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I’m having a hard time grasping this one. Feels like the coastline paradox on a straight line of a known length.
Are irrational numbers even on a number line? Isn’t it definitionally impossible to pick it as a “point along the line”?
Yes, e is between 2 and 3 and Pi is between 3 and 4. There are geometrical lengths corresponding to each number.
>Isn’t it definitionally impossible to pick it as a “point along the line”?
No, it's mathematically possible to have a random process which picks a random real between 0 and n, with equal probability. Imagine it akin to throwing a dart at a line and picking the point it lands on as the number. Since there are only countably many rationals and uncountably many irrationals (i.e. not just infinitely more, but so many that you could never pair off the rationals with the irrationals, there are just too many) on any such length of the real line, chances are the number you end up with is overwhelmingly likely to be irrational.
As we keep burrowing deeper and deeper into an overly complex system that allows people to get into parts of it without understanding the whole, we are edging closer to a situation where no one is left who can actually reason about the system and it starts to deteriorate beyond repair until it suddenly collapses.
How is any human meant to understand a billion lines of code in a single codebase? How is any human meant to understand a world where there are potentially trillions of lines of code operating?
"If you try to rate-limit them, they’ll just switch to other IPs all the time. If you try to block them by User Agent string, they’ll just switch to a non-bot UA string (no, really). This is literally a DDoS on the entire internet."
It requires 7 coins in [ 1 .. 64 ] range to reach 100, but the average of popcnt( 1 .. 99 ) is only 3.19 coins per transaction, way better than 4.1 coins.
The thing I’m tired of is elites stealing everything under the sun to feed these models. So funny that copyright is important when it protects elites but not when a billion thefts are committed by LLM folks. Poor incentives for creators to create stuff if it just gets stolen and replicated by AI.
I’m hungry for more lawsuits. The biggest theft in human history by these gang of thieves should be held to account. I want a waterfall of lawsuits to take back what’s been stolen. It’s in the public’s interest to see this happen.
How is it acceptable to allow these companies to steal all of this copyrighted data and then turn around and use it to enforce their copyrights in the most heavy-handed manner? The irony is unbelievable.