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Mathematics
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2016-08-12 at 10:54 PM UTCMaths is pretty fuckin' dope.
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2016-08-12 at 11:08 PM UTC
Like with all language humans did not create the things these symbol and operations represent. The knowledge was revealed through contemplation not constructed of thought. Much like a horse has existed before we called it such a set of horses existed before either term was defined.
Mathematics is much like religion. Those who fail to see beauty in it are oft ignorant and those who see the beauty in it are oft arrogant. Math is a very useful and nessecary component of the humans understanding of various phenomenon but it cannot truly express everything the human experience has to offer.
Such wisdom. I agree with this sentiment. If the Universe is a computer program mathematics is it's programming language. -
2016-08-12 at 11:23 PM UTCThe Universe is just a big old mathematical clusterfuck made up of 17 fundamental particles governed by 4 rules(forces) with some probability thrown in.
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2016-08-12 at 11:26 PM UTC
The Universe is just a big old mathematical clusterfuck made up of 17 fundamental particles governed by 4 rules(forces) with some probability thrown in.
https://en.wikipedia.org/wiki/Patterns_in_nature
https://en.wikipedia.org/wiki/Rule_30
Sheeeeeit son -
2016-08-12 at 11:28 PM UTC
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2016-08-12 at 11:43 PM UTC
In general, I lean
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The following users say it would be alright if the author of this post didn't die in a fire! -
2016-11-19 at 6:33 PM UTC
Originally posted by Lanny In general I lean nominalist and while that doesn't totally commit one to believing mathematics is invented rather than discovered it lends itself to that conclusion and it is my general inclination. I watched a walk by Philip Wadler and he made this argument about how three or four mathematicians seemed to independently discover the decidability problem and that that was an argument for a discovery model of mathematics. Wadler is a really smart guy but I thought that was kind of a disingenuous move, it fails to acknowledge the distinction between axioms and theorems, the decidability problem is the product of systems in which it emerges, yes we may "discover" new properties of a formal system as in this case but that discovery is predicated on the invention of the system to start with. I'll claim that nothing which is discovered can be fully reduced to invented parts (I recently discovered my phone has a "do not disturb" feature, that's not an argument that my phone or that feature are discovered properties of the universe rather than something invented).
I agree up to a certain point with you. I'm more of an intuitionist than a platonist myself, and I think that axioms are invented and theorems are discovered within the structural limits drawn by the design of the axioms, which is basically what undecidability is all about (I guess that the three mathematicians you were talking about are godel, emil post and turing). So, for instance, working in number theory using the peano axioms rather than the presburger arithmetic is a whole different thing, and that's what I think has been the finishing blow to platonism: the fact that there are undecidable statements within a system implies that there's not such a thing as a perfect bijective function between the mind and the so called perfect platonic realm. Actually, I don't see much difference between religion and platonism since the last one asks for a blind faith in the aforementioned hyperuranion and it makes sense from an historic perspective since platonism stems from the pythagorean mysticism.
One might naturally make some argument from isomorphisms between our mathematics and the world as being evidence that mathematical systems are founded in natural, discovered elements of the world. But this fails too, to model the world post-hoc is not to be discovered. Consider natural languages model the world yet no one would claim that English was "discovered". Likewise the relationship of mathematics to the world is an intentional product of its genesis, it contains similar structures not because it is similar to the world but because it exists to model it.
However I find your critics of the analogy with the "do not disturb" phone feature kinda fallacious. The designers of a phone will know (virtually) every property of the phone they're developing, so there will be nothing to discover. But mathematics is on a whole different level of complexity. When cantor single-handedly created set theory he could have not predicted that the continuum hypothesis is undecidable, so this is something that has been "discovered" by paul cohen, but of course it was already a sort of "built-in feature" of axiomatic space they were working on. I dunno, man, it's fucked up and I'm getting confused, but I'd go as far as to say that the very fact that when you invent a system you cannot virtually know every property means that then everything else from that point forth is discovered.
