Growing up, the lyrics always included the verse as well as the chorus: “… and the joker got away! // Batman in the kitchen // Robin in the hall // Joker in the bathroom // peeing on the wall. // …” but I can’t remember how it ended. does anyone else remember this?
We usually ended it there, but I vaguely recall a version where Batman slips on it (the pee) and breaks his balls; I don't recall the actual verse though.
This is a really cool result! It's computation in a single ball bouncing around a 2-D container, with the infinite state needed encoded in infinite digits of the real number coordinates of the ball (and balls velocity.) Am I reading correctly that the boundary of the billiard table is fractal, with infinite complexity, but the complexity is simple in some sense? Otherwise, a fractal wall encoding a look-up-table of halt/doesn't halt would also do turing computation (better even!) but the paper seems less trivial than this
Embedding state in a real number, and calling it a “length” is a common trick to show that a physical system is TC. Unfortunately, the abstraction (length<->real number) suffers from numerous real-world issues that typically renders any implementation impossible.
I’m not even talking impractical; real numbers are simply too powerful to be resolved in the physical world. Unless you spend a ton of effort talking about quantizing and noise, you are very, very far from a realizable computer.
> real numbers are simply too powerful to be resolved in the physical world
In a sense "real" numbers are in fact not real at all because they can't physically exist. I think we got it wrong when these numbers were named. What we now call the 'whole' numbers should be called 'real', and vice versa. pi is a whole (in the sense of complete) number because it includes ALL decimal places, but because of infinite precision it can never be realized. 2 is a real (as in it is realizable) number because we can have two of something in reality.
I think it outside of implementability, it provides a nice proof that no algorithm can answer questions like “is the trajectory of this ball in this billiard eventually periodic.” Of course it (if I am reading correctly) leaves open that an algorithm could exist assuming the wall isn’t fractal
To answer your literal question of "why do people think..."
For a while there was a widespread standing principle to not assume malice for actions that could be explained as a simple mistake. If only one person follows this policy, it's great. However, so many people were following this policy that it created massive incentives to disguise profit motivated malice as explainable accidents. We're in the midst of a massive backswing against this.
So, there is very little taste for patience when agents of ycombinator make mistakes that benefit a16z such as accidentally removing them from the title of a negative article, due to the billions of dollars entangling ycombinator with the reputation of a16z. This is not because it wasn't an accident- it's because any culture of patience with this will lead (and has led) to an explosion of copycat whoopsies.
reading the paper, I’d say this is a case of hoofbeats meaning horses- people are just getting high and crashing.. Although, this seems like a case where the average is very vulnerable to a ‘spiders georg’ type distortion, especially because of the tolerances people build.
> "average person eats 3 spiders a year" factoid actualy just statistical error. average person eats 0 spiders per year. Spiders Georg, who lives in cave & eats over 10,000 each day, is an outlier adn should not have been counted
Thank you that helps to inject a lot of skepticism. I was wondering how it so easily worked out what Q: A: stood for when that formatting took off in the 1940s
The US is pulling back from NATO and simultaneously re-asserting dominance in the Americas, i.e., the Munroe Doctrine, which has suffered setbacks in recent decades.
i mean, a theory of everything should at least make retrodictions, which afaik string theory never got to. if someone wants to point me to where someone solved e.g. the hydrogen spectrum using a string theory, then I will be wrong but very happy
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