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> What should we consider fundamental?

A fair question, and a full answer would be too long for a comment (though it would fit in a blog post, which I'll go ahead and write now since this seems to be an issue). But I'll take a whack at the TL;DR version here.

AI, ML, and NLP and web design are application areas, not fundamentals. (You didn't list computer graphics, computer vision, robotics, embedded systems -- all applications, not fundamentals.)

You can cover all the set theory and graph theory you need in a day. Most people get this in high school. The stuff you need is just not that complicated. You can safely skip category theory.

What you do need is some amount of time spent on the idea that computer programs are mathematical objects which can be reasoned about mathematically. This is the part that the vast majority of people are missing nowadays, and it can be a little tricky to wrap your brain around at first. You need to understand what a fixed point is and why it matters.

You need automata theory, but again, the basics are really not that complicated. You need to know about Turing-completeness, and that in addition to Turing machines there are PDAs and FSAs. You need to know that TMs can do things that PDAs can't (like parse context-sensitive grammars), and that PDAs can to things that FSAs can't (like parse context-free grammars) and that FSAs can parse regular expressions, and that's all they can do.

You need some programming language theory. You need to know what a binding is, and that there are two types of bindings that matter: lexical and dynamic. You need to know what an environment is (a mapping between names and bindings) and how environments are chained. You need to know how evaluation and compilation are related, and the role that environments play in both processes. You need to know the difference between static and dynamic typing. You need to know how to compile a high-level language down to an RTL.

For operating systems, you need to know what a process is, what a thread is, some of the ways in which parallel processes lead to problems, and some of the mechanisms for dealing with those problems, including the fact that some of those mechanisms require hardware support (e.g. atomic test-and-set instructions).

You need a few basic data structures. Mainly what you need is to understand that what data structures are really all about is making associative maps that are more efficient for certain operations under certain circumstances.

You need a little bit of database knowledge. Again, what you really need to know is that what databases are really all about is dealing with the architectural differences between RAM and non-volatile storage, and that a lot of these are going away now that these architectural differences are starting to disappear.

That's really about it.




> You need automata theory... Turing-completeness... PDAs and FSAs...

Why? I know that stuff inside and out, and across multiple jobs I have used none of it ever. What chance to use this favourite bit of my education did I miss? (Or rather, might I have missed, so that you might speak to the general case)

> You need to know how to compile a high-level language down to an RTL.

Why? Same comment as above.

> You need to understand what a fixed point is and why it matters.

Well, I don't, and I don't. I request a pointer to suitable study material, noting that googling this mostly points me to a mathematical definition which I suspect is related to, but distinct from, the definition you had in mind.

Otherwise... as I read down this thread I was all ready to disagree with you, but it turns out I'd jumped to a false conclusion, based on the SICP context of this thread. Literacy, what a pain in the butt.

In particular, the idea that ((the notion of an environment) is a fundamental/foundational concept) is a new idea to me, and immediately compelling. I did not learn this in my academic training, learned it since, and have found it be very fruitful. Likewise with lexical vs dynamic binding, actually.


>> You need automata theory... Turing-completeness... PDAs and FSAs...

> Why?

So you can write parsers. To give a real-world example, so you can know immediately why trying to parse HTML with a regular expression can't possibly work.

>> You need to know how to compile a high-level language down to an RTL.

>Why?

So that when your compiler screws up you can look at its output, figure out what it did wrong, and fix it.

>> You need to understand what a fixed point is and why it matters.

> Well, I don't, and I don't. I request a pointer to suitable study material

http://ocw.mit.edu/courses/electrical-engineering-and-comput...

Particularly lectures 2A and 7A.


I'm of two minds about this. Everything you mention is great background to have. (Though non-trivial programs can't be reasoned about mathematically much more than biological systems can).

I think this deep background is a great goal. But in another way programming is a craft. You can learn as you go. There are millions of bright people who could do useful, quality work without an MIT-level CS education. They just need some guidance, structure, and encouragement.


> (Though non-trivial programs can't be reasoned about mathematically much more than biological systems can).

I wouldn't be so sure. I once applied for a company that was about proving various safety properties of control and signalling applications (for trains). Sizeable applications. They have problems with the halting problem and combinatorial explosions, but they get around those and do it anyway.


A very vaguely related question: are bindings lexical or dynamic in R? Or would it be fair to say that it's actually both at the same time? Or do we need a new term altogether?

For those unfamiliar with it, in R, environments are first-class objects, and identifier lookup in them is dynamic. But the way those environments are chained for lookup purposes is defined by the lexical structure of the program (unless modified at runtime - which is possible, but unusual) - i.e. if a function's environment doesn't have a binding with a given name, the next environment that is inspected is the one from the enclosing function, and not from the caller. So R functions have closure semantics, despite dynamic nature of bindings.

It would appear that this arrangement satisfies the requirements for both dynamic scoping and for lexical scoping.


> AI, ML, and NLP and webdesign are application areas

On first thought, I do agree. However, they are fundamental applications. Category Theory is categorizing the fundamentals. It uses a lot of the fundamentals on itself, I guess, but that doesn't mean ti me it's inaccessible or useless.


Don't confuse "important" with "fundamental". He probably meant foundational to begin with.

The web for instance is an unholy mess. We can do better for mass electronic publishing. We don't because that huge pile of crap is already there, and it's so damn useful.


Webdesign IMHO is be an extreme example of formatted output. I/O is a fundamental concept.


>What you do need is some amount of time spent on the idea that computer programs are mathematical objects which can be reasoned about mathematically.

Yes please.




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