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    • CommentAuthorloreman
    • CommentTimeOct 10th 2021
     
    Yes. It suddenly struck me, whilst thinking about this, that mathematics is the only discipline I know of where the answers to questions don’t change over time.
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    A bit like religion, in fact. The eternal verities and all that.
    • CommentAuthorBigOilRep
    • CommentTimeOct 11th 2021
     
    Posted By: AngusI'm cool with it as long as we clearly understand the difference between real and real.

    Bigot.
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      CommentAuthorAngus
    • CommentTimeOct 11th 2021
     
    Posted By: BigOilRep
    Posted By: AngusI'm cool with it as long as we clearly understand the difference between real and real.

    Bigot.


    Really?
    • CommentAuthorBigOilRep
    • CommentTimeOct 11th 2021
     
    What do you think?
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      CommentAuthorAngus
    • CommentTimeOct 11th 2021
     
    Some of my best friends are real !
    • CommentAuthorloreman
    • CommentTimeOct 11th 2021
     
    So was Harvey!
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      CommentAuthorAngus
    • CommentTimeOct 11th 2021
     
    What are you rabbiting on about?
    • CommentAuthorBigOilRep
    • CommentTimeOct 11th 2021
     
    Posted By: AngusSome of my best friends are real !

    It's more about the imaginary based community having their choices respected.
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      CommentAuthorAngus
    • CommentTimeOct 11th 2021 edited
     
    I respect imaginary rights! I never believe in someone who self-identifies as imaginary.
    • CommentAuthorenginerd
    • CommentTimeOct 11th 2021
     
    Math may or may not be able to exist merely as a system consistent with itself. Seems like mysticism. Certainly I cannot imagine math being developed without intelligence and things to count and an advantage to counting them.

    That the math we developed has counting in it, and also schroedenger equations for waveform description seems reasonable, because we found some advantage to being able to math those things that way. I carefully read the thread and remain unable to find the awesome part of the fact that our maths, designed to describe things we see, do in fact describe things we see.

    Alien creatures somewhere would presumeably also describe things with their language and their analytical/predictive/modeling/math techniques. As they are describing the same things in the universe, some of it would look something like something that would seem analogous to our language and our math.

    What am I missing? I like being awe-inspired. I find the accomplishments of the human race re math, awe inspiring, but not so much the notion of math or its implied tie to godliness.
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      CommentAuthorAngus
    • CommentTimeOct 11th 2021
     
    What you miss is that our discovery.of interesting things in mathematics, solely on the basis of proving them consistent with the rest of the structure, very often turns out much later to be a useful way to describe or predict material reality. And often not, as well.

    It is just not right to think that mathematics is fundamentally the outcome of attempts to describe the world. It's much bigger.
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      CommentAuthorpcstru
    • CommentTimeOct 12th 2021
     
    Posted By: AngusWhat you miss is that our discovery.of interesting things in mathematics, solely on the basis of proving them consistent with the rest of the structure, very often turns out much later to be a useful way to describe or predict material reality. And often not, as well.

    It is just not right to think that mathematics is fundamentally the outcome of attempts to describe the world. It's much bigger.


    I'm not sure how you can claim that given that we know that most of what we 'know' about the real world via our mathematical models of it are only good approximations rather than absolute truth (we don't have a GUT/GUM and our large and small scale models don't match up). I'm also not sure why it would be surprising that models based on a consistent structure contain things which also turn out to match to that structure. How could they not?
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      CommentAuthorAngus
    • CommentTimeOct 12th 2021 edited
     
    I concede your first point pending developments. Since I won't likely be around long enough to experience the discovery that nature disagrees with mathematics (should that ever happen), it's a safe concession.

    I don't understand the second point. The surprise was that the system based on a sort of aesthetic mental consistency should work on something we found in the road - i.e. external reality.

    Taking that surprise as evidence of something significant leads me to my sense that mathemarics has an existence of its own and we are discovering it much as we discover other aspects of nature. It's all one big universe.
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      CommentAuthorpcstru
    • CommentTimeOct 12th 2021
     
    Posted By: AngusI concede your first point pending developments. Since I won't likely be around long enough to experience the discovery that nature disagrees with mathematics (should that ever happen), it's a safe concession.

