←2007-03-01 2007-03-02 2007-03-03→ ↑2007 ↑all
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01:00:14 <lament> |
01:00:35 <RodgerTheGreat> _
01:00:56 <oerjan> \
01:02:30 <fizzie> I guess I'm left with /, then.
01:03:50 <lament> .
01:05:24 <oerjan> :
01:06:25 <fizzie>
01:06:30 <lament>
01:06:44 <oerjan> oh no, Unicode
01:07:32 <fizzie> I hope my character was a correct U+205D TRICOLON (also called "Epidaurean acrophonic symbol three"); it looks correct elsewhere but not in this terminal. :/
01:08:44 <oerjan> i'm afraid even on second attempt I just got the usual square...
01:13:06 <bsmntbombdood> hi
01:14:57 <oerjan> 'lo
01:40:34 <bsmntbombdood> I wonder how to simplify things like ``SKx
01:41:03 <bsmntbombdood> exstentionaly
01:42:19 <oerjan> well it's simple in lambda calculus, but i don't know about SKI.
01:43:16 <bsmntbombdood> yeah
01:53:21 <bsmntbombdood> ok i've got it to do one variable to I and K
01:54:18 <bsmntbombdood> ``SKx ==> I
01:54:47 <bsmntbombdood> ``S`Kx`Ky ==> `K`xy
01:58:59 <oerjan> and of course ``S`KxI = x
02:01:02 <bsmntbombdood> ?
02:03:57 <bsmntbombdood> can't do ``S`KKI = K yet
02:05:21 <oerjan> why not?
02:05:41 <bsmntbombdood> It's possible, but the algorithm doesn't
02:05:51 <bsmntbombdood> aah, there
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02:08:58 <bsmntbombdood> now for multiple variables....
02:09:05 <SevenInchBread> hmmm... this is interesting...
02:09:41 <SevenInchBread> I accidentally created an algorithm that produces (I think) a circle or maybe an ellipsis (I could only see half of it because the turtle window wasn't big enough)
02:10:01 <SevenInchBread> I'll pastebin it so someone can explain the math behind it.
02:10:26 <bsmntbombdood> fun
02:11:52 <SevenInchBread> http://deadbeefbabe.org/paste/3839
02:12:05 * SevenInchBread is messing around with fractals, thue, and turtles :)
02:14:49 <bsmntbombdood> what are some multiple argument extensional simplifications?
02:15:35 <SevenInchBread> ....uh, what?
02:15:42 * SevenInchBread doesn't understand your lingo.
02:16:11 <bsmntbombdood> ``SKK is extensionaly equal to I
02:16:23 <bsmntbombdood> because ```SKKx = x
02:16:26 <oerjan> i think it may be simpler to convert to lambda calculus, eta-reduce, then convert back.
02:17:01 <bsmntbombdood> I don't understand eta reduction
02:17:24 <oerjan> \x.fx = f where f does not contain x
02:17:59 <bsmntbombdood> oh
02:18:20 <bsmntbombdood> you mean Kf
02:18:33 <oerjan> plus some beta-reductions too, i guess.
02:18:37 <SevenInchBread> so... any clue why the numbers behave in such a way to create a circle(like) shape?
02:18:46 <oerjan> no.
02:19:48 <bsmntbombdood> But a SKI interpreter shouldn't need a lambda calculus interpreter
02:19:50 <SevenInchBread> hmm... changing the right() method call to left() simply makes a smaller circle... weird
02:20:18 <oerjan> let's see.
02:20:38 <oerjan> the only changing parameter is dist.
02:20:52 <SevenInchBread> it just flips back and forth from what I can tell.
02:21:00 <SevenInchBread> to True and False for that condition.
02:21:23 * SevenInchBread breadcrumbs to find out for sure.
02:21:24 <bsmntbombdood> ooh, it does ``S`KxI now
02:22:06 <oerjan> i think i understand.
02:22:09 <SevenInchBread> yup... it just goes back and forth betwen true and false.
02:22:56 <oerjan> essentially dict just fluctuates in some interval.
02:23:38 <SevenInchBread> just... minute enough to... draw a circlish thing?
02:24:18 <SevenInchBread> I looks almost like a perfect circle to me... although it could be oblongated mathematically.
02:24:54 <oerjan> _anything_ that goes through a lot of identical small turtle movements must create a circle.
02:25:30 <oerjan> because each cycle will move by the same amount, then turn the same amount.
02:25:39 <bsmntbombdood> ``S``S`KSK`KI
02:25:46 <bsmntbombdood> is equal to I
02:26:20 <SevenInchBread> ah... yeah that makes sense.
02:26:38 <SevenInchBread> darn... I thought I might have found some weird mathematical pattern.
02:27:10 <oerjan> alas
02:27:11 <SevenInchBread> ... 8, 3, and 5 (the only numbers I used other than phi) are all heavily related with phi.
