Curious to know what makes this "a proper VT100 implementation in the browser, not a JavaScript approximation of one" -- isn't Ghostty also an approximation, just implemented in a different language? Seems unnecessarily pejorative to me.
Readit Newsclintonc commented on Ghostty compiled to WASM with xterm.js API compatibility github.com/coder/ghostty-... · Posted by u/kylecarbs
> The photovoltaic effect is whale oil for the modern age.
What?
Whale oil and solar panels both being signs of high status.
clintonc commented on No reachable chess position with more than 218 moves lichess.org/@/Tobs40/blog... · Posted by u/emporas
Isn't the very first move of any chess game a reachable chess position with more than 218 moves?
The initial board position is certainly reachable (and reached in every game!), but there are only 20 legal moves available: the 16 legal pawn moves for White, and the 4 legal knight moves for White.
clintonc commented on Is mathematics mostly chaos or mostly order? quantamagazine.org/is-mat... · Posted by u/baruchel
> 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].
This argument seems way less convincing to me than the diagonalization argument, because as n is going to infinity that length does become 1.
Then use 1/3 instead of 1/2 for a combined length of 2/3 -- the total length of the intervals can be as small as you like. This hints at the fact that any countable subset of the real numbers is Lebesgue measure zero.
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.
clintonc commented on Is mathematics mostly chaos or mostly order? quantamagazine.org/is-mat... · Posted by u/baruchel
If I had a semester or two of free time I'd love to hit this subject again. I once told my math prof (logician) who made a comment about transfinite cardinals: careful it's powerful but it's power from the devil. I half regret that comment in retrospect.
I've never made peace with Cantor's diagonaliztion argument because listing real numbers on the right side (natural number lhs for the mapping) is giving a real number including transedentals that pre-bakes in a kind of undefined infinite.
Maybe it's the idea of a completed infinity that's my problem; maybe it's the fact I don't understand how to define (or forgot cauchy sequences in detail) an arbitrary real.
In short, if reals are a confusing you can only tie yourself up in knots using confusing.
Sigh - wish I could do better!
There are a couple of strategies for understanding the real numbers. One is to write down a definition of real numbers, for example using rational numbers and Dedekind cuts, hoping that what you're describing is really what you mean. The other is to write down the properties of real numbers as you understand them as "axioms", and go from there. An important property of real numbers that always comes up (either as a consequence of Dedekind cuts or as an axiom itself) is the least upper bound property -- every set which has an upper bound has a least upper bound. That's what gives you the "completeness" of the real numbers, from which you can prove facts like the completeness of the real numbers (i.e., Cauchy sequences always converge), the Heine-Borel theorem (closed and bounded subsets of the reals are "compact", and vice-versa), and Cantor's intersection theorem (that the nested intersection of a sequence of non-empty compact sets is also compact).
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.
clintonc commented on From Finite Integral Domains to Finite Fields susam.net/from-finite-int... · Posted by u/susam
You can get that every integral domain is a field with fewer words by using a higher powered set theory result -- injections on finite sets are also surjections. The cancellation property says multiplication by any element is an injection, so it is also a surjection, i.e., 1 is in the range, so that gives you the multiplicative inverse.
clintonc commented on Boris Spassky: 1937–2025 en.chessbase.com/post/bor... · Posted by u/throwaway81523
Very new to the game, so have mercy on me please, but can anyone explain what's going on with these 0-0-0 and 0-0 moves? I don't understand how or why two pieces can move simultaneously.
It's a special move in chess called "castling". See https://en.m.wikipedia.org/wiki/Castling
clintonc commented on Suckless.org: software that sucks less suckless.org/... · Posted by u/flykespice
From the page about dwm:
> 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.
Love the aesthetic, but I'm having trouble finding key information quickly.
- 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.