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Comment by bananabill | Hacker News Reader

"Why aren't people experts outside of their field?"

No, I'm going to agree that that is 100% within the field of academic computer science. I literally covered all the relevant notation in my freshman year.

What I'm wondering is whether or not there was some other factor going on, because I'm trained as a computer scientist and found nothing particularly objectionable about the formula, other than the f[] application notation. (And as a polyglot programmer, I've long since made my peace with that sort of notation mutation.) And I am by no means well-practiced in that sort of thing; I've been out of school for 14 years now, and only dabble on the side in this sort of thing now. The "forall y there exists an x such that" pattern in the middle is an extremely common recurring pattern, and what surrounds it on either side is also extremely simple.

Did you do it in a few seconds while reading from a slide and listening to a lecturer talk about math? I did the same thing as you and it took me more than 10 seconds to parse through the notation. If someone put this up on a slide during a talk and asked if I 'understood it', the answer would be no. Doesn't mean I'm incapable of understanding it, just that it uses muscles I don't flex very often.

Well, as I was trying to allude to, yeah, I did understand it pretty quickly because it uses a lot of common patterns.

Possibly I'm an extreme outlier, because when I say that I try to keep up with the field a bit, I really do. I really do watch YouTube videos of presentations full of math significantly more complicated than that every so often.

But still, I would also stand by my wondering if there was something else going on here, because it still seems to be grad students in school at the time really should have followed that. When I was in grad school I am quite confident I knew several other students who would have understood that just fine, and I went to "just" Michigan State, not MIT or Berkeley.

'Outside their field' was poor wording on my part. I meant more that it's not the sort of thing that most CS engineers see day to day. People forget things they don't use often.

> CS

> engineers

I think it's important to realize that these are two different things. One is a formal research science, the other deals with practical problem-solving and implementations.

Your typical software engineer likely has a CS degree, but CS researchers and software engineers are two separate populations. Sometimes the same person will do both, but usually not at the same time in their life or for the same organization.

edit: for example, you don't even need a computer to learn computer science fundamentals. A notebook or deck of playing cards will do fine.

As I write this, thearn4's post is fading into the grey, but it's true. That's why I qualified my post with trained as a computer scientist. I have a Master's degree in the field, and I try to keep up with it to some extent, but what I am now is an engineer. Degree or no, I can not currently say "I am a Computer Scientist" with a straight face.

He wasn't talking to software engineers who may have been out of school for a while had time to forget this stuff though; looks like he was talking to a mix of graduate and undergraduate students and some faculty, and I would think stuff like this would be covered during freshman/junior year for sure?

TBH I personally don't always raise hands to such questions though.

This is such a notation issue. If I were to show an implementation of permutations from 1..N in eg Brainfuck (to choose an extreme example), there's no way the mathematicians would get it. Why don't mathematicians learn math??

This issue comes up frequently when I try to read CS papers which explain their concepts using math notation. It's much, much easier to reverse-engineer the concept from a working example written in some notation I can actually read, such as... any programming language, even a programming language I've never formally learned. The math notation is literally Greek to me (if you'll pardon the pun) and does more to obscure than communicate meaning.

Not sure it's just notation but a mater of understanding.

In computer programming "exists" it's a matter of checking all the possibilities and find one, therefore is restricted to finite sets (and realistically speaking quite small the ones).

On the other hand in mathematics there is no such restriction. Existence is just an assumption, if there is at least one, then we go further with the assumption, no meter we talk about finite sets, infinite countable sets or infinite uncountable.

I'm working as a computer programmer for quite a long time and I also find this very annoying seeing people around thinking only finite when they have to solve real problems.

>{f ∈ [1..N ⟶ 1..N] : ∀ y ∈ 1..N : ∃ x ∈ 1..N : f[x]=y}

is not expert-level material.

Didn't read the article, is that supposed to show the properties of a function that is both "1:1" and "onto"? Ie, the set of all inputs is the same as as the set of possible outputs, so for any x in the set, f(x) will return a result that is also in the set?

Didn't major or minor in mathematics but I took a few papers. Time to the read the article and collect my prize or look ignorant under my real name on the web.

EDIT: I was wrong! Though in my defense I had been given the context from TFA I think I would have got it.

But isn't CS one of the formal sciences (together with mathematics, statistics, etc.)? Familiarity with mathematical notation should be pretty foundational for active researchers in the field I would think.

It just doesn't come up very much. The computers abstract it enough that you rarely need to actually look at notation like that. Unless you're doing some real close to the metal work, which the people who kept their hands raised probably were.

You're mixing up programming with computer science. The former is a task that does not necessarily need any math (e.g. web development), the latter is literally math (e.g. category algebra).

Edit: clarification

It doesn't come up because it is too abstract. About the only languages I can think of that will accept existential statements are theorem provers. My favourite is Isabelle/HOL.

In fact, the notation used by the lecturer is sloppy. Numbers 1..N is not a rigorous domain definition. (Unknown if real or natural.)

I'm not sure I buy your claim that mathematical notation is "close to the metal".

Paraphrasing the wise words of my uncle Rick, the rancher. "It is fucking hard to know everything"

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