Shut up and calculate: an extreme mathematical universe
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Re: Shut up and calculate: an extreme mathematical universe
#2I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast.
I yet to have read this essay, but I had two thoughts:
1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machine is implemented. Similarly, this can be case for observers within our universe (humans). So maybe there is, at a high enough level of abstraction, only one mathematically possible universe.
2. The mathematical theorems are shortcuts to computation. For example, I can add two numbers on a computer, or I can use a theorem, which will tell me only some property of the result, but avoids having to do the actual calculation. So if universe is just a computation, one could avoid actually computing it in certain cases by having a theorem that would tell them enough information they need. In other words, you don't actually need to simulate anything in order for objects in simulation to "exist". So there is no need for actual hardware on which the universe runs to exist.
Addendum: So I read the essay, and I disagree that the multiverse is necessary. As I already stated in point 1, it can be the case that all possible mathematical realities are the same at high enough level of abstraction.
Re: Shut up and calculate: an extreme mathematical universe
#3Haven't read the paper but I'm assuming this is the same concept (likely more digestible for the layman) in his book Our Mathematical Universe, which I highly recommend!
Re: Shut up and calculate: an extreme mathematical universe
#4I'm a philosophy noob, but isn't this very similar to Berkeley-style immaterialism?
Re: Shut up and calculate: an extreme mathematical universe
#5I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machin…
A concrete example of #2 is the hashlife algorithm. Intermediate steps can be skipped in a region of space, yet since it implements the CA nothing inside can notice that the computation didn't actually happen.
Re: Shut up and calculate: an extreme mathematical universe
#6I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machin…
If you like the idea of thinking about physical space in computational terms give one of the classics a try, Calculating Space by Konrad Zuse.
Re: Shut up and calculate: an extreme mathematical universe
#7I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machin…
Can you expand on #2? I don't understand maybe the word "theorem" in this context, or perhaps the meaning of "property of the result."
Re: Shut up and calculate: an extreme mathematical universe
#8I like the idea that the reality is just mathematics, I thought about it independently, but it gets weird really fast. I yet to have read this essay, but I had two thoughts: 1. Similar to Turing completeness, actual physical reality might not matter for the internal observer. All Turing-complete machines can calculate same things and observer from the inside of the machine cannot determine on what hardware the machin…
Can you expand on #2? I don't understand maybe the word "theorem" in this context, or perhaps the meaning of "property of the result."
"The complete proof of 2 + 2 = 4 involves 2,863 subtheorems including the 189 above. (The command "show trace_back 2p2e4 /essential" will list them.) These have a total of 27,426 steps—this is how many steps you would have to examine if you wanted to verify the proof by hand in complete detail all the way back to the axioms." http://us.metamath.org/mpegif/mmset.html#trivia
Re: Shut up and calculate: an extreme mathematical universe
#9Earlier quoted context omitted.
Can you expand on #2? I don't understand maybe the word "theorem" in this context, or perhaps the meaning of "property of the result."
"The complete proof of 2 + 2 = 4 involves 2,863 subtheorems including the 189 above. (The command "show trace_back 2p2e4 /essential" will list them.) These have a total of 27,426 steps—this is how many steps you would have to examine if you wanted to verify the proof by hand in complete detail all the way back to the axioms." http://us.metamath.org/mpegif/mmset.html#trivia
Jesus! I guess I'll just stick to 2+2 holy shit this is well beyond me!
Thanks for the link.
EDIT: Nope guess not now I'm knee deep in this thing :P
Re: Shut up and calculate: an extreme mathematical universe
#10The author expands on this concept in his 2014 book (~7 years after the publication of this paper), Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. I've read it, and I would highly recommend it to my fellow HN'rs. I found his multiverse classification scheme [1] very compelling and something that finds its way into my worldview and a lot of my thinking.
[1] https://en.wikipedia.org/wiki/Multiverse#Max_Tegmark.27s_fou...