π in Other Universes
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π in Other Universes
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Re: π in Other Universes
#2> Mathematics can be seen as a logic game. You start with a set of assumptions and you come up with all the logical conclusions you can from that. Then, if someone else finds a situation that fits those assumptions, they can benefit from the pre-discovered logical conclusions. This means that if some conclusions require fewer assumptions, then those conclusions are more generally applicable
This is a really, really nice expression of something my mind's been hovering around for a while.
Re: π in Other Universes
#3IF I've correctly assesed the zeitgeist of HN postings
THEN it follows Terence Tao's Introduction to Measure Theory must be a bullet.
https://news.ycombinator.com/item?id=38064211
But seriously, who's going to read|skim a free 260+ tract on measure theory?
Re: π in Other Universes
#4Not sure about your universe, but here on earth, pi is 2. The length of the equator is 4 times the distance from the pole. (Approx.)
Re: π in Other Universes
#5I must be missing something. In the example of using a sailboat with constant wind and distance, wouldn’t sailing against the wind (let’s call it any constant oppositional force), cause us to get a circle, just shifted from the origin? Not an ellipsis?
Re: π in Other Universes
#6All of these assume your background metric is Euclidean.
If your background 2D metric is a projection of a warped 3D space, you can make π as big as you want by tugging on the centre of the circle.
Re: π in Other Universes
#7Not sure about your universe, but here on earth, pi is 2. The length of the equator is 4 times the distance from the pole. (Approx.)
Sorry, but you're wrong.
Pi is 3. (more accurately, 3.2). https://cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node18.h...
Re: π in Other Universes
#8> Mathematics can be seen as a logic game. You start with a set of assumptions and you come up with all the logical conclusions you can from that. Then, if someone else finds a situation that fits those assumptions, they can benefit from the pre-discovered logical conclusions. This means that if some conclusions require fewer assumptions, then those conclusions are more generally applicable This is a really, really n…
The same principle applies to programming. Functions that know less about their arguments are more generally applicable.
Re: π in Other Universes
#9Not sure about your universe, but here on earth, pi is 2. The length of the equator is 4 times the distance from the pole. (Approx.)
Why stop there? Take the circle with its center at one pole, its radius running an entire meridian, and its perimeter making an infinitesimally tight loop around the other pole. That exhibits a pi that's zero.
Re: π in Other Universes
#10IF I've correctly assesed the zeitgeist of HN postings THEN it follows Terence Tao's Introduction to Measure Theory must be a bullet. https://news.ycombinator.com/item?id=38064211 But seriously, who's going to read|skim a free 260+ tract on measure theory? https://en.wikipedia.org/wiki/Measure_(mathematics)
You don't just read/skim Tao's lecture notes. I used them to teach myself measure theory to skip some prerequisites at university, and they were _hard_. Every other page is a list of exercises. I doubt you would learn much if you didn't take time to solve them. But they are hard exercises.