In July 2019, ICMS hosted a workshop on Category Theory.  During the workshop, Eugenia Cheng (School of the Art Institute of Chicago) gave a public lecture entitled Inclusion-Exclusion in mathematics and beyond: who stays in, who falls out, why it happens and what we could do about it. This is a recording of that talkThis talk has captions.  To turn the captions off, press CC on the bottom toolbar.

Andrew Wiles, one of the world's most renowned mathematicians, wonderfully describes research like exploring a big mansion. You enter the first room of the mansion and it’s completely dark. You stumble around bumping into the furniture but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it’s all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they’re momentary, sometimes over a period of a day or two, they are the culmination of, and couldn't exist without, the many months of stumbling around in the dark that precede them. ​ But more often than not you'll find that by the time you revisit a problem you've literally grown so much (mathematically) that it's trivial.

Slowly, gradually, it dawned on me that what I enjoyed was mathematics. The mathematical aspects of CS were what got me excited and kept me up at night working on projects. ​ The Summer after I graduated, I decided I had too much awesome stuff in my head that nobody wanted to hear me talk about at parties, so I started a blog called Math Intersect Programming ​ If someone offered me this deal to write about math and CS, I would take it in a heartbeat. I would never want to retire.

once we see the formal definition below, it will become clear that mathematical (say, first-order logical) statements, together with proofs of implication, form a category. Even though a “proof” isn’t strictly a structure-preserving map, it still fits with the roughly stated axioms above. One can compose proofs by laying the implications out one after another, this composition is trivially associative, and there is an identity proof. Thus, proofs provide a way to “transform” true statements into true statements, preserving the structure of boolean-valued truth. The section on diagram categeories was fantatsic.

Moreover, a universal property jumps right to the heart of why a construction is important. ​ I want to make this point very clear, because most newcomers to category theory are never told this. Category theory exists because it fills a need. Even if that need is a need for better organization and a refocusing of existing definitions. ​ l One hopes, then, that very general theorems proved within category theory can apply to a wide breadth of practical areas. ​ Could it be that there is some (non-categorical) theorem that can’t be proved unless you resort to category-theoretical arguments? In my optimistic mind the answer must certainly be no. Moreover, it appears that most proofs that “rely” on category theory only really do so because they’re so deeply embedded in the abstraction that unraveling them to find non-category-theoretical proofs would be a tiresome and fruitless process.

The Haskell Pyramid This is the Haskell Pyramid The triangle shape represents the knowledge you may learn about Haskell: wide at the bottom, and acute at the top. The pyramid is tall, heavy, and intimidating.

Die HSR Hochschule für Technik Rapperswil begrüsste zusammen mit Google und Digital Asset rund 300 Informatikerinnen und Informatiker aus der ganzen Welt zum 6. Haskell Hackathon. Die jährlich stattfindende Konferenz knackte zum ersten Mal die 300er-Teilnehmergrenze. Sie richtet sich sowohl an ausgewiesene Experten der Programmiersprache Haskell wie auch an interessierte Anfänger. Studierende der HSR, der ETH und weiterer Hochschulen hatten somit die Möglichkeit, vom 9. – 11. Juni 2017 unmittelbar in die Community einzutauchen. Mehr Informationen unter www.hsr.ch/medien

it's just so much easier for us to broadcast our love now. ​ He is ambivalent about the medium of social photography, arguing that the technology is only a tool that exposes existing fractures in the community and the self. ​ As Jean Baudrillard predicted in the middle of the 20th century, the camera went from changing the way we remember to changing the way we see. ​ To my son and daughters, when you read this one day: I see you and I love you with that eye too.

The most durable role for humans in the near future that’s actually coming, then, involves a strange role reversal with software: Our job is to function as the interfaces between inscrutable automated systems of various scales whose internal operations proceed without our involvement, but can only extend their reach with our help. Instead of eliminating the middleman, digital platforms have solidified that as our permanent role—the most human job of all.

In celebration of one year of Type Classes, annual memberships are half-off through June 30.

