31–40 of 125 posts
In surreal numbers [1], the midpoint between 0 and infinity would be the simplest number greater than 0, which is { 0 | } = 1 [1] https://en.wikipedia.org/wiki/Surreal_number
Can you tell me the hackenbush interpretation of this? sounds cool!
I vaguely remember learning similar fact years ago, but it was phrased something like "There are as many floats in [0, 1] range as in [1, infty]". Leaving aside where exactly "midpoint" of floats lies (either in Ruby's implementation or other languages'): what would be implications of this for writing code dealing with floats? Can I shoot myself in the foot somehow with low precision if numbers I'm using are "too clo…
What you describe is a common problem for video games, because if the engine uses "absolute" floats for everything in the game you effectively lose precision as you move away from the origin. If your maps get very large it gets very noticeable. I remember for instance in No Man's Sky when you traveled very far in a system you'd start to see the various animations become very jerky because the precision would become t…
Isn't this in practise creating a double-precision float by adding a second "significant figure" in a "base float" system?
I vaguely remember learning similar fact years ago, but it was phrased something like "There are as many floats in [0, 1] range as in [1, infty]". Leaving aside where exactly "midpoint" of floats lies (either in Ruby's implementation or other languages'): what would be implications of this for writing code dealing with floats? Can I shoot myself in the foot somehow with low precision if numbers I'm using are "too clo…
What you describe is a common problem for video games, because if the engine uses "absolute" floats for everything in the game you effectively lose precision as you move away from the origin. If your maps get very large it gets very noticeable. I remember for instance in No Man's Sky when you traveled very far in a system you'd start to see the various animations become very jerky because the precision would become t…
There's a lot of interesting problems that arise when making a 3d game vs a 2d one.
In surreal numbers [1], the midpoint between 0 and infinity would be the simplest number greater than 0, which is { 0 | } = 1 [1] https://en.wikipedia.org/wiki/Surreal_number
Edit: also, those infinitesimals were the subject of political and religious controversies in 17th century Europe, including a ban on infinitesimals issued by clerics in Rome in 1632.
Earlier quoted context omitted.
With a finite range, you can bisect directly by splitting in the middle of the range. With infinite ranges, you can't do that; so the usual way is to start with a small number and increase exponentially until you find a number that is too large; which is what is done here. When you got that number, it becomes the upper bound of a finite interval. So that's a two step process, which we can see here. The first 32 is in…
> they could get rid of it by bisecting on [1/n; n] instead of [0; n], as they already know that 1/n (and numbers lower than 1/n) isn't a valid candidate from the first step. Did you mean [n/2; n]?
Paging Dr. Cantor. Dr. Georg Cantor. Paging...
Clearly we'll need to some work in TruffleRuby to be fully compatible. I really hope nobody's code depends on this. Infinity 8.988465674311579e+307 4.4942328371557893e+307 2.2471164185778946e+307 1.1235582092889473e+307 5.6177910464447366e+306 ... 32767.999999999996 16383.999999999998 8191.999999999999 4095.9999999999995 2047.9999999999998 1023.9999999999999 511.99999999999994 255.99999999999997 127.99999999999999 63…
Finally, that settles it: ∞ = 3
This should simplify many things that people have agonized over!
In surreal numbers [1], the midpoint between 0 and infinity would be the simplest number greater than 0, which is { 0 | } = 1 [1] https://en.wikipedia.org/wiki/Surreal_number
TIL: apart from infinity (number, larger than any real number in absolute value) there are infinitesimal (number, less than any real number in absolute value and not a zero). Edit: also, those infinitesimals were the subject of political and religious controversies in 17th century Europe, including a ban on infinitesimals issued by clerics in Rome in 1632.