Re: Physics upgrade.
From: Lefty (Ye_at_h.Right)
Date: 10/16/04
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Date: Sat, 16 Oct 2004 00:49:29 GMT
First, your criticism is most excellent. Perhaps there should be a class on
how to rip things apart to get to the bottom of a problem. I think this
would make a great class.
"Will Twentyman" <wtwentyman@read.my.sig> wrote in message
news:416e7bf1_2@newsfeed.slurp.net...
> Lefty wrote:
>
> >>>>>>>>>>>Axiom 1
> >>>>>>>>>>>No two objects in the physical universe can be identical.
> >>>>>>>>>>>
> >>>>>>>>>>
> >>>>>>>>>>|{ x,y }| = 2 ==> x /= y
> >>>>>
> >>>>>If you are using set theoretic notation, I think that the correct set
> >>>>>theoretic verbage might be that "Any set of exactly identical
> >
> > "physical"
> >
> >>>>>objects contains only one member".
> >>>>>
> >>>>
> >>>>x = y ==> |{ x,y }| = 1
> >>>>
> >>>>As both are logically equivalent, you make quibble.
> >>>>You want to make physics math? Then learn to speak math!
> >>>
> >>>I didn't say that, and I think that your notation is incorrect. I wil
> >
> > not
> >
> >>>check it. Set theory must be modified to fit the physical universe with
> >>>exactness.
> >>
> >>Is notation is correct as far as you have been clear.
> >
> >
> >
> > I think we are headed nowhere with this line of reasoning, I will
restate
> > what I meant.
> >
> > Basically, given Axiom 1, no two objects in the physical universe are
> > identical. Set theory deals mainly with collections which qualify as
sets.
> > This is very strict. If you want abstract members to satisfy set theroy,
> > then they do because they are defined as such. No problem. Cubes can be
> > identical, spheres are indistinguishable - in the mind - as
abstractions. In
> > the universe, you cannot have a collection of identical objects with
> > cardinality greater than 1. An object is identical only to itself.
Universe
> > is a very strange place ! This allows a more rigorous approach to
physics.
>
> Here's the first problem, however: you have not asserted the existence
> of anything. I don't have an issue with things being different from
> each other. I have an issue with not being told anything exists.
Perecisely. I think that there is more work to do. Much more. But I am going
forward very slowly, because there are so many ways to confuse abstraction
with reality. Universe is very different from R3 or R4.
I am trying to make any general statement which can be PROVED somehow. Very
difficult to even contemplate that level of simplicity.
> >>>Consider the set of all yellow houses. Do all the math you want on this
> > set,
> >>>I dont care how much you do. You will always have error because a
> > "yellow
> >>>house" in Beverly Hills is NOT equal to a "yellow house" in South
> > Central
> >>>LA.
> >>
> >>It is up to you to *define* what counts as equal. As it stands now, you
> >>are simply saying that "yellow house" is not a valid object description.
> >
> > This is the thing that everything hinges on. Leveraging the difference
> > between abstraction and generalization. In mathematics, you are free to
be
> > as abstract as you wish. The universe is not so forgiving. You may
exploit
> > generalization to it's fullest, but the physical universe is not
abstract.
> >
> > Axiom 1 is an extremely general statement which can be made about real
> > objects. Furthermore, it is mathematically exact, and it operates on
real
> > objects.
> >
> > I think that you might also be able to say that "All real objects
exist", or
> > "All physical objects have location" or something like that, but valid
and
> > precise statements which encompass the totality of the physical objects
are
> > difficult to make.
>
> However, you need to make at least one or two more axioms. While the
> universe is certainly a model of your axioms, so is the empty set.
Yes. And I dont know which is really more fundamental - uniqueness, or
location. My head is filled with all kinds of wierd garbage on this just
thinking about it.
> > I thnk that you have uniqueness, existence, location, and thats about
it. It
> > is very fundamental stuff. These are the fundamental properties of all
> > objects. You simply cannot get more basic or general that this. This is
the
> > very bottom.
>
> You don't have an axiom guaranteeing existence or discussion location.
It is difficult to be completely blind in terms of where it might go.
Thinking of higher structures like functions or even sets seems too complex
at this time. You have to construct a space/time so that it matches the
current model of physics. It must be elegant, and an absolutely perfect fit.
> >> > Your concept of equality is an abstract one, and you impose this
false
> >>
> >>>belief on physical objects. This is a weakness of every model of modern
> >>>physics. It's actually rather surprising that things are'nt falling
> >
> > apart,
> >
> >>>such a bridges and skyscrapers.
> >>
> >>He didn't impose anything. You have just found that you can use vague
> >>language. Notice also that this is probably *not* how a
> >>physicist/engineer would think about these things.