About isomorphism between math and the real world, those are discovered too and since I think that the so called "pure mathematics" is an hoax and doesn't exist (fuck that faggot of harold hardy), I infer that every mathematical model will eventually be linked to something in the real world (that doesn't necessarily imply the opposite): for instance, category theory, which is known as the most abstract field of math, has been proved useful in many real-world fields (computational linguistics, sorting algorithms, AI and so on): ah, with real-world applications I talk about things that are discovered (such as new physics shit) and things that are invented (such as computer science stuff, artificial intelligence, automata theory). So math could be invented and sometimes only used for other things that have been invented and not discovered. Sounds very autistic.
Originally posted by thelittlestnigger Does the mind have no mathematical properties? Is there any way we could define it as a mathematical object? If I was a smarter man I would say perhaps but all I can say now is I don't know.
Yeah I think we could define the mind as a mathematical object and eventually we will in a much more rigorous way. But we do now by now is that the mind is not a turing machine because we do not crash by bumping into the halting problem when we reason around undecidable statements (at least we can prove that they undecidable, a computer cannot)The following users say it would be alright if the author of this post didn't die in a fire! -
2016-11-19 at 9:34 PM UTCI lean
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2016-11-20 at 4:59 AM UTChow profound your thoughts! I AGREE! I AGREE! I AGREE!
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2016-11-20 at 5:27 AM UTC
Originally posted by antinatalism how profound your thoughts! I AGREE! I AGREE! I AGREE!
Thy thoughts are so profound they confound my innermost being by believing and seeing the beauty of thine mind. Can it be? A soul like me? Is it perhaps destiny, should i flee or run towards this feeling, so appealing in retrospect perhaps freeing? A prospect, unseeing, unseen, to behold and held until death, in the end, is finally dealt.The following users say it would be alright if the author of this post didn't die in a fire! -
2016-11-20 at 6:56 AM UTC
Originally posted by antinatalism the mind is not a turing machine because we do not crash by bumping into the halting problem when we reason around undecidable statements (at least we can prove that they undecidable, a computer cannot)
I dont know about that. I think the halting problem that crashes the mind is much more complex. I would say a traumatic expeience and difficulty processing it is relatively similar to a computer arriving at an undecidable statment. The difference is that the computer needs a human to reboot it whereas the human cannot simply "crash" but must carry on in the face of undecidability. -
2016-11-20 at 8:40 AM UTCAntinatalism, I thanked your post because as far as I can tell it was an authentic, cogent response, not necessarily because I agree with it, but I'm glad my hodunk ramblings on the philosophy of mathematics aren't cast out into the void absent an audience.
Originally posted by antinatalism I guess that the three mathematicians you were talking about are godel, emil post and turing
Replace Post with Church and yee. Honestly I don't know much about Post other than I've heard his name in relation to the history of computability theory.the finishing blow to platonism: the fact that there are undecidable statements within a system implies that there's not such a thing as a perfect bijective function between the mind and the so called perfect platonic realm.
That's an interesting falsification condition for platonism. I'm certainly no platonist but there are complete and consistent formal systems. They may not contain arithmetic, but we could imagine the really hardcore platonist being like "well yeah but fuck arithmetic, here's a mathematics that can't express godel's theorem and BAM!". It would be a poor sort of mathematics, as least from the perspective of a public that expects what we're taught math is in grade school to work, but then it's a poor field that relies on public expectation for its legitimacy.However I find your critics of the analogy with the "do not disturb" phone feature kinda fallacious. The designers of a phone will know (virtually) every property of the phone they're developing, so there will be nothing to discover. But mathematics is on a whole different level of complexity. When cantor single-handedly created set theory he could have not predicted that the continuum hypothesis is undecidable, so this is something that has been "discovered" by paul cohen, but of course it was already a sort of "built-in feature" of axiomatic space they were working on. I dunno, man, it's fucked up and I'm getting confused, but I'd go as far as to say that the very fact that when you invent a system you cannot virtually know every property means that then everything else from that point forth is discovered.
I don't know, what's your experience with the development of commercial software? Nothing in 2016 is proved, almost every commercial software product is shipped with known (although generally minor) bugs, and the expectation that some slipped through the QA process. What are the status of such behaviors? Discovered or invented? They are the inevitable conclusion of the instructions the constitute software although we certainly don't know about them when we're creating same.
