A mathematical definition of the universe

[King_Anarchist]

http://www.alphaomegadimension.net/media/pdf/mathematical_definition_of_universe_ver_3-02_anon.pdf


Abstract:
In this document, the author presents a structure U with the property that
all structures are elementarily embeddable within it. One essential tool is a
version of New Foundations set theory, first developed by Quine, as presented
by Holmes in [4]. The motivation is given by The Mathematical Universe
article by Max Tegmark, [6], in which it is hypothesized that physical existence
is mathematical existence. Consequently, it is hypothesized that the structure
with the aforementioned property could be central in the Mathematical Universe
Hypothesis. Finally, some basic facts about U are explored.

 

[Angleochoas]

If anything is possible, then it is possible that the statement "anything is possible" is false.

In my regard;
Only within it's own possibility.
Which therefore leaves room for countless possibility in and of itself. For in this context;
"anything", as previously aforementioned - would serve it's own possibility structure maintaining the various likely/not-likely outcomes in their varying degrees. Almost seemingly like a balance, counter-balance, or a system of checks and balances (depending on how the mind imagines the metaphor I'd suppose).

I'm not necessarily disagreeing but simply speculating.

 

[King_Anarchist]

It feels somewhat like a koan.

One possible :D problem is that the consequence to the antecedent is in a meta-language and the question of whether or not the 'anything' mentioned in the antecedent is literal.

 

[AcumenImmortalis]

There actually IS a koan I've read that fits that: "When you can do nothing, what can you do?" /ttiforum/images/graemlins/smile.gif

 

[King_Anarchist]

Heh heh. Yep.

 

[Angleochoas]

Only limited to it's own probability

 

[khan2012]

The evidence is not conclusive but it is interesting /ttiforum/images/graemlins/smile.gif


http://www.digitaljournal.com/article/246591/Evidence_of_a_parallel_universe


Data from NASA’s Wilkinson Microwave Anisotropy Probe (WMAP) showed evidence of a huge void in the universe spanning one billion light years. Scientists say this void may be the evidence of another universe beyond our own.

 

[Angleochoas]

then it is possible that the statement "anything is possible" is false.

As well by this statement,

If anything is possible

Then it is possible that the statement "anything is possible" is true.
For just as we reclassify something to have a 'pattern' that it is in sense predictable and not so 'unpredictable', just having more than one variable gives shape to pattern creation.
Taking that in mind, even if we were to settle on a finite universe - does not the amount of photons at least have the potential to fluctuate greatly?[/

The fact that it's not even a constant variable makes it all that much more interesting philosophically to me.

 

[King_Anarchist]

In reply to:
then it is possible that the statement "anything is possible" is false.



As well by this statement,

In reply to:
If anything is possible



Then it is possible that the statement "anything is possible" is true.
For just as we reclassify something to have a 'pattern' that it is in sense predictable and not so 'unpredictable', just having more than one variable gives shape to pattern creation.
Taking that in mind, even if we were to settle on a finite universe - does not the amount of photons at least have the potential to fluctuate greatly?[/
The fact that it's not even a constant variable makes it all that much more interesting philosophically to me.

Absolutely.

However, the statement "if anything is possible then it is possible that the statement "anything is possible" is true" is, on its own, circular.

In the end, word games like the ones I've been playing for so long will not reveal any hidden truths; it seems to be a matter of confirmation bias, words structured in some way are thought to reveal something new but that truth was already there.

May the force be with you always. :D

 

[Angleochoas]

If anything is possible, then it is possible that the statement "anything is possible" is false.

All that the addition to that statement serves to prove, is that the original statement is therefore "true" because of aforementioned variable "false"

.

Binaric thinking, on/off, or metaphorically true/false, left/right - how "long" in duration would be then duration of possibility and in of itself still possibility.

 

[King_Anarchist]

All that the addition to that statement serves to prove, is that the original statement is therefore "true" because of aforementioned variable "false" .

For better or for worse, everything is an inescapable conclusion from the premise that anything is possible. Some pathological example might be "if anything is possible, then it is possible to draw a square circle."

Binaric thinking, on/off, or metaphorically true/false, left/right - how "long" in duration would be then duration of possibility and in of itself still possibility.

