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SetTheorist

114 karma · joined January 18, 2017

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SetTheorist··on Zen-C: Write like a high-level language, run like C
"Damit wird insbesondere zu der interessanten Aufgabe, eine quadratische Gleichung beliebig vieler Variabeln mit algebraischen Zahlencoeffizienten in solchen ganzen oder gebrochenen Zahlen zu lösen, die in dem durch die Coefficienten bestimmten algebraischen Rationalitätsbereiche gelegen sind." - Hilbert, 1900

The use of "variable" to denote an "unknown" is a very old practice that predates computers and programming languages.

SetTheorist··on Aluminium is crucial to vaccines – and safe. Why are US advisers debating it?
I will definitely trust a random, prima facie absurd, claim from an anonymous someone on the internet (with bad grammar, misspellings, and lack of capitalization) over peer-reviewed scientific studies. Yep.
SetTheorist··on Mathematics is hard for mathematicians to understand too
There is an inherent complexity in a lot of mathematics. The compact notation makes it much easier (or even possible) to understand what is going on.

Compare something like

equals(integral(divide(exponentiate(negate(divide(square(var),2))),sqrt(multiply(2,constant_pi))),var,negate(infinity),infinity),1)

vs

$$\int_{-\infty}^{\infty}\frac{e^{-x^2/2}}{\sqrt{2\pi}}dx = 1$$

(imagine the actual generated mathematical formula here :-/ )

it is infinitely easier to grok what is going on using symbolic notation after a minimal amount of learning.

SetTheorist··on Terence Tao: At the Erdos problem website, AI assistance now becoming routine
Experimenting with LLMs, I've had examples like it providing the Cantor Set (a totally disconnected topological space) as an example of a Continuum immediately after it provides the (correct) definition as a non-empty compact, connected (Hausdorff) topological space. This is immediately obvious as nonsense if you understand the topic, but if one was attempting to learn from this, it could be very confusing and misleading. No human teacher would do this.
SetTheorist··on Amid shutdown, Trump administration guts department overseeing special education
Bad. Education and growth of children belongs to the entire country. Full stop.
SetTheorist··on A tutorial for the Mercury programming language
Have you tried diving deeper into languages like Prolog, Haskell, Lisp/Scheme, APL, Forth? These are likely to provide some food for thought different from typical languages used in numerical analysis...
SetTheorist··on A tutorial for the Mercury programming language
Have you tried diving deeper into languages like Prolog, Haskell, Lisp/Scheme, APL, Forth? These are likely to provide some food for thought different from typical languages used in numerical analysis...
SetTheorist··on Largest Mass Resignation in US History as 100k Federal Workers Quit
From "Eternal Fascism: Fourteen Ways of Looking at a Blackshirt" by Umberto Eco. via https://en.wikipedia.org/wiki/Ur-Fascism

I think it is quite evident that the modern far-right movement in the US (including those in power today) can be characterized as fascist.

"The cult of tradition," characterized by cultural syncretism, even at the risk of internal contradiction. When all truth has already been revealed by tradition, no new learning can occur, only further interpretation and refinement.

"The rejection of modernism," which views the rationalistic development of Western culture since the Enlightenment as a descent into depravity. Eco distinguishes this from a rejection of superficial technological advancement, as many fascist regimes cite their industrial potency as proof of the vitality of their system.

"The cult of action for action's sake," which dictates that action is of value in itself and should be taken without intellectual reflection. This, says Eco, is connected with anti-intellectualism and irrationalism, and often manifests in attacks on modern culture and science.

"Disagreement is treason" – fascism devalues intellectual discourse and critical reasoning as barriers to action, as well as out of fear that such analysis will expose the contradictions embodied in a syncretistic faith.

"Fear of difference," which fascism seeks to exploit and exacerbate, often in the form of racism or an appeal against foreigners and immigrants.

"Appeal to a frustrated middle class," fearing economic pressure from the demands and aspirations of lower social groups. "Obsession with a plot" and the hyping-up of an enemy threat. This often combines an appeal to xenophobia with a fear of disloyalty and sabotage from marginalized groups living within the society. Eco also cites Pat Robertson's book The New World Order as a prominent example of a plot obsession. Fascist societies rhetorically cast their enemies as "at the same time too strong and too weak." On the one hand, fascists play up the power of certain disfavored elites to encourage in their followers a sense of grievance and humiliation. On the other hand, fascist leaders point to the decadence of those elites as proof of their ultimate feebleness in the face of an overwhelming popular will.

"Pacifism is trafficking with the enemy" because "life is permanent warfare" – there must always be an enemy to fight. Both fascist Germany under Hitler and Italy under Mussolini worked first to organize and clean up their respective countries and then build the war machines that they later intended to and did use, despite Germany being under restrictions of the Versailles treaty to not build a military force. This principle leads to a fundamental contradiction within fascism: the incompatibility of ultimate triumph with perpetual war.

"Contempt for the weak," which is uncomfortably married to a chauvinistic popular elitism, in which every member of society is superior to outsiders by virtue of belonging to the in-group. Eco sees in these attitudes the root of a deep tension in the fundamentally hierarchical structure of fascist polities, as they encourage leaders to despise their underlings, up to the ultimate leader, who holds the whole country in contempt for having allowed him to overtake it by force.

"Everybody is educated to become a hero," which leads to the embrace of a cult of death. As Eco observes, "[t]he Ur-Fascist hero is impatient to die. In his impatience, he more frequently sends other people to death."

"Machismo," which sublimates the difficult work of permanent war and heroism into the sexual sphere. Fascists thus hold "both disdain for women and intolerance and condemnation of nonstandard sexual habits, from chastity to homosexuality."

