/sci/ - Science & Math

>>10241873
Yeah, I agree with you there in both regards.
(But all that talk made me read some Nick Land, which is fun.)

I have a PhD in physics (theory) and Stirner (Der Einzige und sein Eigentum) had a big influence on my thinking.

We can very well discuss such subject, but Christmas day is a bit unpractical.

But anyway, for starters, what's your "personal philosophy"? What do you make of whatever you read and what's your way?

[math] \forall X.\, \emptyset \notin X \to \exists (f:X \to \bigcup X) .\, \forall (A \in X).\, f(A) \in A [/math]

>When did you decide to dedicate your life to science?
Never.
I decided to dedicate my life to myself.

>>7683589
We have

[math]\sum_{n=0}^\infty a_n = \lim_{m \to \infty} \sum_{n=0}^m a_n[/math]

How many people in this thread could give a definition of

[math] \lim_{m \to \infty} \sum_{n=0}^m a_n[/math]?

The deifnition is some string of 30 symbols in first order logic expressing the convergence idea, and this one involves some abbreviations, like the one for the function giving the norm on the field of real numbers.
Only a few of the math majors and a small percentage of the physicists. All of them have learned it at some point, but never needed to use it.

My point is that even the conventional 18th century infinite sum is a complicated object.

>>7683597
The notion of "the limit doesn't exist" is denoted
"[math]\sum_{n=0}^\infty a_n = \infty[/math]"
but that's just notation - The symbol [math]\infty[/math] doesn't represent a number here that could be equal to some expression. That "=" isn't the one in the axiomatization of a real number field, so we could also write
[math] \neg \exists (y \in R).\ \sum_{n=0}^\infty a_n = y[/math]

Now we can write down other theories of a "sum" that assign a value to it. Of course, then you can't use all the properties of "=" in other calculations relating to the old analysis theory.

Infinite Jest - David Foster Wallace

It's sad that /his/ neglects the other humanities so much...

Anyway, yeah, you can't seem to get around the induction principle
(Just like you e.g. can't prove that it's not the case that 10 minutes ago aliens came to us and implemented memories in our brains that do not involve them + that make most people disregard the possibility that aliens just did this manipulation.)

So you adopt the scientific method as a <method> that has been proven useful.

https://en.wikipedia.org/wiki/Problem_of_induction
http://plato.stanford.edu/entries/induction-problem/
http://plato.stanford.edu/entries/rationalism-empiricism/

Also, Feyerabend reminds me of Feynman...
"Fey" \implies student fucker

It's sad that /his/ neglects the other humanities so much...

Anyway, yeah, you can't seem to get around the induction principle (just like you can't possibly prove that it's not the case that aliens came to us 10 minutes ago and implemented memories in our minds that doesn't involve them and make most poeple disregard that the possibility that aliens just did this is real).
So you adopt the scientific method as a <method> that has been proven useful.

https://en.wikipedia.org/wiki/Problem_of_induction
http://plato.stanford.edu/entries/induction-problem/
http://plato.stanford.edu/entries/rationalism-empiricism/