Is math big or small?
chessapig.github.io
Is math big or small?
1–10 of 34 posts
Re: Is math big or small?
#2Good article.
Math is smaller than the smallest and bigger than the biggest.
Re: Is math big or small?
#3Good article. Math is smaller than the smallest and bigger than the biggest.
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
Re: Is math big or small?
#4> 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.
Re: Is math big or small?
#5Good article. Math is smaller than the smallest and bigger than the biggest.
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
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.
Re: Is math big or small?
#6[flagged]
Re: Is math big or small?
#7Earlier quoted context omitted.
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
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.
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
Re: Is math big or small?
#8Earlier quoted context omitted.
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.
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
[dead]
Re: Is math big or small?
#9> 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 analo…
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?
Re: Is math big or small?
#10> 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 analo…
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?
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.