> >
> >
> >
> > When mathematicians use equality in algebra it is a correct usage of
perfect
> > equality on abstract objects.
> >
> > When an accountant has a pile of dollars and a bag of coins, and he says
> > that one is equal to the other, this works well but is not quite
correct.
> > Even if you have $100 in the pile and $100 in quarters in the bag, you
cant
> > really say that a stack of bills is "equal" to a bag of quarters.
>
> They are equal in the sense that they have the same monetary value.
> They are different in the sense that they have different chemical
> structures. It's a question of which sense is important at the moment.
And, they may have other physical imperfections which give them differing
surfaces, etc. But they have one inescapable difference which absolutely
cannot be overcome. Different locations.
> > Axiom 1 says that
> > No two objects in the physical universe are identical.
> >
> > This usage bypasses ambiguities of equality. It is a statement of broad
> > "inequality". It is an absolute generality, encompassing everything
which
> > exists in the universe. It could be restated "Everything which exists is
> > unique in some way". I think that Axiom1 is basically a statement of
> > uniqueness.
> >
> >
> >
> >>>"yellow house" is an _abstraction_ .
> >>>
> >>>This is fact, not philosophy.
> >>
> >>This is irrelevant to the validity of the set theoretic statements
above.
> >
> > I quote the original poster who said that
> > |{ x,y }| = 2 ==> x /= y
> >
> > I know some set theory, but this notation is unclear to me.
>
> What it is saying is if you have a set containing two symbols for number
> and it has two elements, then the symbols must represent different
numbers.
> > I think that he is defining a set with 2 members. I am not sure that
this
> > would be an easy thing to do in the physical universe. You have to have
a
> > set theory which allows fuzziness in the definition of membership.
>
> No. If you have two objects, they form a set.
If you have two abstract objects they form a set. If you have 2 objects in
physical universe, I'm not so sure. Set membership has to be defined
somehow.
> > Example.
> > Given two exact duplicate Susans, in two separate locations in the
physical
> > universe. What is definition of a Susan ? You have Susan at L1 and Susan
at
> > L2. There are NO identical objects, ahd these two "twins" are different
by
> > virtue of L1<>L2. This affects usage of set theory in real universe.
>
> Your symbols might be Susan1 /= Susan2.
>
> > For a mathematician, you can imagine a collection of imaginary
(abstract)
> > Brunettes. They are all identical twins. They can be identical, because
they
> > are abstract. Set theory works, because they are abstract.
>
> You are generalizing how mathematicians think. We recognize these
> subtleties and differences. We can specify a relation "=" to whatever
> scale of precision is necessary for the desired purpose.
And in R3 or any other abstract place, you can place infinitely many
Brunettes in the exact same location and they remain distinct - by
definition. In the universe, these others would be trivial.
> > I dont think it is so easy to achieve such exactness when applying
theory to
> > real objects, but can be done by avoiding abstraction, and leveraging
> > generality. I dont think it's realistic to modify set theory for this
> > purpose. Set theory itself is a sound tool. The application, however, is
> > typically very loose. True application of set theory would be very
strict.
> > Must fall back on generalizations to make exact statements.
>
> Just define how the theory and the model (reality) correspond with care.
I start jabbering nonsense. It's clear in the head, but looks stupid on
paper.
> >>>>>The axiom describes the physical universe exactly in terms of 0 and
1.
> >>>
> >>>The
> >>>
> >>>>>description is absolutely precise, and it is non-abstract.
> >>>>>
> >>>>
> >>>>It does no such thing.
> >>>
> >>>It does this and more.
> >>
> >>Well, you apparently need to add something about the *model* of this
> >>theory. For example, it might be nice to have some axioms about the
> >>existence of objects and their relationship with each other and
> >>space/time. For example: can two different objects coexist at the same
> >>location at the same time?
> >>
> >>
> >>>Because no two objects can be "equal", or identical, you can only count
> >
> > to
> >
> >>>1. This also implies existence of that thing. If something does not
> >
> > exist,
> >
> >>>then you have 0 of that thing. <<<< Please argue against this directly.
> >>
> >>Can you have sets of objects? What does it mean to count objects?
> >>Normally, you are counting the cardinality of a set of objects.
> >
> > You can have a set with one member. Each object in the universe is a
member
> > of the set containing that object. I dont know if this helps, but it is
> > additional information.
>
> Here's the deal: To formalize "How many yellow houses are there?", I
> would construct a set Y = {x | x is a yellow house}, then the answer to
> the question is |Y|. I don't think the yellow houses are equal, yet I
> can still count them.
One way to look at it.
