HN Theater @HNTheaterMonth

I've literally just started doing this, starting with category theory. Here's what I've been watching:

- https://youtu.be/I8LbkfSSR58?list=PLbgaMIhjbmEnaH_LTkxLI7FMa...

- https://www.infoq.com/presentations/category-theory-proposit...

I'm very, very, very open to suggestions... especially if they're presented from the ground up, and in lots of detail. I'm also quite open to material that can be read rather than watched.

⬐ j2kun

Go read the first few chapters of Algebra Chapter 0, and do the exercises. There's a free copy online somewhere...

This is the book that really demystifies it from the ground up.

⬐ omginternets

Thanks for the suggestion. Is this [0] the book in question?

[0] https://zr9558.files.wordpress.com/2013/11/algebra-chapter-0...

⬐ omginternets

Replying to my own post to say that this book is fantastic. Thank you!

⬐ j2kun

Exactly how I felt the first time I read it :)

⬐ khrm

https://www.youtube.com/watch?v=I8LbkfSSR58&list=PLbgaMIhjbm...

I love this series

⬐ rv11

I read his blog, never new he had some videos.

https://bartoszmilewski.com/2014/10/28/category-theory-for-p...

interesting enough.

⬐ pmoriarty

LtU discussion:

http://lambda-the-ultimate.org/node/5366

⬐ Yxven

As a working programmer that is curious about category theory, I feel like this misses the mark completely. I watched this yesterday, and this is what I remember:

1) I will tell you why category theory is relevant to you, the working programmer.

2) Here are the 2 most important data structures that you don't use in your day job.

3) Look at how they relate in this mathy not applicable way.

4) Conclusion: lambda calculus is awesome.

What I would like to see is:

1) I will tell you why category theory is relevant to you, the working programmer.

2) Here is a realistic but simplified problem and a solution written in python that is obviously the wrong approach to solving the problem. With category theory, we know this is the wrong approach because the math is wrong (and don't go into the math).

3) Here is another example that seems like a decent approach to solving the problem. With category theory, we know this is the wrong approach because the math is wrong (and don't go into the math). Doing it our way has these benefits...

4) Conclusion: learn category theory to become a better programmer.

If you can't do that, find some other way to illustrate the concrete benefits of learning category theory. If there aren't any concrete benefits, it's like telling baseball players they should learn physics to have a better understanding of baseball.

⬐ javitury

Is the diagram at 30:05 right? It says: (A+C)x(B+C)=(A+B)xC However I can't stop thinking it should be: (AxC)+(BxC)=(A+B)xC

⬐ hoprocker

That's how I learned it in grade school, yup.

⬐ nickpsecurity

A nice presentation I found to introduce software engineers to category theory and its areas of application:

http://www.cs.toronto.edu/~sme/presentations/cat101.pdf

I don't know category theory so I can't vet it. My skimming of it did show it was interesting, though.

⬐ emblem21

This is fantastically timed and very well explained. Our company is working deeply with Category Theory right now as we believe programming in the future will find itself focused primarily on the task of orchestrating AI to code.

⬐ adamnemecek

What company is that?

⬐ emblem21

http://www.emblem21.com

⬐ None

None

⬐ usgroup

Intellectual masturbation much?

⬐ Tammy5

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⬐ hellofunk

> a friend of mine referred me to Mr Robert

I think you mean Mr Robot?

⬐ gravypod

Why don't things like Category Theory and Set theory update their terminology to align with more modern words of describing these?

Why is a "function" and "arrow"? A "function" implies an operation that is part of a larger system of organized operations. An "arrow" implies stone age technology. One is infinity more descriptive in my opinion.

Is there a reason for this?

⬐ startling

Functions are one kind of arrow. There are other arrows besides functions.

Renaming "arrow" to "function" is like replacing "number" with "1".

⬐ gravypod

What other types of arrows are there?

