Even if I’d agree with your conclusion, your argument seems quite incorrect to me.
the seeming lack of reliable feedback loops that give you some indication that you are pushing towards something practically useful in the end instead of just a bunch of cool math that nonetheless resides alone in its separate magisterium
That’s what math always is. The applicability of any math depends on how well the mathematical models reflect the situation involved.
would build on that to say that for every powerfully predictive, but lossy and reductive mathematical model of a complex real-world system, there are a million times more similar-looking mathematical models that fail to capture the essence of the problem and ultimately don’t generalize well at all. And it’s only by grounding yourself to reality and hugging the query tight by engaging with real-world empirics that you can figure out if the approach you’ve chosen is in the former category as opposed to the latter.
It seems very unlikely to me that you’d have many ‘similar-looking mathematical models’. If a class of real-world situations seems to be abstracted in multiple ways such that you have hundreds (not even millions) of mathematical models that supposedly could capture its essence, maybe you are making a mistake somewhere in your modelling. Abstract away the variations. From my experience, you may have a small bunch of mathematical models that could likely capture the essence of the class of real-world situations, and you may debate with your friends about which one is more appropriate, but you will not have ‘multiple similar-looking models’.
Nevertheless, I agree with your general sentiment. I feel like humans will find it quite difficult make research progress without concrete feedback loops, and that actually trying stuff with existing examples of models (that is, the stuff that Anthropic and Apollo are doing, for example) provide valuable data points.
I also recommend maybe not spending so much time reading LessWrong and instead reading STEM textbooks.
Even if I’d agree with your conclusion, your argument seems quite incorrect to me.
That’s what math always is. The applicability of any math depends on how well the mathematical models reflect the situation involved.
It seems very unlikely to me that you’d have many ‘similar-looking mathematical models’. If a class of real-world situations seems to be abstracted in multiple ways such that you have hundreds (not even millions) of mathematical models that supposedly could capture its essence, maybe you are making a mistake somewhere in your modelling. Abstract away the variations. From my experience, you may have a small bunch of mathematical models that could likely capture the essence of the class of real-world situations, and you may debate with your friends about which one is more appropriate, but you will not have ‘multiple similar-looking models’.
Nevertheless, I agree with your general sentiment. I feel like humans will find it quite difficult make research progress without concrete feedback loops, and that actually trying stuff with existing examples of models (that is, the stuff that Anthropic and Apollo are doing, for example) provide valuable data points.
I also recommend maybe not spending so much time reading LessWrong and instead reading STEM textbooks.