# What If...



## Capstone (Jan 13, 2014)

...the only truly autonomous 'object' in existence were the universe itself?

 In keeping true to this theoretical principle, there could be no '_whole_ separation' (or 'space') between the many apparent aspects of this singularity. Please, don't misunderstand me here; space would exist, but only in _outer_ relation to the singular material. To analogize this idea, think of a string that's been folded in half. While there would indeed be an area between the halves, the "separation" would not be "whole", because the connection at the delineating point would remain intact. Bear in mind, for the sake of the analogy, the folded string would be the object, the halves its aspects, and space would be the area that exists in outer relation to the totality. From this perspective, its necessary to think of space, not as something that exists _within_ the universe, but as the pure nothingness in outer relation to it. More simply: space wouldnt reside in the universe; the universe would reside _in it_.

Further implications would be, that although maybe infinite in scope, the amount of nothingness that defines the one would be nonetheless 'constant', and moreover, that the theoretical conflation of 'space' and 'time' ...would be erroneous. 

Accordingly, the redshift observations often cited in support of the theory that the universe is expanding would have to be reinterpreted, viewing the apparent increases of the areas between various groupings of cosmological material in deference to the principle that those areas were actually unchanging.

*A Contracting Universe*

In line with the above, space isn't expanding; the universe is contracting (or, perhaps more properly, _rewinding itself_) in relation to space. Another analogy: think of two stationary balls of twine that are both directly connected to a third unseen ball. If one were to wind the hidden ball, the visible balls would shrink in accordance to the amount of material being pulled away from each of them. And as the hidden ball grew larger, the area between the others would seem to be increasing, when in reality the respective sizes of the visible balls would simply be decreasing in a constant space. The speed at which material is pulled away from the visible balls is directly proportional with the rates at which they're decreasing in size, and those commensurate decreases would constitute the impetus for the illusion of expanding space between them. I believe this is essentially what's happening everywhere in the cosmos, and that it's only a matter of time before the 'hidden ball' -- the ultimate re-collector -- becomes visible, if only by virtue of its effects, from nearly any point of view in the cosmos.

*The Principle of Commensurate Distribution*

Commensurate distribution is a vital aspect of my theory. Because all 'things' within a given group are contracting commensurately, the size differential from one second to the next is virtually undetectable _from within_ that group. In reality though, what were 12 inches yesterday (relative E.G. to the group in which humanity resides) aren't the same twelve inches today, because all things in the group -- including the area that qualifies as a 'foot' -- have contracted at paces suited to their surroundings. This explains how and why we (humans) are completely oblivious to the shrinking going on all around us. It is only by _looking outside_ that the various rates of contraction can be measured via redshift observations.

To sum it up: we all know cosmic redshifting shows that groups of material are apparently speeding away from each other. Expansionists presume that "space" isn't constant and that it must be expanding between the groups; I suggest that the groups are shrinking in relation to constant space. The correct answer, as to which idea the redshift "evidence" supports is both -- meaning the issue of 'truth' stands on the veracity of opposing interpretations of the evidence.

Operating FROM the principle of universal oneness is really no different than operating from any other theoretical principle (such as the various _presumptions_ of most  expansionists).


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## Wry Catcher (Jan 13, 2014)

Not to be glib, but how far is up?  If conventional theory is correct, and the universe is expanding, it boggles the mind that there is no end, or conversely, that the expansion will bend back upon itself _from every point on the non Euclidian compass_.


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## Capstone (Jan 13, 2014)

Wry Catcher said:


> ...If conventional theory is correct, and the universe is expanding, it boggles the mind that there is no end, ...



Exactly.

And an end to what? Time? Matter, or maybe just complexity of material formations?

Assuming expansion is occurring from a centralized point (say from the Big Bang outward in all directions), it seems to me that groupings of cosmological material would eventually no longer be able to interact with each other and all of the material within those groups would sooner or later burn out and/or be assimilated by the black holes at the centers of their galaxies. What might happen in a universe full of nothing but black holes (with  infinite amounts of space between them) is anyone's guess, but it doesn't seem to hold a viable formula for the eternal perpetuation of simple matter.



Wry Catcher said:


> ...or conversely, that the expansion will bend back upon itself _from every point on the non Euclidian compass_.



Infinite space coupled with expansion from the center outward could circumvent that eventuality, at least in theory; but that's certainly a problem for any model that doesn't posit a centralized starting point.


