Is math big or small?

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 ...'".

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mkl 5 hours ago | parent | prev | next [-]

> 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.

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aledevv 6 minutes ago | parent | next [-]

I propose a further and different "key to understanding."

I would add: the second thing to decide, besides the scale, is the Plan.

What do we mean, for example, by the "Ethical Plan." By ethical plan, I mean the purpose... "WHAT do I use mathematics for"?

Mathematics can be something immensely BIG if I use it for something important. Or it can be miserably SMALL if I use it for something petty and trivial.

In short: even in this case, greatness depends not only on the scale, but also on the eyes of the beholder, on the Context in which it is applied, and, why not?, also on the Purpose and the ethical plan.

If mathematics were, for example, something at the service of Justice, it would be something immensely Big.

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seanhunter 3 hours ago | parent | prev [-]

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?

	▲	Pay08 42 minutes ago \| parent \| next [-]
		> Also, we haven’t defined measure yet here have we? Kilograms, obviously.
	▲	mkl 2 hours ago \| parent \| prev [-]
		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.

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fuglede_ an hour ago | parent | prev | next [-]

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

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N_Lens 7 hours ago | parent | prev | next [-]

Good article.

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

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lioeters 6 hours ago | parent [-]

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

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contraposit 4 hours ago | parent [-]

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 4 hours ago \| parent [-]
		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

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volemo 2 hours ago | parent | prev [-]

Yes.