2013-03-04T00:18:48 *** srgpqt has quit IRC (Quit: leaving) 2013-03-04T00:26:06 *** _flag <_flag!~flag@69-165-173-172.dsl.teksavvy.com> has quit IRC (Ping timeout: 250 seconds) 2013-03-04T00:39:49 *** _flag <_flag!~flag@69-165-173-172.dsl.teksavvy.com> has joined #aichallenge 2013-03-04T00:48:03 *** djr_ has quit IRC (Quit: Leaving) 2013-03-04T01:22:00 *** sevikkk has quit IRC (Ping timeout: 260 seconds) 2013-03-04T01:45:21 *** _flag <_flag!~flag@69-165-173-172.dsl.teksavvy.com> has quit IRC (Ping timeout: 248 seconds) 2013-03-04T01:54:11 *** Accoun has joined #aichallenge 2013-03-04T02:02:28 *** sevikkk has joined #aichallenge 2013-03-04T02:13:50 *** mceier has quit IRC (Quit: leaving) 2013-03-04T02:28:32 *** foRei has quit IRC (Quit: Bye) 2013-03-04T02:52:16 *** mleise has joined #aichallenge 2013-03-04T03:20:08 *** epicmonkey has joined #aichallenge 2013-03-04T04:01:07 *** mceier has joined #aichallenge 2013-03-04T04:05:15 *** mviel has joined #aichallenge 2013-03-04T04:45:17 *** sigh has joined #aichallenge 2013-03-04T05:09:06 sigh: http://en.wikipedia.org/wiki/Power_function lol 2013-03-04T05:09:23 can you work out what happened there? :P 2013-03-04T05:11:12 hmm? 2013-03-04T05:12:18 some company "Lego Technic" defined some things called power functions 2013-03-04T05:12:31 which are just simple polynomials, not really what I'd expect for a power function 2013-03-04T05:12:50 then they wrote a wiki page about it, claiming that's how power functions are defined in mathematics 2013-03-04T05:12:57 with terrible english and typos 2013-03-04T05:13:26 ahhh\ 2013-03-04T05:13:32 a power function should be like r^x i think 2013-03-04T05:13:46 that would be the intuitive def 2013-03-04T05:14:03 and would make sense to then have "see also exponentiation" 2013-03-04T05:14:57 first few search results for "power function" disagree with you, i think 2013-03-04T05:16:02 c.f. http://mathworld.wolfram.com/TruncatedPowerFunction.html 2013-03-04T05:17:11 why would that be a power function? 2013-03-04T05:17:21 that doesn't make any sense, but must be 2013-03-04T05:17:46 it's raising the variable to a power 2013-03-04T05:17:47 what the internet is defining as power functions are already defined as monomials no? 2013-03-04T05:18:10 what's a name for a^x functions then? :P 2013-03-04T05:19:07 exponentials in the wrong base :P 2013-03-04T05:19:23 http://www.tandfonline.com/doi/abs/10.1080/0020739940250102?journalCode=tmes20 that person is from my uni, but in the abstract he uses power functions as I would define them 2013-03-04T05:22:23 fair enough 2013-03-04T05:22:33 not such a big deal as long as you are clear 2013-03-04T05:23:00 usually I would associate power function with a function of two variables, because that's how it is in most programming languages 2013-03-04T05:23:09 *** Areks has joined #aichallenge 2013-03-04T05:29:22 i've been playing around with ways to formally define a^b for real numbers a and b 2013-03-04T05:29:28 (not both zero) 2013-03-04T05:29:42 it's surprisingly messy whichever way you go about it 2013-03-04T05:30:03 turns out that paper from above is pretty much exactly that, though he assumes a lot of mess 2013-03-04T05:30:06 exp(log(a)*b) isn't good enough? 