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Why do we believe in math?

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  1. #76
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    Quote Originally Posted by wufwugy View Post
    Okay, this might help. Numbers are a concept and me being Thor is a concept. People treat numbers as if they are real and don't treat me as Thor as being real. While it is possible that I am actually Thor, I would agree that numbers seem to be of a true nature regarding reality and me being Thor does not. What, then, distinguishes numbers from me being Thor? What do we think of when we think of the relationship between numbers and reality, and why is that distinct from the idea that I am Thor?

    If this doesn't shine a light on where my brain is trying to go, let me know and I can possibly come up with a different way of putting it.
    More accurate would be "1+2=4" is a concept like "you are thor" is a concept. Neither is true by definition*

    *Perhaps "thor" is sometimes defined merely as the costume? Perhaps dressing as thor on Halloween would make "you are thor" true?
  2. #77
    Quote Originally Posted by JKDS View Post
    I feel like I chose the wrong words to describe my thought.

    When I say people have trouble understanding and conveying math, I don't fault math and I don't mean that math can't do it. I mean that people in general don't understand the definitions, and suck at describing things with math. If you've ever tried to explain something mathematical to another person, you've probably experienced the issue.

    There are many who can competently do this though. And understand it. Those people exist for words too, and when they speak it's beautiful
    No because with maths they are either right or wrong. With language they can take variable meanings from a phrase or more. There is a school of thought that what the artists mean is unimportant compared to what the critic takes from it. They are open to interpretation, some of my favourite quotes I know for a fact I don't take them as the artist means them, that doesn't mean that what I took from it is wrong. In Maths that is 100% not the case.
  3. #78
    Quote Originally Posted by wufwugy View Post
    Oh I remember now why I said numbers can be arbitrary but some systems dont seem to be. I don't know this from my own investigation but it's something I think I have seen from people discussing math (mostly here): there are all sorts of systems of mathematics that are internally consistent yet don't reflect the physical universe. I don't know of what any of them are or even if my statement is correct, but I seem to recall that people have created internally coherent mathematics that are not coherent when applied outside of the system, or something to that effect.
    What is much more common place in maths is for someone to make a list of assumptions and you go from there. This isn't thought to be true it's jus tthought to be a usable approximation of what is going on.

    An example is if you drop a ball from a height you can assume gravity to be 9.81 and you can make great estimations on the speed at the point it makes contact with the earth at pretty much any situation in which you'd drop a ball. Newtons laws of gravity is fucking great, it lets you make loads of predictions which are so accurate but if you don't understand it's limitations you are wrong just like the theory is. Hence why science still uses it for most situations but it certinaly doesn't for those that are known to be wrong such as GPS systems. Einstein loads of great shit comes from it but we know it's not true that doesn't mean it doesn't make loads of great predictions we can use it for.

    All of those thing make assumptions and say them. These are very important because if the assumption isn't true it's wrong this doesn't mean it isn't useful. Ideal gas law is a great example of this.

    Economic models are actually a great example of this in most cases. They make so many assumptions that they are basically nonsense in any actual real life scenario. They aren't wrong but to draw larger conclusions would be. You may recall economics nobel prize giving it to 3 lots of people who all said different outcomes were true because of the same thing and how this was retarded because obviously all three can't be true. Well none of them were ever saying they were always true.
    Last edited by Savy; 06-14-2017 at 02:07 AM.
  4. #79
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    Quote Originally Posted by Savy View Post
    No because with maths they are either right or wrong. With language they can take variable meanings from a phrase or more. There is a school of thought that what the artists mean is unimportant compared to what the critic takes from it. They are open to interpretation, some of my favourite quotes I know for a fact I don't take them as the artist means them, that doesn't mean that what I took from it is wrong. In Maths that is 100% not the case.
    That just means the phrase wasnt as defined as you'd have liked. If a phrase has more than one meaning, it means either more than one meaning exists by definition...or it means someone failed in accurately conveying or understanding the idea.

    How is "the set of all real numbers" any better than "fork"? Do you agree that my sofa would not qualify as a fork?
  5. #80
    Quote Originally Posted by JKDS View Post
    That just means the phrase wasnt as defined as you'd have liked. If a phrase has more than one meaning, it means either more than one meaning exists by definition...or it means someone failed in accurately conveying or understanding the idea.

