00:17:54 -!- Zarutian_ has changed nick to Zarutian. 00:32:10 -!- copumpkin has joined. 00:48:29 -!- Zarutian has quit (Quit: Zarutian). 00:55:34 -!- DHeadshot has joined. 00:56:30 -!- oerjan has joined. 00:59:36 -!- copumpkin has quit (Quit: My MacBook Pro has gone to sleep. ZZZzzz…). 01:03:16 ...why does the Vatican even HAVE an age of consent? 01:03:44 Shouldn't it be, like, "age of the oldest living person, plus 1 day"? 01:04:04 hppavilion[1]: not all people living in the vatican are ordained priests hth 01:04:24 oerjan: I think they are 01:04:29 As in, people who can LIVE there 01:04:37 hm 01:06:12 hppavilion[1]: nope. "Women obtain Vatican City citizenship by marriage (as a baptized Catholic) to their husbands; however such citizenship "lasts only for the duration of their stay" in Vatican City." 01:06:26 oerjan: Wait, what? 01:06:51 Why have actual citizenship that you lose when you leave the country when you can just have traditional visas? 01:06:51 helloerjan 01:06:56 According to the Herald Sun in March 2011, there were "only 32 female citizens" residing in the "smallest state in the world". 01:07:05 *+"" 01:07:08 hellopia 01:07:16 i realized something 01:07:31 p-adic numbers are more limited than what i was thinking for 10's complement 01:08:09 is it a field if i take a: Z->Z/10Z and represent real numbers as sum from -infty to infty of a(i)*10^i 01:08:19 hppavilion[1]: people who lose vatican citizenship automatically gain italian by default (and treaty) 01:08:20 To define what a "Country" is, your criteria has to include Vatican City: The Least Country-Like Country That's Still A Country and EXCLUDE the anti-Vatican City, Hong Kong: The Most Country-Like Country That Isn't A Country 01:08:30 is that a field 01:08:30 oerjan: Interesting... 01:08:45 [wiki] [[Esolang:Introduce yourself]] https://esolangs.org/w/index.php?diff=49721&oldid=49717 * Kenrube * (-7) 01:08:46 quintopia: There was a nice field near my old house 01:09:21 quintopia: the only p-adic fields are the ones from p a prime hth 01:09:39 otherwise, you can easily find a zero divisor 01:09:50 "in some countries in order to be legally defined as a new sex people must first undergo sterilization." 01:09:57 Apparently that's controversial 01:11:02 quintopia: also, p-adic numbers are not reals hth 01:11:10 (Doesn't being transgender defeat the possibility of having children? Like, even if you're a trans man (female anatomy) who is ALSO gay, you probably aren't going to be planning on having children the usual way) 01:12:12 -!- carado has quit (Ping timeout: 265 seconds). 01:12:40 quintopia: the problem with defining multiplication when the number is infinite both ways is that the sum for each resulting digit also gets infinite. 01:13:12 when it's only finite leftwards, each digit only gets a finite sum of possibilities. 01:13:34 -!- izalove has quit (Ping timeout: 265 seconds). 01:14:03 hppavilion[1]: have you considered asking these questions in a forum where people are actually interested in discussing them twh 01:14:40 oerjan: Nope 01:14:52 shocking 01:18:35 quintopia: in particular, for any a,b where a is a 2-adic integer and b is a 5-adic integer, there is a unique 10-adic integer that is equal to a (mod 2^n) and equal to b (mod 5^n) for all n (using the chinese remainder theorem and taking limits) 01:20:10 and if you choose a1=0, b1/=0, a2/=0, b2=0, then the corresponding c1 and c2 become non-zero 10-adics with zero product. 01:20:29 oerjan: i thought the p in p-adic stood for "pooch" tdnh 01:20:31 (maybe i'm not telling you anything you don't know here) 01:21:13 . o O ( shachaf does not get to overuse the word "pooch" any longer ) 01:21:58 oerjan: i think many people who are interested in discussing those questions would be too irritated by the phrasing and implications of the way they're put to answer anyway hth 01:22:00 "Race is a social ruler-and-compass construction" 01:23:28 you should get a twitter account and post your jokes there instead of here. 01:24:17 shachaf: that is possible. 