"Selective populism" – the people, conceived monolithically, have a common will, distinct from and superior to the viewpoint of any individual. As no mass of people can ever be truly unanimous, the leader holds himself out as the interpreter of the popular will (though truly he alone dictates it). Fascists use this concept to delegitimize democratic institutions they accuse of "no longer represent[ing] the voice of the people".

"Newspeak" – fascism employs and promotes an impoverished vocabulary in order to limit critical reasoning.

SetTheorist··on Detached Point Arithmetic
Amusingly, even the numbers in the first example are counter-examples to the author's false claim: neither 0.1 nor 0.2 can be represented thusly.
SetTheorist··on Ukrainian hackers destroyed the IT infrastructure of Russian drone manufacturer
I have no doubt that russian media makes absurd claims like that.

If you actually believe this nonsense, I pity you.

SetTheorist··on Hiding messages in a deck playing cards
Reminds me of the playing-card based encryption system designed by Bruce Schneier for the novel Cryptonomicon .

https://en.wikipedia.org/wiki/Solitaire_(cipher)

SetTheorist··on IPurix: AI-Powered Watermark Removal Without Photoshop Skills
AI used for an unethical and immoral application.
SetTheorist··on Ukrainian hackers destroyed the IT infrastructure of Russian drone manufacturer
No, they do not. Ukrainians have not and do not deliberately target civilians in their war of self-defense against the invading russian army.

Russia consistently and deliberately targets civilians. There is no "both sides" here.

SetTheorist··on Math.Pow(-1, 2) == -1 in Windows 11 Insider build
That's a very misleading description of Banach-Tarski. You need to break up the body into a few (very weird) pieces and maneuver them (via only rigid motions - rotations and translations).
SetTheorist··on Math.Pow(-1, 2) == -1 in Windows 11 Insider build
Paraconsistent logic looks into logical systems that allow contradictions.

A lot of set-theory research is looking into the consequences of various axiomatic assumptions.

SetTheorist··on The new skill in AI is not prompting, it's context engineering
Nitpick: I think you mean that FP arithmetic is not _associative_ rather than non-commutative.

Commutative: A+B = B+A Associative: A+(B+C) = (A+B)+C

SetTheorist··on India launches attack on 9 sites in Pakistan and Pakistani Jammu and Kashmir
In what possible sense can you possible mean that "all wars are defensive"?

And it is absurd to claim that Russia wants peace. It can literally have peace anytime it wants by simply pulling its troops out of Ukrainian territory and ceasing the launching of missiles and drones on the populace.

The US threats on Canada and Greenland are not made with "peace" in mind.

SetTheorist··on Why Is Light So Fast?
Generally, "equivocation" is the fallacy of using the same word with different meanings in an argument.

https://en.wikipedia.org/wiki/Equivocation

SetTheorist··on Let's write a video game from scratch like it's 1987
Don't forget about Turbo Basic!

It was a great language and IDE for a young self-taught programmer.

SetTheorist··on Sierra was captured, then killed, by an accounting fraud (2020)
Latin Vulgate: radix enim omnium malorum est cupiditas

"root of all evil" or "root of all evils" would seem to be more precise translations than "root of all kinds of evils".

The Russian Synodal bible gives: ибо корень всех зол есть сребролюбие which would translate to "root of all evils"

SetTheorist··on Code is run more than read
You've got the subset relationships backwards: Reals are a subset of the field of Surreal Numbers which is a subset of the group of Games. (Probably better phrased as embeddings, rather than subsets, but the point remains...)

Note that Games do _not_ form a field: there is no general multiplication operation between arbitrary games.

SetTheorist··on Ancient Greek terms worth reviving
Your example is patently silly.

Do you really think that Ancient Egyptians didn't have a simple declarative statement that "the sun rises"?

Don't fall into exoticism. Ancient Egyptians were human beings speaking language for the purposes of communication in their day-to-day life, just like we do.

That being said, it definitely could be interesting to see how LLMs would work when trained on different language corpuses and other cultural contexts.

SetTheorist··on These Shapes Are Topologically Equivalent
I'm not sure exactly what you're trying to say (I'm not sure what you mean by "separate" here), but your assertions seem incorrect. Knots can have even or odd crossing numbers, that alone will not tell anything about whether it is an "unknot" or not. Also, if you have two non-trivial knots and "join" them (ie each a knot in a circle, cut each circle in one spot and join the circles at the cuts) you will _never_ get an unknot.
SetTheorist··on A list of developer questions to ask prospective employers
Absolutely. I've done a lot of interviews for different companies, and it is clear when someone is asking a pre-canned list of questions vs. someone who has real questions and genuine interest. I wouldn't give a no-hire recommendation just because someone did that, but it is definitely off-putting. Genuine questions asked out of interest can lead to an interesting discussion which could give a boost to a candidate. (Obviously, actual skills are the most important thing, but when choosing between a couple of candidates, both seeming fits for a role, it could tip the scales.)
SetTheorist··on Taikyoku Shogi
Chu shogi and Tenjiku shogi are other larger (not so ridiculously large) variants of shogi that are quite playable and enjoyable.

Also, people do play crazy games these days, look up "monster wargames". For example "Advanced European Theater of Operations" has 2200 pieces played on 2 poster-sized maps...

SetTheorist··on How many colours were there in a medieval rainbow?
An in-depth analysis of basic color terms across languages:

https://www.amazon.com/Basic-Color-Terms-Universality-Evolut...

(Noting that different languages do have differing numbers of basic color terms.)

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