this great visualisation of homotopy groups might be helpful

A Sphere is a Loop of Loops (Visualizing Homotopy Groups)

https://youtube.com/watch?v=CxGtAuJdjYI

How dis he do all these animations? Any idea?

pretty sure it’s the manim library 3b1b uses (unable to check for certain right now)

and wars can be led in such ways that it never seems like the enemy is attacking the thing over which you would be willing to end the world. aka salami tactics

https://m.youtube.com/watch?v=yg-UqIIvang&pp=ygUOc2FsYW1pIHR...

oof same here brother. chess is killing me. i go cold turkey but i come back eventually. one idea is to replace it with something and then ditch the replacement. or just capitalise next time there’s enough momentum built up for wanting to get rid off of it. i did do it before though, went not playing for months. but when it’s it’s back for good

didn’t open the video, but you can also set double or triple tap on back of your iphone shortcut for this. i have a red filter set up for late night doom scrolling

great article. the information debt and budget seem like very useful things to have in mind

spend 1-2 years learning consistently _any_ undergrad math. id recommend focusing on “mastering” multivariable calculus, dependencies included. but keep taking peaks of higher level stuff or just articles as these. doing this is important as the math can be contextualised in many ways and being exposed to those ways helps you internalise intuitions

would you say that 3 reformulates 1+1+1 in another language? because if yes, such reformulations shouldn’t be disregarded just because they’re “reformulations”. so we can say there are kinds of reformulations which make things incredibly easier, and category theory is one of them

Why do you think category theory makes it easier? That's one thing category theory does not do. How well do you understand the subject?

There is a category theory "school of thought" in many subjects, which believes without solid evidence that category theory must be immensely useful to their subject. But it's often just that: a school of thought. This is the situation of category theory in CS. My concern is that people aren't being honest about this.

you’re right, and I’m in that school of thought, but mainly for math. In essence, I know people who use it in their reaearch and I trust them (and there’s a lot of good people doing good stuff with CT—it’s ubiquitous, so I’m fine with trusting them). I have a beginner understanding of CT, actually I finally started studying it seriously a month ago, after being exposed to it sporadically for some time. I’m not claiming anything about CT in CS, but I’m optimistic about that it can have a more widespread positive effect in it

~”numbers are the abstract notion, the primitive way of counting is a bijection” W. Lawvere

so the way people use “abstraction” sounds more like they are saying “a thing we (we think) are not used to”

many times I’ve wanted to listen to a summarisation of a chapter from a textbook I’m reading. this can be useful in at least 3 ways:

1) it prepares me for the real studying. by being exposed to the gist of the material before actual studying, im very confident that the subsequent real study session would be more effective

2) i can brush up easily on key concepts, if im unable to sit properly, eg while commuting. but even if i were, a math textbook can be too dense for this purpose, and i often just want to refresh my memory on key concepts. and often im tired of _reading_ symbols or words, that’s when id prefer to actually _listen_, in a way, using a muscle that’s not tired

3) if im struggling with something, i can play this 5min chapter explanation multiple times a day throughout the week, while doing stuff, and engaging with it in a casual way. i think this would “soften” the struggle tremendously, and increase the chances of grasping the thing next time i tackle it

also id like a “temperature” knob, that i could tweak for how much in detail i want it to go

I’m both, at times I don’t want to choose, at times I want full control. I didn’t have TV for years (was pushing a decade), but ~2months ago I got myself an analog antenna that has local channels and it’s been a blast: I caught some olympic games, watched Euro cup, couple of movies (I caught “Decision to leave” from my watchlist——tremendous movie), I saw some Anthony Bourdain shows and now I know who the guy is and i enjoyed the show, saw a documentary on war in my country, watched some live streams of city council meetings… Also, I wanted to say this somewhere in this thread I’m not trying to sell tv to you, you caught a stray bullet, but also I’m sharing that I watched it with a different curiosity after so long of not having it, and did have a great time just with those 17 channels of uncurated content, which was the main motivation——to have uncurated content