The Universal Geometric Set

[Russell E. Rierson]

A simple[trivial?] postulate that gives a "Universal Set" and resolves the "set of all sets" paradox[in the geometric sense]:

A circle of radius R, is isomorphic to a circle of radius 1/R.

[1/R]<--->[R]

For any arbitrarily large circle of radius R, there is an exact correspondence with a circle of radius 1/R, such, that the product R*[1/R] = 1

[matt grime]

and this resolves russell's paradox? so where is the set of all sets that do not contain themselves in this construction? and in what sense are you using isomorphism? in what category are your morphisms?

[Russell E. Rierson]

and this resolves russell's paradox? so where is the set of all sets that do not contain themselves in this construction? and in what sense are you using isomorphism? in what category are your morphisms?

I don't think it resolves "russell's" paradox without some more work.

All circles are isomorphic to each other because they have the same shape. Likewise, all squares are isomorphic to each other. Now if sets can be transformed into geometric shapes, more specifically, circles, or "geometric shape-equivalents", the largest possible set with a geometric radius R, has a corresponding twin with radius 1/R.

[matt grime]

well, when you've figured out what it is you're trying to prove let us know.

[Russell E. Rierson]

well, when you've figured out what it is you're trying to prove let us know.

Here is a definition of the "Euler characteristic":

http://en.wikipedia.org/wiki/Euler_characteristic


Graph Theory:

http://en.wikipedia.org/wiki/Graph_theory


If a polyhedron has V vertices, F faces, E edges, and is topologically equivalent to the sphere, the equation is:

V + F - E = 2

2 is the "Euler characteristic" of the polyhedron.

Sets that are members of themselves correspond to a geometric form. Sets that are not members of themselves correspond to a different? geometric form.

Interesting.

[Gokul43201]

I don't think it resolves "russell's" paradox without some more work.

All circles are isomorphic to each other because they have the same shape. Likewise, all squares are isomorphic to each other.

I thought circles were isomorphic with squares - they don't have to have the same shape.

Now if sets can be transformed into geometric shapes,

And the elements of the set transform into...?

more specifically, circles, or "geometric shape-equivalents", the largest possible set with a geometric radius R, has a corresponding twin with radius 1/R.

And I thought the paradox involved the cardinality of the Power Set being bigger than the cardinality of the Set (of all sets). I may be wrong...but what does this have to do with isomorphisms ?

[Russell E. Rierson]

I thought circles were isomorphic with squares - they don't have to have the same shape.

Circles are homeomorphic to squares, not isomorphic...?

http://www.rdrop.com/~half/Creations/Puzzles/TriangleShapes/

And the elements of the set transform into...?

Elements of a set can be characterized as sets. All sets can be associated to geometric forms...?


And I thought the paradox involved the cardinality of the Power Set being bigger than the cardinality of the Set (of all sets). I may be wrong...but what does this have to do with isomorphisms ?

Any circle of arbitrarily large radius R, is isomorphic to a circle of radius 1/R.

The magnitude of R corresponds to the cardinality of the powerset.

Is the set of all geometric forms, a geometric form?

Can Venn diagrams correspond to light cone cross sections?

[Gokul43201]

Can I answer your questions with more questions ?

PS : Yes that should have been homeomorphic. But I'm still not getting the point. What is the resolution of the paradox ?

[Russell E. Rierson]

Can I answer your questions with more questions ?

PS : Yes that should have been homeomorphic. But I'm still not getting the point. What is the resolution of the paradox ?


Set intersection is a type of multiplication of sets.

The intersection of two circles of radius R and 1/R, respectively:

R*[1/R] = 1

R[<-[->[<-[1/R]->]<-]->]


The "Universal Set"

For the continual expansion of power set circle R, there corresponds circle[infinitesimal?] 1/R.

[Hurkyl]

All sets can be associated to geometric forms...?

Not as far as I know.

[Gokul43201]

Set intersection is a type of multiplication of sets.



No, it's not ! It's just a process of picking the common elements.

You can have a set A containing millions of even numbers, and a set B containing thousands of odd numbers and you "multiply" them to get a null set ?

[Russell E. Rierson]

No, it's not ! It's just a process of picking the common elements.

You can have a set A containing millions of even numbers, and a set B containing thousands of odd numbers and you "multiply" them to get a null set ?

Set intersection obeys the distributive law, which is a multiplicative law:

http://www.jgsee.kmutt.ac.th/exell/Logic/Logic31.htm#13

Two sets without common elements are disjoint.

[Russell E. Rierson]

Not as far as I know.


Venn diagrams are circles...

Light cone cross sections are circles, ellipses, etc.

[Hurkyl]

Set intersection obeys the distributive law, which is a multiplicative law:

That doesn't mean set intersection has anything to do with arithmetic multiplication.


Venn diagrams are circles...

Light cone cross sections are circles, ellipses, etc.


And what does this have to do with associating all sets to geometric forms?

[Russell E. Rierson]

That doesn't mean set intersection has anything to do with arithmetic multiplication.


Since the circle of radius R is isomorphic to the circle of radius 1/R, the cardinality of Circle with radius R is on the same line[radius] as the infinitesimal 1/R

1/R 0--------0 R

Since they are on the same line, they intersect. But perhaps a new type of set multiplicative identity needs to be derived?






And what does this have to do with associating all sets to geometric forms?

When two light cones intersect, they become "phase entangled". The intersection is much like a "set" intersection.


In ordinary quantum mechanics, configuration space is space itself
{i.e.,to describe the configuration of a particle, location in space
is specified}. In general relativity, there is a more general kind of
configuration space: taken to be the space of 3-metrics {"superspace",
not to be confused with supersymmetric space} in the geometrodynamics formulation. The wavefunctions[Venn diagrams-light cones] will be
functions over the abstract spaces, not space itself-- the
wavefunction defines "space itself".


The resultant metric spaces are thus defined as being diffeomorphism
invariant. Intersecting cotangent bundles{manifolds} are the set of
all possible configurations of a system, i.e. they describe the phase
space of the system. When the "wave-functions/forms"
intersect/entangle, and are "in phase", they are at "resonance",
giving what is called the "wave-function collapse" of the Schrodinger
equation. the action principle is a necessary consequence of the
resonance principle.

[Hurkyl]

Although you're using the words, you don't seem to be doing mathematics, so I'll move this thread over here.

[matt grime]

Venn diagrams are circles...

no they aren't. what idiot told you that?

[Russell E. Rierson]

no they aren't. what idiot told you that?

