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ec429 comments on The Apparent Reality of Physics - Less Wrong
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Comments (62)
Right, but it doesn't attach little "<exists intensity="200%" />" tags to that pattern.
Well, trivially not, because by giving the example I create a representation. But, does a theorem become true when it is proven? That seems to me to be absurd. Counterfactually, suppose there were no minds. Would that prevent it from being true that "PA proves 2+2=4"? That also seems absurd. I can't prove it's absurd, but that's because a rock doesn't implement modus ponens (no universally compelling arguments).
If X will happen tomorrow, then it is a fact that X will happen tomorrow, even though (ignoring for now timeless physics) tomorrow "doesn't exist yet", and the information "X will happen tomorrow" needn't be represented anywhere to be true; it inheres in the state of the universe today + {equations of physics}. Information which can be arrived at by computation from other, existing information, exists - or perhaps we should move the 'other, existing information' across the turnstile: it is an existing truth that (Information which can be arrived at by computation from foo) can be arrived at by computation from foo. Tautologies are true.
I said information, you said theorem-- I don't think it's the same.
I was expecting you to say something like "the 3^^^3rd digit of pi", and then I was going to say something, but now that I think about it, I think it's time to taboo "exist".
"Theorem Foo is true in Theory T" is information. Though the 3^^^3rd digit of pi is good too; I want to hear what you have to say about it.
Ok... "exist" doesn't have a referent. Any attempt to define it will either be special pleading (my universe is special, it "exists", because it's the one I live in!), or will give a definition that applies equally to all mathematical structures.
I was going to say, it {can be calculated}-exists, but it does not {is extant in the territory}-exist. It certainly has a value, but we will never know what it is. No concrete instance of that information will ever be formed, at least not in this universe. (Barring new phyisics allowing vastly more computation!)
Thanks, I think that's the clearest thing you've said so far.
I think my own concept of "exist" has an implicit parameter of "in the universe" or "in the territory", so it breaks down when applied to the uni/multiverse itself (what could the multiverse possibly exist in?). Much like "what was before the big bang" is not actually a meaningful question because "before" is a time-ish word and whatever it is that we call time didn't exist before the big bang.
But then, how do you determine whether information exists-in-the-universe at all? Does the number 2 exist-in-the-universe? (I can pick up 2 pebbles, so I'm guessing 'yes'.) Does the number 3^^^3 exist-in-the-universe? Does the number N = total count of particles in the universe exist-in-the-universe? (I'm guessing 'yes', because it's represented by the universe.) Does N+1 exist-in-the-universe? (After all, I can consider {particles in the universe} union {{particles in the universe}}, with cardinality N+1) If you allow encodings other than unary, let N = largest number which can be represented using all the particles in the universe. But I can coherently talk about N+1, because I don't need to know the value of a number to do arithmetic on it (if N is even, then N+1 is odd, even though I can't represent the value of N+1). Does the set of natural numbers exist-in-the-universe? If so, I can induct - and therefore, by induction on induction itself, I claim I can perform transfinite induction (aka 'scary dots') in which case the first uncountable ordinal exists-in-the-universe, which is something I'd quite like to conclude.
So where does it stop being a heap?
I'm not saying my universe is special just because it's the one I live in, in fact I can accept the reality of lots of Everett branches in which I don't live in.
More to the point I believe that the reality of those Everett branches preexisted your mathematical models of them, or indeed the human invention of mathematics as a whole. Mathematical structure were made in imitation of the universe -- not vice versa.
Ok, now taboo your uses of "reality" and "preexisted" in the above comment, because I can't conceive of meanings of those words in which your comment makes sense.
The thing about tabooing words, is that we find it easy to taboo words that are just confused concepts (it's easy to taboo the word 'sound' and refer to acoustical experience vs acoustic vibrations), and we find it hard to taboo words that are truly about the fundamentals of our universe, such as 'causality' or 'reality' or 'existence' or 'subjective experience'.
I find it much easier to taboo the words that you think fundamentals -- words like 'mathematical equations', namely 'the orderly manipulations of symbols that human brains can learn to correspond to concepts in the material universe in order to predict happenings in said material universe'
To put it differently: Why don't you taboo the words "mathematics" and "equations" first, and see if your argument still makes any sense
I tabooed "exist", above, by what I think it means. You think 'existence' is fundamental, but you've not given me enough of a definition for me to understand your arguments that use it as an untabooable word.