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## editec (Jan 13, 2014)

> To sum it up: we all know cosmic redshifting shows that groups of material are apparently speeding away from each other. Expansionists presume that "space" isn't constant and that it must be expanding between the groups; I suggest that the groups are shrinking in relation to constant space. The correct answer, as to which idea the redshift "evidence" supports &#8230;is both -- meaning the issue of 'truth' stands on the veracity of opposing interpretations of the evidence.




Okay so the universe isn't expanding, but the content within it is shrinking?


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## Capstone (Jan 13, 2014)

editec said:


> Okay so the universe isn't expanding, but the content within it is shrinking?



Yes.

I think it's important to note though, that "the content within" can only be distinguished from "it" ...in terms of _its_ aspects. To give a linguistic analogy, consider the universe as the only noun that really exists. All other _apparent things_ would be the adjectives that describe it. So, instead of saying something like, "Here is a chair.", I believe it would be more in line with reality to say, "Here the universe is chair-like.". As I see things, the universe IS shrinking; and "all of the content within it", as well as the space _outside_ of it, should be viewed accordingly.


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## Capstone (Jan 13, 2014)

Changing gears from the macro to the micro, quanta too would have to be accounted for in a purely monistic paradigm. This means that "particles" would have to be viewed as peaks, similar to looking down from above on the waves of an ocean and occasionally identifying the very tips of some of those waves. Not a perfect analogy, I know, since there could never be a 'whole separation' between the peaks and valleys at the quantum level of a universal singularity, but I hope you all can at least get some idea as to what I mean.

I don't believe a total disconnect between subatomic particles is necessarily requisite to manipulating some of those peaks, as what I believe happens within the confines of particle accelerators, nuclear power plants, ETC...


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## SmedlyButler (Jan 13, 2014)

I have nagging qualms about using apparent red shift to quantify any model of the universe, dynamic or otherwise. I've only briefly skimmed your post and I have to run now but I will check back and look deeper. It may have relevance to some of my cosmological concerns. Thx.


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## Unkotare (Jan 13, 2014)

The universe is expanding. Not only is it expanding, but it is doing so at an accelerating pace, a phenomenon that is explainable by taking into account dark energy. 


There is a German astronomer who recently posited that the universe isn't moving at all (and never was) but that rather the entire universe is getting heavier. The problem with his theory is that it would require us to throw out the notion that mass = energy.


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## Capstone (Jan 13, 2014)

SmedlyButler said:


> I have nagging qualms about using apparent red shift to quantify any model of the universe, dynamic or otherwise. ...



Appearances _can_ be deceiving, but only when they're interpreted incorrectly.

I think that goes to the heart of the biggest problem with human perception. Too often we make faulty presumptions as much on the basis of what _escapes_ our senses as on what they capture. Did David Blain really penetrate the window of some diner in NYC with a 7 of Clubs from the sidewalk outside? Or did it only seem so by virtue of the failure to see one of his cohorts inside the restaurant sticking the predetermined card to the other side of the glass on cue? Likewise, that we don't directly perceive the physical oneness of reality ...isn't a sound basis for denying its potential reality.

I think you're right, though. Understanding the limitations of perception is as good a reason as any to hold anything "apparent" as suspect in terms of its status as evidential support.


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## Capstone (Jan 13, 2014)

Unkotare said:


> The universe is expanding. Not only is it expanding, but it is doing so at an accelerating pace, a phenomenon that is explainable by taking into account dark energy.



It's fine by me that we disagree.

Where most BB expansion-only models fail, in my opinion, is in their lack of explanatory power where the notion of an eternally self-perpetuating physical universe is concerned. From nothing comes nothing; and given the law of conservation, from any physical something, a state of nothingness could never be derived. This means that something physical has always existed (and something physical will always exist). The task, then, is to discover the impetus for its eternal existence. From an expansion-only model in a pluralistic paradigm, the increasing isolation and consequent lack of interactive capability of the physical building blocks of the universe wouldn't bode well for the existence of matter/energy (dark or otherwise) in the far-off future. 

One of the pluses of my theory, BTW, is that it eliminates the need to posit some _mysterious_ force in order to explain the apparent expansion of space. In my view, the universe is not being pushed apart ad infinitum by 'dark energy'; it's simply recoiling itself in relation to constant space.


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## SmedlyButler (Jan 14, 2014)

to read your post in a little more detail and do a little research. I don't know why you carry this empty baggage around with you  As others have said it doesn't even approach the threshold of a good idea let alone amount to a "theory" And don't try that "My opinion is good as anybody else's". You present no evidence and demonstrate no predictive value to your approach. It is worse than useless-it has cost me 30 minutes of time I will never get back. So do everybody a favor and leave this trash in a dustbin somewhere.