You appear to be acting like an ignorant troll.

http://mathworld.wolfram.com/VennDiagram.html


In general, an order-n Venn diagram is a collection of n simple closed curves in the plane such that

1. The curves partition the plane into 2^n connected regions, and

2. Each subset S of {1,2,3,...,n} corresponds to a unique region formed by the intersection of the interiors of the curves in S (Ruskey).



Actually, spacetime does not really need to be "sliced up" in that it can proceed in discrete steps, yet, still be continuous.

[density 1]--->[density 2]--->[density 3]---> ... --->[density n]


[<-[->[<-[->[U]<-]->]<-]->]
Intersecting wavefronts = increasing density of spacelike slices

As the wavefronts[circles/Venn diagrams] intersect, it becomes a mathematical computation:

2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...2^n


If the universe includes everything that is real and excludes that which is not real, then the universe is the "Universal" set.

You cannot refute the above logic...

[matt grime]

Since when is a simple closed curve necessarily a circle? As you aren't the ignorant one you must surely know that in order to demonstrate all the possible intersections of 4 sets in a venn diagram you cannot use circles. Moreover, surely you, still not being the ignorant one, must also recognise that a venn diagram is not an element of itself, and thus to take the definition you give, and then deduce that a venn diagram is a circle is most definitely not a logical conclusion?


They, circles and closed curves in the plane, certainly aren't even isomorphic, using your particular definition of isomorphic which appears to mean related be some affine transformation when embedded in the plane.

But Im the ignorant troll, so what do I know about affine transformations? Proved Fermat's last theorem yet?

[Russell E. Rierson]

Since when is a simple closed curve necessarily a circle?

Circles are simple closed curves.


http://www.combinatorics.org/Surveys/ds5/VennGraphEJC.html

[matt grime]

Gee, are circles really closed simple curves? you'd have thought they'd have told me that at university. especially after i had to prove the jordan curve theorem....


a closed simple curve is not necessarily a circle a square being a simple closed curve that isn't a circle, an ellipse also being one, which is what you claimed, and what i pointed out was incorrect, which led you to call me ignorant... hmm, i always take preverse pleasure in being insulted by someone who can't understand a implies b is not equivalent to b implies a.

moreover your statement that a venn diagram is a circle is still incorrect, and now we've seen even more things you don't understand.

[Russell E. Rierson]

a closed simple curve is not necessarily a circle


You mean to say, not all simple closed curves are circles.

Wake up.




moreover your statement that a venn diagram is a circle is still incorrect, and now we've seen even more things you don't understand.

:zzz: :zzz: :zzz:

[Tom Mattson]

Matt: You mean to say, not all simple closed curves are circles.

Russell: You mean to say, not all simple closed curves are circles.


Not only did he mean to say it, he did say it. Wake up, yourself, Russell.

He's right, Venn diagrams aren't circles. The definition of a Venn diagram that you quoted doesn't imply that they are, either. The definition of a Venn diagram refers only to the topology of the curves. The definition of a circle, on the other hand, is the locus of all points (x,y) that are equidistant from a fixed point (h,k). They don't mean the same thing.

Why can't you just accept that bit of correction?

[Russell E. Rierson]

Not only did he mean to say it, he did say it. Wake up, yourself, Russell.

He's right, Venn diagrams aren't circles.

Why can't you just accept that bit of correction?


Here is what matt ...said:


a closed simple curve is not necessarily a circle



Yes, it is almost equivalent to: "not all simple closed curves are circles"



The definition of a Venn diagram refers only to the topology of the curves


The Venn diagrams have the property of logical inclusion/exclusion.

In nature, a sphere is the most energy efficient configuration. A 2D slice of that sphere is is a circle.

Yes, I accept correction. But what is the point of arguing and pedantic "nit-picking" over definitions?

[Russell E. Rierson]

http://www.math.ohio-state.edu/~fiedorow/math655/Jordan.html



Jordan Curve Theorem: Any continuous simple closed curve in the plane, separates the plane into two disjoint regions, the inside and the outside.



Interesting...


Jordan-Schönflies Curve Theorem For any simple closed curve in the plane, there is a homeomorphism of the plane which takes that curve into the standard circle.



If the physical universe includes all that exists and excludes that which does not exist, then by definition, the universe is self containing.

A dynamic process.

[Tom Mattson]

Here is what matt ...said:


a closed simple curve is not necessarily a circle




I know what Matt said.


Yes, it is almost equivalent to: "not all simple closed curves are circles"


There's no "almost". The two statements are equivalent.


The Venn diagrams have the property of logical inclusion/exclusion.


No, Venn diagrams have certain connectivity properties, as your Wikipedia definition states. It is the properties of a specific set, together with the set operations, that have logical inclusion/exclusion properties. Those are what determine how the Venn diagram are populated with elements.


In nature, a sphere is the most energy efficient configuration. A 2D slice of that sphere is is a circle.


So? Physics has no bearing on set theory, Venn diagrams, or circles.


Yes, I accept correction. But what is the point of arguing and pedantic "nit-picking" over definitions?

Because in mathematics, definitions are everything.

edit: fixed a quote bracket

[matt grime]

You are subjectively claiming I am nitpicking; perhaps there is another interpretation? Seeing as you managed to misunderstand almost everything that has been written, including failure to understand the important mathematical usage of the word 'necessarily', i'm not going to overly worry about your opinion about what constitutes a 'nit'. Add in to that the fact that most of your own posts are off topic in your own thread...

[Russell E. Rierson]

I know what Matt said.



There's no "almost". The two statements are equivalent.


I disagree.


[1.] "A simple closed curve is not necessarily a circle"


[2.] "Not all simple closed curves are circles"


[1.] and [2.] are different. Not exactly equivalent.

[2.] better fits the context of THIS thread.





No, Venn diagrams have certain connectivity properties, as your Wikipedia definition states. It is the properties of a specific set, together with the set operations, that have logical inclusion/exclusion properties. Those are what determine how the Venn diagram are populated with elements.


A member of the set is included in the "simple closed curve".

That which is not a member of the set is excluded[outside] of the simple closed curve, i.e. a curve that is not necessarily a circle but it does have the property of closure. ...I hope you understand.






So? Physics has no bearing on set theory, Venn diagrams, or circles.


I disagree.

Didn't Ed Witten recieve the Fields medal of mathematics for work he did in mathematical physics?


Physics would not exist without mathematics. Geometry can be expressed in terms of algebra. Einstein was very close to a "unified field theory" explained in terms of geometry.

Here is the relevant quote:

http://physicsforums.com/showthread.php?t=23034&page=1&highlight=einstein+quantum+gravity



[...]