2013-03-04T05:30:18 to do that you first need to define either exp or log 2013-03-04T05:30:28 then show it's bijective (hence the other exists) etc. etc. 2013-03-04T05:30:41 then show all the indice laws etc. 2013-03-04T05:30:52 and that it matches up with the more constructive ways to define it 2013-03-04T05:32:05 ie. a^n = repeated multiplication, a^-z = 1/a^z (negative integer powers), a^(1/n) = unique positive s st s^n = a, a^(m/n) = (a^m)^1/n and show that's equal to (a^1/n)^m etc. etc. 2013-03-04T05:32:31 you have to force a to be non-negative at some point of course without introducing complex numbers 2013-03-04T05:32:41 yeah, fair enough 2013-03-04T05:32:45 :P 2013-03-04T05:32:53 that's just because real numbers are messy 2013-03-04T05:32:57 yep 2013-03-04T05:33:05 there's a reason i prefer algebra to analysis 2013-03-04T05:33:07 it's the mess 2013-03-04T05:33:10 :) 2013-03-04T05:33:40 I just work with integers, and mostly ones that can fit in a 64 bits :P 2013-03-04T05:34:10 oh yeah, a^r = lim_{i->infty} a^q_i where {q_i} -> r 2013-03-04T05:34:14 :P 2013-03-04T05:34:26 which works since Q is dense in R 2013-03-04T05:34:35 yeah 2013-03-04T05:35:11 though not sure if you also need to show the choice of rational sequence converging to r is arbitrary 2013-03-04T05:35:22 that's probably already covered by some general theorem 2013-03-04T05:36:02 what do you mean? 2013-03-04T05:36:16 is that kind of covered by what it means to be converging? 2013-03-04T05:36:26 well you could have {q_i} and {q_i'} both convering to r 2013-03-04T05:36:37 but does that mean lim a^qi = lim a^qi'? 2013-03-04T05:36:41 oh, and that both are equal 2013-03-04T05:36:43 yeah 2013-03-04T05:36:59 i suspect that's covered more generally 2013-03-04T05:37:09 but not sure with what off the top of my head 2013-03-04T05:38:03 all of this started when last week I thought "how to explain what a^b means to first year economics students" 2013-03-04T05:38:03 yeah, seems to be pretty fundamental to any functions of real numbers 2013-03-04T05:38:15 even just defining addition 2013-03-04T05:38:17 i think i might skip trying to explain it, maybe just say use your calculator when not sure 2013-03-04T05:38:25 haha 2013-03-04T05:39:40 repeated mul, inverses for negatives, roots for rationals gives enough of a working knowledge 2013-03-04T05:39:57 that's probably just going to confuse them too tbh 2013-03-04T05:40:02 unfortunately 2013-03-04T05:40:36 they need to at least understand the first two... 2013-03-04T05:40:48 yeah was just about to say i will be giving those 2013-03-04T05:40:52 then all the indice laws etc. 2013-03-04T05:40:57 and how to work with roots 2013-03-04T05:40:59 etc. 2013-03-04T05:41:25 also need to explain what composition of functions are and inverses to explain the relationship between ln and exp 2013-03-04T05:41:40 which the lecturer doesn't do :| 2013-03-04T05:41:56 ah... are you taking tutorials? 2013-03-04T05:42:03 yeah, second year of doing them 2013-03-04T05:42:42 doing multivariable calc and this calc for economics unit (up to about constrained optimisation of bivariate functions, but really simple functions) this semester 2013-03-04T05:43:56 exp, just show the graph, and ln is just an undo function for exp :P 2013-03-04T05:44:27 well same thing for logarithms 2013-03-04T05:44:39 by explaining what undo means you might as well explain what inverse means 2013-03-04T05:44:44 and composition 2013-03-04T05:44:59 logarithm is just counting the number of digits in the number :P 2013-03-04T05:45:14 :P 2013-03-04T05:45:20 *shakes* 2013-03-04T05:46:52 i keep seeing you pop up in philosophy of maths threads 2013-03-04T05:47:00 what school of thought do you actually follow? 2013-03-04T05:47:07 yeah, they keep popping up on my homepage 2013-03-04T05:47:15 i don't even know what the schools of thought are :P 2013-03-04T05:47:27 i'm a "nothing is invented" kind of person though, if that answers your question at all 2013-03-04T05:47:48 well, most things that claim to be invented i don't think are invented anyway 2013-03-04T05:48:07 most things in mathematics, or in general? 2013-03-04T05:48:26 mathematics especially, but in general too 2013-03-04T05:48:43 was chess invented? 