## Search found 2674 matches

- Wed Jul 23, 2008 6:12 am UTC
- Forum: Mathematics
- Topic: Calculus of finite ratios?
- Replies:
**8** - Views:
**1321**

### Re: Calculus of finite ratios?

The general case you're trying for, I think, is where you have an operation G(f)(x) := g(f(x), f(x+1)) for some bivariate function g, and you know that for some integer n, G n (f) is a constant function over the natural numbers. In theory, you can work backwa...

- Tue Jul 22, 2008 2:14 am UTC
- Forum: Mathematics
- Topic: Calculus of finite ratios?
- Replies:
**8** - Views:
**1321**

### Re: Calculus of finite ratios?

You're still only describing a single family of functions, which looks like some kind of nested exponentials (something like \exp(a_0 x + \exp(a_1 x + \ldots)) or worse, I think), the problem being that this isn't a family of functions that is used much in practice, whereas polynomia...

- Tue Jul 22, 2008 1:00 am UTC
- Forum: Logic Puzzles
- Topic: Deal or no deal
- Replies:
**80** - Views:
**17294**

### Re: Deal or no deal

I had a friend who worked up an algorithm that could guess fairly well what the banker would offer as a CS project. I think the Banker uses a "guess" at the personal utility function they expect the average person in the demographic they use is, and then always lowball this value to get t...

- Tue Jul 22, 2008 12:40 am UTC
- Forum: Mathematics
- Topic: Differential Equations question
- Replies:
**8** - Views:
**1388**

### Re: Differential Equations question

That looks a lot better to me.

- Tue Jul 22, 2008 12:19 am UTC
- Forum: Mathematics
- Topic: Differential Equations question
- Replies:
**8** - Views:
**1388**

### Re: Differential Equations question

I don't follow your very first step. Maybe it's because you haven't included enough parentheses? If the original eqn is xy' = (y/x) + [sqrt(x^2 + y^2)]/x then isn't y' = y/x^2 + sqrt[(1/x^2) + (y/x^2)^2] ? No, his reasoning there is fine: \frac{\sqrt{x^2+y^2}...

- Tue Jul 22, 2008 12:15 am UTC
- Forum: Mathematics
- Topic: Differential Equations question
- Replies:
**8** - Views:
**1388**

### Re: Differential Equations question

ln | sqrt( u^2 + 1 ) + u | = ln | x | + c raise both sides to e to get rid of the ln's, and you get (dropping the absolute values at this point for simplicity): sqrt( u^2 + 1 ) + u = x + c e^(a + b) != e^a + e^b Haven't checked where else there might be a mistake. Quick way to check the two solutio...

- Mon Jul 21, 2008 11:57 pm UTC
- Forum: Mathematics
- Topic: Calculus of finite ratios?
- Replies:
**8** - Views:
**1321**

### Re: Calculus of finite ratios?

If you know something about the form of f(x), then you can work out what kind of relationship consecutive values of the function might have. If f(x) is a polynomial of degree < n, then differencing will give you the relationships between coefficients. If f(x) has an exponential form, then ratios wil...

- Mon Jul 21, 2008 11:24 pm UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0452: "Mission"
- Replies:
**88** - Views:
**18261**

### Re: "Mission" Discussion

I'd just like to take a moment to congratulate the person with IP address 88.68.194.102 (apparently in Germany), for at least managing to be original when vandalising the scone Wikipedia article, unlike the four others who all managed, apparently independently, to think that adding the "1 in 6&...

- Mon Jul 21, 2008 9:12 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0452: "Mission"
- Replies:
**88** - Views:
**18261**

### Re: "Mission" Discussion

Am I the only one that feels this comic is a little half-assed? Maybe Randall is going for a greater theme or story that I'm just not privy to, but this comic just didn't do it for me. I don't know, it seems nice to me to have a comic that isn't going to spark again an over-the-top debate in the fo...

- Mon Jul 21, 2008 6:05 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0245: "Floor Tiles"
- Replies:
**252** - Views:
**68899**

### Re: "Floor Tiles" Discussion

I tend to avoid cracks, but I also prefer to step on the same "type" of ground (same substance, colour, etc.) in multiples of two steps, even better if it's a number with a large power of two as a divisor (so 6 is good, but 12 is better, and 16 is awesome). I do the same thing with stairwe...