    How is "the set of all real numbers" any better than "fork"? Do you agree that my sofa would not qualify as a fork?
    No it means it wasn't defined. I have no problem with stuff being defined in multiple ways either as long as it is consistent. Not accurately conveying something means it isn't a definition. You can misdefine things but this is exactly that a mistake.

    Based on your definitions I see no reason to believe your sofa isn't a fork.
  6. #81
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    Quote Originally Posted by Savy View Post
    No it means it wasn't defined. I have no problem with stuff being defined in multiple ways either as long as it is consistent. Not accurately conveying something means it isn't a definition. You can misdefine things but this is exactly that a mistake.

    Based on your definitions I see no reason to believe your sofa isn't a fork.
    We're at an understanding roadblock, but I think we're on the same page. I'll go to bed with this:

    Unlike math, most people DONT agree on the definitions of words. Love means something different to me than to you. Part of this disagreement is because the definitions suck, or we rely on different definitions to begin with. Another part is that people, as a whole, suck at describing things (because of laziness, poor vocabulary, or what have you). But this doesn't mean words aren't like math, it means we have an unrefined and shitty language.
  7. #82
    Quote Originally Posted by JKDS View Post
    We're at an understanding roadblock, but I think we're on the same page. I'll go to bed with this:

    Unlike math, most people DONT agree on the definitions of words. Love means something different to me than to you. Part of this disagreement is because the definitions suck, or we rely on different definitions to begin with. Another part is that people, as a whole, suck at describing things (because of laziness, poor vocabulary, or what have you). But this doesn't mean words aren't like math, it means we have an unrefined and shitty language.
    You're saying language could become a thing like maths where everything is defined etc. Yeah maybe it could. I personally don't think that's better than what we have now, or maybe I would and I just can't see it reaching that point which is fair. On a level language tries to convey shit that is much more complicated than maths but that's a different point I suppose.

    Language is also ever evolving in a way I don't think maths possibly could. I think this is a great thing about language how words can evolve over time to the point where words can mean what they mean and the exact opposite at the same time.

    It's important to realise that it isn't just people don't agree on a definition of a word like love but there is no actual definition. Dictionaries are a great attempt at this but fall so short compared to mathematical definitions it's just bollocks.

    I also want to point out that language is fucking great at what it does. I think humans deserve a great pat on the back at the complexities of language and hwo well they understand them based on context.
  8. #83
    Quote Originally Posted by JKDS View Post
    More accurate would be "1+2=4" is a concept like "you are thor" is a concept. Neither is true by definition*

    *Perhaps "thor" is sometimes defined merely as the costume? Perhaps dressing as thor on Halloween would make "you are thor" true?
    Are you positing something being true by definition makes it true in the ultimate sense? Could you also clarify exactly what "true by definition" means?
  9. #84
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    Quote Originally Posted by Savy View Post
    Do you think words always do accurately describe information?
    Language is a lossy compression algorithm for thought. Words are compressed thoughts rounded to something that most closely resembles the original.
    Our brains have just one scale, and we resize our experiences to fit.

    You wake me up early in the morning to tell me that I'm right? Please wait until I'm wrong.

  10. #85
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    I believe in maths because I'm good at it.

    I also believe in chess.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  11. #86
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    Quote Originally Posted by wufwugy View Post
    If somebody were to ask me to explain why we believe in math, I would say because it is consistent within its own assumptions and because it is useful. I don't know how accurate that is. What is your answer to the question?
    It's more of a "prove me wrong" vibe. 1+1=2. It isn't? Prove me wrong.

    You don't necessarily believe (have to believe?) . If you cannot prove it wrong, then you simply assume it as fact as best as you can understand it and move on
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  12. #87
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    Quote Originally Posted by OngBonga View Post
    I believe in maths because I'm good at it.

    I also believe in chess.
    I believe in morgandawson__ because I love chocolate.

    Also in keyanajenaye.
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    Cogito ergo sum

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  13. #88
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    Hey wuf! This isn't exactly what you're looking for, but I think it'll give you plenty of food for thought when it comes to similarities in the mythological stories of many different cultures.