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## Capstone (Jan 15, 2014)

SmedlyButler said:


> ...You present no evidence and demonstrate no predictive value to your approach. ...



What evidence exists to support the key presupposition of expansionists, namely that space cannot possibly be a constant? 

Predictive value notwithstanding, the theoretical conflation of time and space isn't evidence; it's become a sort of fundamentalist dogma. 

I've presented my approach as more explanatory than predictive for good reason. I'm an amateur philosopher with a 10th grade education, not a science or maths guy, so I really don't know how to formulate predictions. Of course I realize, for many, this amounts to nothing but more reason to dismiss my ideas as the fodder of a bungling ignoramus, and to those people ...I can only offer my warmest welcome to do so.

I do, however, know how to remain true to my preferred philosophical principles (most notably monism); and with those I'll continue my personal quest to understand and describe the reality I perceive, whether anyone else likes it or not.

Thank you, for your 30 minutes. If I could refund them, I would.


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## Unkotare (Jan 15, 2014)

Capstone said:


> I'm an amateur philosopher with a 10th grade education, not a science or maths guy, so I really don't know how to formulate predictions. Of course I realize, for many, this amounts to nothing but more reason to dismiss my ideas as the fodder of a bungling ignoramus, and to those people ...I can only offer my warmest welcome to do so.




Hey, thanks!


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## midcan5 (Jan 15, 2014)

My question is how this fits into to how we live? how we use philosophic ideas and principles to make sense of it all? I agree that the ideas of the universe shown through modern scientific exploration and speculation are interesting. Imagine yourself for a minute in a wayback machine and then consider how the very same universe looked to people of another time? or how it looks today to an uneducated person or to so called primitive cultures? 

"The aim of philosophy, abstractly formulated, is to understand how things in the broadest possible sense of the term hang together in the broadest possible sense of the term."  Wilfrid Sellars


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## editec (Jan 15, 2014)

*Forgive me if I am characterizing this theory incorrectly.

But what it seems to be saying is that the univsere isn't expanding, but instead, everything in it is shrinking.*


Seems to me that's a distinction without a difference.


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## Capstone (Jan 15, 2014)

midcan5 said:


> My question is how this fits into to how we live? how we use philosophic ideas and principles to make sense of it all? ...



Speaking for myself, I think the high degree of adherence to a single principle that holds sway across the spectrum (in my epistemological, ontological, and even ethical bents) ...is kind of a crutch to compensate for my personal inability to reach a depth of general comprehension that had always otherwise eluded me. The transformation of my thought _processes_ in the early 2000's was thus an _almost spiritual_ enlightenment event.

I believe most people move through life with various degrees of adherence to what are at base philosophical ideas and principles, and tend to do so with widely different levels of awareness of that fact. The law-abiding citizen needn't be versed in the ethical treatises of history's greatest philosophers in order to buy into and benefit from the laws that have arisen over time from the ideas hashed-out in those works. 



midcan5 said:


> ...I agree that the ideas of the universe shown through modern scientific exploration and speculation are interesting. Imagine yourself for a minute in a wayback machine and then consider how the very same universe looked to people of another time? or how it looks today to an uneducated person or to so called primitive cultures?



In the many forms it has taken, from humanity's most distant past to the present, I believe 'education' is _destined_ (in the Annunaki sense of the word) to occur in the lives of all conscious beings. Certainly the development of higher education systems seems a natural by-product of the evolution of beings of higher intelligence, but then ...it's not really clear how closely associated the development of an individual's IQ is with the seemingly ever-changing corpora of teachings available at any given point in time to the many cultures that have come and gone. 

In my opinion, form (knowledge) has necessarily followed function (experience, speculation, trial and error, ETC.), and in light of the evident richness and manifest imitativeness of culturally divergent celestial mythologies, it seems to me that speculation and religious dogma would've had to rule the day to which any trip in "the wayback machine" might take us. Not entirely different from what might be seen from the windows of a _here-and-now_ machine.


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## Capstone (Jan 15, 2014)

editec said:


> *Forgive me if I am characterizing this theory incorrectly.
> 
> But what it seems to be saying is that the univsere isn't expanding, but instead, everything in it is shrinking.*
> 
> Seems to me that's a distinction without a difference.



Well, while I suspect it's true that most (if not all) of the 'predictions' made by some inflationary models could be made equally well (in a _mirror image_ sort of way) by a deflationary one, this could only be done by accounting for 'space' as something wholly distinct from 'the universe'. It's that distinction I believe your characterization may be missing. A more appropriate characterization of my view would be: "Space" (which I believe exists, not within, but _in relation to_ the universe) isn't expanding, but instead, "everything in it" (which, in my view, is synonymous to "the universe") is contracting. 

