Substrate

A pause...and then I saw him pop up on my screen, eyes warm and crinkling, smiling widely. “Ahhhhh, there you are!” he beamed, clearly thrilled to see me. It made me happy. He was right: it didn’t feel like a proper reunion until we saw each others' faces. ​ My internet friendships look a lot like my IRL friendships, but they lack corporeality, are impossible for me to get my fingers around. When we hang out in person, our offline interactions look a lot like our online ones: talking, analyzing, processing, thinking out loud, asking questions, reflecting, words, words, words. Our brains are directly wired into one another. Our bodily expressions are confined to heart-eyes, wow, angery, cry, or whichever limited faces our messaging apps allow us to make. We blow blue bubbles at each other. We convey our emotions through slang and punctuation, express our love through memes. ​ Robin talks about making a messaging app for his family, with a grand total of four users, and the joy of building things just for yourself, much like a home cook as opposed to a professional chef.

It is one thing for a proof to be correct; quite another, for a proof to be comprehensible.

It colors the space blue because now it can.

still spinning its one syllable

and my heart— you can't plan on the heart, but the better part of it, my poetry, is open.

Speaker: Tom Leinster (University of Glasgow) Title: An introduction to n-categories Event: Categories, Logic and Foundations of Physics IV (January 2009, Imperial College London) Abstract: I will give an beginners' introduction to n-categories. First I'll explain roughly what an n-category is, and talk about some of the dreams that first led people to want to develop a theory of n-categories. Then I'll go into more detail, leading up to a description of the state of the art and of some of the difficulties involved in trying to make those dreams come true. This is a completely introductory talk, for those who know nothing about n-categories. Experts will be bored senseless.

It’s easy but disorienting, and it makes the home into a very strange space. Until the 20th century, one had to leave the house for almost anything: to work, to eat or shop, to entertain yourself, to see other people. For decades, a family might have a single radio, then a few radios and a single television set. The possibilities available outside the home were far greater than those within its walls. But now, it’s not merely possible to do almost anything from home—it’s also the easiest option. Our forebears’ problem has been inverted: Now home is a prison of convenience that we need special help to escape.

Slides for the course on category theory. Contribute to TallCats/CategoryTheory development by creating an account on GitHub.

Numberphile episode on it, https://www.youtube.com/watch?v=uvMGZb0Suyc.

To understand what it means to be self-compassionate, think about what it means to treat another person compassionately, and then turn that same orientation toward oneself. Viewing one’s problems through the lens of common humanity also lowers the sense of isolation people sometimes experience when they are suffering. It helps to remember that we’re all in this together. ​ Getting older brings undesired changes, many of which involve lapses or failures, as when people can’t remember things or have trouble performing everyday tasks. Even though they would treat their friends’ struggles with kindness and compassion, many older people become intolerant and angry, criticising themselves and bemoaning their inability to function as they once did. Others, meanwhile, seem to take ageing more in their stride, accepting their lapses, and treating themselves especially nicely when they have particularly bad days.

Try to ask one question at as many seminars as possible, either during the talk, or privately afterwards. The act of trying to formulating an interesting question (for you, not the speaker!) is a worthwhile exercise, and can focus the mind. ​ The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere.

as if  I were reading to a match that had to last my life.

If you truly love doing something, it’s always day one. There is no time or place you’ll ever feel you've arrived except in moments. What matters is not your ability, your talent, your achievements (or lack thereof), but that you keep on going and keep serving what you love. Video: https://www.dropbox.com/s/rvidytc7j2u4e41/mircea-day-one.mp4?dl=0

Other handouts can be fond on this page, http://boole.stanford.edu/cs353/handouts.html Mirrored to my Dropbox at https://www.dropbox.com/s/tn5of68rw375ftg/cs353-handouts.zip?dl=0

TIL about Kessler syndrome. https://en.wikipedia.org/wiki/Kessler_syndrome

Diff values with Codable, CaseIterable, and KeyPaths · GitHub

The highly customizable journal system to help you live a more productive, effective life.

For things like papers, tutorials, books, LaTeX is still where it's at, but for HTML I'd like to be able to do things like commutative diagr...

something else entirely going on but no single person can ever know it, so we fall in love. warm with trust

I think that’s what a hobby is supposed to feel like: not an obligation, but a state you’re always returning to. It doesn’t have to be expensive, it doesn’t have to be organized, it doesn’t have to depend on other people. It just has to be yours.

- Inline math, [$]...[/$] - Display math, [$$]...[/$$]

An adjunction is a way to relate two objects a and c, but not directly: C(a,c) Instead, we get two maps, (L)eft and (R)ight, which allow to relate them: C(L(a),c) A(a,R(c)) 1/n The means that there's a pair of arrows, one in each direction, that these two hom-sets are isomorphic. The first example given is currying: a function in two arguments is equivalent to a function of one argument returning another function in the remaining argument. 2/n We can write this like so: C(a✕b,c) C(a,c^b) where L = _✕b, and R = _^b.

that hunt is healing. ​ and you haven’t wasted any time. You just spent time learning. And now it’s time to learn something new.

Finally, I am concerned about the state of pure mathematics research. More and more, results depend on theorems whose proofs are unpublished or sketchy (or even, in places, incorrect). We rely more and more on unnamed teams of experts who have a sufficiently broad overview of an area to be able to tell us with confidence which papers can be trusted. Fashions change, people desert areas, and I am genuinely scared that we are leaving a mess behind in some areas. There are some theorems whose proofs might be difficult or impossible to reconstruct in 20 years’ time.