On Fri, Jun 22, 2018 at 3:30 PM, John Clark <johnkcl...@gmail.com> wrote:
> On Thu, Jun 21, 2018 at 5:09 PM, Jason Resch <jasonre...@gmail.com> wrote: > > >* * >> *The only thing I am asking is:* >> *1) Physics -> Brains, Cars, Atoms, Etc.* >> *2) ??? -> Physics -> Brains, Cars, Atoms, Etc.* >> *Do we have enough information to decide between the above two theories? >> Have we really ruled out anything sitting below physics?* >> > > If I define physics as the thing that can tell the difference between a > correct computation and a incorrect computation and between a corrupted > memory and a uncorrupted memory, and as long as we're at this philosophic > meta level that's not a b ad definition, then I don't think anything > is below physics. > Physical theories are based on induction from observations and experiences. That process won't give us answers to these famous questions, posed by physicists: 1. Leibniz: "*Why is there something rather than nothing?*" 2. Hawking: "*What is it that breathes fire into the equations* and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?" 3. Feynman: "It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? *Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?* " 4. Wheeler: "*Why these equations, and not others?*" If we're to answer these questions, we may need some kind of *metaphysical* theory. Preferably one that is simple, and can explain/predict our observations. The existence of all possible computations may be one possible avenue for this. So far, it is not ruled out, and might even be considered to be partially confirmed. It has the power to answer questions 2, 3 and 4. And for anyone who accepts arithmetical realism/no-cause needed for arithmetical truth, then it can answer 1 as well. > > >> >> >>> Then why is brain damage a big deal? Why do I need my brain to think? >>> >> >> >* * >> *The base computations that implement your brain may be sub-routines of a >> larger computation,* >> > > If true then that is an example of something physics can do but > mathematics can not. And I have to say that is a mighty damn important > sub-routine! > It's not truly doing something math is not, if you take the view that math is what is ultimately "doing physics". > >> >>> Without physics 2+2=3 would work just as well as 2+2=4 and insisting the >>> answer is 4 would just be an arbitrary convention of no more profundity >>> than the rules that tell us when to say "who" and when to say "whom". >>> >>> > >> *For any computation to make sense, you need to be working under some >> definitions of integers and relations between them. * >> > > Definitions are made for our convenience, they do not create physical > objects. > Physical theories are also made for our convenience and they do not tell physical objects what to do. Instead we study physical objects, and try to reason about what laws make sense and describe the phenomenon we observe. It is no different with mathematical theories (a.k.a. axioms and theorems). Mathematicians study mathematical objects, and reason about what laws make sense to describe the phenomenon we observe. When they find sufficient justification, they can amend or extend the fundamental theories (axioms), or even throw them out altogether. > And there are an infinite number of ways integers and the relations > between them could have been defined, > If they were defined differently, they wouldn't be the integers, but some other thing. > so why did mathematicians pick the specific definition that they did? > Because that's the only one that conforms with the physical world, and > thats why mathematics is the best language to describe physics. > Here, we know the definitions are not primary, for we know (since Godel), that the integers are more complex than any finite set of axioms can describe. Is reality not "kicking back", when: It tells us there are things that are true about the integers which are not part of our starting definitions? It tells us no matter how much we might build and develop our theories (axioms) about the integers over time, we know that we will never finish the job. To me, this is strong evidence that math is something objective, which humans explore, rather than define or invent. > >> * > Without that, you can't even define what a Turing machine or what a >> computation is.* >> > > I don't need to describe either one because I've got something much much > better than definitions, examples. > > *>I can imagine a computation without a physical universe. * >> > > I can't. > > > >* * >> *I can't imagine a computation without some form of arithmetical law.* >> > > I can. A Turing Machine will just keep on doing what its doing > regardless of the English words or mathematical equations you use to > describe its operation. > If arithmetical law breaks down, and 0 starts to equal 1, then a Turing machine will do something very different than what would otherwise be predicted. > >> >>> As far as simulation is concerned in some circumstances we could figure >>> out that we live in a virtual reality, assuming the computer that is >>> simulating us does not have finite capacity we might devise experiments >>> that stretch it to its limits and we'd start to see glitches. Or the >>> beings doing the simulating could simply tell us, as they have complete >>> control over everything in our world so they would certainly be able >>> to convince us they’re telling the truth. >>> >>> >> > >> T >> *hey could convince us something strange is going on, but they couldn't >> convince us they weren't lying about whatever they might be telling us >> about the architecture that is running the simulation. This follows >> directly from the Church-Turing thesis. The Church-Turing thesis says any >> program or Turing Machine can be executed/emulated by any computer. >> Therefore, no program or machine can determine whether it is being computed >> by or emulated by any particular Turing machine vs. any other that might be >> emulating it.