Ultimately the substrate from which such behaviors emerge are manifested constructs of the mind. There may be some isomorphism between the contents of our mind, and the language rules are expressed in, and the actual behavior out in the world that we see but we need not speculate some kind of idealized thing which each instance embodies. We can say that we, in a sense, "discover" unexpected properties of systems but ultimately if such behaviors are implied by the systems that house them then I'd argue they share the status as invented or natural that their superior system holds.About isomorphism between math and the real world, those are discovered too and since I think that the so called "pure mathematics" is an hoax and doesn't exist (fuck that faggot of harold hardy), I infer that every mathematical model will eventually be linked to something in the real world (that doesn't necessarily imply the opposite): for instance, category theory, which is known as the most abstract field of math, has been proved useful in many real-world fields (computational linguistics, sorting algorithms, AI and so on): ah, with real-world applications I talk about things that are discovered (such as new physics shit) and things that are invented (such as computer science stuff, artificial intelligence, automata theory). So math could be invented and sometimes only used for other things that have been invented and not discovered. Sounds very autistic.
I'm a little lost on what you're trying to get at here. It does seem like we can come up with formal systems with only trivial relations to the physical world. Consider the toy example of Hofstadter's MU puzzle. It's useful only, in so far as I can tell, as a didactic device. Sure you can say "well that's an isomorph to an educational process" but that seems to render the notion of a "pure" system as, uhh, trivially impossible because at very least you can say any system presented as evidence of pure mathematics serves as a model supporting the notion of a world in which pure systems exist but this trivializes the point to start with.Yeah I think we could define the mind as a mathematical object and eventually we will in a much more rigorous way. But we do now by now is that the mind is not a turing machine because we do not crash by bumping into the halting problem when we reason around undecidable statements (at least we can prove that they undecidable, a computer cannot)
I won't particularly defend the proposition that "the mind is a turing machine" but the fact that we don't implode when faced with a undecidable problem is not conclusive evidence of that fact. Not every turing machine is universal, many turing machines provably halt in a finite number of steps. The halting problem deals with a more general class of machine that is necessarily needed to support human consciousness. Consider the question "can a given turing machine halt with a decision in less than finite N operations?", this is a trivially easy machine to construct and such "timeouts" would seem sufficient to handle the human process of dealing with undecidable problems, at least at an extremely high level.The following users say it would be alright if the author of this post didn't die in a fire! -
2016-11-21 at 6:44 PM UTC
Originally posted by Lanny Antinatalism, I thanked your post because as far as I can tell it was an authentic, cogent response, not necessarily because I agree with it, but I'm glad my hodunk ramblings on the philosophy of mathematics aren't cast out into the void absent an audience.
Post was a bit like the lobachevskij of computability theory, he came pretty close to a result similar to the incompleteness theorems, but godel outspeeded him and that triggered his depression (to be fair, his head was already kinda fucked up)
Replace Post with Church and yee. Honestly I don't know much about Post other than I've heard his name in relation to the history of computability theory.
Originally posted by Lanny That's an interesting falsification condition for platonism. I'm certainly no platonist but there are complete and consistent formal systems. They may not contain arithmetic, but we could imagine the really hardcore platonist being like "well yeah but fuck arithmetic, here's a mathematics that can't express godel's theorem and BAM!". It would be a poor sort of mathematics, as least from the perspective of a public that expects what we're taught math is in grade school to work, but then it's a poor field that relies on public expectation for its legitimacy.
Well, the presburger arithmetic that I mentioned in my previous post is proven to be consistent, complete, decidable at the cost of being much weaker than the peano arithmetic. Basically, the first incompleteness theorem doesn't apply to it. Despite that, platonists are still deluded faggots
Originally posted by Lanny I don't know, what's your experience with the development of commercial software? Nothing in 2016 is proved, almost every commercial software product is shipped with known (although generally minor) bugs, and the expectation that some slipped through the QA process. What are the status of such behaviors? Discovered or invented? They are the inevitable conclusion of the instructions the constitute software although we certainly don't know about them when we're creating same.