2013-03-04T05:48:55 i'm undecided about axioms and even less so definitions 2013-03-04T05:49:10 see the last part of that last sentence :P 2013-03-04T05:49:19 yeah, that was my point :P 2013-03-04T05:49:40 i mean really there's a set of games that could follow such rules 2013-03-04T05:49:44 chess is but one of them 2013-03-04T05:49:50 yup 2013-03-04T05:49:53 *** thestinger has joined #aichallenge 2013-03-04T05:49:55 what's your opinion? 2013-03-04T05:50:04 is opinion even the right word? 2013-03-04T05:50:30 IMO, invention is a type discovery if you look at it abstractly enough 2013-03-04T05:50:46 where iyo is the line drawn? 2013-03-04T05:51:23 here's a general example i'm pedantic to skaters about, is the kickflip invented or discovered? 2013-03-04T05:51:27 you can easily guess where I fall 2013-03-04T05:52:01 for that matter, is the skateboard invented or discovered? 2013-03-04T05:52:27 yeah, I'm of the opinion that the distinction is just one of convenience 2013-03-04T05:52:46 if the search space is abstract enough and large enough, people just call it an invention 2013-03-04T05:53:15 I don't think there is a line 2013-03-04T05:53:17 on a similar note, what's your opinion on patents? 2013-03-04T05:53:49 should nothing be patentable? everything? only those things for which we're socially better off for allowing to be patentable (ie. stuff which requires big money for research) 2013-03-04T05:54:04 the later is individually unfair imo 2013-03-04T05:54:26 perhaps that could be an argument for patentable people subsidising unpatentable people 2013-03-04T05:54:35 patents were useful as a way to encourage people to make their inventions public 2013-03-04T05:54:54 but when it has morphed into the concept of intellectual property it is very harmful 2013-03-04T05:54:58 i don't think many would disagree that that no longer happens 2013-03-04T05:55:06 but there is always the argument that a better patent system exists 2013-03-04T05:55:26 ie. the options aren't necessarily the current patent system or no patent system 2013-03-04T05:55:31 short patent terms are ok 2013-03-04T05:55:39 what about for mathematics? 2013-03-04T05:55:43 ie. Gauss elimination? 2013-03-04T05:55:54 or theorems, definitions etc? 2013-03-04T05:56:10 and if not mathematics, why not compared to something else? see the options listed above :P 2013-03-04T05:56:43 I don;t know where I stand, it's somewhere between no patents and what's socially optimal 2013-03-04T05:56:45 well, I already disagree completely with any sort of software patents 2013-03-04T05:56:48 while individually unfair 2013-03-04T05:57:01 so mathematics is further on that side 2013-03-04T05:57:57 i/we are of course biased 2013-03-04T05:57:59 everyone is 2013-03-04T05:58:04 yup 2013-03-04T05:58:07 it's a pretty messy situation 2013-03-04T05:58:21 however, I do think it is feasible to do away with the entire patent system 2013-03-04T05:58:37 yeah, ramp up publicly funded research 2013-03-04T05:58:42 the researchers will come 2013-03-04T05:58:50 the only compelling argument for keeping it I've heard comes from the pharmaceutical industry 2013-03-04T05:58:55 it's the private funding which is harder without it 2013-03-04T05:58:59 which I think can be managed separatly 2013-03-04T05:59:40 hmmm options for managing separately? I can think of one, but it's almost equivalent 2013-03-04T06:00:09 tax the resulting product, and the creators/discovers/whatever get a "prize" from the government 2013-03-04T06:00:19 or just give the prize for the social gain 2013-03-04T06:00:34 not sure how financially feasible that last one would be 2013-03-04T06:01:27 for pharma? it's easy... they already need approval from the government to make their drugs available... the same process can be used to grant a temporary monopoly 2013-03-04T06:03:01 antimatroid: or just make it so they have