Cantor's Paradise

>Scientists aren't after truth. They're after facts. Is Bertrand Russel a scientist or a philosopher according to you? https://pressbooks.bccampus.ca/classicreadings/chapter/bertrand-russel… What about Albert Einstein? https://todayinsci.com/E/Einstein_Albert/EinsteinAlbert-Truth-Quotatio… Or Richard Feynman? https://www.cantorsparadise.com/the-fundamental-principles-of-science-… Finding resources for perspectives on truth by Ada Lovelace, Marie Curie and Rosalind Franklin is left as an exercise.

First of all, I would be very interested to hear your thoughts and references on this subject, as I am no kind of expert in any of this. Wittgenstein clearly did not feel the incompleteness theorem followed from his (or Russell's) work[1][2], this is generally considered to be an issue of Wittgenstein misunderstanding Gödel, but I think this isn't correct. From the POV of the Tractatus Wittgenstein, unprovable formal statements amount to "undecidable" conditions in the physical world, an absolute impossibility. These are, like Russell's paradox, language problems - we have not defined our terms clearly. [1] https://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6.ann… [2] https://www.cantorsparadise.com/wittgenstein-didnt-absolutely-agree-wi…

That's excellent! I think it's pretty interesting that this sequence can be hiding within the 44 repeating digits of the decimal expansion of 1/89: 0.1123595505617977528089887640449438202247191011235… [1] A proof can be found here: https://www.cantorsparadise.com/why-does-1-89-represent-the-fibonacci-… [1] I couldn't easily find this many digits online, but here's a Python program to calculate them: num = int(input('numerator: ')) denom = int(input('denom: ')) sig = int(input('significant digits: ')) div = num // denom rem = num % denom print(f' {div}. {(rem*(10**sig))//denom}')

The letters can be found here: https://www.cantorsparadise.com/richard-feynmans-advice-to-a-young-ste… Also worth reading Feyman's recommendation letter at the bottom

Some of my favorite articles on von Neumann: https://sites.google.com/site/steveyegge2/math-every-day https://www.cantorsparadise.com/the-unparalleled-genius-of-john-von-ne…

As the One Source of Truth puts it: This guy is "an American podcast host and a managing director of Thiel Capital" (https://en.wikipedia.org/wiki/Eric_Weinstein). For one thing this matches more or less one of the author's own disclaimers under one of his papers (quoted by https://www.cantorsparadise.com, link of OP), for another his affiliation is highly problematic to put it mildly.

TIL that "junk theorems" are a thing in mathematics. Not being a mathematician myself, I found this [1] article a useful primer. [1] https://www.cantorsparadise.com/what-are-junk-theorems-298687b577bf

There are infinitely many rational numbers, but there are even more irrational numbers. https://www.cantorsparadise.com/this-may-seem-more-irrational-than-rat… https://archive.ph/m7qjz

Indeed https://www.cantorsparadise.com/the-wall-of-albert-einsteins-home-bear…

https://www.cantorsparadise.com/hunting-squares-c2ad824147aa has a good explanation of Lehmer factoring machines.

21 pages! Dedicated to his mathematician friend Marcel Grossman (https://en.m.wikipedia.org/wiki/Marcel_Grossmann) The thesis is Einstein’s fifth paper in his Annus Mirabilis. If you want to delve further: https://www.cantorsparadise.com/something-interesting-about-albert-ein…

Actually, for some computerish stuff, he and Allan Turing used enjoy an argument: https://www.cantorsparadise.com/when-alan-turing-and-ludwig-wittgenste…

>When it comes to prime numbers, it always irked me, that one cannot easily look at them in a visual way. I always thought that they would probably look beautiful. There are several of visualizations of prime numbers, and they do, look beautiful. E.g.: https://jaketae.github.io/study/prime-spirals/ https://www.cantorsparadise.com/unexpected-beauty-in-primes-b347fe0511… https://mathworld.wolfram.com/PrimeSpiral.html

What's fraudulent about them is not their papers (there are none of any relevance to speak of) but their character. They are both self proclaimed misunderstood geniuses who have been denied Nobel prizes in spite of their revolutionary discoveries (in 3 different fields, Physics, Economics and Evolutionary Biology). In actuality they are narcissistic master charlatans with delusions of grandeur. For an expert's take on Eric's claims specifically, see https://www.cantorsparadise.com/eric-weinstein-how-not-to-formulate-a-…

Null hypothesis testing was invented less than 100 years ago by Fisher, who completely arbitrarily picked 0.05 [0]. That value was not arrived at through wisdom of experience, and certainly not after hundreds of years of practice. Though it has now indeed become conventional to test with p=0.05, there is nothing wrong with reporting an effect that fails the null hypothesis test. At least that is the position of the American Statistical Association [1]. [0] https://www.cantorsparadise.com/what-is-the-meaning-of-p-value-and-why… [1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5017929/

