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Mathematics is an internally consistent model. Nature is an internally consistent system. We do not understand how nature works (precise factors and their value

Mathematics is an internally consistent model. Nature is an internally consistent system. We do not understand how nature works (precise factors and their values), but we understand how mathematics works, since we designed it for a sole purpose of mimicking and modeling the laws of nature. But know that mathematics (modeling in the broadest sense) only makes sense within its set of axioms and that there are many possible kinds of mathematics out there.

charonn0 14y ago
Math is the ideal tool for understanding how nature works. We see math everywhere in nature, like this hexagram. In principle, we can describe exactly how the hexagram got to be there, through math. But we don't understand why. Can we know whether math yields to nature, or nature yields to math? Does the question even follow?
- JanezStupar 14y ago
  Eh, no what we see in nature are laws of nature in action. And we cannot explain the hexagram exactly because we do not have the formula that produced that pattern. What our models do is to give us an vague idea of what is happening. There are barely any perfect geometric shapes in the nature, at least at the macro level. Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds). But that is kind of sideways thinking, as of all the concepts and ideas that are achievable through mathematics we are mostly interested in those that fit to the world around us and we discard the others. That is the reason why so many people get this "Oh my god it is all connected!" feeling. It is precisely so, because we are mostly interested in the aspects that fit the world we see around us and we selectively discard the aspects that do not fit. In a sense we are writing a story we want to hear.
  - charonn0 14y ago
    But if the math we have is accurate because we have distilled it from the inaccurate, the question remains why is it accurate?
    - JanezStupar 14y ago
      All the math is accurate, we just distilled the parts we like from the parts we don't like. Regarding accuracy let me try again, it is accurate because it is internally consistent. However notion of two apples being 'same' (e.g. completely interchangeable, satisfying the identity) is silly in absolute terms since laws of nature are much more complex.
      - charonn0 14y ago
        it is accurate because it is internally consistent Internal consistency is necessary for accuracy but not sufficient.
  - wfn 14y ago
    > Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds) There are (within academia) alternative views to this one, e.g. Max Tegmark's "Mathematical Universe hypothesis": - http://arxiv.org/abs/gr-qc/9704009 http://arxiv.org/abs/gr-qc/9704009 - http://arxiv.org/abs/0704.0646 http://arxiv.org/abs/0704.0646 - wiki: http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis http://en.wikipedia.org/wiki/Mathematical_universe_hypothesi... The basic idea being, all internally consistent (viz., mathematical) structures exist (whatever the notion pertains to), and those containing 'self-aware substructures' are perceived as physical realities by virtue of those SASes being embedded within a particular given consistent structure (and hence having a from-within vantage point). Sounds fishy, but it's a hypothesis alright, and there have been (AFAIK) some attempts to provide falsifiability conditions (thus making it a testable scientific hypothesis), but one would first have to address the problem of proper operationalization, i.e. defining the damn concepts at hand; it's probably too all-over-the-place for now - but nevertheless interesting and (heh) internally consistent. Also see (for those interested), e.g. http://plato.stanford.edu/entries/computation-physicalsystems/ http://plato.stanford.edu/entries/computation-physicalsystem... (nice overview of related problem spaces)

charonn0 14y ago

Math is the ideal tool for understanding how nature works. We see math everywhere in nature, like this hexagram. In principle, we can describe exactly how the hexagram got to be there, through math. But we don't understand why. Can we know whether math yields to nature, or nature yields to math? Does the question even follow?

JanezStupar 14y ago
Eh, no what we see in nature are laws of nature in action. And we cannot explain the hexagram exactly because we do not have the formula that produced that pattern. What our models do is to give us an vague idea of what is happening. There are barely any perfect geometric shapes in the nature, at least at the macro level. Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds). But that is kind of sideways thinking, as of all the concepts and ideas that are achievable through mathematics we are mostly interested in those that fit to the world around us and we discard the others. That is the reason why so many people get this "Oh my god it is all connected!" feeling. It is precisely so, because we are mostly interested in the aspects that fit the world we see around us and we selectively discard the aspects that do not fit. In a sense we are writing a story we want to hear.
- charonn0 14y ago
  But if the math we have is accurate because we have distilled it from the inaccurate, the question remains why is it accurate?
  - JanezStupar 14y ago
    All the math is accurate, we just distilled the parts we like from the parts we don't like. Regarding accuracy let me try again, it is accurate because it is internally consistent. However notion of two apples being 'same' (e.g. completely interchangeable, satisfying the identity) is silly in absolute terms since laws of nature are much more complex.
    - charonn0 14y ago
      it is accurate because it is internally consistent Internal consistency is necessary for accuracy but not sufficient.
- wfn 14y ago
  > Strictly speaking, math has to yield to the laws of nature as it does not exist outside the laws of nature (as mathematics is in our minds) There are (within academia) alternative views to this one, e.g. Max Tegmark's "Mathematical Universe hypothesis": - http://arxiv.org/abs/gr-qc/9704009 http://arxiv.org/abs/gr-qc/9704009 - http://arxiv.org/abs/0704.0646 http://arxiv.org/abs/0704.0646 - wiki: http://en.wikipedia.org/wiki/Mathematical_universe_hypothesis http://en.wikipedia.org/wiki/Mathematical_universe_hypothesi... The basic idea being, all internally consistent (viz., mathematical) structures exist (whatever the notion pertains to), and those containing 'self-aware substructures' are perceived as physical realities by virtue of those SASes being embedded within a particular given consistent structure (and hence having a from-within vantage point). Sounds fishy, but it's a hypothesis alright, and there have been (AFAIK) some attempts to provide falsifiability conditions (thus making it a testable scientific hypothesis), but one would first have to address the problem of proper operationalization, i.e. defining the damn concepts at hand; it's probably too all-over-the-place for now - but nevertheless interesting and (heh) internally consistent. Also see (for those interested), e.g. http://plato.stanford.edu/entries/computation-physicalsystems/ http://plato.stanford.edu/entries/computation-physicalsystem... (nice overview of related problem spaces)