to license it 2013-03-04T06:03:11 the same thing they do for the "standards essential" patents but for all of them 2013-03-04T06:03:23 they get their money, and people can compete with them (at a tiny disadvantage) 2013-03-04T06:04:07 https://en.wikipedia.org/wiki/Reasonable_and_non-discriminatory_licensing 2013-03-04T06:05:37 even if patents are a good idea, it's silly in general that all the different type of patents are treated the same 2013-03-04T06:06:22 I think it's silly that having a patent gives you a choice to monopolize something 2013-03-04T06:06:47 you should be able to get licensing fees ofc, but why should it throw out competition? unless the government was setting the prices 2013-03-04T06:07:10 yeah, agree 2013-03-04T06:07:11 heavy regulation can sort of work and competition can sort of work, but granting monopolies does not :P 2013-03-04T06:07:46 it's different per industry anyway 2013-03-04T06:08:44 in what way? 2013-03-04T06:09:26 sigh: well, something like the telecom industry where there's a massive barrier to entry for competition 2013-03-04T06:10:01 ah, yeah, i see what you mean now 2013-03-04T06:10:04 competition only works in theory for something like that 2013-03-04T06:10:44 *** coeus_ has quit IRC (Ping timeout: 255 seconds) 2013-03-04T06:11:03 oops, got distracted :P 2013-03-04T06:12:42 * thestinger thinks the telecom stuff should just be treated the same way as roads :P 2013-03-04T06:13:21 * antimatroid agrees with above 2013-03-04T06:13:39 thestinger: you don't want net neutrality? 2013-03-04T06:13:46 not the direct above :P 2013-03-04T06:14:19 antimatroid: well net neutrality is really important when you have corporations that own/run it all 2013-03-04T06:14:28 but not otherwise? 2013-03-04T06:15:00 antimatroid: well it's probably a good policy anyway... I mean otherwise you just open up huge amounts of potential corruption 2013-03-04T06:15:04 who gets to decide on that stuff? 2013-03-04T06:15:16 we used to have telecom as a government run organisation in australia, but then it got privatized 2013-03-04T06:15:41 then why would you want telecom stuff to be treated like roads? or do you also want no toll roads? :P 2013-03-04T06:15:41 sigh: well I think it probably works better as mostly a municipal thing 2013-03-04T06:15:58 fair enough 2013-03-04T06:16:07 antimatroid: we don't really have toll roads :) 2013-03-04T06:16:17 toll roads suck 2013-03-04T06:16:20 i would be curious to see how competing publicly funded organisations went 2013-03-04T06:16:36 the problem with public funding is inefficiency, one component of that is the lack of competition 2013-03-04T06:16:39 antimatroid: they don't even need to be publicly funded though 2013-03-04T06:16:42 they can be self-funded 2013-03-04T06:17:01 lots of government stuff works that way (like the post office in the US - it actually pays into the government) 2013-03-04T06:17:01 self-funded are usually profit driven 2013-03-04T06:17:07 antimatroid: doesn't have to be 2013-03-04T06:17:12 rather than for social purposes 2013-03-04T06:17:16 it usually is 2013-03-04T06:17:59 you also need to work out how to pay people based on their social contribution 2013-03-04T06:18:07 with performance based benefits 2013-03-04T06:18:49 now i'm getting a little far out of what's realistic 2013-03-04T06:18:59 you have to completely change the structure of markets to do that 2013-03-04T06:19:14 which people are quite opposed to after the history of communism 2013-03-04T06:19:15 the unique thing about internet/cellular infrastructure is that it's 99% capital costs 2013-03-04T06:19:22 which the government mostly pays/payed for anyway 2013-03-04T06:19:49 and that's why it's so messed up - they essentially pick and choose whoever is going to profit from