The Joy of Abstraction: An Exploration of Math, Category Theory, and Life | Hacker News Reader

The Joy of Abstraction: An Exploration of Math, Category Theory, and Life

cambridge.org

114 pointsteleforce15 comments

I've been reading through this over the last few weeks. It's not your typical math textbook; the author takes great pains to stretch out the learning curve. Categories aren't even defined until chapter 8, and the presentation still takes multiple pages before we finally get the usual, concise definition.

I think the gradual approach is good, even if you have some familiarity with abstract algebra. Experienced readers might feel a little bored at first, but I still think that's a good sign overall.

I think it's good that the author made it as accessible as possible, but had to pause after a few chapters because they took so long to explain the basics (I was always bad at uni-level math but still studied half a math bachelor before CS).

Do you think it's a good approach to skip to chapter 8+, and come back to the first ones if we're missing something? Or do these first chapters still bring something to people with math education?

For sure, skip ahead :) Math textbooks are not generally meant to be read front-to-back (and math papers even less so). This one lends itself well to a straight-line readthrough, but what's important is what you get out of it.

As the sibling comment notes, if you skip too far ahead, the technical material will make you very well aware of that fact. But I think chapter 8 is a good place to jump in -- the material up to that point is mostly setting up intuitions and analogies. I think those are important to pick up, but they're also the kind of thing you pick up from sufficient exposure to mathematics of any flavor, so there's no harm.

Chapters 9 through 13 show how lots of other things can be seen as categories, so if you're already aware of some of them from undergrad math, you're probably good to go.

I think that's perfectly fine -- skip ahead if you like and return to the earlier chapters as needed. Worst case scenario, the amount of stuff you don't understand will be too much to constantly look up, so you'll have to make a smaller jump. Anyway when learning even more advanced math I think it's totally reasonable to forge your own path through a text (or multiple texts concurrently, if you like)

I've been reading through it and my impression is the same. My background is more in analysis/approximation theory, but I picked this up for bedtime reading and although it's a bit slow going/verbose for me, I think the writing is fantastic given the broad audience this book targets. It seems like a nice introduction for someone curious about abstract math despite some level of math trauma from earlier brushes with it

Are the parts dealing with privelege, gender etc. bearable?

Abstraction is why and how nerds fly. Fly up, look down, name what you see. Repeat over every representation of everything, and go as high as you can stand.

It beats bowling.

Can you give a real life (not related to math) example?

Not the person you replied to, but I've thought about this question myself and I think I've come up with a half decent analogy to explain it. (Someone more qualified can help me iron out any flaws).

Let's say there's an app to order pizza specifically from Dominoes. A generalisation of that idea would be an app to order a pizza from not just Dominoes, but from any food chain that offers pizzas.

An abstraction over that idea would be an app that offers some arbitrary thing in exchange for something that acts as a currency/payment(notice how we've entirely omitted money as a hard requirement).

So in essence, we went from:

An app that maps your money to a Dominoes pizza

Money -> Dominoes pizza at home

to an app that maps your money to any pizza from a food chain(generalisation)

Money -> (Pizza Hut, Dominoes, Papa Johns, ...) pizza at home

to an abstraction over the entire thing

Something to act as a "payment" -> Some return for said payment

An example I can think of for the last would be some service where people can exchange their skillset as a payment with each other. For example, if you know how to cook, you could cook something for a person, and in exchange they could offer a service using their skills to you(mabye help you clean a part of your house). So them cleaning a part of your house acts as a general payment, and you offering to cook for them is a service, it's sort of a abstract barter system over money.

edit: became french for a split second and spelt home as homme

Written by Eugenia Cheng, of the TheCatsters fame. (A great series of short lectures on YouTube.)

How do you download this as a single PDF document? You have to select every chapter you want included in the generated PDF, but the chapters are split over two pages, and moving to the other page to select all its checkboxes unchecks all the checkboxes on the prior page. There doesn't seem to be a way simultaneously select all the checkboxes on both pages for inclusion in the doc.

It’s on libgen, that might be the easiest way

There's a "select all" on the left sidebar. Took me a bit to find it too x)

I've been enjoying this book for the last 2 weeks. It's not an easy read for me. I did a BA in Math about the time negative numbers were discovered and haven't touched math much ever since. But with some effort this book is do-able and has given me very many new insights to chew on. Looking forward to re-reading chapter 14 again again this evening.

How can I get all content in a single PDF for free?

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