Since you raised the topic with the subject header, it's both
instructive and revealing to see what Einstein, himself, had to
say on the subject of quantum gravity at the end of his life:

"One can give good reasons why reality cannot at all be represented
by a continuous field. From the quantum phenomena it appears to
follow with certainty that a finite system of finite energy can be
completely described by a finite set of numbers (quantum numbers).
This does not seem to be in accordance with a continuum theory,
and must lead to an attempt to find a purely algebraic theory for
the description of reality. But [sic] nobody knows how to find
the basis of such a theory."






Because in mathematics, definitions are everything.



You refuse to let the horse out of the starting gate.

[Russell E. Rierson]

You are subjectively claiming I am nitpicking; perhaps there is another interpretation? Seeing as you managed to misunderstand almost everything that has been written, including failure to understand the important mathematical usage of the word 'necessarily', i'm not going to overly worry about your opinion about what constitutes a 'nit'. Add in to that the fact that most of your own posts are off topic in your own thread...


So you promise to go harrass someone else?

Thanks.

[Tom Mattson]

I disagree.


[1.] "A simple closed curve is not necessarily a circle"


[2.] "Not all simple closed curves are circles"


[1.] and [2.] are different. Not exactly equivalent.

[2.] better fits the context of THIS thread.


The two statements are logically equivalent. They needn't have the same wording to be so.


A member of the set is included in the "simple closed curve".

That which is not a member of the set is excluded[outside] of the simple closed curve, i.e. a curve that is not necessarily a circle but it does have the property of closure. ...I hope you understand.


I do understand, and I stick with what I said before: It's not the Venn diagram that has the property of inclusion or exclusion, it's the description of the set, together with binary operators. The Venn diagram by itself can't exclude or include any element from anything.


I disagree.

Didn't Ed Witten recieve the Fields medal of mathematics for work he did in mathematical physics?


What's that supposed to prove?


Physics would not exist without mathematics. Geometry can be expressed in terms of algebra. Einstein was very close to a "unified field theory" explained in terms of geometry.


That's not true at all. Experimental physics is not mathematical, but it's still physics. Of course, doing physics would be very difficult without math, but it certainly could exist without it.


You refuse to let the horse out of the starting gate.

Maybe it's time for you to consider that you really don't understand mathematics all that well. The objects of mathematics, and the rules of inference, are all based on definitions. Get those wrong, and you've got math wrong.

[Russell E. Rierson]

What's that supposed to prove?



http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Witten.html


Basically Witten is a mathematical physicist and he has a wealth of important publications which are properly in physics. However, as Atiyah writes in [3]:-

Although he is definitely a physicist (as his list of publications clearly shows) his command of mathematics is rivalled by few mathematicians, and his ability to interpret physical ideas in mathematical form is quite unique. Time and again he has surprised the mathematical community by his brilliant application of physical insight leading to new and deep mathematical theorems.








Maybe it's time for you to consider that you really don't understand mathematics all that well. The objects of mathematics, and the rules of inference, are all based on definitions. Get those wrong, and you've got math wrong.

Yes, there is much to learn about mathematics.

[matt grime]

I promise to harass you whilst you are spouting inaccurate garbage, Russell, don't worry. Why on earth you chose to cite Ed Witten is a mystery, but then you seem to be beyond the pale of reasonable logical thought and into the realms of the crackpot, so frankly who cares?

[Tom Mattson]

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Witten.html


Again, what is that supposed to prove?

[Russell E. Rierson]

Again, what is that supposed to prove?

You wrote this:


Physics has no bearing on set theory, Venn diagrams, or circles.


Sets "contain" elements, members, etc. Venn diagrams can be represented as conic sections.


A______B

____P____

C______D

A, B, C, and P are "co-moving" i.e. they are at rest with respect to each other. The radius[hypotenuse] from P to the other points{A, B, C, D} is the same length. An expanding circle of light[from point P] reaches A, B, C, and D, "simultaneously". The invariance of "c".





Experimental physics is not mathematical, but it's still physics. Of course, doing physics would be very difficult without math, but it certainly could exist without it.



:zzz: :zzz: :zzz:


There is no experiment unless "numbers" can be attached to the quantity being observed.

Your statement that "experimental physics is not mathematical" is total hog-wash.

Any measurement uses numbers.

Light cones are cutting edge stuff :

http://www.mpi-hd.mpg.de/ilcac/98SPeter_prop/node4.html


It has been known for some time that light-cone field theory is uniquely suited for to address problems in string theory. In addition recently new developments in formal field theory associated with string theory, matrix models and M-theory have appeared which also seem particularly well suited to the light-cone approach

[Russell E. Rierson]

I promise to harass you whilst you are spouting inaccurate garbage, Russell, don't worry. Why on earth you chose to cite Ed Witten is a mystery, but then you seem to be beyond the pale of reasonable logical thought and into the realms of the crackpot, so frankly who cares?


Yes, I suppose it is psychologically healthfull [for you at least] to get in touch withn your inner troll

[Tom Mattson]

You wrote this:


Physics has no bearing on set theory, Venn diagrams, or circles.


Yes, I know what I wrote.


Sets "contain" elements, members, etc. Venn diagrams can be represented as conic sections.


LOL, thanks for the lesson. :uhh:



A______B

____P____

C______D

A, B, C, and P are "co-moving" i.e. they are at rest with respect to each other. The radius[hypotenuse] from P to the other points{A, B, C, D} is the same length. An expanding circle of light[from point P] reaches A, B, C, and D, "simultaneously". The invariance of "c".


This has nothing whatsoever to do with the question I asked. In fact. your entire post looks as though it were written by a random word generator.


There is no experiment unless "numbers" can be attached to the quantity being observed.


False. You can do an experiment without attaching any numbers to the results, and it would still be called "physics".


Your statement that "experimental physics is not mathematical" is total hog-wash.


That's not what an experimental physicist would say. :uhh:


Any measurement uses numbers.


No kidding. That doesn't mean that physics wouldn't exist without mathematics.


Light cones are cutting edge stuff :

http://www.mpi-hd.mpg.de/ilcac/98SPeter_prop/node4.html


???

And what does this have to do with anything being discussed here?

[Russell E. Rierson]

???

False. You can do an experiment without attaching any numbers to the results, and it would still be called "physics".





An experiment is something that can be repeated over and over again. The repetition leads to "equations".

I flip a coin for a large number of repetitions, I notice[observe] certain regularities.


No kidding. That doesn't mean that physics wouldn't exist without mathematics.


Yes it does. Numbers are part of "mathematics".


And what does this have to do with anything being discussed here?


You also appear to act like an ignorant troll.

