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 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?
So, the instructions for Plato boil down to an absurdity: "contemplate the monad; what dyad do you see?" The two sentences should have nothing to do with each other in Platonic terms.
Kilograms, obviously.
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.
He: I think we can agree everything below the average between a Planck length and the size of the observable universe is objectively small, and everything above is objectively large. Using the geometric mean, that average is about 0.12 mm. Therefore my penis is actually large.
She: I shouldn't have married a physicist.
That's... actually kinda cool to know.
The arithmetic mean (what you're thinking of) of 1 and 100 is 50.5.
The geometric mean of 1 and 100 is 10. It gives a sense of the average magnitude.
Of course, I am extra cynical as a number theorist who can't visualize most of my field. I wrote my doctorate on Siegel modular forms, and I can honestly say I have no way to visualize them any further than numbers on a page.
Math is smaller than the smallest and bigger than the biggest.
> The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it. -- Freeman Dyson
https://www.youtube.com/watch?v=EVwQsvof7Hw
Peano arithmetic is sufficiently expressive enough to be equivalent to any possible future theory of mathematics.
Physics, Topology, Logic and Computation: A Rosetta Stone - https://arxiv.org/abs/0903.0340
