## The Universal Geometric Set

 Quote by matt grime 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...
 Recognitions: Homework Help Science Advisor 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?

 Quote by matt grime Since when is a simple closed curve necessarily a circle?
Circles are simple closed curves.

http://www.combinatorics.org/Surveys...nGraphEJC.html
 Recognitions: Homework Help Science Advisor 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.

 Quote by matt grime a closed simple curve is not necessarily a circle

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

Wake up.

 Quote by matt grime 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.

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 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?

 Quote by Tom Mattson 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"

 Quote by Tom Mattson 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?

http://www.math.ohio-state.edu/~fied...55/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.

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Quote by Russell E. Rierson
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
 Recognitions: Homework Help Science Advisor 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...

 Quote by Tom Mattson 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.

 Quote by Tom Mattson 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.

 Quote by Tom Mattson 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:

 [...] 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."

 Quote by Tom Mattson Because in mathematics, definitions are everything.

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

 Quote by 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...

So you promise to go harrass someone else?

Thanks.

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 Quote by Russell E. Rierson 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.

 Quote by Tom Mattson What's that supposed to prove?

http://www-groups.dcs.st-and.ac.uk/~...ns/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.

 Quote by Tom Mattson 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.
 Recognitions: Homework Help Science Advisor 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?

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 Quote by Russell E. Rierson http://www-groups.dcs.st-and.ac.uk/~...ns/Witten.html
Again, what is that supposed to prove?

 Quote by Tom Mattson Again, what is that supposed to prove?
You wrote this:

 Quote by Tom Mattson 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".

 Quote by Tom Mattson 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.

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