* >> > > OK, they could prove they're simulating us but they couldn't prove the > logical hardware architecture of their machine worked the way they said it > did, however in some circumstances they could provide some pretty > compelling evidence that they were telling the truth. For example suppose > they found out how to solve all non-deterministic polynomial time problems > in polynomial time and that's how they were able to make a computer > powerful enough to simulate our universe. And they said they themselves > were being simulated and their simulators told them how to do this and now > they are passing the secret on to us. We try it and pretty soon we have > made our own simulated universe with intelligent, and presumably conscious, > beings in it. After that I’d tend to believe what they said. > That would still be just an algorithm. But in any case, I think you understand my point: "software" can never be certain of the "hardware". Which means we must be humble on the question of where/how our consciousness is being computed. > > >> >>> It was discovered more than 30 years ago that if Quarks didn't exist >>> inside protons then high speed electrons would scatter off protons >>> differently than the way they are observed to scatter. If you assume Quarks >>> don't exist then there are consequences, those high speed electrons will >>> behave in ways that surprise you. In other words physics told you that your >>> assumption was incorrect. >>> >> >> *>Okay. So you do accept relations between mathematical objects can >> support your consciousness?* >> > > A mathematical object is just something that has been defined in the > language of mathematics, > But humans weren't free to define Quarks any way they choose. Quarks are objective, independently existing, mathematical objects. If the same is true of integers (that they are objective, independently existing, mathematical objects), then it might be that we can explain/predict/derive the existence of quarks or other properties of our physical universe from those more basic and more fundamental laws. > J K Rowling defined Hogwarts Castle in the language of English but that > doesn't mean either of them must exist. There are an infinite number of > ways mathematicians could have defined a quark but they picked the one that > physics told them to, the one that scattered electrons the way we see in > experiments. > > >> > >> *Integers (let's go by normal definitions of 0, 1, 2, etc.) have >> properties.* >> > People invented numbers thousands of years ago to count things, if the > laws of physics were different and physical objects spontaneously > duplicated themselves and spontaneously disappeared our "normal definition" > of integers would be very different from what we have now. > Any civilization that must make rational decisions to increase its chance of survival is confronted with the logic of true and false. ("e.g. 'If we don't store food for winter we will starve.') If that civilization reasons logically about true and false, they will develop notions of "and" "or" "not", etc. This leads trivially to the notion of counting "not" operators. An even number of nots is equivalent to 0 nots, and any odd number of nots is equivalent to 1 not. This notion of counting leads directly to the same integers we know and love, regardless of the physics in which that civilization arose. > > >> >> > >> *We can't arbitrarily say "2+2=5", this is playing with strings, not >> integers.* >> > > We can't be arbitrary if we don't want a conflict between mathematics and > physics, but if you take out physics then play away, you can let 2+2 > be anything you want and there are no consequences. > > If you have to assert that "0 = 1" to hold on to your ideas, I would question the legitimacy of those ideas. > > > >> * Would you say that mathematics imposes "meta laws" which must be true >> across all possible/imaginable universes?* >> > > Yes I think so, but the meta laws would be physical not mathematical. > So perhaps the better question to you is: "Might what we consider now as physical laws ultimately be (or be derived from) mathematical laws"? > If we're very lucky we might be able to describe those meta laws > mathematically (although almost certainly not with the mathematics we have > now) > Why not? For example, If conscious experience is ultimately computational in nature, then Turing machines are sufficient to explain all possible experiences. We can already describe Turing machines with our existing mathematics. > but I don't think there is any chance of a pure mathematician ever finding > them, we're going to need physical experiments to give us some hints and I > just hope that doesn't require a particle accelerator the size of the > galaxy. > It will take more work, no doubt. > > > >> >** >> * It is physically impossible to arrange 7 stones into a rectangle* >> > > If there were not 7 stones or 7 of anything in the entire physical > universe the entire concept of "7" would be meaningless. > > If there were 0 physical universes, then wouldn't 0 have meaning? Can zero have meaning without the contrast of 1? Once you have "0 and 1" now you have two unique concepts, so you get 2. Now you have 3 things, (and so on). > > >> > >> * It is physically impossible to move your pencil over a piece of paper >> such that it writes a valid proof that 7 has more than 2 integer factors > >> 0* >> > > Yes, it is a physical law that the physical act described above would be > physically impossible because there are at least 7 physical things in the > physical universe so “7” means something. > > If you have 7 things, then you have 7! = 5040 ways of choosing subsets of those things. So does 5040 have meaning in a universe with 7 physical things? If 5040 has meaning then does 5040! have meaning? > >* * >> *It is an impossible experience to see 7 stones arranged into a rectangle >> (as defined above)* >> > > I'm less sure about that, I've never taken it but with enough LSD I might > be able to experience it. > > > Good point. Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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