Why do you need math to know somethings size?
Started by parsonstreet, 12th June 2019 15:02 in Talk & Chat

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    Default Re: Why do you need math to know somethings size?

    Memnoch
    Trivial example of an absolute size with a mathematical definition: The so-called "potato radius" relates to the maximum size an object can be before its gravity forces it to become a sphere. Of course, smaller objects can be spheres, but objects larger than the potato radius in all directions can't be not-spheres. The potato radius is the same for any object made of normal matter, i.e. atoms. It is an absolute.
    .
    How can this claim be tested?

    Has this transition to a sphere been documented?
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    Default Re: Why do you need math to know somethings size?

    Memnoch
    What problems? Present me with a two or three dimensional object of any shape you choose and I will tell you its area or volume precisely with simple arithmetic..
    A Circle

    I mention this because it's area formula involves Pi which is an irrational number that goes on for infinity.
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    Default Re: Why do you need math to know somethings size?

    parsonstreet
    How can this claim be tested?

    Has this transition to a sphere been documented?
    The asteroids/minor planets bear it out. There are several close to the criticial size which are almost spherical. Everything above that size is spherical and everything below that size is potato shaped. The size was predicted by the mathematical relationship between gravitational and e-m forces, and observation has subsequently supported the prediction consistently.
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    Default Re: Why do you need math to know somethings size?

    parsonstreet
    A Circle

    I mention this because it's area formula involves Pi which is an irrational number that goes on for infinity.
    And I'm guessing that from that you have deduced that any calculation involving Pi will not yield a rational result if the radius is a rational number. Actually that's not quite true, and even if it were, there will always be a yardstick you could use that would yield a rational result. If you follow it through, it stands to reason that some circles must have a rational expression of area in some system of measurement or other because the counterproposition - that there is no such thing as a circle with unit/integer/rational area - is plainly absurd... a circle can be any size. Besides, just because a value may be irrational doesn't mean it isn't absolute and it doesn't mean it's illogical or nonsensical, it just means you can't express it as x/y.
    Anyway, circles are easy but there's a way to do it without involving Pi and which you can use for any shape. For two dimensional shape, you push it into a piece of plasticine to a particular depth, measure the volume of water that fills the indentation, then divide by the depth to give the area.
    And for the volume of a complex 3d shape it's simply submerged displacement.
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    Default Re: Why do you need math to know somethings size?

    Memnoch
    The asteroids/minor planets bear it out. There are several close to the criticial size which are almost spherical. Everything above that size is spherical and everything below that size is potato shaped. The size was predicted by the mathematical relationship between gravitational and e-m forces, and observation has subsequently supported the prediction consistently.
    Where does the earth fit in this pattern?

    It seems that a contrary observation would unseat this theory. As with induction per se.
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    Default Re: Why do you need math to know somethings size?

    Memnoch
    And what exactly do you mean by "absolute area"? What other kind of area is there?
    An area that is not defined by its relationship to something else.

    A human is huge when compared with an ant but tiny when compared with a planet which is tiny when compared to the galaxy etc.

    But also a shape that does not need irrational numbers or infinitesimals to describe it.
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    Default Re: Why do you need math to know somethings size?

    parsonstreet
    Where does the earth fit in this pattern?
    I suppose you're going to object on the grounds that the Earth is not quite a perfect sphere? Well, it would be if it weren't spinning.


    It seems that a contrary observation would unseat this theory.
    A contrary observation would unseat any theory. In this case there are none so far.

    As with induction per se.
    I presume you are referring to inductive reasoning. This isn't because A) the premise provides no evidence, it's a prediction and B) the conclusion is empirical.
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    Default Re: Why do you need math to know somethings size?

    parsonstreet
    Memnoch
    And what exactly do you mean by "absolute area"? What other kind of area is there?
    An area that is not defined by its relationship to something else.
    You're getting hung up on measurement. Granted a statement of size is meaningless without a reference point, but since we live in a universe comprised of more than one object, everything has a reference point. Regardless of which, things still have size even if you're not there to measure them.

    A human is huge when compared with an ant but tiny when compared with a planet which is tiny when compared to the galaxy etc.
    OK, find the most fundamental object that exists and make that your yardstick. The fact that you don't know what that object is is irrelevant. If there were a universe which consisted of only one such object and nothing else, and then another one appeared, the first object would still be the same size it was before.

    But also a shape that does not need irrational numbers or infinitesimals to describe it.
    Why does it matter? There is, as far as anyone knows, no mathematics that can exhaustively describe the gravitational (or any other force) dynamics of a system comprising more than two bodies. That doesn't mean the motions are random, and they're going to carry on happening regardless of how accurately anyone measures them. Your inability to describe something with arbitrary precision doesn't impinge on the fact of its existence.
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