Again, what you are missing is there are other explanations that also will fit the data. As an analogy, if someone draws from a deck of cards and presents the cards as random numbers, you will not be able to deduce what they are doing if you have no prior knowledge of cards, and only a short sequence of draws. There will be many possible explanations and some are simpler than ‘is drawing from a set of 52 elements’.
Yeah, that’s why I used the simplicity argument. Of course there are other explanations that fit the data, but are there other explanations that are remotely as simple? I would argue no, because relativity is just already really simple, and there aren’t that many other theories at the same level of simplicity.
I see that we need to actually do this experiment in order for you to be convinced. But I don’t have infinite compute. Maybe you can at least vaguely understand my point : given the space of all functions in all of mathematics, are you certain nothing fits a short sequence of observed events better than relativity? What if there is a little bit of noise in the video?
I would assume other functions also match. Heck, ReLu with the right coefficients matches just about anything so...
ReLu with the right coefficients in a standard neural net architecture is much much more complicated than general relativity. General relativity is a few thousand bits long when written in Python. Normal neural nets almost never have less than a megabyte of parameters, and state of the art models have gigabytes and terrabytes worth of parameters.
Of course there are other things in the space of all mathematical functions that will fit it as well. The video itself is in that space of functions, and that one will have perfect predictive accuracy.
But relativity is not a randomly drawn element from the space of all mathematical functions. The equations are exceedingly simple. “Most” mathematical functions have an infinite number of differing terms. Relativity has just a few, so few indeed that translating it into a language like python is pretty easy, and won’t result in a very long program.
Indeed, one thing about modern machine learning is that it is producing models with an incredibly long description length, compared to what mathematicians and physicists are producing, and this is causing a number of problems for those models. I expect future more AGI-complete systems to produce much shorter description-length models.
Again, what you are missing is there are other explanations that also will fit the data. As an analogy, if someone draws from a deck of cards and presents the cards as random numbers, you will not be able to deduce what they are doing if you have no prior knowledge of cards, and only a short sequence of draws. There will be many possible explanations and some are simpler than ‘is drawing from a set of 52 elements’.
Yeah, that’s why I used the simplicity argument. Of course there are other explanations that fit the data, but are there other explanations that are remotely as simple? I would argue no, because relativity is just already really simple, and there aren’t that many other theories at the same level of simplicity.
I see that we need to actually do this experiment in order for you to be convinced. But I don’t have infinite compute. Maybe you can at least vaguely understand my point : given the space of all functions in all of mathematics, are you certain nothing fits a short sequence of observed events better than relativity? What if there is a little bit of noise in the video?
I would assume other functions also match. Heck, ReLu with the right coefficients matches just about anything so...
ReLu with the right coefficients in a standard neural net architecture is much much more complicated than general relativity. General relativity is a few thousand bits long when written in Python. Normal neural nets almost never have less than a megabyte of parameters, and state of the art models have gigabytes and terrabytes worth of parameters.
Of course there are other things in the space of all mathematical functions that will fit it as well. The video itself is in that space of functions, and that one will have perfect predictive accuracy.
But relativity is not a randomly drawn element from the space of all mathematical functions. The equations are exceedingly simple. “Most” mathematical functions have an infinite number of differing terms. Relativity has just a few, so few indeed that translating it into a language like python is pretty easy, and won’t result in a very long program.
Indeed, one thing about modern machine learning is that it is producing models with an incredibly long description length, compared to what mathematicians and physicists are producing, and this is causing a number of problems for those models. I expect future more AGI-complete systems to produce much shorter description-length models.