Remember one of the key implications of my approach in the OP: "space doesn't reside in the universe; the universe resides _in it_."


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## SmedlyButler (Jan 15, 2014)

'....if one explanation will do why do you need two? Why is your model different from epicycles (which went to ridiculous levels of complexity to keep the Earth at the centre of things). This is not an appeal to a philosophical principle (parsimony) but sound practise. Physics is not about reality or truth or beauty or anything like that. It is about models that predict things. It is about ways to describe what we can see. If you propose a physical model for something then you make it as simple as possible but no simpler. Not because it makes some fuzzy happy point about complexity in the universe but because that is how you make a useful model. So if your model makes no new predictions, replicates the current model perfectly but requires a whole load of ad hoc synchronisations and stuff then it is a bad model. Not because it violates a world view but because it is harder to use and gives no benefit.

So a direct questions: Why is your model better? What does it simplify? What does it predict or explain that the current models don't?"

*Data Mining is against Site Rules. XXXXXXX*

"Thank you, for your 30 minutes. If I could refund them, I would."- Now it's 45 minutes, please don't increase your debt any further.


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## Unkotare (Jan 15, 2014)

This 'theory' is obviously nothing more than empty communicative diarrhea by some kid trying to feel self-important. It should be treated as such.


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## SmedlyButler (Jan 15, 2014)

Unkotare said:


> This 'theory' is obviously nothing more than empty communicative diarrhea by some kid trying to feel self-important. It should be treated as such.



I was trying to intimate a similar reaction without being cruelly blunt. Maybe your approach is the right one. If he tries to maintain his nonsensical narrative your dismissal will be the proven the way to go.


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## RandomVariable (Jan 15, 2014)

Capstone,

I've had about all I can take of politics for the moment so I will be more than happy to play. Up front my apologies for not taking in more of your theory but the stream needs my foot again soon. First of all let me agree with your concept of oneness. The way I think of it is if I push my hand forward through the air I push the air and it builds up pressure in front and rolls around the sides. As you said about the chair it is the universe. I can pick up the chair and move it to another place but I have not been able to take it out of the universe, separate it from the universe. Your analogy of the string is a little more difficult to work with although it does bring to mind the dual slit experiment. If you are not familiar with that one definitely look it up. It states that an electron and be a wave or a particle or both, it gets really strange. That is on the quantum level however and I will stay with the macro. Going back to the moving hand, there is a place where my and ends and the air begins, whereas when I walk across the room the air is left behind and my hand stays with me so we could say that the hand and the air are different. If I breath the air becomes part of me however and if we are what we eat we are definitely what we breath. A thought though is when an athlete says that the racket, or whatever, feels like part of them. Is it? I don't say either is right or wrong, just thoughts. While I find nothing inherently wrong with your collapsing universe I feel it is created more by your need for analogical connection, I'm one to talk, and you need to unlock your mind more see something outside of the ordinary, so to speak.

I like your thinking very much and hope we can keep this thread going. If you bring up politics however.... 

RV


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## oldfart (Jan 15, 2014)

editec said:


> *Forgive me if I am characterizing this theory incorrectly.
> 
> But what it seems to be saying is that the univsere isn't expanding, but instead, everything in it is shrinking.*
> 
> ...



The math is the same either way as the mapping is 1:1 and reversible.


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## Capstone (Jan 16, 2014)

SmedlyButler said:


> '....if one explanation will do why do you need two? Why is your model different from epicycles (which went to ridiculous levels of complexity to keep the Earth at the centre of things). This is not an appeal to a philosophical principle (parsimony) but sound practise. Physics is not about reality or truth or beauty or anything like that. It is about models that predict things. It is about ways to describe what we can see. If you propose a physical model for something then you make it as simple as possible but no simpler. Not because it makes some fuzzy happy point about complexity in the universe but because that is how you make a useful model. So if your model makes no new predictions, replicates the current model perfectly but requires a whole load of ad hoc synchronisations and stuff then it is a bad model. Not because it violates a world view but because it is harder to use and gives no benefit.
> 
> So a direct questions: Why is your model better? What does it simplify? What does it predict or explain that the current models don't?"
> 
> *XXXXXXX*



*What Goes on at other message boards should stay there. XXXXXXX No Linking to other Message Boards. No discussing them.*
You see, what I'm doing here at the USMB is called trying to get "a better handle on my thoughts". 



SmedlyButler said:


> "Thank you, for your 30 minutes. If I could refund them, I would."- Now it's 45 minutes, please don't increase your debt any further.



You're free to stop wasting your time at any point of your choosing.