    Will that be before or after the creation/discovery of Mathematics is complete?


    I don't understand the second point. The surprise was that the system based on a sort of aesthetic mental consistency should work on something we found in the road - i.e. external reality.

    I have a sheep. I get good at having a sheep and move into the sheep having business. I need to keep track of how many sheep I have, so I invent some numbers - just as many as I need to keep track of my flock and the comings and goings. So I have some numbers and some operators (add/buy a sheep, sell/subtract a sheep). Now in my head I can imagine more sheep than I have and use numbers to think about that. I might realise that there should be numbers for sheep I don't have. Am I surprised when numbers apply to Goats, or atoms?


    Taking that surprise as evidence of something significant leads me to my sense that mathemarics has an existence of its own and we are discovering it much as we discover other aspects of nature. It's all one big universe.


    I think Mathematics is significant as an aspect of thinking - a way to make sense of the sense we have of the material world. It bothers me that we are fundamentally constrained by the tools and language - our 'understanding' of the universe is mediated by constraints that are baked into the ontology of the tools of the 'language' we have available. As the language is generally tuned to communication of common 'understanding' of the material world, it is no surprise to find they have essential properties in common.

    What I do find surprising are unicorns.
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      CommentAuthorAngus
    • CommentTimeOct 12th 2021
     
    Gödel had something to say about when Mathematics would be complete.

    If we have invented mathematics ourselves to take care of our sheep business, then presumably we would have had the option of inventing some other system to take care of our sheep business. I know of no other system than numbers with which to count sheep. If there is only one way to invent mathematics that works, I would call its "invention" a discovery. It implies the existence of a "way that works" which we call mathematics.

    As you know I am a Platonist on the matter. To me the existence of mathematics independent of anybody to think it up is a given. If there were no people would there be three of anything?

    Other than that, we seem to be closer than the continuing argument would imply.
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      CommentAuthorAngus
    • CommentTimeOct 12th 2021
     
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    Looks like this could be turned into some sort of continuous medium deformation - i.e. fluid flow.
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      CommentAuthorpcstru
    • CommentTimeOct 13th 2021
     
    Posted By: AngusGödel had something to say about when Mathematics would be complete.

    That is kind of the point. Does that relate to reality - that either the universe is unsolvable in principle or might never be complete?


    If we have invented mathematics ourselves to take care of our sheep business, then presumably we would have had the option of inventing some other system to take care of our sheep business. I know of no other system than numbers with which to count sheep. If there is only one way to invent mathematics that works, I would call its "invention" a discovery. It implies the existence of a "way that works" which we call mathematics.

    I'd move it back, it seems inevitable from the point that we invent nouns and divide the world into distinct things and relationships between those things.


    As you know I am a Platonist on the matter. To me the existence of mathematics independent of anybody to think it up is a given. If there were no people would there be three of anything?

    Other than that, we seem to be closer than the continuing argument would imply.


    Possibly because the distinction between invented and discovered seems moot. You can equally say Unicorns are discovered in your world because everything must inevitably fall out of the material world as a causal consequence of the existence of the material world. But like Unicorns, to my mind there is a problem when we claim things exist as part of the material world that have no manifestation in the material world other than in our minds and our language. Abstraction does not exist in the material world, it is a construct of our minds, an 'invention' entirely decoupled from the reality of the material world.
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      CommentAuthorAngus
    • CommentTimeOct 13th 2021 edited
     
    I didn't say that mathematics exists in the material world. I said it has some sort of existence in addition to the material world. Both mathematics and the material world are there to explore but are not created by us. I disagree that mathematics is a construct. Though sure you can build bathematical constructs just as you can build material ones.

    The parallel between mathematics and language is false. Language lacks a consistency requirement. You can say anything and there is no way within language to evaluate its validity. Hence unicorns.

    Hmmm. That is not correct. I left it in so you can see what I've gone away to think about.