Twisol

24 ms·

181.
by Twisol 4y ago
As a child, I re-read The Number Devil constantly. It introduced me to some really cool mathematical ideas, couched in a cute story. The very last chapter includes a picture of the Principia Mathematica 's proof of 1 + 1 = 2 -- most
182.
by Twisol 4y ago
I could have made my argument without that line. Thanks for checking me.
183.
by Twisol 4y ago
> (and motivated) Look, that's the important part, right? If I wanted to learn the material, I could. But I'm not really interested in learning the material right now, or following the arguments exactly. It's a great artic
184.
by Twisol 4y ago
Even as someone with mathematical training, my eyes started skipping lines a few paragraphs in. This content is good, for sure, but you have to be in the right headspace to follow along. Quanta's material is serving a different need. Q
185.
by Twisol 4y ago
The first thing I thought of when I saw the name was the opening theme for a 2011 anime called "Phi Brain", which uses the word "misskey" in its lyrics. (I don't think it has any meaning?) Lo and behold, that's
186.
by Twisol 4y ago
For want of context, this is the library described in the article.
187.
by Twisol 4y ago
And CALM stands for Consistency As Logical Monotonicity -- CRDTs evolve monotonically in a certain sense.
188.
by Twisol 4y ago
That makes a lot of sense -- thanks for contributing that nuance!
189.
by Twisol 4y ago
Gravitational attraction still dominates on even fairly large scales, and chemical bonds absolutely dominate over anything expansion could possibly do -- it would contribute an incredibly light force opposing any bonds. So no, we (and our g
190.
by Twisol 4y ago
Yes, true -- the distance between two points doesn't grow linearly, but rather proportionally to itself :D
191.
by Twisol 4y ago
> Rather it's that the rate of expansion of the universe is accelerating, so that we're moving away from parts of it faster than its light can cover the distance to us. From my understanding, it's not that we're movin
192.
by Twisol 4y ago
I think both types can enjoy fun diversions. I think being a "simplifier" just means you can make a distinction between diversions and solutions. For me, every additional moving part has a cost, and that cost needs to be amortized
193.
by Twisol 4y ago
I goofed on my calculations a little bit -- steno boards are designed so that one finger can depress two keys at once, so in principle you can actually hit all 20 keys simultaneously. You can't just hit any two keys with the same finge
194.
by Twisol 4y ago
I also picked up a basic steno keyboard earlier in 2022 (the EcoSteno, I think). I'm no good with it yet (I'm still working through layout drills, honestly), but for me, the draw isn't in transcription or text input specifica
195.
by Twisol 4y ago
As I understand it, submissions are moderated (albeit lightly -- not to the degree of formal peer review). So, since it's on the arXiv, we can assume that the moderators felt it belongs there. I've seen a number of other book-leng
196.
by Twisol 4y ago
> It felt to me more like ‘I had some ideas about programming languages after 20+ years of Haskell and research. Here’s my plan to unify logic programming with more normal functional programming (also we’re getting rid of monads). By the
197.
by Twisol 4y ago
You can sort of justify "the Amazon River" as "the Amazon river" -- i.e. the river that happens to be in the Amazon rainforest. The other two don't really act like "adjective + noun".
198.
by Twisol 4y ago
This is one of those titles that doesn't make sense when HN drops the leading word. It should be: > Why I start taking English classes at the age of 46
199.
by Twisol 4y ago
I'm still waiting (agonizingly) for pattern matching in switch to actually land as a non-preview feature. We're looking at a fourth preview in Java 20 (March 2023), so we probably won't get it for realsies until at least Ja
200.
by Twisol 4y ago
> Category theory is literally the mathematics of boxes (objects), arrows (morphisms), and composition. As I've learned more about category theory (and its applications), I've found string diagrams to be a really nice tool. B
201.
by Twisol 4y ago
"Functor" has been used in multiple ways in different fields. It's apparently a term of art in linguistics; we call C++ classes implementing `operator()` "functors"; Prolog terms have parts called "functors&quo
202.
by Twisol 4y ago
> Mathematics is the mathematics of abstraction. > Category theory is the mathematics of composition. I don't know why you're being downvoted (tone?) but you're right. Categories formalize exactly and only the notion of
203.
by Twisol 4y ago
I second this recommendation; Cheng's book is probably the most approachable of the recent wave of category theory texts which does not assume the whole edifice of abstract algebra as a starting point. Most CT texts introduce categor
204.
by Twisol 4y ago
I think learning the essentials of another field can be more valuable than expected, whether it's a mathematician learning to program or a software engineer learning patterns of abstraction. When you've gone deep on one field, goi
205.
by Twisol 4y ago
> However, it turns out that category theory is equivalent to type theory (ie, what computers use). Just to elaborate on this a little, a program of type B in context of variables of types A1, A2, ..., An, can be modeled as an arrow
206.
by Twisol 4y ago
> you really need to use haskell. Or Scala. They're the only two common-use languages I'm aware of whose type systems are expressive enough to define what a monad (or a category, or a ...) is internally. Of course you can ident
207.
by Twisol 4y ago
I don't know for certain, but I suspect it simplified the language's grammar, since C's "declaration follows use" rule means you can basically repurpose the expression grammar for declarations instead of needing new
208.
by Twisol 4y ago
For sure, skip ahead :) Math textbooks are not generally meant to be read front-to-back (and math papers even less so). This one lends itself well to a straight-line readthrough, but what's important is what you get out of it. As the
209.
by Twisol 4y ago
I've been reading through this over the last few weeks. It's not your typical math textbook; the author takes great pains to stretch out the learning curve. Categories aren't even defined until chapter 8, and the presentation
210.
by Twisol 4y ago
I've seen some imperative code in the wild that looks like this: bool go = true; if (go) doA(&go); if (go) doB(&go); if (go) doC(&go); As a functional thinker, this is "just" an encoding of th

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