That goes for you too, Ukotare.


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## Capstone (Jan 16, 2014)

oldfart said:


> The math is the same either way as the mapping is 1:1 and reversible.



I think that's probably right, but I'm not qualified to understand (much less lay out) the formulas either way. 

Math stopped making sense to me way back when basic algebra first came into the picture.


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## Unkotare (Jan 16, 2014)

Capstone said:


> You're free to stop wasting your time at any point of your choosing.
> 
> That goes for you too, Ukotare.





How about YOU are free to stop wasting EVERYONE'S time?


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## Capstone (Jan 16, 2014)

RandomVariable said:


> ...The way I think of it is if I push my hand forward through the air I push the air and it builds up pressure in front and rolls around the sides. As you said about the chair it is the universe. I can pick up the chair and move it to another place but I have not been able to take it out of the universe, separate it from the universe. [...]



In a 'chain reaction' sort of way, the same could be said of bodies _apparently_ separated by great distances in space, at least within their respective groupings (solar systems, galaxies, clusters, and super clusters). I believe this physical connection only seems to break down between redshifting groups due to a widely-perpetuated falsehood regarding the nature of 'space'.



RandomVariable said:


> ...Your analogy of the string is a little more difficult to work with although it does bring to mind the dual slit experiment. If you are not familiar with that one definitely look it up. It states that an electron and be a wave or a particle or both, it gets really strange. [...]



Part of the reason I now view so-called 'particles' as "peaks" (read: very specific areas _on the tips_ of quantum waves) is because doing so comports very nicely to the implications of the double slit experiment.

The folded string analogy in the OP _is_ pretty limited, so it might be helpful to imagine a version with more dimensions. Ever heard of _Koch's Snowflake_? Think of the string as something with infinite elasticity and closed in the shape of a triangle. In theory, an infinite number of partial iterations of the original shape could arise on either its outer or inner perimeter ...without breaking the closed _and singular_ system. The interaction between this *_multi-aspectual_ (*to coin a phrase) object and  the 'space' on both sides of its perimeter may be more analogous to the bigger picture.



RandomVariable said:


> ...Going back to the moving hand, there is a place where my and ends and the air begins, whereas when I walk across the room the air is left behind and my hand stays with me so we could say that the hand and the air are different. If I breath the air becomes part of me however and if we are what we eat we are definitely what we breath. [...]



Granted, there are many _differences_ available to the *senses (*which are themselves _distinct_ modes of collecting empirical data for the brain to assimilate); in my opinion, the common mistake is to ascribe objective autonomy to the 'things' we perceive and to ideas of which we conceive ...that are neither objective ...nor autonomous. 

When observing the phenomenal world all around us, the question shouldn't be, "What do we see?"; it should instead be, "_What are we missing_ about the true nature of the reality we perceive?", and this is so because of the known limitations of human perception and understanding.



RandomVariable said:


> ...A thought though is when an athlete says that the racket, or whatever, feels like part of them. Is it? I don't say either is right or wrong, just thoughts.



You may be knocking on the door to _solipsism_ here (which is something I _don't_ believe, at least not as its commonly portrayed); but I think I'd characterize the athlete, his or her 'feelings', and the racket ...as 'aspects' of a *_larger whole_ (*AKA the universe).



RandomVariable said:


> ...While I find nothing inherently wrong with your collapsing universe I feel it is created more by your need for analogical connection, I'm one to talk, and you need to unlock your mind more see something outside of the ordinary, so to speak. [...]



Well, since I've already admitted to viewing my chief philosophical modus operandi as "a crutch", I suppose there's no further harm in admitting that my penchant to analogize (when I should be making predictions and scribbling a bunch of mathematical symbols of which I'm presently clueless) might be as much a hindrance to my personal development as it is a means of compensation.

Having said that, I'm guessing not too many would agree that some of the views stated in this thread need to be any more 'out of the ordinary' than they already are. -- *lol*


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## midcan5 (Jan 16, 2014)

Here is a site and this year's question, you may find interesting.

Edge.org

"When thinking changes your mind, that's philosophy.
When God changes your mind, that's faith.
When facts change your mind, that's science."  from edge.org


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## Capstone (Jan 16, 2014)

midcan5 said:


> Here is a site and this year's question, you may find interesting.



Andrei Linde's submission looks pretty relevant, and I love the soccer ball analogy, although I don't really see how the adjacent black and white hexagons on the surface of the whole are analogous to the notion of multiple "universes" (different sets of physical laws notwithstanding). In my view, the soccer ball would represent the universe and the hexagons would be among its aspects; and I think this objection goes a little deeper than one of definitions or semantics.  



