The Universal Geometric Set

Russell E. Rierson

You appear to be acting like an ignorant troll.

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


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

Circles are simple closed curves.


http://www.combinatorics.org/Surveys...nGraphEJC.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

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

Wake up.

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. 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

Here is what matt ...said:

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


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/~fied...55/Jordan.html


Interesting...


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

I know what Matt said.

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

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.

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

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 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.




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 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....uantum+gravity




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

Russell E. Rierson

So you promise to go harrass someone else?

Thanks.

Tom Mattson

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

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.

What's that supposed to prove?

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.

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

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



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

Again, what is that supposed to prove?

Russell E. Rierson

You wrote this:

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".








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