Hacker News Reader

Comment by i-use-nixos-btw | Hacker News Reader

I’m saying this level is perfect. I am not a practicing physicist, but I have a PhD in the theory side of condensed matter from many years ago - mostly focused on numerical simulations.

What is difficult is that most introductions to this topic tend to involve word soup, often employing terminology from category theory and topology that is completely alien to me. The result is that I can’t read a paragraph without looking things up.

And hell, you’ve managed to do that yourself. Homology groups? Simplicial complex? This is sounding more and more like botany to me.

But that’s the best think about intros like this. I’m not one for words, but concepts I can handle.

View on HN

> often employing terminology from category theory and topology that is completely alien to me.

Then it might be worthwhile to learn some basic category theory. Did you know that the language of category theory was introduced to make statements about algebraic topology precise (in particular the notion of so called "natural transformations of functors")?

The thing is, the way I’ve always learned things is by doing. See a problem, and learn different angles to see that problem, different methods to approach it, play around with it some more, and keep probing it until it makes sense through intuition.

The mathematical approach with many introductory texts to this stuff do things completely backwards, from my perspective. They don’t present scenarios, problems, or anything really. They start with definitions, lemmas, theorems. If you’re lucky, they’ll give you proofs. To me, that’s like learning C by reading the standard, and only writing a Hello World program afterwards. Sure, you can get some good understanding that way, but it’s an entirely impractical learning method unless you’re already seasoned in the concepts.

To paint a more complete picture, I came across the concept of polynomial invariants in knot theory, and I managed to get my teeth into that because you can start coming up with problems, solving them, and getting some intuition. That also lead to TL diagrams, winding in (2+1)D, and I could get that down into code pretty easily and again start playing around with it. These are concrete things, and involved memorising nothing other than a handful of relationships.

I tried reading “Category Theory for the Practicing Physicist”, and it was great to begin with - but pretty quickly started just giving names for things. Names for types of categories. Names for types of relationships. Definition definition definition definition. This is through no fault of the author, it’s just how the topic is, and it’s how people who can digest that stuff understand things.

This is thing A. This is thing B. They are related through thing AB. Thing B is related to thing C through thing BC. Thing A is related to C through BCAB. Here’s a diagram. This is a theorem. Ok now on to the definition of thing D.

OK GREAT BUT WHAT DO I DO WITH IT? It’s one hell of an uphill effort for learning nothing in particular - except for words for things. That‘s why I paraphrased Fermi - “if I could remember all the names of these particles I’d have become a botanist”.

>The result is that I can’t read a paragraph without looking things up.... And hell, you’ve managed to do that yourself. Homology groups? Simplicial complex? This is sounding more and more like botany to me.

I'm sorry but what do you expect from an area of research that hasn't entered the vernacular yet?

Like if I go try to read a blog post on cond-mat theory how many mentions of "loop calculations" and "fermions" and "renormalization group" and "analytic continuation" and blah blah blah. Does it make sense for me to complain that the article doesn't speak to me in my vernacular? No of course not - because even if it's an intro article the expectation is that I'm willing to put in some work. If it's too much work for you, ie if you don't know math, then shrug don't try to understand mathematical things I guess.

>I’m not one for words, but concepts I can handle.

How did you manage to get a PhD in theory then?

> I’m sorry but what do you expect

Introductions to be introductions.

> How did you manage to get a PhD in theory then?

Certainly not by being a walking glossary. If that was involved, I’d not have done it.

Same way that everyone does. I gravitated towards a niche, found a new method to analysing it, generalising that method to many more applications and spending the final year trying to ride the metaphorical unicycle on a tightrope hanging high above a cavern of nervous breakdown. The usual.

Now, the way you talk sounds very familiar - I know mathematical physicists who are very much used to throwing mathematical terminology around. But on the theory side, it’s quite rare to generalise that far so early on in an academic career. It’s far more about the concrete application than the abstract viewpoint, unless it’s somewhere where the abstract viewpoint makes a lot of sense.

Reply on news.ycombinator.com