that public investment 2013-03-04T06:21:16 that's a bigger problem though 2013-03-04T06:21:36 universities that take lots of public money, but operate as corporations and patent all their research, etc. 2013-03-04T06:22:01 i realised yesterday too, I don't think astrophysics is implicitly more applicable to people's everyday lives than pure mathematics, yet probably on average attracts more funding. Which is interesting when the claim is that funding increasingly only goes to things which have obvious implicit applications to people's everyday lives. It needs a further caveat, or people somewhat understand the research proposal and think 2013-03-04T06:22:59 whoops /s/implicitly/explicitly 2013-03-04T06:29:00 antimatroid: going back to my school-of-though question... do you think mathematical entities exist, and if so in what sense do they exist? 2013-03-04T06:30:49 sigh: what do you mean by mathematical entity? 2013-03-04T06:31:00 and also what do you mean by exist? :P 2013-03-04T06:31:03 e.g. does the number "1" exist 2013-03-04T06:31:19 i dunno :P 2013-03-04T06:31:28 haha 2013-03-04T06:31:28 it exists as an integer :P 2013-03-04T06:31:41 well existence is something you often prove mathematically 2013-03-04T06:31:48 so obviously you don't mean that kind of existence :P 2013-03-04T06:32:14 right... 2013-03-04T06:32:26 does it exist independent of people? 2013-03-04T06:32:37 well yes 2013-03-04T06:32:37 does it exist independent of the universe? 2013-03-04T06:32:53 define universe? a lot of /r/askscience people say the universe is everything which exists 2013-03-04T06:33:07 making me use something like "observably universe", annoying I know :P 2013-03-04T06:33:25 haha 2013-03-04T06:33:38 I would expect another intelligent species to have mathematics 2013-03-04T06:33:45 hence why I believe it to be independent to people :P 2013-03-04T06:33:53 observable* 2013-03-04T06:33:59 meaning what? 2013-03-04T06:34:07 what meaning what? 2013-03-04T06:34:08 they will have integers too? 2013-03-04T06:34:13 antimatroid: but perhaps unlike ours? 2013-03-04T06:34:20 they will have discovered calculus? 2013-03-04T06:34:25 "god gave us the natural numbers, everything else we constructed" 2013-03-04T06:34:37 sigh: i would expect them to have calculus, depending on how intelligent 2013-03-04T06:34:49 it's the natural way to look at rates of change for functions 2013-03-04T06:34:55 why not, say, non-standard analysis? 2013-03-04T06:35:02 well sure, it may be different 2013-03-04T06:35:07 but they'd have some form of mathematis 2013-03-04T06:35:18 they may have different conventions 2013-03-04T06:35:22 antimatroid: what if they had no discrete math at all :P 2013-03-04T06:35:33 indexing matrices differently, left/right mappings (forcing composition notation etc.) 2013-03-04T06:35:44 which way to integrate around a path 2013-03-04T06:36:21 that would be incredibly fun 2013-03-04T06:36:37 exploring the differences between the mathematics made by two different species on different planets 2013-03-04T06:38:43 you would say we discovered the natural numbers? 2013-03-04T06:38:55 based on your earlier comment? 2013-03-04T06:39:14 it was a quote which is meant mostly as a joke i think :P 2013-03-04T06:39:25 i take it as a joke anyway 2013-03-04T06:39:43 i've seen people take it more seriously :P 2013-03-04T06:40:06 i'm atheist (in the way that asymmetry is to symmetry, ie. not theist) 2013-03-04T06:40:17 but either way, would you say we discovered the natural numbers? they were there before people? 2013-03-04T06:40:38 you already know my answer to that based on other species 2013-03-04T06:40:42 i think we discovered them 2013-03-04T06:41:03 perhaps we invented peano axioms etc though? 