Is math big or small?(chessapig.github.io)
26 pointsby robinhoustona day ago3 comments
  • mkl2 hours ago
    > When Illustrating a mathematical idea, the first thing you need to decide is the scale.

    I have spent much of my life illustrating mathematical ideas, and scale is never the first thing I decide. Most commonly it stays abstract and there is no scale; it's flexible and I can zoom in and out at will. Sometimes I will choose a scale partway through or towards the end of an explanation, if I want to use a specific analogy, but I can comfortably rescale it to something else - the scale is never fixed.

    Interesting to see such a different view.

    • seanhunter34 minutes ago
      Totally agree. I really enjoyed the article, and the illustrations are really cool but scale is just something I don’t even consider. Even the very first question baffled me, when it said “Picture a torus. Is it big or small?”

      I answered an unambiguous “yes”.

      Also, we haven’t defined measure yet here have we? What does it even mean for something to have scale without measure?

      • mkl5 minutes ago
        Right, I immediately saw a torus - it was light blue (that's trivial to change, but I can't have no colour if it's visual) - but it could have been the size of a bacterium or the size of a galaxy. Without any context or application, the size is undefined.
  • N_Lens4 hours ago
    Good article.

    Math is smaller than the smallest and bigger than the biggest.

    • lioeters4 hours ago
      It's also deep, it goes all the way to the bottom.

      > The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it. -- Freeman Dyson

      • contraposit2 hours ago
        Weird Things Happen When Math Gets Too Expressive

        https://www.youtube.com/watch?v=EVwQsvof7Hw

        Peano arithmetic is sufficiently expressive enough to be equivalent to any possible future theory of mathematics.

        • lioeters2 hours ago
          Even before I started the video, I had a feeling it was going to lead to a kind of "introspective" mathematics that can reason about its own reasoning. I was not disappointed, thank you.

          Physics, Topology, Logic and Computation: A Rosetta Stone - https://arxiv.org/abs/0903.0340

  • trendbuilder2 hours ago
    [flagged]