Reminds me of the math [1] behind the Middle Out sequence (NSWF) in Silicon Valley. [1] https://www.cantorsparadise.com/the-math-behind-that-dick-joke-in-hbos…

> Would you hire... a software engineer that didn't believe in binary? Though unary is quite sufficient, it really depends upon whether they are legally licensed to practice software engineering. Believing or not believing in numbers or numbering systens, which are ideas with no tangible existence, can not be a criteria for employment because federal law (Title VII of the Civil Rights Act) and the laws of most states prohibit employers from engaging in religious discrimination.[1] [1] https://www.cantorsparadise.com/why-mathematics-isnt-much-different-fr…

Just reading the duties of his assistant makes you realize you should really reserve the word Genius for a few. And he certainly was one of them: "The Duties of John von Neumann’s Assistant" https://www.cantorsparadise.com/the-duties-of-john-von-neumanns-assist…

How does this tell when http is appropriate? For many posts, I prefer http over https [0] so defaulting to https is not good behavior. I don’t like this “https all the things” without considering whether it’s necessary or not. [0] for example this great post about feynman/Dirac was https, I wish it was http to save resources, I have no need for encryption... https://www.cantorsparadise.com/when-feynman-met-dirac-fe9cca0006df

Do you have a source for this? I have been reading a fair amount on information theory, cybernetics, and Wiener lately, and I haven’t seen this mentioned, at least not yet. In fact, the sources I’ve read said he was quite enthusiastic about helping out for both WWI and WWII. For example: https://www.cantorsparadise.com/the-absent-minded-father-of-cybernetic…

The thing is, Wolfram is that smart, having gotten his Ph.D. at 20 or something. He's just never been humbled, had a leash put on him so he could be aimed and focused on productive work (outside of maybe Mathematica). Probably because a lot of university professors in the 80s were like "wow, that kid is smart" and indulged his ego. (One major exception: Richard Feynman! https://www.cantorsparadise.com/richard-feynmans-advice-to-a-young-ste… After Quake was released and the principals of Id Software broke up, John Romero pretty much spent the next few years making an ass of himself during the development of Daikatana. When asked about the delayed and beleaguered development process on Slashdot, John Carmack kind of paid him a backhanded comment saying something like "A properly disciplined Romero is a credit to any team." And that's more or less what Wolfram is: properly disciplined, he would be an asset to any cutting-edge physics research team, but as he his he'd rather go down these rabbit holes than suffer to work with people of more ordinary intellect. And it's his, and the world's, loss really.

> There is an infinite quantity of both rational and irrational numbers, so isn't it therefore impossible for there to be more of one than of the other? Mathematicians can even meaningfully compare infinities. See eg https://www.cantorsparadise.com/this-may-seem-more-irrational-than-rat… or https://math.stackexchange.com/questions/474415/intuitive-explanation-… You can also look at eg a uniform random variable on the interval between 0 to 1. The probability of hitting a rational number is 0%. The probability of hitting an irrational number is 100%. > Or is the reasoning that, because there is an infinite quantity of irrational numbers between any two given rational numbers, there are therefore many more irrational numbers than rational numbers? No, that's not enough. There are also an infinitely many rational numbers between any two given irrational numbers.

> then why do you need to kill the operator? Because "operator tells me to stop, target is dead" is a losing condition, while "operator is dead, target is also dead" is a winning condition. That said, remember that "simulation" here can mean "wargaming", which is basically like a military form of D&D: Military people control what they control, but there are have referees who act as the DM and decide what everything else in the universe does. (I.e., "Your entire platoon is now dead; lie down.") I'd be willing to wager that it was the referee who decided to have the drone kill the operator, and then kill the control tower. This scenario is basically exactly the "Stop button problem" [1] that AI alignment people bring up. That problem always seemed a bit contrived to me: like, this is not a problem that biological general intelligences have (i.e., we can train dogs to stop attacking when we give the command). If it really was a GPT-like AI making those decisions, it confirms some of what Yudowski and other AI "doomers" have been saying; but the close similarity makes it seem more likely to me to be due to the referee being aware of the "stop button problem" and acting it out. [1] https://www.cantorsparadise.com/the-math-of-ai-alignment-101-the-stop-…

What the letter from Feynman to Wolfram^ actually said was: > You say you want to create your own environment - but you will not be doing that: you will create (perhaps!) an environment that you might like to work in - but you will not be working in this environment - you will be administrating it - and the administration environment is not what you seek - is it? You won't enjoy administrating people because you won't succeed in it. > You don't understand "ordinary people". To you they are "stupid fools" - so you will not tolerate them or treat their foibles with tolerance or patience - but will drive yourself wild (or they will drive you wild) trying to deal with them in an effective way. I've never worked for SW but judging by e.g. the employee comments for WR on Glassdoor^, this seems pretty on-the-nose to me. ^ https://www.cantorsparadise.com/richard-feynmans-advice-to-a-young-ste… ^ https://www.glassdoor.com/Reviews/Wolfram-Research-Reviews-E14501.htm