I agree.

 

[Packerbacker]

Dear Angleochoas:

Would you please not take up writing text books--they are difficult enough.

 

[Angleochoas]

Packer, not sure what you mean, but I'll remember that

For better or for worse, everything is an inescapable conclusion from the premise that anything is possible. Some pathological example might be "if anything is possible, then it is possible to draw a square circle."

Okay, good point. Now a question;

Is that shape a circle, a sphere, or polygons?

:eek:

P.S.

I'm more surprised you didn't use the metaphor of triangles to circles, then squares

 

[Packerbacker]

Gasp! You've used the Sacred Symbol of the Great Goo-oo-roo--The Great Blue Ball-- in a profane setting where it can be seen by infidels. I suspect there will be a fatah put on your head by believers. Flee now, while there is still a chance to escape!

 

[King_Anarchist]

Okay, good point. Now a question;

Is that shape a circle, a sphere, or polygons?

That image is a collection of pixels which approximate squares, which are polygons.

P.S.

I'm more surprised you didn't use the metaphor of triangles to circles, then squares

If I said "then it is possible to draw something that is both a circle and a 100-gon" one might say "maybe you can" due to the closeness of the two... So saying a triangle would be the most "dramatic" demonstration of an "impossible feat".

 

[Angleochoas]

Gasp! You've used the Sacred Symbol of the Great Goo-oo-roo--The Great Blue Ball-- in a profane setting where it can be seen by infidels. I suspect there will be a fatah put on your head by believers. Flee now, while there is still a chance to escape!

I hope to never experience the punishment of the great blue ball :eek:
(That's almost tasteless wit, but not quite

). lol.

 

[King_Anarchist]

I just realized that I can greatly simplify this. I don't think I need to resort to exotic set theories which will make it a bit less objectionable. woot

 

[Angleochoas]

A set theory is great for known variable problem solving.
How do you plan on attaining absolute quantities to use a theory to support a theory?
Is this theory 'daisy chaining'?

Prior to getting into the "complicated" sets, I'd like to know your stance on finite vs. infinite as well so we have a good understanding on the possibility of your sets to work upwards from to be part of such an all encompassing expression.

 

[King_Anarchist]

A set theory is great for known variable problem solving.
How do you plan on attaining absolute quantities to use a theory to support a theory?

Not exactly sure which absolute quantities you're referring to. What I try to do is detail what is, essentially, a structure containing* all other structures. Assuming the mathematical universe hypothesis (which was argued to follow from the external reality hypothesis by Tegmark), such a structure basically represents the universe.

*Containing isn't quite right but it might suffice for this discussion.

Is this theory 'daisy chaining'?

If you mean that it depends on other theories then yes absolutely.

Prior to getting into the "complicated" sets, I'd like to know your stance on finite vs. infinite as well so we have a good understanding on the possibility of your sets to work upwards from to be part of such an all encompassing expression.

Finite/infinite are jargon words in math which may or may not correspond to what one might intuitively call finite/infinite. Within the context of math there are ways to define these terms.

If we've developed the machinery to define the set of natural numbers and one-to-one correspondences, then a set is finite if there is a 1-1 correspondence between it and any set of the form {0,1,...,n}. A set is called infinite if it is not finite.

Another approach is to start by defining an infinite set first. A set is infinite if there is a 1-1 correspondence between it and a proper subset of it. (Proper subset of a set means a subset in which at least one element of it is absent.) Then a set is finite if it is not infinite.

 

[Angleochoas]

Not exactly sure which absolute quantities you're referring to. What I try to do is detail what is, essentially, a structure containing* all other structures. Assuming the mathematical universe hypothesis (which was argued to follow from the external reality hypothesis by Tegmark), such a structure basically represents the universe.

This christmas, I'll bring you a box, and you show me how sets can predict the contents.
Without known variables.

There's lot's to still find? No?
IE;
http://georgewashington2/universe-is-weirder-than-i-thought.html

That's just a couple 'examples of a definate or indefinate amount of possibility?
Time has a factor with that question, does it not?

Then to even liken our universe with an xmas present - would be more likened to Pandora's box? ^^