2013-03-04T06:41:08 ie. ways to construct them 2013-03-04T06:41:11 but not the actual numbers 2013-03-04T06:41:13 yup, just clarifying... because now I want to know what it means to discover them 2013-03-04T06:41:17 but i still don't think so 2013-03-04T06:41:29 "I want to know what it means to discover them" ? 2013-03-04T06:41:39 can you further qualify what you mean? 2013-03-04T06:41:58 well it's our interpretation of fundamental concepts 2013-03-04T06:42:15 maybe an alien species would have arrived at an entirely different system of doing things from the same basis 2013-03-04T06:42:18 well, we can discovered a fossil in the ground by seeing it... obviously we didn't "see" the natural numbers somewhere? 2013-03-04T06:42:22 or did we? 2013-03-04T06:42:36 counting things 2013-03-04T06:42:53 they're isomorphic to that notion? 2013-03-04T06:42:56 antimatroid: what if you're only able to perceive the probability of things being somewhere? :) 2013-03-04T06:43:26 counting, not necessarily... what is the point of an infinite set just to count obects? 2013-03-04T06:43:29 and your senses are really terrible and throw in noise everywhere 2013-03-04T06:43:33 seems wastefull 2013-03-04T06:43:46 ahh, well infinity is the notion of "never ending" 2013-03-04T06:43:53 that and counting give the natural numbers 2013-03-04T06:44:04 that infinity anyway :P 2013-03-04T06:44:14 well, I'll never have an never ending amount of apples... why would I need a never ending amount of numbers just ot count them? 2013-03-04T06:44:28 "what's the largest number" 2013-03-04T06:44:32 add that question in to the mix 2013-03-04T06:44:51 then you'd get N :P 2013-03-04T06:45:10 N? 2013-03-04T06:45:18 the natural numbers 2013-03-04T06:45:23 \mathbb{N} happy? 2013-03-04T06:45:31 ah 2013-03-04T06:45:53 I don't know the largest number... just like I don't know the number of apples 2013-03-04T06:46:09 that's just it, you can always add 1 to a number 2013-03-04T06:46:13 so there is no largest number 2013-03-04T06:46:17 hence numbers are never ending 2013-03-04T06:46:19 giving the natural numbers 2013-03-04T06:46:45 but why would I *need* all those numbers, just for counting? I don't have that many objects? 2013-03-04T06:47:07 next you'll be telling me there are numbers below 1 2013-03-04T06:47:12 *** mleise1 has joined #aichallenge 2013-03-04T06:47:27 I can't have less than 1 apple 2013-03-04T06:47:48 sigh: negative vs positive is a unit then 2013-03-04T06:48:07 i think the order of events would be as follows: 2013-03-04T06:48:07 1. associate "counting" things with natural numbers 2013-03-04T06:48:07 2. be mathematically minded and ask "what's the largest number" and care just for its own sake 2013-03-04T06:48:07 3 .... 2013-03-04T06:48:07 4. Natural numbers 2013-03-04T06:48:18 negative numbers come in from additive inverses 2013-03-04T06:48:41 sigh: i'm going to make the assumption that there exists members of the species who are "mathematically minded" 2013-03-04T06:48:45 :P 2013-03-04T06:49:02 *** mleise has quit IRC (Ping timeout: 252 seconds) 2013-03-04T06:49:45 FYI, took a long time for humans to accept negative numbers... was only in the last mellinium 2013-03-04T06:50:08 and 0 for that matter 2013-03-04T06:50:23 that's 1000 years? 2013-03-04T06:50:40 *millenium, yup 2013-03-04T06:51:12 what's to accept? 2013-03-04T06:51:18 they're the additive inverses 2013-03-04T06:51:21 :P 2013-03-04T06:52:00 same reason why people find it hard to accept imaginary numbers 2013-03-04T06:52:18 that's because people call them imaginary numbers and people insist on visualising things :P 2013-03-04T06:52:51 if you define i = sqrt(-1) and construct if from there you can't really not accept it 2013-03-04T06:52:56 only not understandit 2013-03-04T06:53:05 true, but historical it's not always been the case that 1 has had a square root 2013-03-04T06:53:29 hey my sister wrote an essay about the 0. 