    Crash Course: Mythology
  14. #89
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    Quote Originally Posted by MadMojoMonkey View Post
    For me the curious part is the lack of clear answer to the question: do humans invent math or discover it?
    We invent it and discover it tho
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  15. #90
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    Quote Originally Posted by Savy View Post
    I think we can all agree that's definitely wrong.
    Hahaha
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  16. #91
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    Quote Originally Posted by Savy View Post
    Ultimately tell me what is and isn't a plate. If you can list literally everything as one or the other or give me some grander meaning as to the word plate I'm all ears.

    If you can convey some sort of an idea as to what a plate is then that's kind of my point about language.
    Yeah, you and I have similar conceptions of a plate, and we may find some edge-cases to argue over, but my sense of a plate and your sense of a plate are pretty close. The difficulty is when we try to definitively square-away plate-ness between each other.
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  17. #92
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    Quote Originally Posted by wufwugy View Post
    Okay, this might help. Numbers are a concept and me being Thor is a concept. People treat numbers as if they are real and don't treat me as Thor as being real. While it is possible that I am actually Thor, I would agree that numbers seem to be of a true nature regarding reality and me being Thor does not. What, then, distinguishes numbers from me being Thor? What do we think of when we think of the relationship between numbers and reality, and why is that distinct from the idea that I am Thor?

    If this doesn't shine a light on where my brain is trying to go, let me know and I can possibly come up with a different way of putting it.
    Because when I have 5 rocks and 5 other rocks and pair them rock for rock, I see the 5-ness is true.
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  18. #93
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    Quote Originally Posted by MadMojoMonkey View Post
    I don't see how touch and sight are relevant, here. These properties are true of all ideas and emotions.

    Black holes fit the bill, too. I believe they exist.
    Black holes can be sensed.

    I believe either math exists or the idea of identity is total hogwash. Either everything is all one, or countability is a property of the universe.
    If it is meaningful to count things, then math exists.
    I cannot accept that I am actually you and it is only a fault of my our perception which makes me think I'm not.

    Furthermore, I posit that if there are multiple universes, then that is proof that math exists, at least in-between the universes (where there is clearly countable-ness going on)
    Multi-verses can't [to my limited knowledge].
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  19. #94
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    Quote Originally Posted by MadMojoMonkey View Post
    I haven't researched this in years. Start with google.

    On the one hand, smart people have to think long and hard to figure out new cool stuff in mathematics, so it seems like it's an inventing process, mentally.

    On the other hand, it seems like extreme hubris to think an alien species could come to Earth, we show them our math, and they're, "Who would've ever suspected there was order in the universe? Look at this, guys!" If it's just there to be sussed out, more of a discovery process than invention.

    Big names in mathematics disagree over how it feels in the moment. Some even posit spiritual guidance or epiphany.
    Was the wheel invented or discovered?
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  20. #95
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    Quote Originally Posted by JKDS View Post
    I feel like I chose the wrong words to describe my thought.

    When I say people have trouble understanding and conveying math, I don't fault math and I don't mean that math can't do it. I mean that people in general don't understand the definitions, and suck at describing things with math. If you've ever tried to explain something mathematical to another person, you've probably experienced the issue.

    There are many who can competently do this though. And understand it. Those people exist for words too, and when they speak it's beautiful
    Yeah, there are understandings that are wordless. And then we have to go through all the trouble of getting those understandings across to someone else.

    Messy business. People could argue over the communicae for centuries. Oh right, they do, and they're called lawyers.
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  21. #96
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    Quote Originally Posted by Poopadoop View Post
    "Discovered" makes more sense to me than "invented." Like, if we hadn't come along and starting counting on our fingers and toes, there would be no maths? Meh. There might not be maths textbooks, but there would still be maths.

    An epiphany doesn't imply an invention. By definition, an epiphany means you just realised (discovered) something.

    Somewhere out there are a bunch of equations that no-one has discovered yet, but which are invariably true. Even something like 13478342470 + 234890584325 might never have been calculated, but I would hardly say if I solved it, that would make me an "inventor" of maths.

    p.s. The exception to the rule would be Ong, who does invent his own maths.
    It's like you want to discount humans for inventing things and recognize humans for discovering things. People are doing it, why pick at these nits?
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  22. #97
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    Quote Originally Posted by JKDS View Post
    The question, in essence, is asking why we believe in "words".
    Fucking bullseye. Jkids, you're too good.
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  23. #98
    Quote Originally Posted by a500lbgorilla View Post
    It's like you want to discount humans for inventing things and recognize humans for discovering things.
    Well no, it's not like that. All I said was if something already exists you can't really invent it, you can only discover it. As far as giving people credit for one versus the other, there's no value judgment implied in what I said; you're reading things into my words that aren't intended.

