/sci/ - Science & Math

I'd go with Math, but it's kinda of not comparable. Basic needs like wanting to eat, sleep and have sex are sort of orthogonal to cultivated passions.
Is the girl in the the webm really beautiful or is it just that you feel yourself get a hardon from spotting fertility via youthful skin and perky bouncing tits?
I'd could imagine if you ask a young Bob Dylan to either lose his ability to get off of girls or lose the ability to hear and write songs, he'd go with dropping sex. Who are you, and where can you go, if you lose this thing that makes the core path of your life. Or could he imagine to start over in a completely new direction? I may get a few beer with friends at night, knowing it'll help get more talkative with chicks, who have what I need, but when I'm drunk on the dancefloor, watch the scene, I mostly start thinking of math - say because the emerging dance formation of the group naturally opens up questions in the realm of Ramsey theory.
I'd rather never never bang a woman again than not be able to do and read math, because the former is something you repeatedly crave and lose when you come, the second one is something that build on itself and the satisfaction is lasting - not returning like bodily urges.

>>7509906
Here's a more ad hoc way of smoothing than analytical continuation, that leads to the value.

http://www.wolframalpha.com/input/?i=Limit[z%2F%281-z%29^2-1%2FLog[z]^2%2Cz-%3E1]

>>7509864
Purely classically,

<span class="math"> \sum_{k=0}^\infty k [/spoiler]

is the same as the limit of z to 1 of

<span class="math"> \sum_{k=0}^\infty k z^k [/spoiler]

namely undefined (or infinity).

On the other hand, for any |z|<1, you have the expansion

<span class="math"> \sum_{k=0}^\infty k z^k = \frac{z}{(z-1)^2} [/spoiler]

http://www.wolframalpha.com/input/?i=Sum[k+z^k%2C{k%2C0%2CInfinity}]

Now if you define a forward average <span class="math"> \langle f(k) \rangle [/spoiler] of a function via

<span class="math"> \langle f(k) \rangle := \int_{k}^{k+1} f(k') \, dk' [/spoiler]

you might consider

<span class="math"> \sum_{k=0}^\infty ( k z^k - \langle k z^k \rangle ) = \frac {z} {(z-1)^2} - \frac {1} {\log(z)^2} [/spoiler]

Both functions <span class="math"> \frac {z} {(z-1)^2} [/spoiler] and <span class="math"> \frac {1} {\log(z)^2} [/spoiler] are singular at z=1 themselves, but the later is actually growing faster by a slight amount:

Purely classically, -1/12 is only the limit as z approaches 1 value of this,
i.e. the sum, but only "regularized" by subtracting the smooth surroundings.
The limit is in the first link, but you can actually draw the sharply rising graphs of the two and see how the difference close to z=1 remains -1/12.

The original speech is actually available!

You wouldn't believe it, Hilbert has the friendliest voice and a funny accent.

http://math.sfsu.edu/smith/Documents/HilbertRadio/HilbertRadio.mp3

>Wir müssen wissen. Wir werden wissen!
is the end of the speech, at 3:55.

>>6588886
I personally didn't find the haskell.org page too helpful, and the book is an introduction to, and implementation of logic in, Haskell. While I like the clear writing and examples of the book, it is really about classical logic and not cats, types of computation.

>>6588883
donno.

>>6588874
For types and lambda calculus, Simon Thompson "Type Theory & Functional Programming" is nice, and for category theory Goldblatt "Topoi: The Categorial Analysis of Logic" is soft and suitable. The first book is online, the second not, but Awodey "Category theory" is, which is a computer scientist.
The first two steps how the subjects connect is
http://www.alpheccar.org/content/74.html
The beauty that is typed lambda calculus can live without categories, but once you understand the latter, you have many ways to use it to view the former. If you're really mathy, you can then throw away everything but category theory and rediscover language logic and computation within it.
The Haskell founders were not interested in structural math in the above sense, but I very much enjoyed reading this paper on how the specification came about
http://www.scs.stanford.edu/~dbg/readings/haskell-history.pdf

What you wrote is not very concrete. Which major and semester?
If there are some connections you can hardly see but know are there, ask right away.