- Mon Jul 21, 2008 4:03 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0452: "Mission"
- Replies:
**88** - Views:
**18261**

### Re: "Mission" Discussion

This guy seems to be going from having a lassez-faire attitude to the world, to being completely mad and pastry-obsessed. Not that there's anything wrong with pastry. (And I knew I should have bought those scones half an hour ago so I could make a "Randall get out of my head" line!)

- Fri Jul 18, 2008 6:59 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0451: "Impostor"
- Replies:
**381** - Views:
**105322**

- Fri Jul 18, 2008 4:56 am UTC
- Forum: Mathematics
- Topic: Interesting real number I generated
- Replies:
**9** - Views:
**2265**

### Re: Interesting real number I generated

It does raise an interesting point - given an arbitrary sequence (a_0, a_1, ..) from OEIS and an integer n, does the number \sum_{k=0}^{\infty}{n^{-k}\mbox{mod}{\left(a_k, n\right)}} have any interesting properties, and does it relate to any previously studied real numbers? For sequences lik...

- Fri Jul 18, 2008 1:17 am UTC
- Forum: Logic Puzzles
- Topic: An input/output puzzle thread
- Replies:
**77** - Views:
**6757**

### Re: An input/output puzzle thread

My chemistry definitions are a bit rusty, but didn't the Deuterium/Tritium thing only show, if anything, that our function doesn't just involve atomic #, row, column, and # of electrons? More to the point, we didn't rule out atomic mass, as that (IIRC) is a function of (among other things) neutrons...

- Fri Jul 18, 2008 1:11 am UTC
- Forum: Logic Puzzles
- Topic: Probability puzzle... genetics based
- Replies:
**24** - Views:
**3810**

### Re: Probability puzzle... genetics based

Why doesn't it stay at 50% given that the chance of the children have it shouldn't affect whether he has it or not? Since, the question is whether his chances change or not, and not about the chance of both him and his children having it. This is worded slightly differently depending on whe...

- Fri Jul 18, 2008 12:53 am UTC
- Forum: Logic Puzzles
- Topic: An input/output puzzle thread
- Replies:
**77** - Views:
**6757**

### Re: An input/output puzzle thread

My chemistry definitions are a bit rusty, but didn't the Deuterium/Tritium thing only show, if anything, that our function doesn't just involve atomic #, row, column, and # of electrons? More to the point, we didn't rule out atomic mass, as that (IIRC) is a function of (among other things) neutrons...

- Fri Jul 18, 2008 12:35 am UTC
- Forum: Mathematics
- Topic: Statistics and time series
- Replies:
**4** - Views:
**1306**

### Re: Statistics and time series

The document that basically explains the approach I used when I was doing time series analysis is an Australian Bureau of Statistics publication entitled An Introductory Course on Time Series Analysis . It's mostly concerned with monthly and quarterly series, though, so you'd have to do some work to...

- Thu Jul 17, 2008 3:33 am UTC
- Forum: Mathematics
- Topic: Calculus I homework problem help
- Replies:
**4** - Views:
**1057**

### Re: Calculus I homework problem help

The fact that there is a (presumably local) maximum at f(2) = 1 actually gives you two and a half bits of information: (1) that f(2) = 1 (2) that f'(2) = 0 (2 1/2) that in the neighbourhood of x = 2, f(x) is concave down, implying that f''(2) < 0. Perhaps you missed one or the other? You should end ...

- Wed Jul 16, 2008 5:48 am UTC
- Forum: Mathematics
- Topic: Infinite Series, Quadratic Term in the denominator
- Replies:
**10** - Views:
**2015**

### Re: Infinite Series, Quadratic Term in the denominator

By the way, I took the Ratio Test to check for convergence and it was inconclusive. I am running on the assumption that is convergent since the answer to the Euler series converged absolutely on an exact value. You can use the comparison test to see that your series converges. Each term in your ser...

- Fri Jul 11, 2008 5:15 am UTC
- Forum: Logic Puzzles
- Topic: Logic related puzzle
- Replies:
**10** - Views:
**2218**

### Re: Logic related puzzle

Or maybe it didn't, because on Sunday he had lamb roast.