> [...]In the example given above, we were talking about black and white. But in physics, the number of different states of matter (the number of "colors") can be exponentially large. The best candidate for the "theory of everything" that is presently known to us is string theory. It can be successfully formulated in space-time with 10 dimensions (9 dimensions of space, and 1 time). But we live in the universe with 3 dimensions of space. Where are other 6? The answer is that they are compactified, squeezed into something so small that we cannot move in these directions, which is why we perceive the world as if it were 3-dimensional.
> 
> From the early days of string theory, physicists knew that there are exponentially many different ways to compactly the extra 6 dimensions, but we did not know what can prevent the compactified dimensions from blowing up. This problem was solved about 10 years ago, and the solution validated the earlier expectations of the exponentially large number of possibilities. Some estimates of the number of different options are as large as 10[to the]500[th]. *And each of these options describes a part of the universe with a different vacuum energy and different types of matter.*
> 
> In the context of the inflationary theory, this means that *our world may consist of incredibly large number of exponentially large "universes" with 10[to the]500[th] different types of matter inside them.* [emphasis Capstone's]



So, he goes from String Theory's multiple "part" of a singular "universe" (albeit parts with widely divergent physical attributes) to an inflationary model's "incredibly large number of exponentially large 'universes'" (yes, I noticed his use of quotation marks there), without explicit clarification as to what constitutes a "universe" in either paradigm.  

Then he seems to switch indiscriminately back and forth between "parts" and "universes", as if nobody should even take notice:



> [...] A pessimist would argue that since we do not see other parts of the universe, we cannot prove that this picture is correct. An optimist, on the other hand, may counter that we can never disprove this picture either, because its main assumption is that other "universes" are far away from us. And since we know that the best of the theories developed so far allow about 10[to the]500[th] different universes, anybody who argues that the universe must have same properties everywhere would have to prove that only one of these 10[to the]500[th] universes is possible.



It isn't clear from his writing how the uniformity (or lack thereof) of the universe's physical properties has any bearing whatsoever on the question as to how many "universes" could possibly exist.



> [...]The relation between our properties and the properties of the world is called the anthropic principle. But if the universe were given to us in one copy, this relation would not help. We would need to speculate about the divine cause making the universe custom built for humans. Meanwhile, in the multiverse consisting of many different parts with different properties, the correlation between our properties and the properties of the part of the world where we can live makes perfect sense.



That any number of areas in which different rules hold sway may indeed exist in the universe, and as a result, physically different bodies may be confined to their respective _hexagons_, isn't an argument (anthropic or otherwise) in favor of multiple universes. It just isn't. 

Thanks, for the link.


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## SmedlyButler (Jan 16, 2014)

You just won't give it up will you. You've tried to run this scam on multiple sites in the past and never been accorded any more than scorn for your empty nonsense. You don't have a "theory". You have strung together words used by real theoreticians in a completely deceitful attempt to garner intellectual credibility. It's just too transparent. Again, remember this? "It is good to see that you disagree with Maxwell, Lorentz, Einstein, Riemann, Ehrenfest, Weyl, Minkowski, Penrose, Schrödinger and Hawking.Since their work is backed up by rigorous mathematics and your opinion is not, a reasonable person will go with them."  Now,  confronted with the vast literature and profound mathematical implications of string theory your response is "It just isn't" an argument for any model. "It just isn't"- that's some well thought criticism.  You are either a perfect example of one obsessed with delusions of grandeur or a grandiose charlatan. Or both.

Would you like me to post links for the sites you have tried this posing on in 2009-2010 for example or do you keep the URLS as souvenirs?


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## Capstone (Jan 16, 2014)

SmedlyButler said:


> [...]Again, remember this? "It is good to see that you disagree with Maxwell, Lorentz, Einstein, Riemann, Ehrenfest, Weyl, Minkowski, Penrose, Schrödinger and Hawking.Since their work is backed up by rigorous mathematics and your opinion is not, a reasonable person will go with them."



Yes, and I'm absolutely fine with other people dismissing my opinions on the basis of failings I've openly admitted time and again, but such dismissals aren't going to stop me from theorizing and opining to the best of my abilities.



SmedlyButler said:


> Now,  confronted with the vast literature and profound mathematical implications of string theory your response is "It just isn't" an argument for any model. "It just isn't"- that's some well thought criticism.



My criticism was that String Theory's affirmation of the possibility of multiple physically-divergent parts of the universe, coupled with Linde's musings on the anthropic principle, isn't an argument in favor of multiple universes (not "for any model").

At least get it right. 