As far as I know, the main reason why mathematics approach such as formal verification, model checking, automated bug fixing and so on are not very much used in the debugging process is because of the rice's theorem that shows that the only properties of a program that are algorithmically decidable are trivial, therefore making any in-depth analysis impossible with this kind of techniques. But yeah, your argument makes sense and in fact I was talking more about perception than from a factual perspective.
Originally posted by Lanny Ultimately the substrate from which such behaviors emerge are manifested constructs of the mind. There may be some isomorphism between the contents of our mind, and the language rules are expressed in, and the actual behavior out in the world that we see but we need not speculate some kind of idealized thing which each instance embodies. We can say that we, in a sense, "discover" unexpected properties of systems but ultimately if such behaviors are implied by the systems that house them then I'd argue they share the status as invented or natural that their superior system holds.
Again, fair point. anyway, that made me think at a quote of a (((coen)))'s brothers movie, a serious man, about mathematics being "the art of the possible" and that guy of mathematica, stephen wolfram, when said that math is basically an historical artifact where there's absolute freedom (within the rules of logic), and from this space of "all possible mathematics", given by all the possible consistent axiomatic systems, you pick each time the most appropriate model to describe a scientific theory\whatever (an example of that could be the use of non-euclidean geometry for special relativity)
Originally posted by Lanny I'm a little lost on what you're trying to get at here. It does seem like we can come up with formal systems with only trivial relations to the physical world. Consider the toy example of Hofstadter's MU puzzle. It's useful only, in so far as I can tell, as a didactic device. Sure you can say "well that's an isomorph to an educational process" but that seems to render the notion of a "pure" system as, uhh, trivially impossible because at very least you can say any system presented as evidence of pure mathematics serves as a model supporting the notion of a world in which pure systems exist but this trivializes the point to start with.
I dunno what exactly I was rambling about cuz, full disclosure, the combination of alcohol + short attention span made me switch to full stream of consciousness mode, but trying to guess, I was just praising the beauty of the autism underlying math, invented by man, used to build other systems, built by man, instead of using math models to investigate the nature and shit. Btw, I've read hofstadter's godel escher bach years ago but I remember that the MU puzzle was recreational mathematics à la martin gardner: other than that, no serious mathematics field lies under the category of "pure mathematics" for a long time
Originally posted by Lanny I won't particularly defend the proposition that "the mind is a turing machine" but the fact that we don't implode when faced with a undecidable problem is not conclusive evidence of that fact. Not every turing machine is universal, many turing machines provably halt in a finite number of steps. The halting problem deals with a more general class of machine that is necessarily needed to support human consciousness. Consider the question "can a given turing machine halt with a decision in less than finite N operations?", this is a trivially easy machine to construct and such "timeouts" would seem sufficient to handle the human process of dealing with undecidable problems, at least at an extremely high level.
Right. However, if we consider machines that never halts and for which the halting problem is decidable, so deciders, finite state machines (DFA and, I guess, NFA too) and so on, that decidability appears to be only theoretical given the amount of computations required to run that task, and it doesn't seem that the mind takes all this effort to reason about those problems. that's why I'd think about models that can simulate parallelism more efficiently than a TM. btw, I remember roger penrose shilling for a computational mind theory based upon quantum computation, but I don't much about that and I'm not even aware whether the church-turing thesis still applies to quantum computing. -
2016-12-01 at 2:39 AM UTCjedi kabbalah number games
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2016-12-04 at 8:54 AM UTCmmethmatics
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2016-12-04 at 8:54 AM UTCtinnematics
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2017-03-16 at 10:07 PM UTCsacred mathemaics donot lie
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2017-03-16 at 10:36 PM UTCi say math is a human discovered system of measurement that can be applied in one form or other to just about anything. the variables we measure using math existed before we discovered it, but the system itself dint exist until humans devised it.
a more interesting question is do animals count and to what degree. some studies suggest that some do. -
2017-03-22 at 1:23 AM UTCI like math for two reasons.
1. Triangles
2. The question is trivial and left as an exercise for the reader. -
2017-03-29 at 3:43 PM UTCdeep and interesting thread until scro and bling came in and killed it.