2013-03-04T06:53:36 ah, now that's a very philosophically loaded statement 2013-03-04T06:53:37 well actually it was our mother... 2013-03-04T06:53:57 it implies complex numbers were invented and not discovered yeah? :P 2013-03-04T06:54:13 of course in europe the zero was some kind of devil's stuff 2013-03-04T06:54:19 otherwise historically -1 had a square root, just hadn't been discovered :P 2013-03-04T06:54:30 ok, it has not aways been accepted that x^2 = 1" 2013-03-04T06:54:35 has a soltuion 2013-03-04T06:54:37 *solution 2013-03-04T06:54:42 you keep accidentally a - 2013-03-04T06:54:49 *sigh* 2013-03-04T06:55:03 not always been known* i would say 2013-03-04T06:55:14 even with negative numbers, Diophantus (namesake for Diophantine equations) considered negative numbers to be "false" and that equations like 4x + 20 = 0 were absurd. 2013-03-04T06:55:16 x² = 1 has a Unicode solution 2013-03-04T06:55:25 antimatroid: can't you just show people complex numbers on a 2d plane? 2013-03-04T06:55:31 why can't it be visualized? 2013-03-04T06:55:50 well sure, but it's not the kind of visualisation people are used to or expect 2013-03-04T06:56:15 hmmm accepted might work 2013-03-04T06:56:42 A few days ago I though that it's all a matter of which mathematical 'grammar' you use. 2013-03-04T06:57:05 i'd say there's possibly often a gap between something being known and something being accepted 2013-03-04T06:57:24 i care about what is, so it is what's known that i care about :P 2013-03-04T06:57:42 known is pretty loaded too 2013-03-04T06:57:50 physicists and mathematicians would have different notions 2013-03-04T06:57:59 antimatroid: sure... but my main point was that if you consider us a "mathematically minded" species, it took us an awfully long time to accept these concepts 2013-03-04T06:58:07 e.g. a subtraction like 4-2, can exist in a grammar that only allows natural numbers and addition by saying: 4=2+2 2013-03-04T06:58:21 I didn't mean that 2013-03-04T06:58:35 and often only when it was shown to be useful, like complex numbers for solving cubics 2013-03-04T06:58:47 I meant there exists members of the species like me who consider the properties of mathematics useful to study by themselves 2013-03-04T06:58:53 and zeroes for economic calculations ^^ 2013-03-04T06:59:53 antimatroid: sure the properties are interesting to study... but how did you decide from that there was no largest number? 2013-03-04T07:00:18 sigh: I don't think something has to be useful for it to be accepted, certainly not today 2013-03-04T07:00:36 look at non-standard analysis and higher category theory :P 2013-03-04T07:00:56 i don't think people would say what they're doing is "wrong", merely that it's not (currently) useful 2013-03-04T07:01:01 no, not today... but I meant useful in the mathematical sense as well 2013-03-04T07:01:03 and some of it probably is useful 2013-03-04T07:01:53 but historically, the question of whether "-1" exists or "0" exists or "i" was not just a question of definition 2013-03-04T07:01:55 so many loaded words :P 2013-03-04T07:02:07 yup :P 2013-03-04T07:02:48 that's another complaint, people using loaded mathematical words when explaining stuff to non-mathematicians which have more general definitions 2013-03-04T07:03:38 like the (cardinal) number of real numbers being larger than the (cardinal) number of rational/etc. numbers 2013-03-04T07:03:42 or almost always 2013-03-04T07:04:24 or even saying there's more reals than rationals is kind of loaded without defining what we mean by more in the way of bijections 2013-03-04T07:04:36 *** mceier has quit IRC (Quit: leaving) 2013-03-04T07:04:55 sure, but that's not too bad