the right answer?" and the section on the fundamental theorem of calculus. It was worth studying maths just to be able to appreciate the humour...
Fri Dec 18, 2009 10:13 pm UTC
Forum: Movies and TV Shows
Topic: Avatar: the most heavily promoted film since I-don't-know...
Replies: 686
Views: 81210

### Re: Avatar: the most heavily promoted film since I-don't-know...

Just saw this film yesterday. As everyone has noted the story is cheesy, derivative, preachy and predictable. But who cares? Go see it anyway. It's definitely the most cinematic thing I've ever seen on a screen, and one of the most entertaining as well. Just for god's sake make sure you see it in 3D...
Wed Nov 04, 2009 3:55 pm UTC
Forum: Mathematics
Topic: Fancy Arithmetic
Replies: 11
Views: 1512

### Re: Fancy Arithmetic

I certainly wouldn't go back to square one because you don't have distributivity. That would be like saying "Rats, not all groups are Abelian, might as well quit!" I recently took a course on something called "additive combinatorics" in which sums and products of sets are heavily...
Wed Nov 04, 2009 1:09 pm UTC
Forum: Mathematics
Topic: Vector spaces, subspace test, and the zero vector
Replies: 8
Views: 1825

### Re: Vector spaces, subspace test, and the zero vector

Here's an example where it's not obvious that the set is empty We'll look at the vector space R 3 . Now let S be the set span<\{ (a,b,c) : \quad a,b,c \in \mathbb{Z}, \quad a,b,c > 0 \quad \exists n > 2 \quad s.t. \quad a^{n} + b^{n} = c^{n} \}> In other words, any linear combination* of sol...
Tue Nov 03, 2009 10:31 pm UTC
Forum: Mathematics
Topic: Hyperbolic tangents ate my variable! [SOLVED]
Replies: 6
Views: 1008

### Re: Hyperbolic tangents ate my variable!

If you're hoping to rearrange the equation into something of the form y = f(x) then I can show that it can't be done: Note that tanh is an odd function, in that tanh(-x) = -tanh(x). From this it very quickly follows that if (x 0 ,y 0 ) solves your equation, then so does (x 0 ,-y 0 ). That means that...
Tue Nov 03, 2009 8:05 pm UTC
Forum: Mathematics
Topic: Hyperbolic tangents ate my variable! [SOLVED]
Replies: 6
Views: 1008

### Re: Hyperbolic tangents ate my variable!

EDIT:

Do you have to find y as a function of x in order to be able to plot?

(is this homework?)
Tue Nov 03, 2009 7:32 pm UTC
Forum: Logic Puzzles
Topic: What do these words have in common?
Replies: 97
Views: 8992

### Re: What do these words have in common?

Cosmologicon: (not really a spoiler, just two lists of words) IN: escape, hot, tall, wintry, Jobs, qwantz OUT: elope, cold, short, balmy, Gates, xkcd Assuming this is right, (a) I'm delighted because I normally fail hard at this kind of thing, and (b) I'd be curious to know h...
Thu Oct 22, 2009 11:36 am UTC
Forum: Mathematics
Topic: Blindly sharing out a cake.
Replies: 5
Views: 836

### Re: Blindly sharing out a cake.

This will always distribute the cake unfairly. You can see this because when the first person turns up, they will already have their fair share, and then the next time they take cake they will have more cake than they should. On the other hand, without doing any maths at all, if we assume that the o...
Sun Oct 18, 2009 2:08 pm UTC
Forum: Mathematics
Topic: Limit Superior
Replies: 4
Views: 1574

### Re: Limit Superior

In reply to your earlier question about the sequence you invented, you are correct that there is no real number y such that lim sup x n = y Depending on your approach you can either say that the lim sup is undefined or that it is -\infty . With reference to the "second" definition of the l...
Wed May 27, 2009 2:04 am UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 2985

### Re: A question about random walks

Well, we can't reach 0 without first hitting 1. So in fact, P(hit 0 starting from 2) = P(hit 1 starting from 2)*P(hit 0 starting from 1) I don't trust this reasoning. The events aren't independent. You're probably right to be suspicious, but in fact they are. This is a consequence of the so-called ...
Tue May 26, 2009 11:40 pm UTC
Forum: Mathematics
Topic: A question about random walks
Replies: 33
Views: 2985

### Re: A question about random walks

Unless I've wildly misunderstood, I'm sure there's a much simpler analysis possible here. Let P be the probability of hitting 0, starting from 1. Then by conditioning on the first move, we have the following equation: P = q + p * P(hit 0 starting from 2) But what is P(hit 0 starting from 2)? Well, w...
Thu Jan 29, 2009 4:00 pm UTC
Forum: Mathematics
Topic: Massively Collaborative Mathematics
Replies: 20
Views: 2223

