Is math big or small?

mkl•about 6 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.

seanhunter•about 4 hours 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?

mkl•about 4 hours 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.

lefra•about 1 hour ago

A first-year physics teacher once told the class something that stuck with me (paraphrasing): "Nothing is big or small by itself. I want you to always follow these words with 'compared to ...'".

fuglede_•about 3 hours ago

I've always loved this recording of Thurston talking about branched coverings and knot complements using big knots: https://www.youtube.com/watch?v=IKSrBt2kFD4

N_Lens•about 8 hours ago

Good article.

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

lioeters•about 7 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

contraposit•about 5 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.

lioeters•about 5 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

volemo•about 3 hours ago

Yes.

Is math big or small?

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