[Tom Mattson]

An experiment is something that can be repeated over and over again. The repitition leads to "equations".

I flip a coin for a large number of repetitions, I notice[observe] certain regularities.


Observation is not the same as doing mathematics.


Yes it does. Numbers are part of "mathematics".


Again, simply attaching numbers to measurements is not the same thing as doing mathematics.


You also appear to act like an ignorant troll.

Guess what? So do you. :uhh:

Seriously, so what if I appear that way to you? You said the same thing to Matt Grime. He is a PhD student in mathematics, and I am a PhD student in physics. Given that you seem to be struggling to understand both of those two disciplines, it hardly seems unsettling that you should say that.

[Russell E. Rierson]

Seriously, so what if I appear that way to you? You said the same thing to Matt Grime. He is a PhD student in mathematics, and I am a PhD student in physics. Given that you seem to be struggling to understand both of those two disciplines, it hardly seems unsettling that you should say that.


edited after second thoughts:

Thank you for your perspective Tom Mattson

[Russell E. Rierson]

False. You can do an experiment without attaching any numbers to the results, and it would still be called "physics".


A measurement is "numerical": e.g. distance, length, time, force, counting repititions, counting quantities, weight, mass, colour-wavelength, symmetric/asymmetric/anti-symmetric patterns, volume, area, etc.


Distinctions or differentiating between quantities is inherently LOGICAL/MATHEMATICAL.

My[Phd student] interlocutors only response has been "that aint true".

What can I say...

College aint what it used to be?

[matt grime]

A measurement is "numerical": e.g. distance, length, time, force, counting repititions, counting quantities, weight, mass, colour-wavelength, symmetric/asymmetric/anti-symmetric patterns, volume, area, etc.


Distinctions or differentiating between quantities is inherently LOGICAL/MATHEMATICAL.

My[Phd student] interlocutors only response has been "that aint true".

What can I say...

College aint what it used to be?

that isn't what you've been saying before, and our replies do not reflect what you claim we have said.

In fact I believe we are pointing out that you do not konw what a venn diagram is, nor that you understand the usage and meaning (if they are different) of 'necessary' and that you stated all simple closed curves were circles, which is obviously wrong.

I don't recall ever using or seeing the word 'distinction' before in this thread and I certainly can't imagine I needed to use 'measurement' at any point other than in this post.

You are distinguishing between things, and you are inherently unmathematical. At least you are consistent in your inconsistency.

[Russell E. Rierson]

In fact I believe we are pointing out that you do not konw what a venn diagram is, nor that you understand the usage and meaning (if they are different) of 'necessary' and that you stated all simple closed curves were circles, which is obviously wrong.



Nope. I never said simple closed curves were "only" circles.

But your continual berating is very distracting. Hopefully you can put that education to good use and say something constructive.

[Tom Mattson]

A measurement is "numerical": e.g. distance, length, time, force, counting repititions, counting quantities, weight, mass, colour-wavelength, symmetric/asymmetric/anti-symmetric patterns, volume, area, etc.

Distinctions or differentiating between quantities is inherently LOGICAL/MATHEMATICAL.


No one denies that numbers are attached to measurements, but as I said, measuring and doing mathematics are two different things. Also, one could do experimentation qualitatively, without numbers. Did you know that there is not a single equation in any of Michael Faraday's lab notebooks? And yet who would say that he did not do physics?


My[Phd student] interlocutors only response has been "that aint true".


Well, that's not really fair. We have explained ourselves.

[Russell E. Rierson]

Did you know that there is not a single equation in any of Michael Faraday's lab notebooks? And yet who would say that he did not do physics?



Didn't Michael Faraday discover somethiong like "field" lines of force? If his notebooks contained diagrams, then he was thinking in terms of vectors.

Vectors are mathematical.

[Tom Mattson]

Didn't Michael Faraday discover somethiong like "field" lines of force? If his notebooks contained diagrams, then he was thinking in terms of vectors.

Vectors are mathematical.

You keep stating the obvious, as if it proves what your are saying, but it doesn't. No one denies that physical forces can be described by vectors, and quite well at that. But it is not the case that physical forces are vectors. One is the map, and the other is the territory: they aren't the same thing.

[Russell E. Rierson]

You keep stating the obvious, as if it proves what your are saying, but it doesn't. No one denies that physical forces can be described by vectors, and quite well at that. But it is not the case that physical forces are vectors. One is the map, and the other is the territory: they aren't the same thing.


Faraday was an experimentalist who thought in "mathematical" terms, even though he was not formally trained in physics or mathematics.

You concede then?

OK...

[Tom Mattson]

Faraday was an experimentalist who thought in "mathematical" terms, even though he was not formally trained in physics or mathematics.


That's just it: He thought in physical terms. It is you who is imposing the mathematical viewpoint onto this.

An experimentalist with no training or interest in mathematics looks at Faraday's apparatus and sees coils, batteries, wires, magnets, capacitors, inductors, etc. He hooks them up and he sees wires being attracted and repelled, ammeter needles deflecting, etc.

You look at those things, and you see vectors, whose line integrals you can compute and whose divergence you can calculate. There's nothing wrong with that (indeed, I see the same thing), but there's also no reason to think that everyone is going to see it that way. Further, there's further no reason to think that such people aren't "doing physics".

The statement "Physics would not exist without mathematics" is simply false. In fact I think a better case could be made for the converse.


You concede then?

OK...

Why should I? :confused:

[Russell E. Rierson]

That's just it: He thought in physical terms. It is you who is imposing the mathematical viewpoint onto this.




Faraday visualized field lines of force; directed line segments. Vectors in simple form.

In certain respects, physical existence is mathematical. If not, then why does mathematics explain the world so well?

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_t he_Natural_Sciences


"The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning."



An arbitrary n-dimensional surface, a curve, can be defined by a parametric equation:

x^a = x^a(u) , (a = 1,2,...,n) where u is the parameter with x^1(u),x^2(u),...,x^n(u) denoting n functions of u. A subspace/surface of m dimensions has (m < n) degrees of freedom, depending on m parameters according to the parametric equations:

x^a = x^a(u^1 , u^2 ,..., u^m) , (a = 1, 2,...,n)

When m = n-1 the subspace is called the hypersurface:

x^a = x^a(u^1 , u^2 ,..., u^n^-^1), (a=1, 2,..., n)


If the manifold with n degrees of freedom is restricted to a hypersurface of an n-1 subspace, its coordinates must satisfy the constraint:

f(x^1 , x^2,..., x^n) = 0

Intersecting "level surfaces" or simple closed curves, of n-1 dimensions with radius R and 1/R, respectively, form in-phase standing waves. A geometric "universal set".