⬐ systoll

State machines & object dependencies [and function composition, and... categories] are often drawn as directed graphs. When drawn like that, the circles/boxes represent objects, and the arrows represent arrows. The name comes from that kind of representation.

You can call them morphisms, too.

⬐ gravypod

Then from what I'm understanding it's not an "arrow", it's something closer to a "step" or a "process". Some method to get from one location to another. An arrow means nothing without background information. If I say it takes "10 arrows to get from A to x(A)" as a way to explain there are 10 things happening in the function X, then wouldn't it be better to say it takes "10 steps/processes to get from A to x(A)"?

> The name comes from that kind of representation.

The representation, the way I conceive it, is a mode for displaying computational or data in a spacial manor. As such relating a computational or mathematical process to a spacial terminology would be a "step" not a stick with a rock at the end of it.

⬐ kian

Does step help when thinking of the objects as individual data elements, the arrows as cons-links, map being a functor that respects cons-links [i.e. does not change the structure of the list]? The problem here is that implying process, ordering, or anything else is too narrow of a definition for what an arrow/morphism can be used to represent. That's why arrow (a thing that points to another thing), or morphism (a thing that helps define the shape) are actually better terms. Because Category Theory isn't about the things, it's about the relationships between the things, how these can be composed, and how higher-order operators that respect these relationships [and the new ones they represent for even higher-order operators] can form new relationships which can also be composed.

⬐ sanctus

Given any set with a partial ordering you can construct a category whose objects are the elements of that set and that has an arrow from a to b if and only if a <= b.

⬐ catnaroek

Some examples of categories whose arrows aren't functions:

(0) Any monoid can be viewed as a category with a single object. The arrows from the object to itself are the monoid's elements.

(1) Any preorder can be viewed as a category such that, between any two objects, there is at most one arrow, precisely when the source is less or equal than the target.

(2) Given a directed graph, or more generally a quiver[0], there is a small category[1] whose objects are the quiver's nodes, and whose arrows are the paths (finite sequences of edges) from a source node to a target node.

[0] https://en.wikipedia.org/wiki/Quiver_(mathematics)

[1] https://en.wikipedia.org/wiki/Free_category

⬐ tobbe2064

The word function has a sort of precis mening in math as a rule mapping each NUMBER in some domain to some NUMBER in a codomaon. The word arrow however can refer to any directed relation including less than or divides or what not, as long as they are composable and associative

⬐ tobbe2064

Further math is sort of a stone age technology

⬐ jonsterling

wtf are you on about? That is not how math works.

⬐ tobbe2064

I apologise for my drunken and incorrect silliness.

Aside from that, would you please enlighten as to what you meant by "that's not how math works"?

⬐ jonsterling

Sorry for my harsh comment; here's what I'm thinking of...

In math, you are dealing with many different kinds of object, not just numbers. In fact, one of the big realizations that led to modern mathematics is that not all mathematical objects can even be coded as numbers!

Your remark about "arrow" being more general than function is correct; but functions do not map only between sets of numbers, but between arbitrary sets, some of which contain elements that are not numbers, or even encodable as such.

⬐ None

None

⬐ GFK_of_xmaspast

Bronze age, sure, but stone age might be pushing it.

⬐ startling

That's not even true. Functions can map between lots of things, not necessarily numbers.

⬐ RGamma

Category theory uses weird terminology all over the place partly because it needs to distance itself from concepts that are "sort of like in set theory but not quite" and there are a lot of concepts that need naming thusly. Browse https://ncatlab.org/nlab/show/category+theory and you'll see a ton of examples of this.

W.r.t the "modernity" of the terms: I think category theorists are glad if they find any word that fits the concept in their minds. "Mathspeak" is not supposed to be intuitive to outsiders (and everyone is such an outsider at one point), but once you get more into it the names do start to make sense.

Generally mathematics is a field that breaks everyday-intuition constantly. Having a technolect, a "foreign language in a language" if you will, helps coping with that.

