Thanks for the game, I really enjoyed it and finally trying out some things I learned in practice. The solution I submitted was the best possible team according to a XGBClassifier calibrated with sklearn.CalibratedClassifierCV. Calibration performance on a test set and evaluating a solution with a different model (Dense NN) did make me realize that the solution is unlikely to be performant, but it was worth a try.
You can just pretend that ω is finite and plug it into the formula for the partial sum.n∑i=1i=12n2+12n, so ω∑i=1i=12ω2+12ω. If they were to give the ith odd number amount of fish on the ith day (1,3,5,7,9...), then you would have ω2 amount of fish, because n∑i=12i−1=n2. The two links I posted about the handling of infinite divergent series go into greater detail (eg. the question of the starting index).
You can absolutely count your fish that way with the help of hyperreals! ("growing promise" stream would be 12ω2+12ω though)
I think https://en.wikipedia.org/wiki/Hyperreal_number#The_ultrapower_construction is a good introduction. https://math.stackexchange.com/questions/2649573/how-are-infinite-sums-in-nonstandard-analysis-defined and https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3459243 address the handling of infinite divergent series with hyperreals and https://arxiv.org/pdf/1106.1524v1.pdf talks about uniform probability over N (among other things).
The Lost Temple of Lemarchand:
The Infernal Den of Cheliax:
The Goblin Warrens of Khaz-Gorond:
One common outcome (though not universal) in my simulations was that the carni/omnivores kill the non invincibles, then the pure carnivores starve to death and then the minimal size invincibles outcompete to extinction the non-minimal invincibles (which also includes the omnivores, the multi-herbivores and the animals able to migrate). I'm curious on how many biomes this outcome will play out.
Furthermore, It is also not inconceivable to me that an adversary might be able to use the hash itself without cracking it. For example, the sha256 hash of some information is commonly used to prove that someone has that information without revealing it, so an adversary, using the hash, could credibly lie that he already possesses a launch code and in a possible counterfactual world where no one found about the client side leaking the hash except this adversary, use this lie to acquire an actual code with some social engineering.
"Attention Lesswrong! With trickery I have acquired a launch code capable of destroying your site. As proof here is the sha256 hash of it: <hash>.
This is not a trick, I will leave plenty of time for you to check with your EA buddies that the hash is valid before you need to meet my demands.
I demand a launch code capable of destroying the EA forum sent to me until <time> or I will nuke this site and to this I precommitted. I won't reveal what I plan to do with the launch code you will send to me, but by basic game theory your interest is in sending it to me as your site's destruction is not certain that way.
I can't prove it to you, but irl I precommitted to nuking the site if my demands are not met and also that I won't send any more messages to prevent useless debating.
I hope you will make the correct choice!"
Counterclockwise, I've never heard anyone use it for clockwise.
Is it that intuitive to you that you should name the rotating object's direction using the movement of the top of the object? I think I would get confused with your words after a while. I just use "positive" and "negative" direction.
I was the one who first shared the notes on reddit. Unfortunately, I did not know that recording the speech was against the wishes of Sam Altman, but I should have checked why there was no recording (at the time I simply thought that no one bothered to do it). I'm sorry, fwiw I deleted the post.
I didn't know about Ramanujan primes and I enjoyed this article about them, so thanks!
One small note: I was a bit confused about whether the magic line's endpoints are included in the magic line. Initially, I thought they both are, but the formal definition says that the lower endpoint is not included. Maybe others were also confused.