/sci/ - Science & Math

>be a completely different type of unit
you can measure length in time units, just multiply by the speed of light c.

>>8583939
I did my PhD among aerospace engineers and then they all go to Bosch or Daimler (south of Germany, duh) and by now I did "freelance programming" a bunch of times and it appears to me you can't run out of jobs with some basic programming knowledge. That's where my perspective is coming from.

In fact my cross product problem is related to a freelancing job on something like GPS navigation (I always use those work-from-home jobs to write a sort of encyclopedic notebook for when I have to come back to it).

So reporting back on this, I'm somewhat surprised by this finding:

We have
[math] b = M(a,b)\,a [/math]
with
[math] M(a,b) = \frac{1}{||a||}\left[(\frac{a}{||a||}\times b)\times + (\frac{a}{||a||}\cdot b)\, 1_3\right] [/math]
and here, basically, [math] M = W(a,b) + h(a,b)\, 1_3 [/math] and what this does it factoring b into a part [math] h(a,b)\,a [/math] that points into direction a but has length |b|, and some other term [math] W(a,b)\,a [/math].

But this means that given ANY function
[math] f: {\mathbb R}^n \to {\mathbb R}^n [/math]
you can always "factor out" the argument by writing

[math] f(a) = M(a,f(a))\,a [/math]

In one dimension (in a ring), this can only be done via
[math] M(a,f(a)) := \frac{f(a)}{a} [/math]
and this decomposition matrix M above is one generalization of that, one that keeps the linearity.

Well anyway, back to the question if all such maps have to look like that. Well in any case I reminded myself that only in n=3 can we represent rotation generators (skew-symmetric linear maps, for which dim=n(n-1)/2) with a (rotation) vector and the cross product, so I'll fix n=3.

I have two coding jobs - one is for a group at a research facility (muh superconducting qubits experiments) and one "data science" (looking at traffic data and doing statistic).
The first is badly paid (PhD student salary/hour) and the second one is "do it at home and present what you find" (i.e. I don't do shit for the money I get).
I'll quit both jobs eventually, but I'll drop the latter sooner, because I rather spend 5 more hours reading homotopy type theory or whatever papers than having extra money I don't know what to do with. (I'm not so interested in traveling.)
My point is probably that it may seem odd that simple jobs get paid more, but TO BE HONEST the simple coding jobs are relevant and the academics jobs are fapping around with stuff you enjoy. Of course, quantum computers, curing cancer, understanding spread of diseases... blabla. no, those are shills to get grant money. science is masturbation. I already like fapping all day more than looking at actually city statistics to the extent that I rather not get paid. If you were to study in Göttingen (or whatever the American equivalent is), then you're moving to a city with 1/3 student population, parties, fucking around - it's fair that the code monkeys get paid more, and more relevant (and hopefully organized so that those hours are not wasted), while uni is mostly fun and reading cool stuff.

Possibility of a universal Turing machine
Fractal geometry
Random matrices was a cool trick too
Schrödinger equation, Dirac equation, Feynman diagrams
and finally, more mindfuck and more unexpected than Gödel imho:
Riemann zeta function continuation counting primes

>>8324294
Well it's true, I have no reason to make it up.

I was in the Magic the Gathering community, which is comparatively strong in Vienna where I live, and people took it seriously (we went to the UK, Netherlands, Italy, just in the hope to win a few thousand euros at tournaments).
The Poker scene is close to that, a prominent example being
https://en.wikipedia.org/wiki/Jon_Finkel
and everybody could make an online account and if you had enough money you'd play against.. I don't know...Ben Affleck or people like that who do it as a hobby.
So I grew up with at least 10 people who made their living off of poker, starting with 14 and many are about 30 now. It pays okay, but you spend 8h a day in front of a computer and essentially do a machines job, and then there are some real life tournaments from time to time, but you sit in a Casino where there is no distinction between night or day - and all those guys don't have any sort of job experience now and do the same all day.
Upside is that those who are better than other do have some proper money and travel around like it's nothing.