[matt grime]

nxn matrices and nxn matrices of nonzero determinant are manifolds, one has one fewer degree of freedom than the other, yet they have the same dimension (that of the dimension of its tangent space at any point).

We'll leave the rest as specious nonsense at this stage

[Tom Mattson]

Faraday visualized field lines of force; directed line segments. Vectors in simple form.


I can see that my comment went in one ear and out the other.

Once again: it is you who is imputing the mathematical interpretation onto this.


In certain respects, physical existence is mathematical. If not, then why does mathematics explain the world so well?


First, a question is not a valid argument. Second, mathematics isn't used "explain" the world at all. It is used to describe the world. And third, your position as to the nature of existence is neither a scientific viewpoint nor a mathematical one. It is a philosophical viewpoint, and a rather bad one at that, as it is a form of idealism that mistakes the ideal forms used to describe the physical reality, for the physical reality itself.

Anyway, the point that led up to this line of discussion was my response to your comment that energy arguments could somehow be invoked in set theory. They can't. Physical arguments are of no use whatsoever in proving mathematical results, because math is not physics, and vice versa.


http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_t he_Natural_Sciences


I have read the Wigner article more than once. Do you know why he calls the effectiveness of mathematics "unreasonable"? It's because no one can explain it. That is precisely why the article is not of any use in proving your assertions.


Intersecting "level surfaces" or simple closed curves, of n-1 dimensions with radius R and 1/R, respectively, form in-phase standing waves.


Incorrect. First, "standing waves" are physical phenomena. And second, even if you mean that they are "standing wave solutions to the wave equation" (which are bona fide mathematical objects), your analysis here by no means proves such a thing. You haven't even specified the parametric equations, nor a dynamical equation that they are supposed to satisfy.


A geometric "universal set".

What is so "universal" about this set?

I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

[wespe]

In certain respects, physical existence is mathematical. If not, then why does mathematics explain the world so well?

... mathematics isn't used "explain" the world at all. It is used to describe the world.

Sorry for the intrusion. That was once one of my misconceptions (about relativity, but same thing). Best way to make it clear is to think that math was invented to get answers in the physical world. That is, to describe it, not to explain it. Because, things don't happen in physical world because of math says so, it's the other way around. Math is abstract anyway. So when you simplfy or rearrange equations, it may not have a physical meaning, maybe two forces are canceling each other out, but they sill exist, the answer you get is still correct.

[Russell E. Rierson]

Incorrect. First, "standing waves" are physical phenomena. And second, even if you mean that they are "standing wave solutions to the wave equation" (which are bona fide mathematical objects), your analysis here by no means proves such a thing. You haven't even specified the parametric equations, nor a dynamical equation that they are supposed to satisfy.



What is so "universal" about this set?

I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

It is one interpretation of the "Wheeler-Feynman Absorber" theory. I will not give the equations on a silver platter. :eek: :eek: :eek:

[Tom Mattson]

It is one interpretation of the "Wheeler-Feynman Absorber" theory. I will not give the equations on a silver platter. :eek: :eek: :eek:

:uhh:

First of all, you have not presented anything that could be called an interpretation of any physical theory. And second, the Wheeler-Feynman Absorber theory is not a secret.

You keep throwing technical terms around, but you don't seem to have the foggiest idea of what any of them mean.

Has it occured to you to go into the Math and Physics Forums and ask people for help? This place is loaded with people who can do just that.

[Russell E. Rierson]

I can see that my comment went in one ear and out the other.


Here is a quote of Oliver Heaviside, talking about Michael Faraday:


"And it is a noteworthy fact that ignorant men have long been
in advance of the learned about vectors. Ignorant people, like
Faraday, naturally think in vectors. They may know nothing of their
formal manipulation, but if they think about vectors, they think of
them *as* vectors, that is, directed magnitudes. No ignorant man
could or would think about the three components of a vector
separately, and disconnected from one another. That is a device of
learned mathematicians, to enable them to evade vectors. The device
is often useful, especially for calculating purposes, but for general
purposes of reasoning the manipulation of the scalar components
instead of the vector itself is entirely wrong."











First, a question is not a valid argument. Second, mathematics isn't used "explain" the world at all. It is used to describe the world. And third, your position as to the nature of existence is neither a scientific viewpoint nor a mathematical one. It is a philosophical viewpoint, and a rather bad one at that, as it is a form of idealism that mistakes the ideal forms used to describe the physical reality, for the physical reality itself.



Mathematics is a meta-language. Yes, mathematics "describes" the physical universe and it also "explains" :

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=explain&x=15&y=16



EXPLAIN

1 a : to make known b : to make plain or understandable <footnotes that explain the terms>

2 : to give the reason for or cause of

3 : to show the logical development or relationships of

:eek:

Here is an interesting paper by Max Tegmark that you have probably read before?

http://www.hep.upenn.edu/~max/toe.pdf

Here is a quote about the equivalence of mathematical existence with physical existence:


Our proposed TOE can be summarized as follows:

Physical existence is equivalent to mathematical existence.

What precisely is meant by mathematical existence, or
ME for brevity?

A generally accepted interpretation of
ME is that of David Hilbert:

Mathematical existence is merely freedom from contradiction.
In other words, if the set of axioms that defne a mathematical
structure cannot be used to prove both a statement
and its negation, then the mathematical structure
is said to have ME.



"Mathematical existence is merely freedom from contradiction" The universe must make sense.

Faraday recognized that action at a distance was absurd, and he solved the problem with the "field" concept.

You are saying that fields are not mathematical structures? I disagree. You are saying that Faraday didn't think mathematically? I disagree.




Anyway, the point that led up to this line of discussion was my response to your comment that energy arguments could somehow be invoked in set theory. They can't. Physical arguments are of no use whatsoever in proving mathematical results, because math is not physics, and vice versa.


The laws of physics could be described as laws of geometry. The constants of physics could be described as constants of geometry. That is what Einstein was trying to do, yes?




I have read the Wigner article more than once. Do you know why he calls the effectiveness of mathematics "unreasonable"? It's because no one can explain it. That is precisely why the article is not of any use in proving your assertions.

Then Wigner's paper is also useless for Max Tegmark's writings and I wasn't trying to prove assertions with it.




Incorrect. First, "standing waves" are physical phenomena. And second, even if you mean that they are "standing wave solutions to the wave equation" (which are bona fide mathematical objects), your analysis here by no means proves such a thing. You haven't even specified the parametric equations, nor a dynamical equation that they are supposed to satisfy.


