In mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.

Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.

I've been a professor of mathematics at Harvard and at Yale. At Yale for a long time. But I'm not a mathematician only. I'm a professor of physics, of economics, a long list. Each element of this list is normal. The combination of these elements is very rare at best.

Think not of what you see, but what it took to produce what you see.

If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).

There are very complex shapes which would be the same from close by and far away.

If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.