01:27:06 shachaf: I did. It got locked because I looked like a bot. 01:27:19 aha 01:28:23 -!- digin4 has joined. 01:28:50 shachaf: ? 01:29:58 hppavilion[1]: Being trans is orthogonal to getting medical treatment for being trans. *Additionally*, what those countries require includes destruction of any frozen sperm or eggs. 01:30:22 Ah, yes, that's overdoing it 01:30:44 pikhq: Yes, but my point is that if you ARE trans, you probably aren't going to go using the equipment for cisgendery things 01:30:59 If you're a trans-man, you probably aren't going to go around using your uterus 01:31:03 Likely, but why should the state mandate it? 01:31:10 pikhq: I was getting there 01:31:11 I mean, requiring that is stupid 01:31:17 -!- izabera has joined. 01:31:21 my server died 01:31:40 actually no because apache is alive 01:31:52 It probably makes clerical stuff easier (so you don't have to note that the mother is a man), but if your clerications are set up so you can't do that via compartmentalization, you're doing it wrong. 01:32:12 but irc died, ssh is dead, cloudatcost's control panel is dead 01:32:57 hppavilion[1]: Additionally, it is *shockingly* difficult to get medical treatment for being trans in many different cases. And sterilization can be part of those medical treatments... 01:34:18 And again, we are talking about legally enforcing a potentially-unnecessary medical treatment just to have your gender identity recognized. 01:34:22 Which is pretty shitty. 01:36:54 don't say just.. 01:41:00 -!- izalove has joined. 01:42:09 IT'S ALIVE 01:44:34 i did nothing... 01:44:38 still can't access it 01:45:03 we'll be fine as long as it doesn't start shouting BRAINS 01:46:19 BRAINS 01:46:21 BRAAAAINS 01:46:29 AAAAAAAAAA 01:46:39 <_46bit> hppavilion[1]: I'd like to point out that when you say "Yes, but my point is that if you ARE trans, you probably aren't going to go using the equipment for cisgendery things" in reference to reproduction, it feels like you're forgetting non-straight relationships altogether 01:47:11 <_46bit> and that's all I'll say about that. it's too late and this is a wrong venue for this conversation. 01:48:00 _46bit: No, I covered that earlier; it's just that even if you're a trans man AND gay, you probably aren't going to want to carry a baby because that's pretty much 100% womanly 01:48:00 <_46bit> there was a time I created a Linux container with lxc and the hosts /dev devices all vanished 01:49:09 If people can be trans-gender, can I be trans-race? 01:49:27 I'm sure I could get the SJWs to support it, but only if I wasn't white as-is 01:49:51 ("I /identify/ as Pakistani") 01:49:51 <_46bit> figures you had that agenda 01:50:01 _46bit: That just occurred to me now 01:50:09 It wasn't part of my agenda 01:50:33 -!- izalove has quit (Changing host). 01:50:33 -!- izalove has joined. 01:51:12 (Hm, if trans people need to legally change their gender, I think that's already a sign of your society doing something wrong- the law incorporates gender into it. Unless it's just changing whether they say "Mr." or "Ms." on notices) 01:51:16 hppavilion[1]: You'd think that, but there are trans men who have actually gone off hormones in order to carry a baby. 01:51:28 pikhq: Huh, that's interesting 01:51:32 And a tiny bit bizarre 01:51:36 People are complicated. 01:51:40 (More so than transgenderism in general, that is) 01:51:48 pikhq: Oh, really? This changes everything! 01:51:54 :) 01:51:56 What's the computational complexity of people? 01:52:02 O(???) 01:53:04 O(nermous) 01:54:32 -!- digin4 has quit (Quit: Leaving). 01:55:40 -!- DHeadshot has quit (Ping timeout: 244 seconds). 