    If I had said something along the lines of "Newton didn't accomplish much because all he did was discover gravity, not invent it." then you would have a point.


    Quote Originally Posted by a500lbgorilla View Post
    People are doing it, why pick at these nits?
    The question was raised regarding whether maths are invented or discovered, and I offered an answer. If you prefer to believe people invent maths, then by all means feel free.
  24. #99
    Quote Originally Posted by a500lbgorilla View Post
    Yeah, you and I have similar conceptions of a plate, and we may find some edge-cases to argue over, but my sense of a plate and your sense of a plate are pretty close. The difficulty is when we try to definitively square-away plate-ness between each other.
    What's quite funny to me is that whilst posting in this thread I was really drunk and I seemingly mostly made sense. I sent some text messages around the same time and they mostly didn't.

    Quote Originally Posted by CoccoBill View Post
    Language is a lossy compression algorithm for thought. Words are compressed thoughts rounded to something that most closely resembles the original.
    I like this.
    Last edited by Savy; 06-18-2017 at 02:11 AM.
  25. #100
    Quote Originally Posted by a500lbgorilla View Post
    Was the wheel invented or discovered?
    Invented. If only there was a career in this.
  26. #101
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    Quote Originally Posted by Poopadoop View Post
    Well no, it's not like that. All I said was if something already exists you can't really invent it, you can only discover it. As far as giving people credit for one versus the other, there's no value judgment implied in what I said; you're reading things into my words that aren't intended.

    If I had said something along the lines of "Newton didn't accomplish much because all he did was discover gravity, not invent it." then you would have a point.




    The question was raised regarding whether maths are invented or discovered, and I offered an answer. If you prefer to believe people invent maths, then by all means feel free.
    Maths doesn't exist without someone to codify it. And once someone lays down the rules to describe math, they begin to explore where those rules take them.

    edit: remember, there are entirely useless maths.
    Last edited by a500lbgorilla; 06-18-2017 at 07:48 AM.
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  27. #102
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    Quote Originally Posted by Savy View Post
    I like this.
    Me too.
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  28. #103
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    Maths doesn't exist without someone to codify it.
    Of course it does. The ratio of the circumference to the radius is pi, and that was true before someone figured it out.

    Maths is like language. The word mountain describes something that it physical. The word itself is not the mountain, the word is merely the noise we associate with the physical object that is a mountain.

    Without the word mountain, mountains still exist.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  29. #104
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    Great, maths is discovered.

    Just like a wheel was always a wheel before someone created it.
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  30. #105
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    Further, where there are two mountains... it doesn't require someone to be able to count for there to be two mountains there.

    All we invented was the words to descirbe the concpets that we're trying to describe. The mountain exists, just as one and two exist. All we need to do is create the language to communicate these concepts.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  31. #106
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    Quote Originally Posted by a500lbgorilla View Post
    Great, maths is discovered.

    Just like a wheel was always a wheel before someone created it.
    No. Someone had to conceive the wheel, someone had to manipulate physical objects in order to create the object they conceive.

    That is not what is happening with maths, nor with language. With language, we see something, then we create a word for it. We don't manipulate rock to create mountains so we can give it a name... mountains were discovered, not invented.

    The wheel was invented becuase it wasn't "found" lying around, and then someone said "I'll call this the wheel".
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  32. #107
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    Quote Originally Posted by OngBonga View Post
    No. Someone had to conceive the wheel, someone had to manipulate physical objects in order to create the object they conceive.

    That is not what is happening with maths, nor with language. With language, we see something, then we create a word for it. We don't manipulate rock to create mountains so we can give it a name... mountains were discovered, not invented.

