On 6/24/2018 6:43 PM, Jason Resch wrote:
On Fri, Jun 22, 2018 at 3:30 PM, John Clark <[email protected]
<mailto:[email protected]>> wrote:
On Thu, Jun 21, 2018 at 5:09 PM, Jason Resch <[email protected]
<mailto:[email protected]>>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?*"
"The reason that there is Something rather than Nothing is that
Nothing is unstable."
-- Frank Wilczek, Nobel Laureate, physics 2004
1. 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?"
"What is there? Everything! So what isn't there? Nothing!"
--- Norm Levitt, after Quine
1. 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?*"
"Because the world is made of physics, not logic."
- Brent Meeker
1. Wheeler: "*Why these equations, and not others?*"
"These are the ones we invented to describe what we've seen."
- Vic Stenger
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.
How would that be any better or worse than "all possible set theory" or
"all possible phsyics" or "all possible novels"?
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.
All your questions are number 1. However, I would point out that
Feynman's question implies that computationalism must be false.
>>
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".
Sure, and it's not truly doing something that music is not, if you take
the view that music 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.
That's not what Bruno says. He takes Peano's axioms to be just one
possible axiomatization of the integers and he assumes the integers
exist (somehow) independent of whatever definition may be given, i.e
they are "a first class object".
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?
That's not reality, it's logical inference...which never reaches
anything not implicit in its premises.
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.
So is being infinite a known attribute of reality? Space appears to be
infinite too.
To me, this is strong evidence that math is something objective, which
humans explore, rather than define or invent.
My mathematician friend, Norm Levitt used to say, "That's what
mathematicians think Monday thru Friday. On the weekend they philosophize."
/
>
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.
A Turing machine is a mathematical abstraction. It doesn't "do"
anything. If it "exists", it "exists" in a timeless Platonia.
>>
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.
I'm glad they don't teach that to neurosurgeons.
>>
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.
?? They can't be both mathematical objects defined within a theory and
independently existing? "Independently" can only refer to independence
from theory. My chair exists independent of theory because I can define
it ostensively.
If the same is true of integers (that they are objective,
independently existing,
Independent of what? Above you thought they were dependent on the
axioms set.
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.
No it doesn't. Counting is theory laden (as is all application of
mathematics). If I plan a party for the high school swim team and the
high school tennis team I need to count up the members. I count 8 on
the swim team and I count 9 on the tennis team. So the party must be
for 17. I'm sure you can see why this doesn't work. It's because one
needs an interpretation of the theory to say what is a unit.
>
/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.
First, that's confusing. A Turing machine is an abstract bit of
mathematics. It isn't "described" as a real machine might be; it is
mathematics. Second, it's like saying English is sufficient to explain
all possible experiences. The trouble of course is that good
explanation explains the difference between the actual and the possible.
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's that "and so on" that is problematic.
Brent
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