01:55:48 O(1) 01:57:19 O(1/0) 01:59:58 -!- heroux has quit (Ping timeout: 244 seconds). 02:00:08 -!- heroux has joined. 02:01:48 The worst complexity I've ever seen was Worst Sort 02:01:59 Which is O(n!!!!!...) 02:02:08 The number of factorials depend on the exact implementation 02:03:31 <_46bit> :D 02:04:14 <_46bit> I got a couple of factorials in something the other week, then wondered why n=154000 took so long 02:12:54 Unless your name actually is "Mr." or "Ms." then they should omit that 02:13:23 Slereah: bah factorials are insignificant compared to the power of ackermann. 02:13:59 -!- augur has quit (Remote host closed the connection). 02:14:14 zzo38: now i'm wondering if there are any languages where any of those are names. 02:14:31 well, probably without the period, anyway. 02:16:52 apparently Mr. is the artist name of a japanese guy 02:19:22 oerjan: i was onbviously not talking about p-adics 02:19:38 i dont know why you said so much about them 02:19:52 quintopia: because you didn't have the dignity to stop me hth 02:20:07 i wasnt able to. i was at work 02:20:20 anyway, i think the infinite sum for one digit thing i mentioned is what makes it break down to have it twosided. 02:20:36 but abt the infinite sum thing: why is it a problem as long as the sums converge? 02:20:45 -!- Frooxius has quit (Ping timeout: 265 seconds). 02:21:20 how do make them converge? especially in the reals. 02:21:51 *do you 02:22:13 for general Z -> Z/10Z, there's no reason to expect them to. 02:22:21 why wouldnt they converge? as long as we assume that all finite numbers have an infinite string of 0s or 9s on the left... 02:23:29 ok but then you're basically just using a strange way of writing ordinary decimal. 02:24:05 which gives a field (the reals), but not a unique representation. 02:24:18 (strange for negatives, that is.) 02:25:43 The infinite product 2*2*2*2*2*2*2*2*... converges in the 2-adics 02:26:08 to 0, even. 02:26:52 "§ (lower case: ſ) is the 19.5þ letter of ðe Eŋgliʃ alphabet" 02:28:54 oerjan: yes a strange representation for ordinary decimal is exactly what i meant when the other day i said "10's complement" 02:29:09 one where addition works for subtraction 02:29:52 the fun bit is that ...999.999... is negative zero 02:29:59 OUCH 02:30:33 food -> 02:30:48 (okay technically it's just an alternative representation for zero, but it's more fun to call it negative zero) 02:31:25 -!- augur has joined. 02:31:32 I should probably learn about p-adics 02:31:46 quintopia: It's -1 + 1 02:31:56 FireFly: I prefer the vc-adics 02:32:00 I don't think there is a distinct negative zero 02:33:00 what about the drug-adics 02:34:08 I like how the ackermann function grows faster than any primitive-recursive function 02:34:28 And any stack of factorials is primitive-recursive 02:45:52 -!- Phantom_Hoover has quit (Quit: Leaving). 02:53:41 did you know that 4^(4^4)cm is wider than the observable universe? 02:55:06 x^(x^x) goes 0, 1, 16, 7.6*10^12, wider than the observable universe 03:05:31 -!- DHeadshot has joined. 03:16:30 quintopia: 0^0 != 0 unless explicitly stated to be 03:17:04 Also, that's 3^(3^3) presumably 03:19:58 quintopia: pft, TREE() grows much faster 03:30:41 > 3^(3^3) 03:30:44 7625597484987 03:31:44 > length "625597484987" 03:31:46 12 03:31:48 confirmed 03:44:34 -!- hppavilion[1] has quit (Ping timeout: 255 seconds). 04:17:10 > exp 3 04:17:16 20.085536923187668 04:17:55 > 4*(log (4^4)) / log 10 04:18:00 9.632959861247397 04:18:21 4^(4^4) is a 9 digit number then? 04:18:25 Or rather 10 digit 04:19:33 -!- izabera has quit (Quit: WeeChat 1.5). 04:22:38 > 4^(4^4) 04:22:45 1340780792994259709957402499820584612747936582059239337772356144372176403007... 