A Medium publication on mathematics, science and computing history, with stories about figures like Feynman, von Neumann, Turing and Dijkstra.
HN links it for biographical pieces and math explainers, such as Feynman's letter to Stephen Wolfram and von Neumann's genius.
> 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-button-5f53aaebccc0
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-stephen-wolfram-1985-d572dc360c18)
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.
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-stephen-wolfram-1985-d572dc360c18
^ https://www.glassdoor.com/Reviews/Wolfram-Research-Reviews-E14501.htm
> 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-rational-317fe1a9cbd or https://math.stackexchange.com/questions/474415/intuitive-explanation-for-how-could-there-be-more-irrational-numbers-than-rati
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.
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.annotate
[2] https://www.cantorsparadise.com/wittgenstein-didnt-absolutely-agree-with-g%C3%B6del-s-theorems-and-russell-s-paradox-and-he-was-right-a5883750f925
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-sequence-7e09873533c3
[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}')