November 3, 2011
Computational irreducibility is like prime numbers in a sense, right? So as long as it has pockets of reducibility, it is not the fundamentally irreducible thing? It’s not the universe that’s computationally irreducible, it’s…?
It’s the processes that go on. OK, so what is the universe? Is the universe the underlying code from which you can generate the universe? Or is it these dynamic processes that are going on inside the universe today? Or is it just one slice of those dynamic processes? This is the universe as it is today, whatever that means. What computational irreducibility talks about is how much information—if you want to predict what the universe is going to do, if you want to predict some aspect of what the universe is going to do, then you have to go from that underlying rule. You actually have to run it and see what the universe does. So, for instance, one of the types of things is, you might say, Is warp drive possible? And you might say, well, gosh, if you have the underlying theory of the universe, you should be able to answer whether warp drive is possible, but probably it isn’t easy to answer. Probably that will be one of these questions for which it’s effectively undecidable, because what you’ll be reduced to from a mathematical point of view is to say, Does there exist some configuration of material which has this property and that property and that property given these underlying rules for how things can be set up? And that can be an arbitrarily difficult question to answer. And that’s an example of what it means for there to be computational irreducibility. The thing with computational irreducibility is, what it tells you is that in order to find the outcome of some process, you have to follow through some number of steps. And that you can’t always arbitrarily reduce the amount of computational effort that’s needed.