My back pain continued today. I did manage to get some things done, but was too tired to do any math besides reading more of Infinite Powers.
One thing Strogatz relates in that book is that Greek mathematicians emphasized geometry partly because they had no way of expressing irrational numbers, such as $\pi$, except in geometric terms: as lengths, areas, and their ratios. If you think about it, that has not changed much. We may have discovered more contexts in which $\pi$ or $\phi$ crop up, but we can still only express them exactly as solutions to particular problems. Any effort to write them down in isolation is only an approximation.
and approximations are a pain in the back. Here’s hoping your approximation can be rounded to the point of bluntness. {If bluntness has a point (used though it may be to make one.)}
An interesting thought. What is the difference between saying something pointedly and saying it bluntly? Perhaps level of intent to be impolite?
And I thought I was just playing with homonyms.
What a great discovery! The blunt and pointed piece of language I encountered a couple of days ago said,
“What’s the difference between assertive and aggressive?”
“Gender.”