Screaming into the void, I guess, but PSA. Don't use buttons for links. In my case, I couldn't right-click and copy the URL, but there are a lot of other reasons not to do this.

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# Author likes go

Ok, cool story bro...

# Go is compiled

Nice, but Python also has syntax and type checking -- I don't typically have any more luck generating more strictly typed code with agents.

# Go is simple

Sure. Python for a long time had a reputation as "pseudocode that runs", so the arguments about go being easy to read might be bias on the part of the author (see point 1).

# Go is opinionated

Sure. Python also has standards for formatting code, running tests (https://docs.python.org/3/library/unittest.html), and has no need for building binaries.

# Building cross-platform Go binaries is trivial

Is that a big deal if you don't need to build binaries at all?

# Agents know Go

Agents seem to know python as well...

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Author seems to fall short of supporting the claim that Go is better than any other language by any margin, mostly relying on the biases they have that Go is a superior language in general than, say, Python. There are arguments to be made about compiled versus interpreted, for example, but if you don't accept that Go is the best language of them all for every purpose, the argument falls flat.

As the "evidence" piles up, in further mathematics, physics, and the interactions of the two, I still never got to the point at the core where I thought complex numbers were a certain fundamental concept, or just a convenient tool for expressing and calculating a variety of things. It's more than just a coincidence, for sure, but the philosophical part of my mind is not at ease with it.

I doubt anyone could make a reply to this comment that would make me feel any better about it. Indeed, I believe real numbers to be completely natural, but far greater mathematicians than I found them objectionable only a hundred years ago, and demonstrated that mathematics is rich and nuanced even when you assume that they don't exist in the form we think of them today.

Even using 1/2, the set that remains is nonempty due to the Cantor intersection theorem. The total length of the intervals is 1, which means that the remainder has no "interior" (i.e., contains no open interval), but the converse is not true: removing intervals whose lengths sum to less than one does not mean that the remainder will contain any interval. This is the consideration that allows you to create what are called "fat Cantor sets" -- the middle thirds Cantor set has Lebesgue measure zero, but by removing smaller intervals you can get other, homeomorphic sets that have positive measure.

The diagonalization argument is an intuitive tool, IMHO. It is great if it convinces you, but it's difficult to make rigorous in a way that everyone accepts due to the use of a decimal expansion for every real number. One way to avoid that is to prove a little fact: the union of a finite number of intervals can be written as the finite union of disjoint intervals, and that the total length of those intervals is at most the total length of the original intervals. (Prove it by induction.)

THEOREM: [0, 1] is uncountable. Proof: By way of contradiction, let f be the surjection that shows [0, 1] is countable. Let U_i be the interval of length 1/2*i centered on f(i). The union V_n = U_1 + U_2 + ... + U_n has combined length 1 - 1/2*n < 1, so it can't contain [0, 1]. Another way to state that is that K_n = [0, 1] - V_n is non-empty. K_n also compact, as it's closed (complement of V_n) and bounded (subset of [0, 1]). By Cantor's intersection theorem, there is some x in all K_n, which means it's in [0,1] but none of the U_i; in particular, it can't be f(i) for any i. That contradicts our assumption that f is surjective.

Through the right lens, this is precisely the idea of the diagonalization argument, with our intervals of length 2*-n (centered at points in the sequence) replacing intervals replacing intervals of length 10*-n (not centered at points in the sequence) implicit in the "diagonal" construction.

> Because dwm is customized through editing its source code, it's pointless to make binary packages of it. This keeps its userbase small and elitist. No novices asking stupid questions.

...sucks less than what? :) Simple is good, but simpler does not necessarily mean better.

- Is this a "traditional" RPN calculator?

- Does it have bonus features, like symbolic processing?

- Is it programmable?

I believe outcomes would be better if kids used RPN calculators when learning, and programmable is definitely a plus.

- I use TurboTax because it's helpful, but I'm not happy or proud to use it (because it shouldn't need to exist).

- I use TikTok, but it doesn't make me feel good because I know I'm exposing myself to manipulation and data privacy concerns.

- I drive a [REDACTED] car, but it doesn't make me feel good because I always feel scammed when I take it in for maintenance.

I do feel good about my Brother printer, though -- Toner is reasonably priced, and I don't feel like they're trying to squeeze every dime out of me that they can; it's just a good reliable printer that does what I ask it and keeps out of my way otherwise.

I'm interested in all kinds of answers: Software, hardware, services, tools, toys, anything!

Comments URL: https://news.ycombinator.com/item?id=42797363

Points: 13

# Comments: 16

I like that just will search upward for the nearest justfile, and run the command with its directory as the working directory (optional -- https://just.systems/man/en/attributes.html -- with fallback available -- https://just.systems/man/en/fallback-to-parent-justfiles.htm...). For example, I might use something like `just devserver` or `just testfe` to trigger commands, or `just upload` to push some assets -- these commands work from anywhere within the project.

My life wouldn't be that different if I just had to use Make (and I still use Make for some tasks), but I like having a language-agnostic, more ergonomic task runner.

:-D

We can play a lot of games with "what is a symbol", but compactness pervades many of the models that we use to describe reality. The crux of the argument is not necessarily that the symbols themselves are compact as sets, but that the *space of possible descriptions* is compact. In the article, the space of descriptions is (compact) subsets of a (compact) two-dimensional space, which (delightfully) is compact in the appropriate topology.

In your example, the symbols themselves could instead be modeled as a function f:[0,1]^2 -> [0,1] which are "upper semicontinuous", which when appropriately topologized is seen to be compact; in particular, every infinite sequence must have a subsequence that converges to another upper semicontinuous function.

Much of the fun here comes from the Tychonoff theorem, which says that arbitrary products of compact spaces is compact. Since the *measurement space* is compact, the topology of the domain is not as important, as long as the product topology on the function space is the appropriate one. (Mystically, it almost always is.)

Milnor is a titan in his fields, so any conjecture he has made would be called Milnor's conjecture.

Are skilled pragmatists undervalued? Maybe, but this article doesn't do an good job of making me believe that.