SmedlyButler said:


> Would you like me to post links for the sites you have tried this posing on in 2009-2010 for example or do you keep the URLS as souvenirs?



I haven't denied spreading around and testing my ideas on other message boards over the years. That's actually how I've learned many things over the past decade or so. This isn't embarrassing to me at all, so suit yourself. It's your time you'd be wasting, not mine.


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## SmedlyButler (Jan 16, 2014)

Obviously you haven't learned anything. You have refined your already prodigious misdirection and prevarication skills a little. that's some progress, becoming a more artful phony. Make no mistake, that's what you are. A two bit phony.


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## SmedlyButler (Jan 16, 2014)

What happens in Vegas....
"What Goes on at other message boards should stay there. XXXXXXX No Linking to other Message Boards. No discussing them."
Your original post was a copy from various other sites. That fact is fair game. You're obviously a psycho. I don't want to push you over the edge to do something dangerous in that dark world you inhabit. I'll leave you alone for a while.


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## Capstone (Jan 17, 2014)

SmedlyButler said:


> Your original post was a copy from various other sites. That fact is fair game. ...



Moderators:

Since the statement above was allowed to stand, I should also be allowed to answer it. 

The OP in this thread IS for the most part a copy of a template of my own ideas, which I originally authored and have posted on an eclectic mix of discussion boards over the past several years. This I've done in order to subject those ideas to a mixture of minds from diverse backgrounds and with various levels of interest and/or expertise in different areas. There's also a distinct possibility that my template has been used without my knowledge or consent by others, as well as one instance in which it was used with my permission by an individual who credited me in the original post of that thread. 

As for the allegation that I'm a 2-bit phony, I can only ponder as to how I've warranted that charge. A phony what? Here and elsewhere, I've openly admitted to my personal deficiencies in formal education and methodology. I've also admitted to the weaknesses of my theories and have welcomed others to dismiss them on those grounds, whenever they've seemed so inclined. I guess that makes me a _phony_ 10th grade dropout with a penchant for admitting personal and ideological facts that are in no way beneficial to the portrayal of myself as someone of any importance or scientific credibility! 

What the hell ever...


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## Unkotare (Jan 17, 2014)

Capstone said:


> SmedlyButler said:
> 
> 
> > Your original post was a copy from various other sites. That fact is fair game. ...
> ...





[ame=http://www.youtube.com/watch?v=SLk4Ia0otko]Family Guy - OMG WHO THE HELL CARES! - YouTube[/ame]


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## Capstone (Jan 18, 2014)

Strictly for the benefit of those who care (Without presuming that any such people exist, Unkotare!),  having experienced it 'myself', I understand the natural compunction at the thought of universal physical oneness. There's a _loneliness_ at the heart of monism that has to be wrestled with in order to discover its underlying beauty. It may be the case that all of the universe's conscious perspectives (or 'minds') have been predisposed to buck against any notion that might seem to threaten the physical autonomy of the 'bodies' from which each and every one of us have arisen. Yes, we (aspects) have individual 'minds' that tend to be very protective of the physical means responsible for our very existences (plural) and consequent abilities to interact with agents of intelligence _other than oneself_. Nobody wants to be alone. This seems as good a candidate as any for maybe the primary reason monism has so few adherents (in the western world especially) and why it's generally snubbed in contemporary metaphysics, despite the coherence, wide-sweeping methodological applicability, and logical consistency ...in which lies its beauty.

In the words of Jonathan Schaffer (from his 2007 entry in the _Stanford Encyclopedia of Philosophy_): "_the entire monistic tradition is often dismissed as being somewhere between obscure and ridiculous. But there are serious arguments for monism._"

To those who wonder what justification could possibly exist for adopting a monistic worldview in the first place, I suggest that it might well offer the _only_ ontology that can survive a thorough going over from _Occam's Razor_. From on top of that foundational principle, the logic of oneness can flow unabated across the entire philosophical spectrum. No other philosophical school of thought offers the right to claim the principle of parsimony as its primary justification.

Beyond that, the ideas that arise from a monistic methodology tend to be naturally simpler than those that come from other paradigms. One example of this can be seen by the fact that my theory of the universe eliminates the need to posit a _mysterious_ force in order to explain the apparent expansion of space. Thus, the principle of parsimony not only justifies one's initial adoption of this worldview; it continuously provides reason to maintain it.

True enough, I've been scorned for "carrying this baggage" around with me over the years, but I've yet to be offered a sound enough reason to drop it. Appeals to authority/popularity, name-calling, and even thinly-veiled threats over the past several years have only strengthened my grips on the handles. 