- Fri Jul 11, 2008 5:03 am UTC
- Forum: Mathematics
- Topic: The Furlong/Farad/Fortnight/Faraday system of units
- Replies:
**4** - Views:
**2507**

### Re: The Furlong/Farad/Fortnight/Faraday system of units

Random832 wrote:According to wikipedia, another version is that c_{0}and G (along with 1/4πε_{0}) are both set to 1 (i.e. [0]) and time, distance, mass, and charge are all the same quantities, with the dimension [1].

True. Which means that, for example, the Sun weighs 1.5 kilometres.

- Fri Jul 11, 2008 1:42 am UTC
- Forum: Mathematics
- Topic: Question About the Pythagorean Theorem
- Replies:
**40** - Views:
**7320**

### Re: Question About the Pythagorean Theorem

I can't help shake the feeling that some of the "proofs" are running around in circles - that the fact that they prove the Pythagorean Theorem is only because they're defined in a system that was designed such that it would hold. For example, the norm and complex number proofs both rely on...

- Fri Jul 11, 2008 1:38 am UTC
- Forum: Mathematics
- Topic: The Furlong/Farad/Fortnight/Faraday system of units
- Replies:
**4** - Views:
**2507**

### Re: The Furlong/Farad/Fortnight/Faraday system of units

The general idea is a form of dimensional analysis - to be able to convert from one system to another, they need to be of the same dimension. So for example, in general relativity one often works in "geometric units", where the main dimensions are length (generally in metres, but you could...

- Thu Jul 10, 2008 3:35 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0447: "Too Old For This Shit"
- Replies:
**95** - Views:
**19493**

### Re: "Too Old For This Shit" Discussion

You want to talk about basics, then start telling me about pseudocode, documentation, design and analysis, test beds, thorough testing, error control and handling, abstraction - none of these things are tied to a particular technology. In the context of the above, yes, knowledge of any given langua...

- Wed Jul 09, 2008 4:04 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0446: "In Popular Culture"
- Replies:
**144** - Views:
**43826**

### Re: In Popular Culture Discussion

Looks like Randall's admitted his mistake.

- Wed Jul 09, 2008 3:21 am UTC
- Forum: Mathematics
- Topic: Linear problem.
- Replies:
**6** - Views:
**1455**

### Re: Linear problem.

Hint 1:

As you've proven (since the set doesn't contain the origin), the set cannot be a vector subspace of R^4, so its span is bigger than itself.

Hint 2:

(dim span S = 4) iff (S = R^4) iff (the standard basis vectors of R^4 can be written as linear sums of elements of S)

As you've proven (since the set doesn't contain the origin), the set cannot be a vector subspace of R^4, so its span is bigger than itself.

Hint 2:

(dim span S = 4) iff (S = R^4) iff (the standard basis vectors of R^4 can be written as linear sums of elements of S)

- Tue Jul 08, 2008 4:11 am UTC
- Forum: Logic Puzzles
- Topic: 2 + 2 = 5
- Replies:
**175** - Views:
**54554**

### Re: 2 + 2 = 5

phlip wrote:Doesn't INT() round down in BASIC? Try setting X to 2.9 instead.[/pedantry]

Good point, although then I could just set X to 2.5, and remove the INT around X + X, thus perfecting the statement given above that it's true "for sufficiently large values of 2".

- Mon Jul 07, 2008 7:23 am UTC
- Forum: Logic Puzzles
- Topic: 2 + 2 = 5
- Replies:
**175** - Views:
**54554**

### Re: 2 + 2 = 5

Apologies for BASIC code - translate to the programming language of your choice.

10 LET X = 2.4

20 PRINT INT(X); " + "; INT(X); " = "; INT(X + X)

RUN

10 LET X = 2.4

20 PRINT INT(X); " + "; INT(X); " = "; INT(X + X)

RUN

- Sun Jul 06, 2008 7:01 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0445: "I Am Not Good with Boomerangs"
- Replies:
**132** - Views:
**40555**

- Fri Jul 04, 2008 4:26 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0445: "I Am Not Good with Boomerangs"
- Replies:
**132** - Views:
**40555**

### Re: "I Am Not Good with Boomerangs" discussion

Try reading the comic from every possible direction for extra laughs. Top left to bottom right is pretty surreal... The columns each tell an interesting story - the 1st one is about the frustration of a man who keeps throwing boomerangs, but never gets them to return. The 4th, as Randall suggests, ...