### Re: Massively Collaborative Mathematics

If I were to hazard a guess, I'd say it might be on computational complexity (but not something ridiculous like P != NP) This is on the basis that: The problems in this area are often understandable without PhD-level expertise. He's about to lecture a non-examinable graduate course on computational ...
Tue Jan 27, 2009 10:18 pm UTC
Forum: Mathematics
Topic: Interesting sequences (Catalan, maybe?)
Replies: 42
Views: 3430

### Re: Interesting sequences

It's very well-known, but you could look at the sequence. 1, 1/4, 1/9, 1/16, 1/25, ... And show that it sums to pi 2 /6 There is loads of history behind this problem so there's plenty to discuss that's of interest to a casual audience. In my opinion, the nicest proof of this uses Fourier analysis, b...
Thu Jan 22, 2009 4:29 pm UTC
Forum: Mathematics
Topic: Stats homework question
Replies: 4
Views: 778

### Re: Stats homework question

Both wrong! OP, you've found Pr(crashed in Sisk AND not found in Sisk), when you want Pr(crashed in Sisk GIVEN not found in Sisk) For this you need Bayes' Theorem. Joe, right start but your calculation of Pr(not found in Sisk) is wrong. You write P(~f) = P(~f|~c) + P(~f|c)P(~f) = 0 + 0.25 when in fa...
Wed Dec 03, 2008 5:26 pm UTC
Forum: Mathematics
Topic: Theorems named after the wrong people
Replies: 21
Views: 8755

### Re: Theorems named after the wrong people

In the 17th century, James Gregory also worked in this area and published several Maclaurin series. It was not until 1715 however that a general method for constructing these series for all functions for which they exist was finally provided by Brook Taylor, after whom the series are now named. Con...
Wed Oct 29, 2008 7:44 pm UTC
Forum: Mathematics
Topic: Proving a sequence problem
Replies: 5
Views: 1108

### Re: Proving a sequence problem

This happens to be identical to the problem of finding the chromatic polynomial of a cycle graph . If you know some graph theory then you should be able to prove that formula (which is correct!) using those ideas. To finish Lul Thyme's proof (assuming it's correct), all you need to do is to show tha...
Fri Jun 13, 2008 11:04 pm UTC
Forum: Logic Puzzles
Topic: Deal or no deal
Replies: 80
Views: 17623

### Re: Deal or no deal?

There is an incredibly detailed analysis of deal or no deal in this paper . One small part of the paper is a study of the distribution of banker's offers. In the versions of the game they analysed (US, Dutch and German), the banker's offer starts miles off the expected value and gets closer and clos...
Tue Jun 10, 2008 11:22 am UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3113

### Re: Infinite Dimensional Hypersphere

A flat 3-sphere can be seen as the interior of a flat 2-sphere with opposite points on the surface defined as being identical. Whats more, a flat 2-sphere can be seen as the interior of a flat 1-sphere (a circle) with opposite points on the perimeter defined as identical. If you say that some of th...
Tue Jun 10, 2008 10:32 am UTC
Forum: Mathematics
Topic: Infinite Dimensional Hypersphere
Replies: 26
Views: 3113

### Re: Infinite Dimensional Hypersphere

The closed unit ball of \ell^2 (or indeed any infinite dimensional normed space) is non-compact. Is that enough for there to be no uniform probability measure on it? Intuitively I can't see how there can be a uniform measure on a non-relatively compact set, but as has been pointed out, trying to th...
Sun Jun 08, 2008 9:42 pm UTC
Forum: Mathematics
Topic: Theorems named after the wrong people
Replies: 21
Views: 8755

### Theorems named after the wrong people

I always think it's a great honour to have a theorem named after you. Your name gets to be associated forever with something that is immutable and true - this is, in my opinion, pretty cool. However, mathematicians have a habit of naming theorems after the wrong people. Example: Taylor's theorem - n...
Sun Jun 08, 2008 8:42 pm UTC
Forum: Mathematics
Topic: Your Axiom of Choice is SILLY
Replies: 60
Views: 8826

### Re: Your Axiom of Choice is SILLY

Fact: for a very long time I thought it was called the axiom of choice because everyone got to choose whether or not they thought it was true.

Of course, now I realise that it simply *is* true and that's all there is to it!
</religious beliefs>
Sun Jun 08, 2008 4:21 pm UTC
Forum: Mathematics
Topic: Your Axiom of Choice is SILLY
Replies: 60
Views: 8826

### Re: Your Axiom of Choice is SILLY

*snip* Not once in that article are there any references to attempted proofs of this "axiom", which I find astounding. Thus, I attempt to do so now: Everyone knows that the size of a Cartesian product is the product of the size of the sets in the product, right? I shouldn't need to prove ...
Tue Jun 03, 2008 9:39 pm UTC
Forum: Mathematics
Topic: Combining estimated probabilities
Replies: 10
Views: 1466