04:22:48 Oh, no 04:22:55 My calculation was clearly wrong =P 04:23:08 > log(4^(4^4)) / log 10 04:23:15 154.12735777995834 04:23:19 spam 04:23:24 Sorry 04:32:06 <\oren\> rebooted my computer now my blutoth mouse is working 04:32:40 -!- hppavilion[1] has joined. 04:33:44 <\oren\> why is blutoth such an unreliable thing 04:39:55 -!- DHeadshot has quit (Ping timeout: 255 seconds). 04:41:16 -!- hppavilion[1] has quit (Ping timeout: 255 seconds). 04:45:02 -!- `^_^v has joined. 04:45:23 -!- hppavilion[1] has joined. 04:45:36 I'm a tad unclear on the exact rules of ± 04:46:32 -!- copumpkin has joined. 04:46:36 ±1 is {-1, 1} 04:46:58 and 5±2 is {3, 7} 04:47:08 But then things start to break down 04:47:32 Is (1±i)^2 {2i, -2i} or {2i, -2i, 1-i}? 04:48:20 -!- copumpkin has quit (Client Quit). 04:48:58 s/1-i/2/ 04:49:12 (2i = (i+1)^2, -2i = (i-1)^2, 2 = (1+i)(1-i)) 04:52:53 hppavilion[1]: the former. 04:53:22 But if you just make it normal numbers, (2±3)^2 feels like it should be 5^2 = 25 or (-1)^2 = 1, but if you try it the fun way you get those two AND 13 04:53:24 oerjan: Oh 04:53:49 you don't get to expand ^2 like a macro when the content is multivalued. 04:53:53 Why? Is there a fixed reason, or is it just because everything is nicer? 04:54:04 Ah, right 04:54:51 oerjan: So you have to solve&separate the inside first, THEN macronize it on each separate result? 04:54:59 > let a +- b = [a+b,a-b] in (^2) <$> (x +- y) 04:55:04 [(x + y) * (x + y),(x - y) * (x - y)] 04:55:13 yeah 04:55:24 > let a +- b = [a+b,a-b] in (*) <$> (x +- y) <*> (x +- y) 04:55:30 [(x + y) * (x + y),(x + y) * (x - y),(x - y) * (x + y),(x - y) * (x - y)] 04:56:18 -!- izalove has quit (Read error: Connection reset by peer). 04:58:37 -!- izabera1 has joined. 04:58:59 oerjan: Argument of the day: If there's more than one ± (e.g. a±b±c) do you have to treat them all the same (so a+b+c OR a-b-c), or can they mix (So a+b+c, a+b-c, a-b+c, OR a-b-c) 05:00:55 -!- izabera1 has quit (Changing host). 05:00:55 -!- izabera1 has joined. 05:01:07 -!- izabera1 has changed nick to izalove. 05:02:35 hppavilion[1]: mixing is allowed. 05:02:47 oerjan: OK 05:03:11 oerjan: what about the thing where you use +- in one place and -+ in the other place 05:03:16 So then WTF is ∓‽ 05:03:19 oh right 05:03:22 to indicate that the same choice is used respectively in both 05:03:27 s/WTF/WÐF/ 05:03:32 shachaf: yeah hm 05:03:44 hppavilion[1]: ok there's exceptions, darn 05:03:49 -!- bibibi has joined. 05:04:03 >:) 05:04:10 `unidecode ∓ 05:04:11 [U+2213 MINUS-OR-PLUS SIGN] 05:04:54 i think we're heading into "if you do this you get to explain your notation" territory. 05:05:13 agreerjan 05:06:28 Ah, yes 05:06:37 agreerjan^2 05:07:49 -!- `^_^v has quit (Quit: This computer has gone to sleep). 05:09:01 * oerjan suddenly envisions putting indices on the signs 05:09:32 oerjan: now write a monad for it hth 05:11:12 oerjan: There's also ⋇ btw 05:11:15 no, i don't think so. 05:11:18 oerjan: Huh, that actually works 05:11:28 `unidecode ⋇ 05:11:30 [U+22C7 DIVISION TIMES] 05:11:46 fiendish 05:12:05 ж 05:12:31 write a subscript after a ± or ∓ to link it to all others with that sign; all ±s with the same index are + and - at the same time, all ∓s with the same index are + and - at the same time and never the same as ±s with the same index 05:12:40 `unidecode ж 05:12:43 [U+0436 CYRILLIC SMALL LETTER ZHE] 05:13:04 hppavilion[1]: but of course. although at this point multiplying by {-1,1} valued variables s_i is probably more standard. 05:13:42 oerjan: Well yeah, but that's no fun 05:14:00 oerjan: Is there an operator set, like Sigma and Pi? 05:14:09 Which would give you the set of a bunch of things. 05:14:15 oerjan: Oh, and what if we need "only 2 out of these 3 can be + at once; the other has to be -, but it doesn't matter which 2 are +" 05:14:32 I guess that's just an alternative way to write set comprehensions. 