Re:Ask HN: What are the most fundamental books on computer s...
by beagle3 on Monday October 21, 2019 @12:22PM
(#21314091)
Mathematics has a (mostly linear) historical progression, not logical progression.
It very often happens that the shortest, simplest derivation is discovered a century after the original discovery.
E.g. if you define exp(x) as \sum_0^\inf \frac{x^n}{n!}, a crazy amount of things that (historically) took a lot of effort to derive, become exceptionally simple and straightforward.
Now, historically, it didn't make sense to define it that way (especially because limits and infinite sums were only rigourously defined much later). But complexity wise, it is much simpler to first define limits and only then the exponent as an infinite sum.
> But you quickly head into patterns and conventions that started out as someones opinion on how things should be set up, rather than some fundamental principle.
That's not computer science. That is indeed philosophy, specifically software engineering philosophu. Science, it is not.
It very often happens that the shortest, simplest derivation is discovered a century after the original discovery.
E.g. if you define exp(x) as \sum_0^\inf \frac{x^n}{n!}, a crazy amount of things that (historically) took a lot of effort to derive, become exceptionally simple and straightforward.
Now, historically, it didn't make sense to define it that way (especially because limits and infinite sums were only rigourously defined much later). But complexity wise, it is much simpler to first define limits and only then the exponent as an infinite sum.
> But you quickly head into patterns and conventions that started out as someones opinion on how things should be set up, rather than some fundamental principle.
That's not computer science. That is indeed philosophy, specifically software engineering philosophu. Science, it is not.