The question becomes, what does "is" mean ? Does "is" mean 2 houses exactly
equal ? Or does "is" mean they can differ in shape, as long as both are
yellow. I find this maddeningly ambiguous. It is no problem in abstract
world. Two abstract houses are exactly identical. Two physical universe
"yellow houses" are very different.
Mathematical toys match up with abstract playground PERFECTLY. I need a math
which matches up with physical universe the same way. This is tricky.
> >>>The universe has been opened. I have given you a rock to stand on. You
> >>>should stop arguing about this and immediately begin building. The
> >>>foundation is solid.
> >>
> >>Solid but inadequate for concluding anything. You have not asserted the
> >>existence of objects within space/time.
> >>
> >>
> >>>I have a question for the world. I want to prove, by means of RIGOROUS
> >>>proof, whether space/time is continuous or not. I must know this. I
have
> >>>given you a place to start. Do not torture me to build this proof
> >
> > myself. I
> >
> >>>dont know if I have the strength or the ability to do it. I do not know
> >
> > if I
> >
> >>>will live long enough to see it. I need help.
> >>
> >>Right now you don't have enough axioms to come close to determining
> >>that. It seems likely that whether it is continuous will end up being
> >>an axiom, or equivalent to an axiom.
> >
> > I'm not sure. Space/time is a wierd place. Not the same as R3 or R4 I
> > suspect.
>
> It is, but at the moment you need some axioms to begin describing it.
>
> > I do not completely understand all the the ramifications which Axiom 1
> > implies for the physical universe.
>
> Not much. For example: it does not imply the existence of objects.
Also, you are thinking like a mathematician. Not a physicist. This axiom is
basically a real universe axiom. Different critter.
If I have this axiom, I can take it to the lab and use it on real universe
objects. Cant do that with an abstraction.
In my construction, 1 and 0 are not just abstract numbers. They are
something new. They match universe exactly. Their meaning is enhanced to
imply existence somehow. Counting higher then 2 introduces ambiguity and
error in the universe.
You guys train to swim around in abstract imaginary world where you can do
anything you want. Physical uiverse has wierd rules. Cant just define things
into existence.
Brutal, trying to constantly separate the two worlds. So many things seem
intuitive and safe to deploy. But I dont even trust counting higher than 1.
> > I am not talking about the effects of an axiom upon abstractions. I am
> > talking about the implications for real objects. Very different.
>
> Here's the thing: an axiom doesn't affect the universe. It can
> potentially affect our understanding of the universe.
> > Consider this - "No two reals on the interval [0,1] are identical."
<<<
> > [abstract]
> >
> > It is true that there are sets which have properties which make them
> > groupable in ways, for example the set of all transcendentals on [0,1],
the
> > set of all rationals on [0,1], the set of all irrationals on [0,1], etc.
> > <<<<< [abstract]
> >
> > But in a sense, "No two distinct reals on the interval [0,1] are
identical."
> > is a very true statement. It can be made precise with algebra by saying
"For
> > all x1, x2 in [0,1] where x1 <> x2, we have x1 <> x2" . A tautology.
<<<<<
> > [abstract]
> >
> > Is Axiom1 a tautologie ? I am not sure at this time. <<<<<<
[non-abstract]
>
> It is closer to a description of what it means to consider objects equal.
>
> > I am having a hard time considering sets from the universe where nothing
can
> > be identical. <<< [non-abstract]
> >
> > It carries over somehow to the physical universe. You can prove things
> > rigorously about [0,1], and might be able to create rigorous proofs
> > regarding space/time. Someone needs to prove something about
space/time -
> > using Axiom 1. I dont care who. I'm going to grab my copy of Adv. Calc.
by
> > Buck and find a proof which can be adapted to space/time. I'm tired of
> > talking. It needs to be performed.
>
> The axioms exist seperate from what you are hoping will be a model of
> them. Reality is the model, but your axioms may or may not have
> anything to do with it.
Thats the problem. Current physics is one big collection of models.
Approximations. Best guesses. Reasoned algebraic statements. We use calculus
every day, but dont even know if space is continuous. Physics is out on a
limb by doing this. Must fill the gaps somehow.
In calculus, the fabric of R3 is just numbers. I have thrown out the
numbers, and replaced that fabric with space/time continuum. Now I need to
understand the rules. I dont want to do calculus on R3. I want to do physics
in space/time.
I have to take a break. I'm losing my mind. When I think about using
rigorous analytic proofs on space/time fabric, I get very motivated. One
must know the fundamentals about the space to do this, and every single step
must be absolutely unambiguous.
I'm going into so much new ground, It's hard to keep my head from
exploding.
I'm got things to do in the foundry -
Talk soon,
Will K
- Next message: David C. Ullrich: "Re: Natural Densities are Probabilities"
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- In reply to: Will Twentyman: "Re: Physics upgrade."
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