On Thu, Jun 21, 2018 at 2:49 PM, John Clark <[email protected]> wrote:
> > > On Thu, Jun 21, 2018 at 1:32 PM, Jason Resch <[email protected]> wrote: > > > ** >> *We can use physical analogies to reason about mathematics,* >> > We can't reason about ANYTHING without physics, that's why our physical > brain is so handy. > > "This is not to say the physical laws are discarded and we are dealing with a pure idealism where anything goes. Quite the opposite. We would look at the statistics of all computer programs that replicate your conscious experience (we would find most of them correspond to a system that has Hydrogen atoms, and relativity, and billions of years of evolutionary history, etc.) and due to those statistics, we can recover stable laws." 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? > >* * >> *but doing so cannot prove that physical things are more fundamental than >> mathematical things.* >> > > 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, such as the emulation of the evolution of the Shrodinger equation on our Hubble volume. > > >> *> Accept for one second that a platonic computation could be >> conscious. * >> > I'll be damned if I understand how a unique platonic computation could > even exist much less be conscious. I don't see any way to tell the > difference between the one correct platonic computation from the infinite > number of incorrect ones. > >From the definitions of addition and multiplication. > 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. Without that, you can't even define what a Turing machine or what a computation is. I can imagine a computation without a physical universe. I can't imagine a computation without some form of arithmetical law. > > >> > ** >> *(we can debate this later) Accepting this premise, do you agree that >> the conscious computation cannot determine whether it is running on a >> platonic computer vs. a physical computer? * >> > To answer that question I'd have to have at least some understanding about > how a platonic computer could work, and I have absolutely no idea. > Let's discuss this later. Accepting the premise that such a platonic computer could compute something (I know you don't accept this) does the rest follow? I think we need to settle this question first, otherwise there is no point in going any farther as the consequences won't follow. > 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. > They 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. > >* * >> *If I run software, any software, it can never perform any computation >> that can reveal to it anything about what is ultimately executing it. I >> might run a Nintendo game,* >> > If I'm a intelligent being living in that Nintendo game I could figure out > that my enviroment was unbounded but finite and consisted of 57,344 cells > arranged in a 256 by 224 grid with each cell having a finite number of > states, and from that figure out the minimum size memory the simulating > computer would have to have. > Yes. But the normal definition of a Turing machine assumes a tape of unlimited memory. So while you can determine a certain minimum necessary memory, you can't decide any Turing machine from any other (that has an unlimited tape). > People have done something similar with our own observable universe > and figure that the computer simulating its running on must have between > 10^122 and 10^124 bits of memory. > > The only thing I know about how the hardware of this universe simulating > computer works is that it must have some way of telling the difference > between a correct computation and a incorrect computation and between a > corrupted memory and a uncorrupted memory. Actually that might not be a bad > definition of "physics". > Okay. > > >> *You are willing to accept that relations between quarks and electrons >> can implement and support your consciousness.* >> > > Yes, > > > > ** >> *Quarks and electrons are fundamentally mathematical objects (they can't >> be described in terms of anything simpler than their mathematical >> properties). * >> > > 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? > > >> *>Integers are also mathematical objects (they can't be described in >> terms of anything simpler than their mathematical properties).* >> *Why do you think that the only mathematical objects that can sustain >> computation are quarks and electrons?* >> > > Because Platonic integers can be arranged in any way but quarks and > electrons can not be, when they can not we call that "wrong"; when the > wings of your airplane fall off that is physics telling you that one of > your calculations was wrong. Without physics Platonic integers are never > wrong, 2+2=3, 2+2=4, 2+2=5 its all fine, one relation is as good as another. > This is where I disagree. Integers (let's go by normal definitions of 0, 1, 2, etc.) have properties. We can't arbitrarily say "2+2=5", this is playing with strings, not integers. Here is a question I would like to know your answer on. Would you say that mathematics imposes "meta laws" which must be true across all possible/imaginable universes? For example, here are some examples of mathematical meta-laws, imposing limits on what is physically or experientially possible: - It is physically impossible to arrange 7 stones into a rectangle (but not linear) representation (i.e. being arranged in two dimensions of a Euclidean geometry into a fully populated set of rows and columns with # rows and # columns > 1) - 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 - It is an impossible experience to see 7 stones arranged into a rectangle (as defined above) - It is an impossible experience to observe a valid proof that 7 has more than 2 integer factors > 0 Do you think such meta-laws must be true and respected in every possible physical universe? If not can you think of any such meta-laws that would necessarily be true and enforced in any possible world? Jason -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
