On Sun, Jun 24, 2018 at 9:43 PM, Jason Resch <[email protected]> wrote:
>* Leibniz: "Why is there something rather than nothing?"*
By "nothing" Leibniz meant a vacuum, today we know far more about the
vacuum than he did. Nothing, that is to say zero, is far too precise a
number for quantum mechanics, it permits a violation of the law of
conservation of energy and mass but only for a very short time. Empty space
is not empty, it is a sea of virtual particles popping into and out of
existence. This may seem like a theologian talking about how many angels
can dance on the head of a pin but it is not because it can be detected
experimentally. And if you have an infinite amount of time to play around
with even some jaw droppingly unlikely things will happen, maybe even the
Big Bang.
You could argue that all modern science has done is prove the vacuum is not
nothing and although Leibniz was wrong about that the question remains
valid, but I would say expecting science to explain how a nothing that is
so nothing that it doesn't even have the potential of ever becoming
something is unreasonable. Even a omnipotent omniscient God couldn't do
that, it would be like asking Him to make a rock so heavy he can't lift it.
> >
> *Hawking: "What is it that breathes fire into the equations?*
The equations are a description of how the physical world reacts in certain
specific situations written in the language of mathematics and contain no
fire.
>
> *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?"*
That is exactly why I think the field of Quantum Computers has such
enormous potential.
> *>Wheeler: "Why these equations, and not others?"*
>
Like the English language both fiction and nonfiction can be written in the
Mathematical language and both can be grammatically correct, mathematicians
are interested in both but physicists are only interested in the nonfiction
stories,
> >
> *The existence of all possible computations may be one possible avenue for
> this. *
>
That's not the answer that's the problem. How can you pick out the one
correct calculation from the infinite number of incorrect calculations if
you don't have physics to help you?
> >* *
> *It's not truly doing something math is not, if you take the view that
> math is what is ultimately "doing physics".*
>
As you point out, the answer a Turing Machine spite out depends on its
program not what its made of, you can make one with silicon or vacuum tubes
or mechanical gears or even Lego blocks, but you can't make one out of pure
numbers, it you could be Intel wouldn't need silicon, and it does.
>
>> >>
>> 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.
>
Yes, but physical theories do tell **us** what those physical objects will
do under a certain range of conditions, outside of that range we ned to
find a better theory.
> >>
>> 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.*
>
But why did mathematicians pick that definition instead of one of the
infinite number of alternative ones it could have chosen? Because physics
told them that was the most eloquent one to use in writing nonfiction
stories about the world. There is nothing wrong with with fiction, it has
its charms, but that was not the sheep herder 10,000 ago who invented
numbers was thinking about, he just wanted to manage his flock and be able
to determine if one was missing. And physicists have decided to concentrate
on the nonfiction and let mathematicians get on with their literary
pursuits and weave their beautiful fictional tales .
*>*
> *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?*
>
Godel discovered that reality is telling us that if our mathematical tale
contains no plot holes then there is no way to expand the story so that it
includes everything all the characters are doing when they are off stage.
As for determining if the story is fiction or nonfiction that can only be
determined by physical experiment
*>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.*
>
Arithmetic doesn't tell matter what to do, matter tells mathematicians the
best way to construct arithmetic.
> >**
> *I think you understand my point: "software" can never be certain of the
> "hardware". *
>
I understand what you're getting at and agree with it but I would add
although it can't know specifics it can know there must be something hard
enough in the hardware that it can poked andbe changed and a bit of
information can be stored in it. There is nothing hard in the integer "7"
so the is no way to poke it and change it, and without change there can be
no intelligence. Although the integer "7" is eternal it has no memory,and
without memory there can be no 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.*
>
Yes exactly, physics told humans there is only one way to define a Quark
if they want to be consistent with experimental results. Physics is like a
straightjacket that stops us from doing many things and that includes going
down blind alleys. But pure mathematicians are free to do anything, that
means they are in in a infinite landscape with no hints from physics or
from anything else about which direction would be most fruitful to travel.
>* *
> *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*
>
I agree completely, if you want to physically survive in the physically
world you'd better use the integers we have in dealing with physical
problems and not one of the infinite number of different ways p-adic
arithmetic would let you define integers even though they would every bit
as logically consistent as the integers we know and love today.
>>
>> 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? *
>
Well for example the mathematics of String Theory have gotten so complex
that nobody knows how to proceed, we need new mathematical that lets us cut
through the mess and untangle things so it can actually make a prediction
that can be tested. Who knows maybe some p-adic numbers could be useful in
doing that, but even then we'll still use regular old integers when we want
to count sheep or figure out if the bridge will collapse if we try to cross
it.
>**
> *If there were 0 physical universes, then wouldn't 0 have meaning? *
>
Yes, but Quantum Mechanics
says you can't have zero energy and if there is energy something exists,
nevertheless zero remains a useful fiction because things can get mighty
damn small.
>* *
> *Can zero have meaning without the contrast of 1? *
>
If zero has a meaning that exists then one thing exists, and if the
meaning of zero is "nothing exists" then then what zero is saying is untrue.
>
> 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?
>
As far as we know neutrinos are the most numerous thing in the observable
universe, there are about 10^89 of them, the power set of 10^89 neutrons is
a vastly larger number even then that but its still finite. and so is the
power set of the power set and any finite number of iterations after that,
and so it doesn't even scratch the surface of the set of all integers, much
less all the real numbers from to 1, which makes me suspect the real
numbers are like zero, a useful fiction.
John K Clark
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