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ithinkso

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I don't doubt the results but I cannot imagine how that can be true, I'm not fit but I've had many 20+hours hikes to the high mountain peaks but if I run to a bus stop when I'm late I'm tired beyond belief and I just cannot maintain running, have to stop

This is actually a harmful definition, both (1,1) and (0,2) tensors can be written as a matrix but they are very different. It's like calling vector an array but vectors require vector space and arrays are just arrays. It doesn't help that std::vector is very common in CS but 'pushing back' to a mathematical vector just doesn't make any sense

Although I do agree with your overall sentiment

the problem is "just" gaining traction and having a good plan for moderating The Stuff People On Internet Will Upload. See GitTorrent for another (unrelated) example of a good idea that never gained traction.

maybe there is a reason why github gained traction

Finding a cycle is hard!

I mean, it is easy in the size of the graph, you constructed implicitly an exponentially large graph, I don't think it's in the spirit of GP point where the hamiltonian cycle is exponentially (in the size of the graph) hard to find

The most unique thing about 4-dimensional space imho is that some simple manifolds like e.g R4 have uncountably many differential structures possible, in lower dimensions there is only one, in higher - finitelly many.

When push comes to shove I'm not sure we have enough experimental physicists...

Your 'duh's escalated quite quickly, I had a Euclid postulates feelings when reading it - first four are 'duh' and then the fifth one comes swinging.

(by the way I think you have your Newton's law order wrong, that's the second one you're referering to)

Coffee or tea will taste better to you if you put a lot of work into it.

This is very true but, tangentially, this is the opposite when you make drink/food for others. I found that you get the best effect when you spend a lot of effort to cook and perfect the dish but when asked, you have to pretend you basically winged it and it wasn't a hassle

Matplotlib 3 years ago

Tangential but a thing about defaults - when I was at uni, in a lot of labs we were doing data analysis and plotting in something called Origin. I absolutely loved the defaults there, to this day I can recognize if it was plotted using origin and I had visceral reaction if I'd see something done in Excel. Sane defaults are very important and I'm not sure why they are often afterthoughts

Algebra 3 years ago

If you want the equation

x + 1 = 0

to have a solution, you need to invent negative numbers, now if you want the equation

x^2 + 1 = 0

to have a solution, you need to invent complex numbers and 'i'. (Also, complex numbers, turns out, are enough for higher powers as well)

The line and plane are just convenient representations of R and C but there is nothing inherently profound about them, in my opinion

(The arrow functions iconically: there is an informal logical path from A to B. It does not denote formal implication.)

In other words, how far has one to analyse a claim of the form 'from property A, B follows' before assenting to it depends on the agent.

Or just prove the implication instead of inventing 'informal logical paths'

None of what you said is true except for

Mathematical proof is really just for convincing other mathematicians

which is precisely the point of a proof, but 'convince' means something different than you seem to think it means (in the field of mathematics)

Moreover, mathematicians rarely prove anything from axioms, they start from other statements which are considered more trivial.

Not more trivial but from the ones already proved and those closer to the thing you are proving. There is no need to go back to the axioms if you know, and can reference, proof of step N-1, just go from there.

There is also this 'misconception' that mathematical theorems follow from the axioms. They do, of course, but the axioms were choosen just right to make things that were working to still work, with some weird consequences like axiom of choice

Also, it turns out that this area was already well understood. There are no free lunches with entropy.

If I ever go mad and I breach the 'crankpot line' this will be it. There is something in entropy that I just can't fully grasp even though I understand (or I can convince myself that I do) Shannon, Kolmogorov etc.