05:14:36 >:D 05:14:42 ℝ is the set of real numbers 05:14:55 shachaf: just use a big union sign and braces. 05:14:59 ℝ^k is a k-dimensional space, because a set S to a power k means a k-tuple of items from S 05:15:26 (presumably, all sets work like this, where multiplication of sets is just a tuple of the values- nothing more than Cartesian product) 05:15:39 oerjan: i,i {}_{(i,j) \in {1,2,3} x {5,6,7}} { i+j } 05:15:52 k is, generally, a natural number 05:16:50 But are there definitions for k < 0 &| k ∉ ℕ? 05:17:02 `unidecode ℝ 05:17:03 [U+211D DOUBLE-STRUCK CAPITAL R] 05:17:20 oerjan: Your font is terrible hth 05:18:04 shachaf: Wait, wðf does ðat notaʃon mean‽ 05:18:25 Please stop being annoying. 05:18:26 -!- shachaf has left. 05:18:34 wait, what? 05:18:41 Did I do something? 05:18:49 hppavilion[1]: it's putty, it doesn't support using more than one font. 05:18:55 Oh? 05:19:26 @tell shachaf I'm sorry, though I'm not exactly sure what in particular I did. :( 05:19:30 Consider it noted. 05:19:49 i can paste it into my browser and it shows fine. 05:20:43 hppavilion[1]: shachaf's irc client has even bigger problems with unicode than mine hth 05:20:49 Oh 05:21:18 also, i don't know generalization for k < 0. 05:21:27 So is ℝ^k defined for anything other than k ∈ ℕ 05:21:28 OK 05:21:40 oerjan: Anything for k ∉ ℕ? 05:22:01 i recommend not using those fancy chars as i've already pointed out i cannot read them easily. 05:22:42 Ah, right 05:22:51 Anything for k \nin |N? 05:22:54 but assuming you're asking about complexes, that seems as hard as negatives. 05:23:44 you can do infinite cardinals, obviously :) 05:24:12 oerjan: No, I mean like 2.5. Is there any generalization that /somehow/ supports something that looks like a 2.5-tuple? 05:24:58 not that i know of. now if you were just asking about any set with that dimension, i'd point you to fractals. 05:25:03 (Preserving the generic properties that doing types like this has; (S^n, S^m) is pretty much equivalent to S^(n+m) 05:25:07 ) 05:25:37 I have a feeling no, but you never know 05:27:54 me too 05:28:50 <\oren\> hppavilion[1]: well, if you had a S = R^2.5, then the tuple (x,y) where x and y are in S would be a member of R^5 05:29:03 Yes, they would, wouldn't they? 05:29:13 it's a little bit like those fractional bits in TURKEY BOMB, i suspect - they don't really exist individually. 05:30:11 (and trits) 05:30:46 Wait, I suppose R^(-1) (aka "anti-R" and typically written Я (the Cyrillic backwards-R, of course)) would basically be a quotient type of the Unit Type and the Reals (Quo[Unit,Real]) 05:31:08 But I still don't really know WTF a quotient type is 05:31:17 quotient types of singleton sets tend to still be singleton sets hth 05:31:28 *quotients of 05:32:44 <\oren\> so you need a set R^0.5 such that to specify a member of R, two members can be used. 05:32:45 now i'm reminded about those people who said they could define a reversible computation system where the types were a field. but they never explained how they avoided the obvious contradictions, so they probably didn't. 05:33:57 oerjan: Oh? Including where we're assuming the singleton is the (pardon my arithmetic) numerator? 05:34:11 \oren\: Yeah, basically 05:34:27 (R^0.5, R^0.5) has to pretty much directly correspond with R 05:34:55 (I suppose I could make it... no, that won't work) 05:35:09 well there were units, i think 1 may have been just the computation that makes input and output equal 05:35:25 Q can be represented by (Z, W) ips 05:37:32 (I suppose (R^(-1), R) would have to be the unit type, and that doesn't seem right- if all else fails, you just always use the same value in the first place every time and the second place can be any real number, so the limit being 1 possibility seems impossible) 05:37:42 now come to think of it there may be an obvious way to cheat based on R being the same cardinality as R^2. it probably won't give something very nice. 05:38:15 Yeah, true 05:38:24 and it'll still break for getting R^0 = R^a x R^(-a) 05:38:26 Quotient type of R and R^2 or somesuch? 