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Cake day: 2024年2月6日

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  • i can kinda understand “liking the idea” in the same way that I “like” the very simple currency systems in single-player video games, where you do work (fight monsters, collect items, win Pokemon battles) and are automatically rewarded with currency you can use to buy items, which are always reasonably-priced because the game developers balanced it that way. It’s just that these systems have nothing to do with reality. But that simplistic view of money is pretty much all that’s left of cryptocurrencies if you look past the get-rich-quick scheme.














  • If the growth is superexponential, we make it so that each successive doubling takes 10% less time.

    (From AI 2027, as quoted by titotal.)

    This is an incredibly silly sentence and is certainly enough to determine the output of the entire model on its own. It necessarily implies that the predicted value becomes infinite in a finite amount of time, disregarding almost all other features of how it is calculated.

    To elaborate, suppose we take as our “base model” any function f which has the property that lim_{t → ∞} f(t) = ∞. Now I define the concept of “super-f” function by saying that each subsequent block of “virtual time” as seen by f, takes 10% less “real time” than the last. This will give us a function like g(t) = f(-log(1 - t)), obtained by inverting the exponential rate of convergence of a geometric series. Then g has a vertical asymptote to infinity regardless of what the function f is, simply because we have compressed an infinite amount of “virtual time” into a finite amount of “real time”.