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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 com
by revskill 1y ago
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"
- novaRom 1y agoAnd especially when we mix different categories. Like saying about any infinity as about an object is misleading, because it's rather a process
- Sharlin 1y agoInfinities (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.)
- random_ta 1y agoSure, if you accept reifying concepts into objects as valid. But that is a gateway to misery.
- Sharlin 1y agoWhat'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.
- revskill 1y agoObject in OOP ?
- Sharlin 1y agoMathematical objects, like numbers, sets, matrices, functions, …
- kbrkbr 1y agoI 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?
- vharuck 1y agoIt 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.
- glial 1y agoNot just Euclid - even Newton's Principia used geometric demonstrations, rather than algebraic ones.