05:38:39 Yep 05:39:05 R^0 has to be the unit type (or empty tuple, or whatever. Are those all the same in whatever type theory we're using?) 05:39:36 -!- Sgeo_ has joined. 05:40:35 Sgello 05:40:48 i dunno, i don't know all type theories. 05:40:55 Sgeo_: I'm trying to figure out if -1-space is a reasonable thing 05:41:59 for some kinds of dimension measures, there is _one_ reasonable -1-space, the empty set. 05:42:52 -!- Sgeo has quit (Ping timeout: 265 seconds). 05:44:05 (e.g. the measures where you define the dimension to be n if a space can be split up with subspaces of dimension n-1) 05:54:46 -!- MoALTz has joined. 06:01:33 oerjan: I suppose negative time dimensions would be measured in hertz? 06:03:36 -!- copumpkin has joined. 06:04:50 well the idea certainly does. 06:09:45 -!- copumpkin has quit (Quit: My MacBook Pro has gone to sleep. ZZZzzz…). 06:09:55 -!- hppavilion[1] has quit (Ping timeout: 255 seconds). 06:09:56 -!- wob_jonas has joined. 07:04:06 -!- hppavilion[1] has joined. 07:19:33 -!- clog has quit (Ping timeout: 240 seconds). 07:24:09 % is a stupid symbol 07:24:35 It basically indicates "Hey, the previous number is a proportion of a whole, not a count. Oh, and we multiplied it by 100 for no apparent reason at all" 07:25:43 no no, that symbol indicates the following number is a job number, not a pid, and also, if this appears as the command, then there's an implicit fg command before it 07:27:29 wob_jonas: I'm trying to remember if there's a way to express logarithms using exponentiation and division alone 07:27:41 % is obviously the division remainder operator 07:27:45 I seemed to remember it being (1/b)**x, but then I realized that's stupid 07:27:49 FreeFull: Yes, it's that too. 07:28:30 FreeFull: And log*_b(x) is the iterated logarithm remainder operator 07:29:56 (an easy way similar to how roots are x**(1/k)) 07:30:23 hppavilion[1]: Let's just regard % to mean "divided by 100". The population of the US is 318.9%%% 07:30:57 er, that was wrong 07:30:59 Cale: Isn't it usually multiplied? 07:31:17 Cale: Use antipercent (a mirrored percent sign) for that 07:31:19 The population of the US %%% is 318.9 07:31:21 yeah 07:31:27 (or just put a percent at the beginning) 07:31:32 yeah 07:31:48 Cale: Do you know of an easy way to logarithmicate? 07:32:31 -!- carado has joined. 07:32:55 I also created the constant u (the Deranged Euler Constant) today 07:32:55 -!- augur has quit (Remote host closed the connection). 07:33:06 Well, log_b x = log_a x / log_a b 07:33:28 So if you know the right constant to multiply by, you can do it roughly by counting digits 07:34:08 Yes, I've got that 07:34:22 The problem is I want to do it simply 07:34:26 (I might just import log) 07:34:51 Oh, simply in terms of what? 07:35:30 <\oren\> no % is the modulo operator, duh 07:36:04 <\oren\> i wish c++ had made % and ^ work the right way with floats 07:36:32 \oren\: Yeah, Cale said that 07:36:34 (roughly) 07:36:53 I didn't say that :) 07:37:32 https://en.wikipedia.org/wiki/Logarithm#Arithmetic.E2.80.93geometric_mean_approximation -- this method might be good 07:37:39 If you're implementing an algorithm 07:38:23 Yeah, I just gave up and imported it 07:38:36 I was hoping to avoid it as a dependency, but oh well 07:39:06 ln(x) = log_e(x), lb(x) = log_2(x), lg(x) = log_10(x), ld(x) = log_u(x) 07:43:16 huh? 07:43:24 i know ld as log_2 07:43:29 what is u? 07:44:10 myname: ISO recommends lb for log_2 07:44:22 meaning what 07:44:24 (not sure where that 'd' came from anyway...) 