I agree with Michael Faraday and Albert Einstein. Action at a distance is totally absurd. Geometry solves that problem.



What is so "universal" about this set?


Again, I will repeat the first axiom:

If the physical universe includes all that is real and excludes all that is not real, then the physical universe is the universal set.

References for the first axiom:

Chris Langan

www.ctmu.org

Lee Smolin

"Three Roads to Quantum Gravity"


Refute the first axiom. You are a mentor.



I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

That is your opinion? Refute it mathematically.


First of all, you have not presented anything that could be called an interpretation of any physical theory. And second, the Wheeler-Feynman Absorber theory is not a secret.

You keep throwing technical terms around, but you don't seem to have the foggiest idea of what any of them mean.

Has it occured to you to go into the Math and Physics Forums and ask people for help? This place is loaded with people who can do just that.


Yes, I will ask for help. One question at a time.

Thank you.

[Tom Mattson]

Here is a quote of Oliver Heaviside, talking about Michael Faraday:


So what? Even if I leave alone the fact that Heaviside and Faraday were not contemporaries, the fact remains that this does not one thing to prove your ridiculous assertion that physics would not exist without mathematics, and neither does it do anything for your equally ridiculous assertions that physical arguments can be used in mathematical proofs. Why won't you just concede that fact, instead of bringing up these silly arguments?


Mathematics is a meta-language. Yes, mathematics "describes" the physical universe and it also "explains" :


Oh does it? Let's look at what you cite as evidence.


EXPLAIN

1 a : to make known b : to make plain or understandable <footnotes that explain the terms>


Mathematical models don't do that. That's what observation does.


2 : to give the reason for or cause of


Nope, mathematical models don't do that either.


3 : to show the logical development or relationships of


OK, mathematical models do that, to a certain extent. But they most definitely don't do that in the most fundamental degrees of freedom, whch is what would be required for an "explanation".


Here is an interesting paper by Max Tegmark that you have probably read before?

http://www.hep.upenn.edu/~max/toe.pdf


Yes, I've read it. Do you really think that a student in theoretical physics hasn't read the articles by Tegmark and Wigner?


Here is a quote about the equivalence of mathematical existence with physical existence:


Here's a novel idea: How about you stop trying to prove your ponits with quotes, and start trying to prove them with arguments. :surprise:


You are saying that fields are not mathematical structures? I disagree. You are saying that Faraday didn't think mathematically? I disagree.


1. I am saying that physical fields, and the mathematical fields used to describe them, are not the same thing.

2. I am not saying that Faraday didn't think mathematically. I am saying that there is no reason to think that your assertion, "Physics would not exist without mathematics", is correct.


The laws of physics could be described as laws of geometry. The constants of physics could be described as constants of geometry. That is what Einstein was trying to do, yes?


That's what he did with GR, and he tried to do it with his attempt at a unified field theory in the 1950's. Still, none of that information lends any credence to the math-o-phille position that mathematical forms acutally exist in nature. That is an unfounded belief.


Then Wigner's paper is also useless for Max Tegmark's writings and I wasn't trying to prove assertions with it.


Then why did you quote it in response to my challenge of your assertion?


I agree with Michael Faraday and Albert Einstein. Action at a distance is totally absurd. Geometry solves that problem.


I agree that action at a distance is absurd. But I would say that geometry describes the problem. I would also be so forward as to say that Faraday and Einstein would agree with that.


Again, I will repeat the first axiom:

If the physical universe includes all that is real and excludes all that is not real, then the physical universe is the universal set.

References for the first axiom:

Chris Langan

www.ctmu.org

Lee Smolin

"Three Roads to Quantum Gravity"


What are you talking about? Axioms don't need references or proofs. They just need logical arguments to flow from them. What you quote here proves nothing.


Refute the first axiom. You are a mentor.


I don't even care about refuting "the first axiom", if nothing can be derived from it.


Tom: I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

Russell: That is your opinion? Refute it mathematically.


It's not my opinion, it is a fact. You want me to prove mathematically that the gibberish you have posted is wrong? Why should I? Instead why don't you stop screwing around and post something with some actual reasoning behind it?

[Russell E. Rierson]

So what? Even if I leave alone the fact that Heaviside and Faraday were not contemporaries, the fact remains that this does not one thing to prove your ridiculous assertion that physics would not exist without mathematics

:uhh:


Nice try.


From the quote of Tegmark and Hilbert: Hilbert defines mathematical existence as "freedom from contradiction"

If mathematical existence equals physical existence:


Physical theories must be free of contradiction.

Physical theories would not exist without mathematics.

Physics must be free of contradiction









Mathematical models don't do that. That's what observation does.


Are you saying that "observation" is not a mathematical process in itself?

eye<-------[photons]------->observed phenomena






Here's a novel idea: How about you stop trying to prove your ponits with quotes, and start trying to prove them with arguments. :surprise:


I am not proving[or trying to prove] points with quotes. This thread started out as a question and was moved to TD. Now I am trying to "develop" the theory. Or more correctly, I am trying to develop a hypothesis



2. I am not saying that Faraday didn't think mathematically. I am saying that there is no reason to think that your assertion, "Physics would not exist without mathematics", is correct.


Earlier, you said this about Faraday:



That's just it: He thought in physical terms.


Now you agree that he thought in mathematical terms also :devil:

Thanks.


That's what he did with GR, and he tried to do it with his attempt at a unified field theory in the 1950's. Still, none of that information lends any credence to the math-o-phille position that mathematical forms acutally exist in nature. That is an unfounded belief.


It is not a "belief". It is a hypothesis. Perhaps I should have stated that expilcitly.





I don't even care about refuting "the first axiom", if nothing can be derived from it.

Thanks for the help.

[Tom Mattson]

:uhh:


Nice try.


I have no idea of what you mean by that.


From the quote of Tegmark and Hilbert: Hilbert defines mathematical existence as "freedom from contradiction"

If mathematical existence equals physical existence:


Physical theories must be free of contradiction.

Physical theories would not exist without mathematics.

Physics must be free of contradiction


Was this supposed to be an answer to what I was saying? If so, then I don't see how. All you are doing is starting from your peculiar brand of idealist philosophy, and drawing conclusions from it. I wasn't wondering about the consequences, I was wondering what made you think the statement,

"Mathematical existence equals physical existence,"

was true in the first place.


Are you saying that "observation" is not a mathematical process in itself?

eye<-------[photons]------->observed phenomena


Yes, observation is not a mathematical process.


