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Comment by revskill | Hacker News Reader

We need a word-less world of math where all meaning is derived from figures. WOrds are confusing.

"If you can't describe the meaning using only pencils and compass, you don't mean it"

And especially when we mix different categories. Like saying about any infinity as about an object is misleading, because it's rather a process

Infinities (transfinite cardinals) in the sense used by the article are absolutely objects. We’re not talking about infinite sums or other sequences and their limits. (And limits aren’t really “processes” either – the limit of the sequence 0.9, 0.99, 0.999, … is exactly 1, as a well-known example which nonetheless is controversial among people who don’t know what limits are.)

Sure, if you accept reifying concepts into objects as valid. But that is a gateway to misery.

What's the difference? How is the concept of a transfinite cardinal less of an object than, say, the concept of a set? Or a real number? All are well enough defined that you can do useful math with them, and that's really all that matters.

Object in OOP ?

Mathematical objects, like numbers, sets, matrices, functions, …

I can think of N as a process in a sense, because I can keep adding a number. But I can't think of R as a process like this, specifically because there is no surjective mapping from N to R.

How would you think of R as a process?

It is amazing what Euclid was able to prove and, frankly, even imagine using just geometric figures.

Nowadays, we have symbolic notation. The only research articles I read are for epidemiology, so I don't know how much notation is used in pure math journals. But I can't remember seeing any notation in those articles beyond what one would encounter in high school. I guess authors see more value in deceptive narrative and descend into strict logical languages only when necessary.

Not just Euclid - even Newton's Principia used geometric demonstrations, rather than algebraic ones.

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