07:44:32 But u is the Deranged Euler Constant 07:44:32 dualis 07:44:40 Oh 07:45:04 e is defined as (or at least can be calculated with) the sum of the reciprocals of all factorials from 0 to infinity 07:45:30 what does the b in lb stands for? 07:45:31 u is the same, but with subfactorials instead (and we just ignore subfact(1) because that causes divide-by-zeroes) 07:45:35 myname: 'binary' 07:45:53 that's horrible 07:46:04 @let agm x y = head [u | (u,v) <- iterate (\(u,v) -> ((u+v)/2, sqrt (u*v))) (x,y), abs (v - u) < 1e-10] 07:46:08 Defined. 07:46:21 myname: It's the only name Wikipedia even knows 07:46:27 https://en.wikipedia.org/wiki/Binary_logarithm 07:49:22 the german entry has lb also listed as ld for logarithmus dualis 07:49:33 > pi / (2 * agm 1 (2^^(2-16) / exp 1)) - 16 * log 2 07:49:36 1.0000000011791865 07:50:04 myname: ISO 80000 recommends base 2 is lb and base 10 is lg. If we're going to have an ld other than the Deranged Logarithm, ld should be base 10 and lg base 2 07:50:44 I find it kind of weird that log bases are even a thing. 07:51:10 Cale: they aren't. base e, base 2, and base 10 are the only useful ones. 07:51:10 how so 07:51:17 Cale: Why? 07:51:19 We usually don't bother giving special names or indices to scalar multiples of a function. 07:51:29 Cale: sqrt(2) 07:51:56 ah, so it's weird for the bases to have special names, not the existence of the bases as such 07:52:10 Well, even the bases are pretty weird 07:52:13 wob_jonas: I don't think base 10 is even very useful outside of the fact that we all count that way 07:52:23 not really 07:52:26 (When not in computers, you can just drop the index entirely for roots for square roots) 07:52:31 hpp: it's useful for calculating in my hand because the numbers are in base 10 07:52:31 Cale: How? 07:52:35 we do have the same for roots 07:52:36 Like, whenever you would have written log_10 x, you could have just done away with the concept of log bases altogether and written log x / log 10 07:52:41 which is really not so much worse 07:52:49 I know base 10 logarithms, not base e ones 07:52:49 wob_jonas: I forget, how does one do log 10 in one's head? 07:53:13 Cale: It's cleaner and less confusing 07:53:19 Cale: it does make the concept less understanding imho 07:53:35 While equivalent, it's confusing 07:53:47 yeah 07:53:55 Because defining log_b x as k s.t. b^k = x is understandable 07:54:01 hpp: you learn the exponential sequence 1, 1.25, 1.6, 2, 2.5, 3.15, 4, 5, 6.3, 7.9, 10 to compute approximate base 10 logarithms and exponentials, and you use them to compute approximate multiples of large numbers when you want to do approximate calculations 07:54:04 I do it all the time 07:54:05 try explaining kids why you divide by the stuff you have as your basis 07:54:14 Defining it as however the hell base change works is impossible to understand 07:54:29 hppavilion[1]: That works if you can define b^k appropriately, but how do you want to do that? :) 07:54:56 Usually we define b^k as exp(k log b) 07:55:06 Cale: Tell them how exponents work, then tell them how it works if they're negative, then explain square roots, then general roots, then rational powers 07:55:18 s/how exponents/how natural exponents/ 07:55:26 So what does 2^sqrt(2) mean? 07:55:58 Cale: If you want a meaningful representation, you just round it off as with all other irrational numbers 07:56:03 it's very useful when I only want approximate magnitudes 07:56:06 Round it off and pretend it's a rational 07:56:32 obviously if I want a more precise calculation, I use a computer 07:57:18 Well, how do we know that rounding it off is okay at all? 07:57:37 The same way you find the circumference of a circle given its diameter; you don't find an infinite series that yields the answer when completed, you just say pi is 3.14159, multiply by that, and say "close enough" with a little footnote 07:57:50 If we don't know how x^y is defined for irrational y in the first place, we can't justify any means of approximating it 07:59:50 Cale: We hold off the actual proper definition for irrational y until they've taken some calculus 08:00:20 Oh, I highly recommend not talking about logarithms at all until one has had some calculus. 