### Re: Combining estimated probabilities

This is a wishy washy "solution" which eliminates the above inconsistency. Also to me it feels intuitively right. Imagine that Nick and Eliezer both got their estimates from some sort of sample of 100 trials. In Nick's trials, he had the bill 15 times and Eliezer had it 85 times. In Elieze...
Tue Jun 03, 2008 7:06 pm UTC
Forum: News & Articles
Topic: Rachel Ray's bad fashion sense linked to terrorism
Replies: 50
Views: 5716

### Re: Rachel Ray's bad fashion sense linked to terrorism

Whoa - methane isn't _created_ by beef - well, it is, but I assume you're talking about it in terms of global warming, which means you're thinking of it in terms of atmospheric carbon. A cow cannot put any more carbon into the atmosphere than the plants it eats took out of the atmosphere (in the fo...
Sun Jun 01, 2008 2:05 pm UTC
Forum: Logic Puzzles
Topic: Triathalon of the titans (solutions)
Replies: 3
Views: 1864

### Re: Triathalon of the titans (solutions)

The first bit: f(n) = (n + 1)/(3n - 1) Now, regrettably, I must revise instead of ploughing ahead. If you're interested, I noticed that the terms were a decreasing sequence. Naturally (being an analyst) I assumed they approached a limit, looked at the large term that you gave and guessed the limit w...
Thu May 29, 2008 12:52 pm UTC
Forum: Mathematics
Topic: A Matter of Steam-Powered Math
Replies: 29
Views: 3136

### Re: A Matter of Steam-Powered Math

For any normal chunk of mass, we can say it is made up of fermions. Now you might argue with me about whether the uncertainty principle applies (I would say it does, and that it disallows zero volume), but the Pauli exclusion principle would most definitely apply to a hypothetical zero-volume chunk...
Wed May 28, 2008 8:06 pm UTC
Forum: Mathematics
Topic: A Matter of Steam-Powered Math
Replies: 29
Views: 3136

### Re: A Matter of Steam-Powered Math

It's clear that there can't be a definition of volume in QM in the standard sense. For a "normal" shape/object, the volume is (mathematically) defined to be the measure of the set of points that are part of the object. (A measure in 3-dimensional space is a real-valued function on (some) s...
Wed May 07, 2008 2:57 pm UTC
Forum: Logic Puzzles
Topic: Getting your fair share
Replies: 49
Views: 10737

### Re: Getting your fair share

The following is a solution which works for an arbitrary number of people and doesn't assume a long cake or incremental cutting ability. This solution assures that each person has the ability to act such that he gets a fair share of cake, no matter how all of the other people choose to act. For n p...
Mon May 05, 2008 9:14 am UTC
Forum: Mathematics
Topic: Linear Algebra
Replies: 5
Views: 1243

### Re: Linear Algebra

Great! Enjoy

Wasn't sure whether your course was more computational or more pure in style.
Mon May 05, 2008 8:28 am UTC
Forum: Mathematics
Topic: Linear Algebra
Replies: 5
Views: 1243

### Re: Linear Algebra

Try here (maybe too advanced based on what you're saying) http://www.dpmms.cam.ac.uk/site2002/Teaching/IB/LinearAlgebra/ or A1b-A1d from here (especially c and d) http://www.damtp.cam.ac.uk/user/examples/ The exercises in the first link are substantially more advanced, I recommend looking at the sec...
Fri Apr 25, 2008 2:37 pm UTC
Forum: Logic Puzzles
Topic: Nails and String [solutions]
Replies: 24
Views: 5547

### Re: Nails and String [solutions]

rhino: Your solution doesn't work. EDIT: May have misread skeptical's drawing. And yes, I tested this, assuming you accept some incredibly liberal definitions of "picture", "nail", and "string". True! Hmm. Skep: not sure what you mean by "loop around the other n-2...
Fri Apr 25, 2008 2:03 pm UTC
Forum: Logic Puzzles
Topic: Nails and String
Replies: 11
Views: 6150

### Re: Nails and String

Here is my understanding of the problem: Version 1: Wrap the string around 2 nails in such a way that the picture hangs, but removing either nail causes the picture to fall to the ground. Version 2: Wrap the string around 3 nails in such a way that the picture will not hit the ground if only one nai...
Fri Apr 25, 2008 11:57 am UTC
Forum: Logic Puzzles
Topic: Nails and String [solutions]
Replies: 24
Views: 5547

### Re: Nails and String [solutions]

For the easiest case: http://img218.imageshack.us/img218/2162/nailsnstringhr1.gif PS: behold my phenomenal MS Paint skills! Edit: also, I think this is a really interesting problem. Completely stuck on all the harder versions though! I expect that the "real maths" will be in or around the ...
Thu Feb 28, 2008 5:57 pm UTC
Forum: Forum Games
Topic: how many kinds of fruit can you list? goal= >100.
Replies: 56
Views: 12089

### Re: how many kinds of fruit can you list? goal= >100.

Cloudberry
Physalis

Physalis are really tasty!
Kinda expensive though.

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