Stoller’s basic thesis is that private equity transforms corporations from institutions that make things and employ people into vehicles for extracting value, shifting that value toward a company’s owners, and then discarding whatever’s left. ​ In this climate, value of any kind is hard to confine to bounded places, even though much of the infrastructure of our society is still set up to operate under that assumption.

Experiencing your feed without numbers is such a fundamentally different thing. You evaluate every bit of content, not in the context of external approval (how many Likes or the numerical influence of the creator), but simply in the act of its consumption. but for all organic usage, let's make it a numbers-free space. Compensation (stock or cash) based on increased usage and engagement targets has to be somehow changed. I'm not sure what that exactly looks like, but I am certain that as long as this isn't fixed, even with the implementation of the first four planks, we’re still going to be facing the same challenges

Seems like `Publisher.handleEvents(receiveSubscription:receiveOutput:receiveCompletion:receiveCancel:receiveRequest:)` is Combine’s `do` equivalent. https://developer.apple.com/documentation/combine/publisher/3204713-handleevents

Introduction Terminal and Initial objects Terminal and initial objects 1 Terminal and initial objects 2 Terminal and initial objects 3 Products and Coproducts Products and coproducts 1 Products and…

A dependent type is a type that is parameterized by a value. Lots of languages have types that are parameterized by other types, like `List`, but those are not dependent types. Dependent types are parameterized by instances of types.

Whenever I mentally parse `protocol SomeProtocol: SomeOtherProtocol`, it’s meant to imply `SomeProtocol` adds additional requirements onto another protocol, namely `SomeOtherProtocol`’s. What’s odd about class-constraining protocols is that it’s been a weird historical inconsistency in Swift where the term to the right of the `:` _isn’t_ a protocol and instead a reserved word. All reference types implicitly conform to `AnyObject`, which, being a protocol, makes it a more consistent way of class constraining than remembering the special `: class` trick. This merging of concepts was lightly mentioned in [SE-0156](https://github.com/apple/swift-evolution/blame/93abb54833e2d9ee7ee842882f6104a867de3069/proposals/0156-subclass-existentials.md#L134) (link to specific line).

Shit sucks sometimes but it is pretty cool to be alive in NYC right now, seems like everyone I meet is pouring their hearts and souls into music, photography, or a new business idea, and it’s special to see how careers grow and friends help each other along the way. I am frustrated with myself beca

This piece reminded me of a [recent addition](https://github.com/jasdev/thoughts/commit/4103afc7ee992e86b52ecfe28b14549ef1287e5a) to my Daily List, “write for yourself and Distillations.” By keeping Twitter usage ephemeral, it might be easier to [keep stock](http://snarkmarket.com/2010/4890) on my own domain.

Xcode 11 beta 5 has brought lots of changes to SwiftUI, and we'd like to take a moment to provide corrections to our episodes based on these changes.

CAUTION: Monoid fever is contagious.

Grothendieck views the mathematician and the problem as complimenting each other, the mathematician using the problem’s natural structure in its solution, rather than striking it with a foreign, invasive method. My view is that any problem that has resisted repeated direct attack from problem solvers, should naturally be of interest to theory builders. If you can’t solve a problem directly, then grow a crystal of theory around the problem and then hope that the solution you are looking for can be located somewhere inside the crystal. This is hard because the same person needs to know about both category theory and the problem domain, which is quite a heavy demand on a human brain.

I think we should levy a fee for category theorists to use the word “just”

Category theory is just a special case of edge-labelled digraph theory

Andrej Bauer raises a question whether Hask is a real category. I think it’s a legitimate question to ask, especially by a mathematician or programming languages researcher. But I want to look closer at how a (probably negative) answer to this question would affect Haskell and its community.

The retweet lived and Reader died, but the underlying pattern was the same; once it was handed over to the corporation, everyone lost control.

ME: *responds to DM* ME: *checks off todo item* PERSON: *writes back* ME: ME: *makes new todo item*

They replied, “Yeah of course you are.”