⬐ gravypod

> "Mathspeak" is not supposed to be intuitive to outsiders

Isn't that antithetical to the entire concept of an organized science? As I understand we're meant to make commutative models of the world around us that have predicative properties. If it's not possible to easily communicate your model, then there isn't much of a point in using the terminology.

Think back to Newton's notations of calculus. They are improper and poor ways to demonstrate the information that is being spoken about [0]. I don't know anyone who doesn't actually use Leibniz's notations.

I don't think anyone can convince me that "Mathspeak" should be unintuitive.

[0] - ttps://en.wikipedia.org/wiki/Notation_for_differentiation#Newton.27s_notation

⬐ Koshkin

To be honest, Category Theory is the last thing a software developer ("working hacker") should worry about learning. It is indeed a fun subject, it has grown into a large branch of algebra, it has connections with functional programming (lambda calculus) etc. But if one wants to be a good programmer, there is so much of really useful and important (and difficult) stuff to learn before you can even come to appreciate what, if anything, knowing Category Theory can do to improve your software engineering skills, that I would dare to characterize it just as an obscure subject that in all likelihood is not worth spending your time on.

⬐ a-saleh

I thing that if you are the sort of person that really likes design patterns, the sort of applied category-theory that the likes of Erik Meijer, Bartosz Milewski, Rúnar Bjarnason or Gabriel Gonzalez talk about is actually a good next step after the GOF Desing Patterns :-)

⬐ danidiaz

Some basic notions of folds/unfolds, algebraic data types and recursion schemes are great to have, I think.

⬐ Nydhal

I'm curious, what should come before as a far as a mathematical subject ? Graph theory ? Number theory ?

⬐ Koshkin

The purely mathematical subjects that are deemed important for programmers are parts of the so-called Discrete Mathematics. The Wikipedia article on it lists what is included. It is a vast collection of topics, but discerning what would be more important (or interesting) for you should not be hard.

⬐ tnecniv

Depends on what you do. I work in robotics, so probability and linear algebra are the two most indispensable subjects I know. Graph theory might be a little more generally applicable.

At the end of the day, you don't need a lot of math to write CRUD apps. The more math you know, though, the more approaches you'll have to formulate and solve problems.

⬐ Jaxan

A lot of linear algebra is implemented using graph theory, using things like sparse matrices.

⬐ SomeStupidPoint

A lot of graph theory is implemented as linear algebra, using things like adjacency matrices.

⬐ westoncb

There isn't a specific branch of mathematics you need to know in order to learn Category Theory. Its main role is in providing a way of describing other parts of mathematics (similar to the way set theory and certain logics are commonly used to formulate definitions and proofs). In other words, it's a kind of 'foundation,' so there isn't really anything under it. (This is my understanding anyway—please correct me if I'm wrong here.)

That said, it will probably be rather difficult to comprehend if you haven't been exposed to a good amount of other work in pure mathematics first. If you wanted one other more introductory subject, I'd recommend checking out Abstract Algebra (lots of other mathematics are expressed in its terms, also; so independent of Category Theory it would probably be time well spent. https://en.wikipedia.org/wiki/Abstract_algebra).

⬐ ajamesm

Category theory doesn't make someone a better Java applications developer, which is EXACTLY why they should be learning it

⬐ AvenueIngres

I agree it isn't directly useful but I think that is good common knowledge to have and a little exposure can only help.

⬐ willtim

Have you actually watched the presentation? If not, I encourage you to do so. Category theory and abstract algebra help us understand what it means to build composable and reusable software components with well defined semantics. There is already ample focus on algorithms and discreet math at university courses, but very little of the above. This is despite the fact that modern software development is becoming more about composing existing code and less about reimplementing classic algorithms. So given the already ample focus on the topics you suggest, I think we can forgive Phil Wadler for giving a very brief glimpse into a promising subject that most hackers would dismiss as obscure/irreverent.

⬐ Toidiu

Interesting talk from an academic point of view but still left me confused as to how we should 'think in functional terms.