upvote
"The Rees algebra is an algebra over Z[t^−1]"

Such a small sentence and yet it means very little to me. I understand some constituent pieces, but I don't understand what Z is here other than a 'ring' and I don't really grasp how t^-1 converts this into a generalized family of algebra. It would take me a lot of effort to understand this and use it practically. I find that fascinating because it really is such a small statement that seems perfectly cromulent, but there's a lot packed in there that someone like me is totally missing.

I suppose there may be similar concepts in computer science, but nothing comes to mind that ever stumped me. To be frank, the field has been relatively accessible to me because it hasn't been too challenging. Not sure if that's a personal aptitude thing or it is genuinely simpler.

reply
You are comparing TCP a relatively basic topic in the grand scheme of computing with Rees_algebra which is fairly specialized, we could take a simpler topic more foundational and clearer to understand and compare them.

I can understand that this feels like one is so much more complicated part of it is also how the articles were written, wikipedia is not known for quality maths explanations.

But beyond that this comparison to me feels unfair.

Let's take Euclidean algorithm or just modular arthimetic for example what a lot of computing even is based on I feel like that's a fairer comparison. No?

Perhaps that's too easy but I just find this specific comparison very unfair to both Math's intuitive-ness and Computing's complexity. Perhaps I am the one being delusional.

reply
I think you are snagging on thinking this is an observation about difficulty, time-to-mastery, or mental firepower requirements. It's not.

It's a plain observation that math exists on mostly it's own path with little to zero overlap with our lived experiences. If mathematics was a vector, it would have similar magnitude to other vectors, but it's direction would be much more removed from the typical knowledge pack, forcing you to get really close to the origin before you can "hop" over to that math vector. Other "knowledge" vectors, by virtue of being more bunched up, are closer together much further up, if that poor analogy at all makes sense.

reply
Mathematics has a lot of knowledge points that do connect to the "real world" very deeply, but perhaps the nature of their linkage to other mathematical pieces of knowledge is best left to the mathematicians. But we can still use the pearls of wisdom that come out of the process.
reply