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> But, there are no circles in the world, empirically Only if you have an overly strict definition of circle. I don't think it is wrong to call the outline of

> But, there are no circles in the world, empirically Only if you have an overly strict definition of circle. I don't think it is wrong to call the outline of a ball a circle, or the shape you do if you take an Y shaped object and rotate it along one of those branches, it isn't a perfect circle but it is still a circle.

mtlmtlmtlmtl 3y ago
And crucially, lots of things like the ones you mentioned are often not better approximated by an ellipse than a circle(I realise circles are just a subset of ellipses).
- DiscourseFan 3y ago
  >I realise circles are just a subset of ellipses Ah, but in a circle the circumference is always equidistant to the centre, which is never true of an ellipse. I suppose there is only one circle in the world.
  - jibalt 3y ago
    > Ah, but in a circle the circumference is always equidistant to the centre, which is never true of an ellipse. It's never true of an ellipse that isn't a circle. i.e., this is a--ahem--circular argument.
    - DiscourseFan 3y ago
      You can't just decide that the circle is contained in the set of all ellipses. Anyway its a philosophical argument, you can't "prove" mathematically that circles are ellipses or vica versa. Why do circles need to be ellipses anyway, why can't they be absolutely different? If they were absolutely different, then circles would be purely ideal, and yet an organizing principle (or as the say in Greek, an ἀρχιτεκτονική, from when we receive the word architecture). The only way to understand this, ontologically, is if we take the world to be in a constant tension with the "earth," as Heidegger puts it (cf. The Origin of the Work of Art), the thing in which the "rifts," which is the actual discourse of idealism, come about. You know, I thought about it for a moment, and I don't think the visual circle is even universal. The schema of the circle may be, but the circle itself never appears. See this article below[0]. [0]https://en.wikipedia.org/wiki/Molyneux's_problem https://en.wikipedia.org/wiki/Molyneux's_problem
      - trealira 3y ago
        I'm not who you replied to, but the reason circles are ellipses is because the definition of a circle is equivalent to the case of an ellipse where both foci have the same x, y coordinates. You can read about all the definitions of an ellipse on Wikipedia. https://en.wikipedia.org/wiki/Ellipse https://en.wikipedia.org/wiki/Ellipse Functionally, they might not be the same if you're programming them. For example, if you have a circle class with members detailing its center and its radius, it might be more efficient to draw an instance of it than an instance of an ellipse class that has two foci members that just happen to have the same values.
        DiscourseFan 3y ago
        I was just wondering about this the other day, it turns out Gödel actually got really into phenomenology later in his life... https://plato.stanford.edu/entries/goedel/goedel-phenomenology.html https://plato.stanford.edu/entries/goedel/goedel-phenomenolo... Also, that definition of a circle as an ellipse via locus points (which you mentioned) still requires defining ellipses by an imaginary, ideal circle--even if transcendental (and I've mentioned elsewhere, the circle never appears). The circle that appears is always already an ellipse, empirically, so in pure mathematical terms as I've said the ellipse is actually absolutely different from the circle, which always exceeds it. In order for the circle and ellipse to be set in relation one must be forced to be analytically composed under the other. Edit: Its clear that phenomenology was the most important philosophical influence on the modern theory of computation, but its curious to me that those that study pure math and physics haven't, for the most part, realized that yet, even as they employ computers to do so much of their work.
        trealira 3y ago
        > Also, that definition of a circle as an ellipse via locus points (which you mentioned) still requires defining ellipses by an imaginary, ideal circle--even if transcendental (and I've mentioned elsewhere, the circle never appears). How so? I don't understand. It seems like the opposite to me: because a circle can be defined as a special case of an ellipse, then a circle is defined in terms of ellipses, not the other way around. The definition of an ellipse is a generalization of the definition of a circle.
DiscourseFan 3y ago
There is only one definition of a circle, and its universal. Anything else is not a circle.
- jibalt 3y ago
  There is not only one definition of a circle. There are many definitions, all of which are consistent with each other.
  - DiscourseFan 3y ago
    Ok, but there is only one circle
    - jibalt 3y ago
      Obviously not.
      - DiscourseFan 3y ago
        If there were two circles, the second would be isomorphic to the first, therefore, in pure geometry there is only one circle. I suppose by some sort of empirical measure, there would be circles of different sizes, but as we already stated, empirically observed circles are actually ellipses, so in fact there is actually only one circle.

mtlmtlmtlmtl 3y ago

And crucially, lots of things like the ones you mentioned are often not better approximated by an ellipse than a circle(I realise circles are just a subset of ellipses).

