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This is the classier form of the "who would win in a fight between Thanos and Darkseid" internet discussions. But yes, physics is amazing, but it doesn't exist

This is the classier form of the "who would win in a fight between Thanos and Darkseid" internet discussions. But yes, physics is amazing, but it doesn't exist alone. Math is particularly important, but also chemistry and engineering all co-exist in a positive feedback loop. (If I had to isolate the single greatest insight in the modern world, it would be Descartes introducing the notion of number as different than "the length of a line segment". This change in perspective made possible all the math and physics that came after. This perspective is now so common as to be invisible, so for someone to see something so foundational, but so unknown, it is really remarkable.)

civilized 5y ago
Could you elaborate on what Descartes did? He's known as the inventor of coordinate geometry, which seems to rely on the notion of number as the length of a line segment (two number lines placed perpendicular to one another uniquely identify any point on the plane). Are you talking about his work on algebra or other things?
- javajosh 5y ago
  https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematical_legacy https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematic... I will look up the specific paper where he proposed that a squared number need not represent only an area, for example.
  - civilized 5y ago
    Ah, I get it now. Descartes suggested that the representation of numbers need not be dictated by the geometric interpretation of how they were calculated. For example, a^2 doesn't have to be represented as an area, even though geometrically it would be the area of a square.
    - javajosh 5y ago
      The "paper" was La Géométrie[1], originally published as an appendix(!) to another work, Discourses on the Method [2]. Not sure why all the downvotes. Oh well. 1 - https://en.wikipedia.org/wiki/La_G%C3%A9om%C3%A9trie https://en.wikipedia.org/wiki/La_G%C3%A9om%C3%A9trie 2 - https://en.wikipedia.org/wiki/Discourse_on_the_Method https://en.wikipedia.org/wiki/Discourse_on_the_Method

civilized 5y ago

Could you elaborate on what Descartes did? He's known as the inventor of coordinate geometry, which seems to rely on the notion of number as the length of a line segment (two number lines placed perpendicular to one another uniquely identify any point on the plane). Are you talking about his work on algebra or other things?

javajosh 5y ago
https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematical_legacy https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes#Mathematic... I will look up the specific paper where he proposed that a squared number need not represent only an area, for example.
- civilized 5y ago
  Ah, I get it now. Descartes suggested that the representation of numbers need not be dictated by the geometric interpretation of how they were calculated. For example, a^2 doesn't have to be represented as an area, even though geometrically it would be the area of a square.
  - javajosh 5y ago
    The "paper" was La Géométrie[1], originally published as an appendix(!) to another work, Discourses on the Method [2]. Not sure why all the downvotes. Oh well. 1 - https://en.wikipedia.org/wiki/La_G%C3%A9om%C3%A9trie https://en.wikipedia.org/wiki/La_G%C3%A9om%C3%A9trie 2 - https://en.wikipedia.org/wiki/Discourse_on_the_Method https://en.wikipedia.org/wiki/Discourse_on_the_Method