02:27:28 <SevenInchBread> ...I picked them mainly because they're a few of my favorite numbers.
02:27:57 <oerjan> i believe any change in the constants which doesn't cause dist to diverge will still produce a circle.
02:28:51 <SevenInchBread> until then I just got freaky scribble patterns... for an unrelated alg using a bunch of randomly pieced together computations.
02:29:11 <oerjan> you might change dist by functions that don't match quite as well as *= prod and /= prod
02:29:51 <SevenInchBread> **= and /= maybe :)
02:29:56 <oerjan> then dist could change in a more complicated pattern.
02:30:40 <SevenInchBread> hmmm..
02:31:09 <SevenInchBread> changing it to exponentiation makes the circle spin in a very tight spiral to the right... like the original except veering to the right very slightly each loop.
02:31:37 <oerjan> oh.
02:31:50 <SevenInchBread> still a cyclic interval though... the distance is simply being gradually altered.
02:32:35 <oerjan> i think that must be roundoff errors in the Turtle graphics. It they were perfect you couldn't go in a particular direction.
02:32:43 <oerjan> *If
02:33:01 <SevenInchBread> could be floating point?
02:33:07 <oerjan> yeah
02:33:16 * SevenInchBread uses Python's decimal format thing.
02:33:21 <SevenInchBread> just to see.
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02:36:40 <SevenInchBread> hmm... switching to decimal representation made exponentiation no longer work with phi as the exponent.
02:38:13 <SevenInchBread> decimal.InvalidOperation: x ** (non-integer)
02:40:08 <bsmntbombdood> yessss it works now
02:40:55 <bsmntbombdood> ``S``S`KSK`KI ==> I
02:42:20 <SevenInchBread> bah... using Decimal just makes the floating point math done in the turtle module screw up.
02:42:20 <bsmntbombdood> sweet
02:43:41 <bsmntbombdood> It's noticably slower now though
02:44:37 <bsmntbombdood> `x`x`x`x`x`xx takes like 1.5 seconds
02:44:44 <SevenInchBread> hmmm... is decimal arithmetic considerably slower than good ol' floating point?
02:45:44 * bsmntbombdood disappears
03:08:29 <SevenInchBread> I was thinking for Sophia I could automatically convert between floating point, long intergers, short integers, and decimally-represented numbers without having to worry about it.
03:09:21 <SevenInchBread> ...as long as there's a way to predict which floating point operations won't be accurate... you could convert to decimal format for the operations.
03:10:10 <bsmntbombdood> ...huh?
03:11:41 <SevenInchBread> decimal format... instead of binary floating point.
03:12:04 <SevenInchBread> it basically mimics "schoolhouse" algorithms for doing math... so it's more accurate but takes more time
03:12:25 <oerjan> decimal format is not that much better.
03:13:00 <oerjan> you'll have to round off eventually, in any case.
03:15:11 <oerjan> adding more bits increases accuracy just as much as adding more decimals.
03:15:37 <bsmntbombdood> rationals for the win
03:15:43 <SevenInchBread> It's mostly used in nitpicky computations... like finance and science...
03:15:53 <oerjan> yeah, but even they only work for arithmetic
03:16:03 <oerjan> just finance, i think.
03:16:14 <SevenInchBread> yeah... mostly finance.
03:16:29 <oerjan> and that's not really because decimals are more accurate.
03:16:39 <SevenInchBread> more... precise? or something like that?
03:17:01 <bsmntbombdood> because .1 has to be 1/10
03:17:22 <oerjan> it's because financial calculations are strictly defined by old traditions from before there were binary computers.
03:18:00 <bsmntbombdood> this simplifier is sloow now
03:19:05 <SevenInchBread> aaah.... legal standardization more so than any gains in accuracy.
03:19:30 <bsmntbombdood> ``````````aaaaaaaaaaa takes like 5 minutes to return
03:19:44 <oerjan> the more simplifications you try to catch the closer you get to having to solve the halting problem :)
03:19:54 <bsmntbombdood> heh
03:20:15 <oerjan> although that does sound like maybe you need a better algorithm
03:20:22 <oerjan> or maybe you have bugs.
03:20:27 <bsmntbombdood> maybe
03:20:34 * SevenInchBread is reading up on number representations.
03:20:43 <oerjan> as in, repeating work bugs
03:21:10 <bsmntbombdood> yeah, there is one
03:23:50 <bsmntbombdood> http://pastebin.ca/377911
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13:59:54 <EgoBot> 42
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23:00:18 <GregorR> I wrote a runtime ELF loader 8-D
23:00:35 <GregorR> It segfaults mysteriously >_> ... but only after the program has finished.
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←2007-03-01 2007-03-02 2007-03-03→ ↑2007 ↑all