I'd say that (or rather 'mathematics') is just 'the orderly manipulations of symbols'. Or, as I prefer to phrase it, 'symbol games'.
That's applied mathematics (or, perhaps, physics), an entirely different beast with an entirely different epistemic status.
Manipulations of symbols according to formal rules are the ontological basis, and our perception of "physical reality" results merely from our status as collections of symbols in the abstract Platonic realm that defines the convergent results of those manipulations, "existence" being merely how the algorithm feels from inside.
Yup, still makes sense to me!
I understand "symbols" to be a cognitive shorthand for our brains representation of structures in reality. I don't understand the meaning of the word "symbols" in the abstract, without a brain to interpret them with and map them onto reality.
This doesn't really explain anything to me, it just sounds like wisdom.
Think in terms of LISP gensyms - objects which themselves support only one operation, ==. The only thing we can say about (rg45t) is that it's the same as (rg45t) but not the same as (2qox), whereas we think we know what (forall) means (in the game of set theory) - in fact the only reason (forall) has a meaning is because some of our symbol-manipulating rules mention it.
As I understand it ec429’s intuition goes a bit like this:
Take P1, a program that serially computes the digits in the decimal expansion of π. Even if it’s the first time in the history of the universe that that program is run, it doesn’t feel like the person who ran the program (or the computer itself) created that sequence of digits. It feels like that sequence “always existed” (in fact, it feels like it “exists” regardless of running the program, or the existence of the Universe and the time flow it contains), and running the program just led to discovering its precise shape.(#)
Now take P2, a program that computes (deterministically) a simulation of, say, a human observer in a universe locally similar(##) to ours, but perhaps slightly different( ###) to remove indexing uncertainty. Applying intuition directly to P2, it feels that the simulation isn’t a real world, and whatever the observer inside feels and thinks (including about “existence”) is kind of “fake”; i.e., it feels like we’re creating it, and it wouldn’t exist if we didn’t run the program.
But there is actually no obvious difference from P1: the exact results of what happens inside P2, including the feelings and thoughts of the observer, are predetermined, and are exclusively the consequence of a series of symbolic manipulations or “equation solving” of the exact same kind as those that “generate” the decimals of π.
So either: 1) we are “creating” the sequence of decimals of π whenever we (first? or every time?) compute it, and if so we would also “create” the simulated world when we run P2, or 2) the sequence of digits in the expansion of π “exists” indifferently of us (and even our universe), and we merely discover (or embody) it when we compute it, and if so the simulated world of P2 also “exists” indifferently of us, and we simply discover (or embody) it when we execute P2.
I think ec429 “sides” with the first intuition, and you tend more towards the second. I just noticed I am confused.
(I kind of give a bit more weight to the first intuition, since P2 has a lot more going on to confuse my intuitions. But still, there’s no obvious reason why intuitions of my brain about abstract things like the existence of a particular sequence of numbers might match anything “real”.)
(#: This intuition is not necessarily universal, it’s just what I think is at the source ec429’s post.)
(##: For example, a completely deterministic program that uses 10^5 bit numbers to simulate all particles in a kilometer-wide radius copy of our world around, say, you at some point while reading this post, with a ridiculously high-quality pseudo-random number generator used to select a single Everett “slice”, and with a simple boundary chosen such that conditions inside the bubble remain livable for a few hours. This (or something very like it, I didn’t think too long about the exponents) is probably implementable with Jupiter-brain-class technology in our universe even with non-augumented-human–written software, not necessarily in “real-time”, and it’s hard to argue that the observer wouldn’t be really a human, at least while the simulation is running.)
(###: E.g., a red cat walks teleports inside the bubble when it didn’t in the “real” world. For extra fun, imagine that the simulated human thinks about what it means to exist while this happens.)
No, I'd say nearer the second - the mathematical expression of the world of P2 "exists" indifferently of us, and has just as much "existence" as we do. Rocks and trees and leptons, and their equivalents in P2-world, however, don't "exist"; only their corresponding 'pieces of math' flowing through the equations can be said to "exist".