> 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.

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.

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?