I am not proving[or trying to prove] points with quotes. This thread started out as a question and was moved to TD. Now I am trying to "develop" the theory. Or more correctly, I am trying to develop a hypothesis


Then why do you respond to comments with quotes and links that have no relevance to the discussion? Why not just post an argument? If you are here to devlop a theory, you don't seem to be trying very hard.


Earlier, you said this about Faraday:

Now you agree that he thought in mathematical terms also :devil:

Thanks.


He probably did. So what? It still doesn't mean that physics would not exist without mathematics.


It is not a "belief". It is a hypothesis. Perhaps I should have stated that expilcitly.


A belief is nothing other than a hypothesis that is held to be true, without any evidence.

I feel compelled to echo Matt's earlier thought: When you have figured out what it is you want to prove, let us know.

[hello3719]

Mathematics is THE LANGUAGE that express human thoughts in the most logical way. Physics is the study of what exists. You can consider an observation made in an experiment to be part of the mathematical terminology, but in our mathematical system they aren't always included.
Also if you meant to say that "existence" is due to mathematics it isn't true since language isn't by definition the root of existence.

[Russell E. Rierson]

I was wondering what made you think the statement,

"Mathematical existence equals physical existence,"

was true in the first place.



Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.



Yes, observation is not a mathematical process.


Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".

Ergo, it follows that your statement: "observation is not a mathematical process" is false.



Then why do you respond to comments with quotes and links that have no relevance to the discussion? Why not just post an argument? If you are here to devlop a theory, you don't seem to be trying very hard.


This appears to be your personal, biased opinion? Elitism? Feigned ignorance? The quotes and links ARE relevant to the discussion.


He probably did. So what? It still doesn't mean that physics would not exist without mathematics.



[1.] Physics would not exist without an ability to describe phenomena.

[2.] The description of phenomena must be logically consistent[free of contradiction].

[3.] Mathematical existence is defined as freedom from contradiction.


[4.] Mathematics describes phenomena.

Therefore

Physics would not exist without mathematics.




A belief is nothing other than a hypothesis that is held to be true, without any evidence.

If the hypothesis cannot be tested, then what good is it?



I feel compelled to echo Matt's earlier thought: When you have figured out what it is you want to prove, let us know.

:zzz: :zzz: :zzz:



If the universe includes all that is real and excludes that which is not real, then the universe is the "universal set".

Background Independence:


The description of any entity inside the real universe can only be
with reference to other things in the universe. Space is then
relational, and the universe, self referential. For example, if an
object has a momentum, that momentum can only be explained with
respect to another object within the universe. Space then becomes an
aspect of the relationships between things in reality.

Physicist Lee Smolin says that space becomes analogous to a sentence, and it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it.

For example, relationships like object-subject or adjective-noun. So
there are many different grammatical structures composed of different
arrangements of words, and the varied relationships between them.


If the universe is closed, the "information" or entangled quantum
states cannot leak out of the closed system. So the density of
entangled quantum states, continually increases, as the entropy must
always increase. While to us, it is interpreted as entropy or lost
information, it is actually recombined information, to the universe.

Shannon entropy.

Since entropy can also be defined as the number of states within a
region of space, and the entropy of the universe must always
increase, the next logical step is to realize that the spacetime
density, i.e. the information encoded within a circumscribed region
of space, must be increasing in the thermodynamic direction of time.


The entropy of thermodynamics and entropy of Shannon, are equivalent
concepts, because the number of arrangements that are counted by
Boltzmann entropy reflects the amount of Shannon information needed
to implement any particular combination, or arrangement. The two
entropies also appear to have superficial differences.

Thermodynamic entropy is interpreted in units of energy divided by
temperature, while, the Shannon entropy is interpreted in terms of
dimensionless bits. This seems to point towards a computational/language structure for reality.


The Heisenberg uncertainty principle follows directly from the Cauchy-Schwartz inequality for scalar products. By quantizing spacetime geometry, it seems that the wavefunctions/waveforms aren't based on a background space. The wavefunction space, can be thought of as the space of square-
integrable wavefunctions over classical configuration space. Geometric quantization can be constructed, via fiber bundles.

[Tom Mattson]

Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.


OK, fine.


Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".

Ergo, it follows that your statement: "observation is not a mathematical process" is false.


No, it doesn't follow. You are in dire need of a lesson in elementary logic. It is a simple, obvious fact that denying the statement "physical existence = mathematical existence" and affirming the statement "physical observations must be noncontradictory" are compatible.


Tom: Then why do you respond to comments with quotes and links that have no relevance to the discussion? Why not just post an argument? If you are here to devlop a theory, you don't seem to be trying very hard.

Russell: This appears to be your personal, biased opinion? Elitism? Feigned ignorance? The quotes and links ARE relevant to the discussion.


No, they aren't relevant. You consistently respond to comments with links that have the correct buzzwords, but do not connect to those comments in the slightest. Anyone who knows anything about mathematics or physics can see this.


[1.] Physics would not exist without an ability to describe phenomena.

[2.] The description of phenomena must be logically consistent[free of contradiction].

[3.] Mathematical existence is defined as freedom from contradiction.


[4.] Mathematics describes phenomena.

Therefore

Physics would not exist without mathematics.


Russell, do yourself a huge favor and take a course in logic. This argument is so asinine, I am astounded that a would-be mathematical theorist would even post it.


If the hypothesis cannot be tested, then what good is it?


Exaclty my point: Your belief that physical existence is equivalent to mathematical existence cannot be tested. Ergo, it is no good.


If the universe includes all that is real and excludes that which is not real, then the universe is the "universal set".

Background Independence:

The description of any entity inside the real universe can only be
with reference to other things in the universe. Space is then
relational, and the universe, self referential. For example, if an
object has a momentum, that momentum can only be explained with
respect to another object within the universe. Space then becomes an
aspect of the relationships between things in reality.

Physicist Lee Smolin says that space becomes analogous to a sentence, and it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it.

For example, relationships like object-subject or adjective-noun. So
there are many different grammatical structures composed of different
arrangements of words, and the varied relationships between them.


If the universe is closed, the "information" or entangled quantum
states cannot leak out of the closed system. So the density of
entangled quantum states, continually increases, as the entropy must
always increase. While to us, it is interpreted as entropy or lost
information, it is actually recombined information, to the universe.

Shannon entropy.

Since entropy can also be defined as the number of states within a
region of space, and the entropy of the universe must always
increase, the next logical step is to realize that the spacetime
density, i.e. the information encoded within a circumscribed region
of space, must be increasing in the thermodynamic direction of time.


The entropy of thermodynamics and entropy of Shannon, are equivalent
concepts, because the number of arrangements that are counted by
Boltzmann entropy reflects the amount of Shannon information needed
to implement any particular combination, or arrangement. The two
entropies also appear to have superficial differences.

