3 ms·

I don't know nearly as much abstract algebra as I would like to, but when I read "A cyclic abelian group" I thought, "hold on, aren't all cyclic groups abelian?

I don't know nearly as much abstract algebra as I would like to, but when I read "A cyclic abelian group" I thought, "hold on, aren't all cyclic groups abelian?" And I remembered correctly, they are. So there's that suspicion, never far away when dealing with something cryptocoin-related, that maybe they're trying to bedazzle more than explain. Honestly, who can follow this who doesn't already know it?

tux3 3y ago
I think they meant it the other way around. They wanted to talk about abelian groups, and here specifically a cyclic (abelian) group. It would be silly to talk about a cyclic group that is specifically abelian, all cyclic groups are abelian. But not all abelian groups are cyclic. They could have kept it implicit, but not everyone might know that fact, so it doesn't really hurt
shakow 3y ago
> "hold on, aren't all cyclic groups abelian?" And I remembered correctly, they are. Yes, but not all abelian groups are cyclic.
renonce 3y ago
> that maybe they're trying to bedazzle more than explain I don't know much abstract algebra as well but I have studied elliptic curve pairings before, so from what I can tell, every sentence in the article counts (maybe not every word, though). The article may sound bedazzling to a reader not experienced in the subject, but its complexity can totally be justified by the complexity of technical details that it tries to explain clearly. That said, it's indeed hard to distinguish between a bedazzling article and an article that actively tries to explain concepts as clearly and concisely as possible. I do have such feelings with many AI papers these days, but not this one.
- vintermann 3y ago
  It doesn't help if you explain things accurately, if you're explaining it in such a way that no one would understand it who didn't already understand it. One key concept this text skips over, that I at least can't remember from any of the stuff I've read, is elliptic curves. Sure, you learn about abelian groups in an abstract algebra course. And you certainly learn about multiplicative subgroups of the integers modulo a prime. But do you learn about elliptic curves in a basic abstract algebra class these days? I mean maybe we should since they've become so important in cryptography, but I don't think we do.

tux3 3y ago

I think they meant it the other way around. They wanted to talk about abelian groups, and here specifically a cyclic (abelian) group. It would be silly to talk about a cyclic group that is specifically abelian, all cyclic groups are abelian. But not all abelian groups are cyclic. They could have kept it implicit, but not everyone might know that fact, so it doesn't really hurt

shakow 3y ago

> "hold on, aren't all cyclic groups abelian?" And I remembered correctly, they are. Yes, but not all abelian groups are cyclic.

renonce 3y ago

> that maybe they're trying to bedazzle more than explain I don't know much abstract algebra as well but I have studied elliptic curve pairings before, so from what I can tell, every sentence in the article counts (maybe not every word, though). The article may sound bedazzling to a reader not experienced in the subject, but its complexity can totally be justified by the complexity of technical details that it tries to explain clearly. That said, it's indeed hard to distinguish between a bedazzling article and an article that actively tries to explain concepts as clearly and concisely as possible. I do have such feelings with many AI papers these days, but not this one.

vintermann 3y ago
It doesn't help if you explain things accurately, if you're explaining it in such a way that no one would understand it who didn't already understand it. One key concept this text skips over, that I at least can't remember from any of the stuff I've read, is elliptic curves. Sure, you learn about abelian groups in an abstract algebra course. And you certainly learn about multiplicative subgroups of the integers modulo a prime. But do you learn about elliptic curves in a basic abstract algebra class these days? I mean maybe we should since they've become so important in cryptography, but I don't think we do.