though 2013-03-04T07:05:22 better than most discussions about dimensions which come up in askscience :P 2013-03-04T07:05:27 lol 2013-03-04T07:05:35 or tensors 2013-03-04T07:05:46 (which i still don't understand properly) 2013-03-04T07:05:59 to be fair, physicists define them differently to mathematicians 2013-03-04T07:06:12 i know they're to bilinear transformations what matrices are to linear transformations, but that's about it 2013-03-04T07:06:30 sigh: i wish more people on both sides were aware of that 2013-03-04T07:06:43 weren't you going on an on about tensors a while back? 2013-03-04T07:06:48 like you wrote your own library? 2013-03-04T07:06:56 you've used that library 2013-03-04T07:06:59 it was just for nd tables 2013-03-04T07:07:23 neither the mathematicians or physicists notion of tensor 2013-03-04T07:07:44 ah 2013-03-04T07:08:12 and even then it might have been stupid I think, I should have just used a map from vectors of integers to utility values or something like that 2013-03-04T07:08:26 or maps from strategy profiles to utility values would be better 2013-03-04T07:08:28 fair enough 2013-03-04T07:19:54 *** mcstar has joined #aichallenge 2013-03-04T07:20:05 antimatroid: are you all right? 2013-03-04T07:24:13 mcstar: yes, why? 2013-03-04T07:25:06 i just read your mistake on 'power functions' and why would you think that a company has anything to do with that article? 2013-03-04T07:25:40 look at the top of the article 2013-03-04T07:25:43 lego technic-power functions are completely unrelated 2013-03-04T07:25:51 it links to them from that page 2013-03-04T07:25:57 jesus 2013-03-04T07:26:07 do you know what disambiguation is? 2013-03-04T07:26:35 similarly named articles can link to eaach other without any connection between them besides their names 2013-03-04T07:27:17 (also that article is particularly shitty, but thats another topic) 2013-03-04T07:27:35 *** mceier has joined #aichallenge 2013-03-04T07:37:29 that conversation is pretty long, ill finish later 2013-03-04T07:37:33 *** mcstar has quit IRC (Quit: mcstar) 2013-03-04T07:40:24 *** _flag <_flag!~flag@69-165-173-172.dsl.teksavvy.com> has joined #aichallenge 2013-03-04T07:48:59 *** _flag <_flag!~flag@69-165-173-172.dsl.teksavvy.com> has quit IRC (Ping timeout: 252 seconds) 2013-03-04T07:50:48 *** mcstar has joined #aichallenge 2013-03-04T07:51:24 antimatroid: i wanted to share a puzzle with you, and now i almost forgot http://xorshammer.com/2008/08/18/hardest-logic-puzzle-ever/ 2013-03-04T07:51:53 bit of a letdown, it isnt that hard 2013-03-04T07:51:59 but the rest is funny 2013-03-04T08:10:27 antimatroid: did you read it or are you too damn busy? 2013-03-04T08:10:37 this is fun, haven't seen it before: "This sentence is false and it has a well-defined truth-value." 2013-03-04T08:10:45 gave the puzzle statement a read 2013-03-04T08:10:50 but otherwise too busy sorry 2013-03-04T08:11:08 not a problem, just thought it might interest you 2013-03-04T08:11:17 sigh seems interested for you :p 2013-03-04T08:11:42 i havent seen many of those sentences 2013-03-04T08:12:14 the actual "Hardest Logic Puzzle Ever" isn't mentioned on the page directly though 2013-03-04T08:12:22 there's a link to teh wiki 2013-03-04T08:12:23 also, i didnt gave the same answer, "If I asked you question Q, would you say “yes”?" 2013-03-04T08:12:28 yeah 2013-03-04T08:13:06 *** amstan has quit IRC (Quit: Konversation terminated!) 2013-03-04T08:13:32 mcstar, that's not the actual "hardest" puzzle 2013-03-04T08:13:49 i thought it was isomorph to it 2013-03-04T08:13:59 no, it's a much much simpler version 2013-03-04T08:14:52 in the actual puzzle, there is a third person who answers randomly, and you also don't know which word means yes and which means no 2013-03-04T08:15:32