08:01:02 Of course, the highschools don't do that because they're big fans of confusing people and making them think they're "bad at math" by introducing things with circular definitions :) 08:01:31 and leaving out all the content of mathematics, which is the proofs 08:01:43 hpp: no, we don't. we give one of the two definitions for exponentiating reals _before_ calculus, 08:02:00 wob_jonas: That works too 08:02:01 You need some sort of limit 08:02:14 Cale: I'm not even in Calculus yet and I get logarithms fairly well. I couldn't tell you the exact rule for irrational powers, but otherwise I get it. 08:02:23 If you really want to scrape by, you can use the least upper bound property directly. 08:02:25 -!- diginet has quit (Quit: diginet has quit!). 08:02:37 -!- diginet has joined. 08:02:39 the definition where you extend exponentiation from rational exponents to real exponents such that it's monotonous in the exponent 08:03:16 wob_jonas: How do you know that extension is unique? 08:03:39 and even without calculus, it's possible to prove that on rational exponents it's monotonous, so an extension exists, and with a bit more work, it's even possible to prove that the extension is unique 08:04:05 Cale: without calculus, you do stuff with inequations to effectively prove that it's continuous on rationals 08:04:21 and prove that way that the extension at any point is unique 08:04:46 or you just take it at faith at that point and prove it later after you've done some basic calculus, which is still not circular 08:04:47 I've never seen a highschool introduce enough concepts to actually make the thing work. 08:05:09 Well, some presentations aren't circular, but just leave out details, those are the better ones 08:05:12 Cale: I could recommend a good textbook, but all the good books at highschool level I know are in Hungarian 08:05:32 I'm sure in some parts of the world, they do a better job than in the US and Canada 08:05:37 how much mathematics do you read in Hungarian? 08:05:40 none 08:05:49 then I won't recommend textbooks 08:06:37 Unfortunately, schools in the US *seem* to like introducing logarithms quite quickly. I think this is for historical reasons, though. 08:06:41 The best way to do it, imo, is just to wait until you have the integral 08:06:49 and/or power series 08:06:54 one or the other will do well enough 08:07:04 Logarithms used to be a practical requirement for a lot of calculation, after all. 08:07:24 Yeah, it's sort of a silly hold-over from the times when people actually used log tables 08:07:47 Note that you also need to know that exponentiation is continuous to be able to define logarithms 08:07:49 and so you'd need some sort of hazy idea of what they were about in order to use them to multiply numbers faster 08:08:05 so it's definitely needed, but it's still possible to just leave the proof for later in a high school 08:08:16 wob_jonas: You need to know that the integral of a continuous function is continuous :) 08:08:29 and the integral of a positive function is monotone 08:08:29 Even if you didn't really get them, it was worth at least having the directly relevant properties shoved in your head. 08:08:35 Cale: no, the power series is the other definition, and you need to know both in any case, and prove them equivalent 08:08:47 Well, depends on how you go about things 08:08:52 Cale: what integral? 08:09:01 integral from 1 to x of 1/t dt 08:09:19 You can take that as the definition of log x 08:09:27 um... yes, but I don't think that really helps you 08:09:27 and work everything out from there 08:09:53