Thermodynamic entropy is interpreted in units of energy divided by
temperature, while, the Shannon entropy is interpreted in terms of
dimensionless bits. This seems to point towards a computational/language structure for reality.


The Heisenberg uncertainty principle follows directly from the Cauchy-Schwartz inequality for scalar products. By quantizing spacetime geometry, it seems that the wavefunctions/waveforms aren't based on a background space. The wavefunction space, can be thought of as the space of square-
integrable wavefunctions over classical configuration space. Geometric quantization can be constructed, via fiber bundles.

Be sure to let me know when you want to present a logical argument for your ideas on geometric set theory. :uhh:

[Russell E. Rierson]

No, it doesn't follow. You are in dire need of a lesson in elementary logic. It is a simple, obvious fact that denying the statement "physical existence = mathematical existence" and affirming the statement "physical observations must be noncontradictory" are compatible.



You agree that physical observations must be non-contradictory.

You must also agree that descriptions of physical existence must be
non-contradictory since observations must be non-contradictory.

We can drop the label "mathematical existence"
if it puts a burr in your saddle.


:eek: :eek: :eek:


In other words, you appear to be arguing semantics, not physics.

[Tom Mattson]

It has occured to me that, just because you use terms such as "modus ponens", it just might not be the case that you understand them. So, I am going to go into more detail on these arguments.


Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.




Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".

Ergo, it follows that your statement: "observation is not a mathematical process" is false.


It does not follow. Let's see why, formally.

The fundamental statements of the argument are these:

p: Mathematical existence is equivalent to physical existence.
q: Physical existence is free from contradiction.
r: Observation is free from contradiction.
s: Observation is not a mathematical process.

Your argument proceeds as follows:

1.) p-->q (Premise)
2.) q-->r (Premise)
3.) Therefore, ~s (Conlcusion)

That this is a non-sequitir is obvious to anyone with any familiarity with logic. The basic statements of the premises do not even appear in the conclusion, which makes the conclusion totally unconnected to the statements cited to support it. Furthermore, it is a simple fact that conclusions of valid arguments cannot contain statements that do not appear in the premises, but this argument does. You can test it for validity yourself by determining the truth table for the compound statement:

[p-->q]^[q-->r]-->(~s)

You will see that the statement is not tautological, and so the argument cannot be valid.

But perhaps you didn't mean to include a new term in the conclusion, and that it only looks like you did due to a poor choice of words?


[1.] Physics would not exist without an ability to describe phenomena.


OK, so formally this is an "if-then" statement:

If physics exists, then it has the ability to describe phenomena.

I'll contract it to:

p: Physics exists.
q: Physics has the ability to describe phenomena.

So we have:

1.) p-->q.


[2.] The description of phenomena must be logically consistent[free of contradiction].


Since this is not a compound statement, it will be denoted by a single logical variable:

2.) r


[3.] Mathematical existence is defined as freedom from contradiction.


Same here.

3.) s


[4.] Mathematics describes phenomena.


And here.

4.) t


Therefore

Physics would not exist without mathematics.


And this is equivalent to the "if-then" statement:

If physics exists, then mathematics exists.

The antecedent was already denoted as "p". Let the consequent be "u". So we have:

p-->u.

And your argument proceeds as follows:

1.) p-->q (Premise)
2.) r (Premise)
3.) s (Premise)
4.) t (Premise)
5.) Therefore, p-->u (Conclusion)

This argument has the same malady as the first one, though to a lesser extent (one logical variable from the premises actually occurs in the conclusion!). But this argument is not valid either, which you can verify using a truth table.

On to your next post:


You agree that physical observations must be non-contradictory.

You must also agree that descriptions of physical existence must be
non-contradictory since observations must be non-contradictory.


Yes.


We can drop the label "mathematical existence"
if it puts a burr in your saddle.


It puts a burr in my saddle because it is irrational.


In other words, you appear to be arguing semantics, not physics.


No, logic is not semantics. Furthermore, you aren't even arguing physics. The position "physical existence is equivalent to mathematical existence" is a philosophical position, not a scientific or mathematical one.

[Russell E. Rierson]

That this is a non-sequitir is obvious


Thanks for the help :devil: :devil: :devil:

[1.] Mathematics is a meta language.

[2.] Language is descriptive.

[3.] Language must be free of contradiction. Mathematics is also defined as a descriptive system that has "freedom from contradiction".

[4.] Mathematics describes physical existence/processes/events.

[5.] Observation is a physical process.

[6.] Mathematics describes observations.

[7.]A description of an observation must be free of contradiction-following from [3.]

[8.] Observation must be free of contradiction.

[8.] A description is an abstract representation of a physical system. The description must be as exact as possible.

[9.] An exact description implies equivalence between abstract structures and physical systems.

[10.] If the exact description exists, then physical existence is a meta-language. A self descriptive entity, free of contradiction. The universe is equivalent to its[exact] description.


:eek: :eek: :eek:

[matt grime]

9. equivalence?

of course there's then the problem that you cannot prove that any model *exactly* fits the system, so it's all vacuous.

then there's the fact that language needn't be free or contradiction. cleave means to split apart or to stick together...

[Russell E. Rierson]

9. equivalence?

of course there's then the problem that you cannot prove that any model *exactly* fits the system, so it's all vacuous.

then there's the fact that language needn't be free or contradiction. cleave means to split apart or to stick together...

A meta language[mathematics] must be "free" of contradiction does it not? Cleave and ...cleave are relativised to the context of the "situation".

The only certainty is uncertainty :eek: :eek: :eek:

X = certainty

The only X is not-X ?

A contradiction. But what we understand about reality, must make sense.

We must assume? that a non-contradictory description [stratified variables]of reality exists.

X = certainty, exists, even if it is an incompletely constructed map by self aware systems within the universe...?

[Russell E. Rierson]

I was thinking in terms of nested "hyper-realities" , where the algorithim arises spontaneously, analogously to a quantum fluctuation description.

These nested hyper curves are level-surfaces, analogous to resonating phase spaces:

[<-[->[U]<-]->]

The laws and constants of physics become the laws of geometry. Any measured piece of reality is observed to be constructed of discrete units. The resonating wave functions are the infinite number of possible combinations of position Dx, and momentum Dp.

A quantum computer "algorithm".

Overlapping waves become phase entangled. There are two types of wave "motion", which becomes a mixed wave form. Both transverse and longitudinal wave propagation occurs.

Hypothetically speaking, of course :eek: :eek: :eek: