I remember Eliezer wrote an earlier essay to the effect that GR is a really simple theory, in some information-theoretic sense, and therefore we should optimize our theories based on their information-theoretic complexity. But what’s being missed here is that GR (and SR and Newtonian physics and arithmetic . . .) are simple stated on its own terms. That’s WHY it’s a paradigm shift. If you tried to state GR strictly as a modification of Newtonian mechanics in a global coordinate system, you would either fail, or you would end up with something incredibly complex that would appear implausible by information-theoretic counts.
The bits that you fail to count, when looking at a simple theory, are the bits required to represent the entire worldview, which don’t seem like they’re information because they’re just how you look at the world.
What you’re trying to do is find a local optimization in theory-space, but all you’re working with is a projection of theory-space onto the sub-space that is our current way of thinking, and then you find your objective function is not quite zero, but you wave your hands and say, “Hey! It’s lower than what we had before! Why did it take people 30 years to reach this not-quite-minimum when all they had to do was descend the gradient?” I think a lot of people would rather just wait around for someone to come along with an answer that really does minimize the objective function.
Somehow you have to hit upon the right projection of theory-space that happens to include all the right variables. If you have a mistress, I invite you to retire to a cottage with her for a month and see if that helps.
Seriously, agreeing with Caledonian.
I remember Eliezer wrote an earlier essay to the effect that GR is a really simple theory, in some information-theoretic sense, and therefore we should optimize our theories based on their information-theoretic complexity. But what’s being missed here is that GR (and SR and Newtonian physics and arithmetic . . .) are simple stated on its own terms. That’s WHY it’s a paradigm shift. If you tried to state GR strictly as a modification of Newtonian mechanics in a global coordinate system, you would either fail, or you would end up with something incredibly complex that would appear implausible by information-theoretic counts.
The bits that you fail to count, when looking at a simple theory, are the bits required to represent the entire worldview, which don’t seem like they’re information because they’re just how you look at the world.
What you’re trying to do is find a local optimization in theory-space, but all you’re working with is a projection of theory-space onto the sub-space that is our current way of thinking, and then you find your objective function is not quite zero, but you wave your hands and say, “Hey! It’s lower than what we had before! Why did it take people 30 years to reach this not-quite-minimum when all they had to do was descend the gradient?” I think a lot of people would rather just wait around for someone to come along with an answer that really does minimize the objective function.
Somehow you have to hit upon the right projection of theory-space that happens to include all the right variables. If you have a mistress, I invite you to retire to a cottage with her for a month and see if that helps.