on cultivating gardens in our lives

the horses running until they forget that they are horses.

As opposed to a textbook, real maths is highly non-linear. ​ As we will see throughout the post, personalization (and the engagement inherent in it) is essential to the success of the lecture.] ​ [Before the third, I ask the class whether the first two alone are enough. If I get nods, I draw a random collection of dots and lines, with the lines not at all connected to the dots, and they see we need some statement of incidence.] ​ Since we will always draw constellations as a picture, we can just use the picture as our “function.” ​ Compare this to being given the definitions and propositions in the established mathematical language. To an untrained, uninterested student, this is not only confusing, but boring beyond belief! They don’t have the prerequisite intuition for why the definition is needed, and so they are left mindlessly following along at best, and dozing off at worst.

Left to its own devices, the human brain resorts to one of its most emblematic tricks, maybe one that helped make us human in the first place. It time-travels. ​ The whole sequence is a master class in temporal gymnastics. ​ The PET scanner allowed us to appreciate, for the first time, just how complex this kind of cognitive time travel actually is. ​ “Apparently, when the brain/mind thinks in a free and unencumbered fashion,” she wrote, “it uses its most human and complex parts.” ​ Amos Tversky once joked that where probability is concerned, humans have three default settings: “gonna happen,” “not gonna happen” and “maybe.” We are brilliant at floating imagined scenarios and evaluating how they might make us feel, were they to happen. But distinguishing between a 20 percent chance of something happening and a 40 percent chance doesn’t come naturally to us. ​ The Homo prospectus theory suggests that, if anything, we need to carve out time in our schedule — and perhaps even in our schools — to let minds drift.

Refactor Camp 2019, Day 1, Drew Austin: "The City as Weakly-Escaped Reality (Revisiting the Holey Plane)"

Maybe technology made it all too easy to slide into a life I wasn’t meant to have. ​ We still have to make our way in the world, alone, save for our technology built from other people’s frozen choices. ​ I spent so much time trying to organize the life that I thought I wanted. It wasn’t the same as living.

“That sucks” is negativity. “That sucks, here’s why, and here’s how to fix it” is criticism, ​ Someone with an informed, critical opinion is, in my experience, far less likely to be negative than someone not as informed. If anything, critical thinking adds dimension to an appreciation of the world around you.

Here’s the thing: the hero is the most damaging person on a team, particularly on a team that’s supposed to be writing high-availability or otherwise mission-critical software. ​ The hero is a human patch. ​ When a team can rely on a hero, they don’t need to grow and learn collectively. They don’t need to get better. They can coast along, which serves no one in the end. ​ You’re clearly managing someone highly motivated, but you need to shape that motivation into something more constructive.

🎶 A collection of types and functions that enhance the Swift language. - swift-prelude/Sources/Optics at 8cb25510cd54be91d28f0466e37f337aca815b74 · pointfreeco/swift-prelude

“Race to the Top; what a horrid metaphor for education. A race? Everyone is on the same track, seeing how fast they can go? Racing toward what? The top? The top of what? Education is not a race, it’s an amble. Real education only occurs when everyone is ambling along their own path.” —Peter Gray ​ 2. Always work (note, write) from your own interest, never from what you think you should be noting or writing. Trust your own interest.

in addition to this act of pressing “send,” there’s also a visual cue to suggest the end of a transmission: “Text messages and tweets already have a terminus, which is just the fact that they exist in little ‘bubbles.’” For these reasons, when a period is used, it can sometimes feel angry. ​ saying ‘end transmission’ instead of just ending it

I’ve always found the PDF to be the calmest of digital formats—

In the post-Facebook era, which many of us are already living in, there is no single platform, or place, where we can even expect to find everyone we know, and it wouldn’t surprise me if there never is again in our lifetimes. ​ The increasingly-maligned model of VC-funded, loss-leading hypergrowth in the pursuit of market dominance, understood another way, is a quest to create voids that matter, voids that will hurt if we let them emerge by rejecting the product currently filling them ​ The residue of buildings and cities determines what gets built on top of them, and if we’re conscientious, we’ll build with a more distant future in mind.

This PR introduces some concept that were done by our friends at PointFree ❤️ combine and pullback for Reducer and Feedback Store class that has minimal set up of the state machine Context is abil...

In last last week's episode of PBS Infinite Series, we talked about different flavors of multiplication (like associativity and commutativity) to think about when multiplying things that aren't numbers. My examples of multiplying non-numbers were vectors and matrices, which come from the land of algebra. Today I'd like to highlight another example: We can multiply shapes!

So if you feel inadequate whenever some form of the “achievement Olympics” comes up, don’t. We live in a society that is assesses people by what their lives produce, not what it takes to live them. Inner work is ignored unless it explains some outer work.

I need a strategy that bends, not breaks, while still holding me accountable over time. It should supply pressure smoothly and flexibly. So now I start each habit with a low weekly goal: e.g. meditate once per week, any day. That bar is low enough that I don’t have to schedule it or do anything special. Once that stabilizes, I ratchet up the target frequency.

One of my sisters, after having seen my pictures with a new outfit or after trying on makeup, said it was like watching me “bloom” into a new person. And i do feel like a completely different person than i was over the summer; those days feel impossibly far away now. ​ However, this kind of puts me between worlds: i’m hesitant to go back to my “old home”, but i still have yet to establish a “new home” of my own.

adding equalizers and coequalizers to a cartesian closed category amounts to enriching the corresponding type system with refinement types and quotient types respectively.

Paper wasn’t supposed to be cool. Then math came along.

and while I’m so glad that I did, I feel like those wounds are still open and won’t close until the book is out in the world and in people’s hands.

This primer exists for the background necessary to read our post on RSA encryption, but it also serves as a general primer to number theory. Oh, Numbers, Numbers, Numbers We start with some easy de…

Clearly it is vastly more logical and practical for a few people to develop the lessons really well, and put them [online]. ​ The teaching role of universities, especially for large popular subjects, will inevitably change from providing primarily learning content to providing primarily assessment, support and certification.

we are going to see an increasing number of academics thinking not so much about their paper CV, but rather about their [videos].

I’ve realized that a big part of the problem with mathematics education around the world might be that: the second piece of the picture—algorithmic computation—is a lot easier to teach than either the first—conceptual understanding—or the third—problem solving.

I am in Austria right now; having spent a week in Innsbruck visiting Hans-Peter Schroeker and Manfred Husty, I am now in Graz at the Technical University, and I am talking with Anton Gfrerrer, Sybi…

Programming languages lie at the intersection between the binary, deterministic, silicon world of computers and the inexact, chaotic, organic world of human consciousness and communication. To me, functional programming is the practice of applying mathematical formalisms to real-world programming problems.

And yeah, I think that sense of future shock is what has disappeared, which was in retrospect a very rapid turnover of styles one was accustomed to. ​ Music is the site where the major symptoms of cultural malaise can be detected I think. ​ what’s missing is a popular experience of newness.