2024-03-22 15:20:26 might be neat to see a single binary *nix userspace like busybox written in forth. having a shared nucleus, i'll bet you could make it laughably small.
2024-03-22 15:38:25 also, this : postpone{ postpone { postpone postpone ; immediate oh, forth, never change.
2024-03-22 18:35:12 Wow... the things people get themselves into.
2024-03-22 18:35:14 https://www.bbc.com/news/world-us-canada-68630987
2024-03-22 18:36:09 My newest granddaughter was born yesterday. My first was born during covid, and had had some complications - it was MONTHS before we got to meet him. We scurried right over yesterday to meet this one, though.
2024-03-22 18:40:13 This is an interesting little Python program:
2024-03-22 18:40:15 a = 0 ; b = 1 ; p = 1
2024-03-22 18:40:17 while True:
2024-03-22 18:40:19 for i in range(1000000):
2024-03-22 18:40:21 a += 2 ; p *= a/b
2024-03-22 18:40:23 b += 2 ; p *= a/b
2024-03-22 18:40:25 print(p)
2024-03-22 18:41:04 I started that running yesterday. It converges to pi/2 - it's known as the Wallis series. Just using the default digits Python prints out, that seems to converge to seven decimal places, but to then be unable to nail down the remaining digits.
2024-03-22 18:41:59 It's kind of odd behavior - it will lock in on a value for a dozen or so iterations, and then jump away and recoverge to a different value for a dozen or so iterations. And of course "one iteration" is actually 2 million iterations - I'm adding two terms each time through the loop and only printing every million loops.
2024-03-22 18:42:29 So it will stay stable for 20-30 million terms, and then jack around for a while.
2024-03-22 18:42:42 I'm curious as to what's triggering those excursions.
2024-03-22 18:43:00 What I EXPECTED it to do was to converge every printed digit and then never change anymore.
2024-03-22 18:43:03 floating point foo?
2024-03-22 18:43:08 Possibly.
2024-03-22 18:43:48 I can probably add some code to detect those hiccups, but that'll slow it down a fair bit.
2024-03-22 18:44:15 But it's really the most interesting aspect of the little experiment, so I may do that.
2024-03-22 18:44:46 It's pretty fascinating to me that just playing around with inteers somehow manages to connect up with pi.
2024-03-22 18:44:56 There's no circle in sight here.
2024-03-22 18:47:46 Another interesting I noted was that when I first started it the first several decimal places converged quite quickly, and then it slowed down a *lot*.
2024-03-22 18:48:17 It didn't seem to be gradual as I would have expected - something basic seemed to change in there at some point.
2024-03-22 19:04:22 The series it's implementing looks like this written out:
2024-03-22 19:04:23 https://i0.wp.com/mindyourdecisions.com/blog/wp-content/uploads/2016/10/wallis-formula-for-pi.png?fit=1200%2C675&ssl=1
2024-03-22 19:05:04 What's interesting is that every single denominator eventually disappears, because somewhere further on down the line you find a numerator that's double the denominator.
2024-03-22 19:06:08 But if you run the product out far enough to find that numerator, then you always have a run of not-yet-canceled denominators, and that's just enough to keep it down around pi/2.
2024-03-22 19:07:55 And that gets longer and longer; you add two numerator terms to come to where you can cancel the next denominator term.
2024-03-22 19:09:04 Even numbers in numerators that are multiples of four persist long term - the in between ones all wind up becoming 2.
2024-03-22 19:09:36 "just playing around with inteers somehow manages to connect up with pi" the basic series for PI are all like that
2024-03-22 19:09:51 Like 4/1 - 4/3 + 4/5 - 4/7 etc or whatever it is
2024-03-22 19:09:53 Yeah, I know.
2024-03-22 19:10:50 Congrats on granddaughter
2024-03-22 19:11:01 In some cases I've seen presentations where they can show a connection to a circle, but I haven't seen that for all of them, and I've never been convinced those are "causal" so to speak. I feel like there may be some fundamental number theory thing going on that we haven't gotten hold of yet.
2024-03-22 19:11:10 :-) Thanks. She's lovely.
2024-03-22 19:57:43 congrats!
2024-03-22 19:57:45 what's her name?
2024-03-22 20:00:12 This is interesting reading https://en.wikipedia.org/wiki/Indiana_pi_bill
2024-03-22 20:09:49 Missiles can hit targets with Pi = 3 though
2024-03-22 20:10:26 And cos x = 1 approximation