    The wheel was invented becuase it wasn't "found" lying around, and then someone said "I'll call this the wheel".
    How didn't Newton manipulate a thing to develop his understanding of mechanics?
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  33. #108
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    Newton didn't invent gravity, nor did he invent the laws of motion. He discovered the laws of motion, and observed gravity. He didn't even discover gravity, he just explained it (rather well but not nearly perfectly).
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  34. #109
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    Quote Originally Posted by OngBonga View Post
    Newton didn't invent gravity, nor did he invent the laws of motion. He discovered the laws of motion, and observed gravity. He didn't even discover gravity, he just explained it (rather well but not nearly perfectly).
    He invented how to describe gravity.

    And in the same vein, maths is both invented and discovered.

    Just like how Goodyear invented a way to make wheels real.
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  35. #110
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    Quote Originally Posted by a500lbgorilla View Post
    He invented how to describe gravity.
    No he didn't. He didn't invent the words he was using. He merely figured out how to apply the maths to his concepts, he solved the puzzle better than anyone else for a long, long time. But he didn't invent anything, with the possible exception of a slightly flawed intepretation of physical laws that already existed. I suppose that he was wrong means he did invent something! But, that's just pedantry.

    There's a clear distinction between inventing and discovering. I know you like to wrestle with language and philosophy, but inventing something involves direct manipulation to create something that didn't previously exist, other than in theory.

    The wheel actually isn't the best example, because it's possible that a circular piece of debris was found and used for the purpose, which would make it a discovery. Let's talk about the light bulb. That's a very clear "invention". Is it also a "discovery"? The discovery is what's going on inside the head. The invention is the creation of a concept, it's applying the discovery to the physical world.

    Nobody is creating maths, just applying it or describing it.

    nd in the same vein, maths is both invented and discovered.
    Only the words used to describe maths are invented.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong
  36. #111
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    Mathematics is the queen of sciences, without it it is impossible, this is the basic science
  37. #112
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    Quote Originally Posted by DietelByaneth View Post
    Mathematics is the queen of sciences, without it it is impossible, this is the basic science
    Mathematics is not a science.

    Mathematics is not based on experimental observations, but on propositions, or axioms. Mathematics supposes its axioms are true and draws logical conclusions based on those axioms. If an axiom causes inconsistencies, it is discarded from that corner of mathematics, which is reminiscent of scientific processes, but not enough. Whether or not those axioms represent anything which could be observed is not relevant. Only the internal consistency of the logical mathematical system is relevant.

    In the sciences, for any statement to be considered "true" (true in quotes, because science doesn't produce true statements, only statements not yet shown to be false), it must match experimental observations. It is not enough that a statement adds or does not disrupt the logical consistency of the science's other statements.
  38. #113
    Why are the mathematics axioms assumed true?
  39. #114
    Quote Originally Posted by wufwugy View Post
    Why are the mathematics axioms assumed true?
    Because someone said if you assume a b and c then d, ohh shit e f g h i j too, maybe even x y and z.

    And no one has had a problem with a b or c at any point in time and we're onto zzzzzzz
  40. #115
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    Pretty much what Savy said.

    Mathematical statements begin, "If you assume..." which is formally saying, "For the sake of the following discussion, that statement is absolutely true."

    The thing is that math is very tight with its axioms. Simpler, more intuitive statements are preferred in most cases.

    E.g.
    Assume identity is not an absurd idea, i.e., that 'things' in the broadest sense, can be told apart, i.e. that if we were to talk about "this" thing, we would know that we're not talking about "that" thing, and vise versa, because we can tell these are different things.

    That's more formally stated in mathematical axiom, but that's the gist of the fundamental principle which gives rise to all of algebra.

    Whether or not this is true, or any reflection of reality is coincidental. That coincidental relationship can make humans more or less interested in studying it, but it doesn't change that the relationship between reality and numbers is not formally required in any part of mathematics.
  41. #116
    OngBonga's Avatar
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    Jul 2010
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    I dunno, I think maths is sort of science. I think it's like a chess opening database compared to an endgame tablebase... science is the study of openings... it develops, and new openings become superior to what were once considered optimal. Maths is like the tablebase, working backwards, slowly figuring out all possible outcomes, starting with the most basic and becoming ever more complicated.

    Either way, it's all doing the same thing... figuring chess out.
    Quote Originally Posted by wufwugy View Post
    ongies gonna ong

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