8,771 reputation
22040
bio website gottwurfelt.wordpress.com
location San Francisco, CA
age 30
visits member for 4 years, 2 months
seen 3 hours ago

Quantitative analyst and math blogger.


Jul
16
comment Determine which mean is smaller over two non-normal distributions
You want the Mann-Whitney U test: en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U
Jul
16
comment Packing rectangles in a grid
There are good heuristics for packing a car with suitcases. (I don't know what these are, but my father does. I've seen him do it.)
Jun
24
comment Probability that random subspaces intersect
And if $a + b < d$ (for example, two lines in 3-space) this will be zero. The nontrivial case is $a+b = d$.
Jun
11
comment Unexpected approximations which have led to important mathematical discoveries
Not exactly what you're asking, but Noam Elkies has a short explanation of why $\pi^2 \approx 10$: math.harvard.edu/~elkies/Misc/pi10.pdf
Jun
3
comment Using math for interior decorating with lamps
The response to a light stimulus isn't directly proportional to the stimulus. Rather it's proportional to the logarithm of the stimulus - this is the "Weber-Fechner law" (en.wikipedia.org/wiki/Weber%E2%80%93Fechner_law). So maybe work with $\log (a^{-2} + b^{-2} + c^{-2})$. This is both psychophysically more realistic and won't diverge as badly around the lights themselves. In particular you can calculate the average light level in the room, which you couldn't do without the logs.
May
9
awarded  Pundit
Dec
14
comment How many citations to read before convergence?
When you start seeing the same papers over and over again, that's when you're done.
Dec
6
comment How to shuffle a deck of cards?
So now we just need $n^n/n!$ to not be an integer. It's not.
Dec
6
answered How to shuffle a deck of cards?
Nov
28
comment “How long 'til we get there?” Road trip puzzle
US road signs do have text on them, so if there were a town called "Speed Limit" this could theoretically happen.
Nov
27
comment Dividing a range into major and minor divisions
You're welcome! Glad to hear it works - I was pretty much just thinking out loud and didn't do any testing, so I could have said something stupid.
Nov
27
comment “How long 'til we get there?” Road trip puzzle
You might find the ending of Billy Jonas's song "Wichita" to be of interest. Lyrics at billyjonas.com/index.php?page=songs&display=57 .
Nov
27
answered Dividing a range into major and minor divisions
Nov
25
comment Entropy of a binomial distribution
A comment: the entropy of the normal distribution with variance $\sigma^2$ is ${1 \over 2} \log (2\pi e \sigma^2)$, which can be computed by a fairly straightforward integration. Perhaps using Stirling's approximation you can reduce the computation of the entropy of the binomial to this same integral plus some error terms. (I haven't actually tried to do this.)
Sep
21
awarded  Custodian
Sep
4
answered Proving an equality involving compositions of an integer
Sep
4
comment “Rules of thumb” to decide which convergence test is most appropriate
One good rule of thumb is to apply the "easiest" tests first -- so if it looks easy to take the ratio of consecutive terms, take ratios. (This includes if $a_n$ contains factorials, since most of the factors will cancel.) If $a_n$ contains $n$th powers, try the root test first.
Aug
31
answered A couple of asymptotics exercises
Aug
31
comment A couple of asymptotics exercises
You only need it for real $z$. If you're willing to assume that $\Gamma(z)$ is an increasing function (which follows from the definition of $\Gamma$ as an integral) then it will suffice to show that $z! \ge (z+1)^{(z+1)/2}$ for large enough integers $z$. This lower bound is bigger than the previous one by a factor of about $\sqrt{ez}$, which is pretty much negligible. (At some point, if you're going to worry about this sort of thing, you should just throw in the towel and use Stirling.)
Aug
31
answered A couple of asymptotics exercises