- Wed Jul 02, 2008 1:23 am UTC
- Forum: Mathematics
- Topic: Neural network x^2 equivalent
- Replies:
**11** - Views:
**2038**

### Re: Neural network x^2 equivalent

Given 'enough' nodes, a sigmoid neural network with a single hidden layer can approximate any continuous function Theorem 2.3.1: http://www.sztaki.hu/~csaji/CsBCs_MSc.pdf Of course, this doesnt necessarily mean that a neural network is the best way to do it. For the specific case of x^2, why not tr...

- Tue Jul 01, 2008 5:19 am UTC
- Forum: Mathematics
- Topic: Your Axiom of Choice is SILLY
- Replies:
**60** - Views:
**8469**

### Re: Your Axiom of Choice is SILLY

Correct me if I'm wrong (and I almost certainly am), but isn't "the product of a countable number of non-empty sets is non-empty" also provable in ZF? It's only when you get to "the product of an uncountable number of non-empty sets is non-empty" that you need choice ... or so my...

- Wed Jun 25, 2008 7:45 am UTC
- Forum: Science
- Topic: The Ten Commandments
- Replies:
**15** - Views:
**2786**

### Re: The Ten Commandments

I assume you mean "such that the product of the uncertainties in measurement are less than [math]\frac{\hbar}{2}[/math]".

- Wed Jun 25, 2008 7:22 am UTC
- Forum: Individual XKCD Comic Threads
- Topic: 0439: "Thinking Ahead"
- Replies:
**164** - Views:
**27409**

### Re: "Thinking Ahead" Discussion

A little late, but here's the alternative take on the strip: That's Journal Girl, engaging in her own brand of nerd sniping before going out on her date with Black Hat Guy. After all, he beat her at the "land mines in the driveway" trick, so she needed to build up a little confidence. This...

- Mon Jun 23, 2008 3:05 am UTC
- Forum: Mathematics
- Topic: Geohashing help - finding correlation
- Replies:
**4** - Views:
**1204**

### Re: Geohashing help - finding correlation

Presumably an ordinary least squares regression on the two variables separately. You can do it in Microsoft Excel, if you know what functions to use (I don't use Excel any more, so I don't know what functions they might be, but a quick look in OpenOffice Calc gives INTERCEPT and SLOPE).

- Mon Jun 23, 2008 2:59 am UTC
- Forum: Mathematics
- Topic: Cosine for x?
- Replies:
**17** - Views:
**2756**

### Re: Cosine for x?

OK, I've thought of a method that uses numerical integration. I'm not 100% convinced of its accuracy, but here goes: First, assume that x \in (0, \pi/2) , and if it isn't then use modulus as described earlier (0 and \pi/2 are degenerate cases that you can test for and give exact solutions fo...

- Mon Jun 23, 2008 2:23 am UTC
- Forum: Mathematics
- Topic: Cosine for x?
- Replies:
**17** - Views:
**2756**

### Re: Cosine for x?

I can't help but think that there'd be some sort of trick using the fact that sin and cos are (up to a sign factor) derivatives of each other. So if you had 1st order approximations for each, you could feed those into each other to give quickly-converging 2nd order approximations for both. My brain ...

- Wed Jun 18, 2008 5:19 am UTC
- Forum: Mathematics
- Topic: Basic statistics problem
- Replies:
**6** - Views:
**1462**

### Re: Basic statistics problem

You won't get anywhere just using 68/95/99.7, because that's not fine-grained enough. In this case, the 68/95/99.7 rule is enough. In most cases, you would be right. To give a little more detail, the 68/95/99.7 rule is based on a symmetrical interval - e.g. the interval from two sd's below the mean...

- Wed Jun 18, 2008 5:16 am UTC
- Forum: Mathematics
- Topic: Probability question...
- Replies:
**5** - Views:
**1476**

### Re: Probability question...

Take your solution for (b), and first note that E(T) doesn't change when N = lambda is a constant rather than a random variable. However, what happens to V(T)?

- Sat Jun 14, 2008 1:13 pm UTC
- Forum: Mathematics
- Topic: ln(x) = x
- Replies:
**16** - Views:
**3217**

### Re: ln(x) = x

If you have an equation with a repellor solution, you can often[1] transform it to another equation with the same solution, but where it is an attractor. Does iterating arcos(log(x)) give you the correct solution? [1] Sadly, I can't remember of often actually means "always", and I can't re...