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I am a mathematician who is using category theory all the time in my work in algebraic geometry, so I am exactly the wrong audience for this write-up!

I think that talking about "bad definitions" and "confusing presentation" is needlessly confrontational. I would rather say that the traditional presentation of category theory is perfectly adapted to its original purpose, which is to organise and to clarify complicated structures (algebraic, topological, geometric, ...) in pure mathematics. There the basic examples of categories are things like the category of groups, rings, vector spaces, topological spaces, manifolds, schemes, etc. and the notion of morphism, i.e. "structure-preserving map", is completely natural.

As category theory is applied more broadly in computer science and the theory of networks and processes, it is great that new perspectives on the basic concepts are developed, but I think they should be thought of as complementary to the traditional view, which is extremely powerful in its domain of application.


An essay from Paul Graham which explores this idea and the future trends:

The Acceleration of Addictiveness


Thank you for putting so much time into spelling out your work and thought process !

Question: Did you try to assess whether converting existing software/platforms or joining/taking over existing online communities would be better (along the various metrics you care about) ? If so, what were your conclusions ?


I tend to disagree with the idea that a depressed individual should seek flow activities.

Indeed, when I raised up the notion of Flow with my therapist (treatment for depressed moods and anxiety), she was familiar with it but observed that the basic elements of flow : concentration, accurate and adaptive sense of challenge, internal motivation... were the first victims of depression and that I should not expect to get into flow states before I got those back !


"De notre naissance à notre mort, nous sommes un cortège d’autres qui sont reliés par un fil ténu."

Jean Cocteau

("From our birth to our death, we are a procession of others whom a fine thread connects.")


An especially important example of macro choice that deserves some thought is the choice of a professional activity. See 80000 Hours:


For me, the strongest argument in favor of evolutionary psychology is how well it works for explaining social behaviours of non-human animals. I think this is important background material to understand where evolutionary psychologists come from. I recommend parsing through the following textbooks:

Animal Behaviour, Alcock

An Introduction to Behavioural Ecology, Krebs and Davies

(Disclaimer: I have only read Alcock, but Krebs and Davies is supposed to be stronger and better organized from a theoretical point of view - Alcock has wonderful examples.)

Of course, human social behaviour is orders of magnitude more diverse and complicated than in any other species - and even for other primates, one already needs to adopt the point of view of sociology and social psychology to get a good picture. But the premise that culture somehow freed us from all this background of behavioural adaptations is very strange, especially given the tendancy of the evolutionary process to recycle everything in sight into new shapes and patterns.


As far as major scientific facts go, I am surprised that evolution has yet to be mentioned. Let me try:

"All the complexity of Life on Earth comes from a single origin by the following process: organisms carry the plan to reproduce and make copies of themselves, this plan changes slightly and randomly over time, and the modified plans which lead to better survival and reproduction tend to outcompete the others and to become dominant."


The example about stacks in 1.2 has a certain irony in context. This requires a small mathematical parenthese:

A stack is a certain sophisticated type of geometric structure which is increasingly used in algebraic geometry, algebraic topology (and spreading to some corners of differential geometry) to make sense of geometric intuitions and notions on "spaces" which occur "naturally" but are squarely out of the traditional geometric categories (like manifolds, schemes, etc.).

See for a very short introduction focusing on the basic example of the moduli of elliptic curves.

The upshot of this vague outlook is that in the relevant fields, everything of interest is a stack (or a more exotic beast like a derived stack), precisely because the notion has been designed to be as general and flexible as possible ! So asking someone working on stacks a good example of something which is not a stack is bound to create a short moment of confusion.

Even if you do not care for stacks (and I wouldn't hold it against you), if you are interested in open source/Internet-based scientific projects, it is worth having a look at the web page of the Stacks project (, a collaborative fully hyperlinked textbook on the topic, which is steadily growing towards the 3500 pages mark.


Been there, done that survey...

I'm curious about the results.

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