DiscourseFan 3y ago
>I realise circles are just a subset of ellipses Ah, but in a circle the circumference is always equidistant to the centre, which is never true of an ellipse. I suppose there is only one circle in the world.
- jibalt 3y ago
  > Ah, but in a circle the circumference is always equidistant to the centre, which is never true of an ellipse. It's never true of an ellipse that isn't a circle. i.e., this is a--ahem--circular argument.
  - DiscourseFan 3y ago
    You can't just decide that the circle is contained in the set of all ellipses. Anyway its a philosophical argument, you can't "prove" mathematically that circles are ellipses or vica versa. Why do circles need to be ellipses anyway, why can't they be absolutely different? If they were absolutely different, then circles would be purely ideal, and yet an organizing principle (or as the say in Greek, an ἀρχιτεκτονική, from when we receive the word architecture). The only way to understand this, ontologically, is if we take the world to be in a constant tension with the "earth," as Heidegger puts it (cf. The Origin of the Work of Art), the thing in which the "rifts," which is the actual discourse of idealism, come about. You know, I thought about it for a moment, and I don't think the visual circle is even universal. The schema of the circle may be, but the circle itself never appears. See this article below[0]. [0]https://en.wikipedia.org/wiki/Molyneux's_problem https://en.wikipedia.org/wiki/Molyneux's_problem
    - trealira 3y ago
      I'm not who you replied to, but the reason circles are ellipses is because the definition of a circle is equivalent to the case of an ellipse where both foci have the same x, y coordinates. You can read about all the definitions of an ellipse on Wikipedia. https://en.wikipedia.org/wiki/Ellipse https://en.wikipedia.org/wiki/Ellipse Functionally, they might not be the same if you're programming them. For example, if you have a circle class with members detailing its center and its radius, it might be more efficient to draw an instance of it than an instance of an ellipse class that has two foci members that just happen to have the same values.
      - DiscourseFan 3y ago
        I was just wondering about this the other day, it turns out Gödel actually got really into phenomenology later in his life... https://plato.stanford.edu/entries/goedel/goedel-phenomenology.html https://plato.stanford.edu/entries/goedel/goedel-phenomenolo... Also, that definition of a circle as an ellipse via locus points (which you mentioned) still requires defining ellipses by an imaginary, ideal circle--even if transcendental (and I've mentioned elsewhere, the circle never appears). The circle that appears is always already an ellipse, empirically, so in pure mathematical terms as I've said the ellipse is actually absolutely different from the circle, which always exceeds it. In order for the circle and ellipse to be set in relation one must be forced to be analytically composed under the other. Edit: Its clear that phenomenology was the most important philosophical influence on the modern theory of computation, but its curious to me that those that study pure math and physics haven't, for the most part, realized that yet, even as they employ computers to do so much of their work.
        trealira 3y ago
        > Also, that definition of a circle as an ellipse via locus points (which you mentioned) still requires defining ellipses by an imaginary, ideal circle--even if transcendental (and I've mentioned elsewhere, the circle never appears). How so? I don't understand. It seems like the opposite to me: because a circle can be defined as a special case of an ellipse, then a circle is defined in terms of ellipses, not the other way around. The definition of an ellipse is a generalization of the definition of a circle.

DiscourseFan 3y ago

There is only one definition of a circle, and its universal. Anything else is not a circle.

jibalt 3y ago
There is not only one definition of a circle. There are many definitions, all of which are consistent with each other.
- DiscourseFan 3y ago
  Ok, but there is only one circle
  - jibalt 3y ago
    Obviously not.
    - DiscourseFan 3y ago
      If there were two circles, the second would be isomorphic to the first, therefore, in pure geometry there is only one circle. I suppose by some sort of empirical measure, there would be circles of different sizes, but as we already stated, empirically observed circles are actually ellipses, so in fact there is actually only one circle.