Beauty is a subjective valuation, People. An honest look in the mirror might just reveal that _truth_ doesn't always correspond to even your own current notions of beauty.

Thanks, for reading...


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## Capstone (Jan 20, 2014)

From my approach in the OP (with 'space' as something wholly distinct from the universe's physical properties and modes of existence - including 'time'), I see 'motion' as a function of time, with distance traveled along a given axis as a function of relative temporal regularity. Yes, I realize the terms "relative" and "regularity" seem potentially contradictory, but only until one considers that what's "relative" here are any number of unique _experiences_ of time.

*An analogy*

Imagine the dial (face) of a 3-hand analog clock, giving special attention to its second hand. Watch it tick...tick...tick...for just a moment with your minds' eyes. Notice that the distances incrementally traveled by the second hand grow exponentially larger from the central axis point (where all three hands are attached to a common rotating substrate) outward along the length to the very tip of the second hand. In a very real sense, then, microbes sitting on the second hand closer to the turning point would be experiencing the passage of time at an _ever-so-slightly_ accelerated rate (and yes, 'aging' faster) than their cohorts sitting further out towards the tip. The same increment of time would have elapsed for all of the microbes, but their experiences of that increment would be unique to each one of them on the basis of

position (along a common dimensional axis),
distance traveled (above a lower dimensional substrate which I'll call "available area")
speed (which is determined by considering the various distances of area covered in relation to a common increment of time).


Accordingly, this available area would serve as a lower-dimensional backdrop for the propagation of material formations, but not by way of disconnection from the simple fabric from which all of the aspects of the universe are formed. The only 'thing' disconnected from the universe is space. The interaction between the universe and space is thereby limited to the 'outermost skin' of all material forms. This is not to say that regions of space can't be '_partially_ isolated' by material forms and processes, (as I believe occurs in the eyes of certain vortex formations -- the proverbial doughnut holes of the cosmos), but the isolation could never be complete.

I believe that time and space are ontological problems, but even this is open to debate, in my mind. I haven't yet vetted these aspects of my ontology, so any help (by way of suggestion, refutation, or otherwise) would be much appreciated.


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## Capstone (Jan 22, 2014)

In search of a model of mathematics to facilitate my inability to comprehend much beyond remedial arithmetic (here again, this isn't laziness, but a means to compensate for something lacking in the way that my mind works), I recently stumbled upon the work of Marko Rodin (click on the icon in my signature line). His simplification by way of reducing multiple-digit numbers to their respective single-digit bases (1-9) via numerological addition, and then assigning all numbers physical positions (charting them, at least in part, on the basis of mirror symmetry), has flipped-on a light switch in my mind.

Please, bear in mind: my interpretation of this method could well be wrong in several respects.

To begin with, as I understand him, Rodin establishes the means for determining what he calls "archetypal values" (for the future purposes of this discussion, 'AV') as follows:


8x1=8 (in this case, the sum is equivalent to the AV, because it's already a single-digit number)
8x2=16 (and since 1+6=7, the AV of 16 is 7)
8x6=48 (4+8=12, 1+2=3, so the AV of 48 is ultimately 3)

When applied across the multiplication tables, this method reveals a mirror symmetry between the AV's of the multiples of 1 and 8, 2 and 7, 3 and 6, and 4 and 5. 

Numerologically-reduced Multiples of 1 and 8

1x1=(1) *1* ------------- 1x8=*8*
2x1=(2) *2* ------------- 2x8=(16) *7*
3x1=(3) *3* ------------- 3x8=(24) *6*
4x1=(4) *4* ------------- 4x8=(32) *5*
5x1=(5) *5* ------------- 5x8=(40) *4*
6x1=(6) *6* ------------- 6x8=(48, 12) *3*
7x1=(7) *7* ------------- 7x8=(56, 11) *2*
8x1=(8) *8* ------------- 8x8=(64, 10) *1*

9x1=(9) 9 ------------- 9x8=(72) 9 

The number 9 is set apart by virtue of 'self-similarity'. That is, 9 multiplied by any single-digit number (with value) will invariably render an AV of 9. This phenomenon serves as the basis for Rodin's unique positioning of 9 on his geometrical chart.

Beyond that, notice that the AV's of the multiples of 1 (1,2,3,4,5,6,7,8) are mirror opposites in relation to those of 8 (8,7,6,5,4,3,2,1). 

As already mentioned, the same holds true for sets 2 and 7, 3 and 6, and 4 and 5, although it should be noted that the mirror symmetry between 3 and 6 has the additional feature of being expressed in repeating sequences of three (3,6,9,3,6,9,3,6,9 / 6,3,9,6,3,9,6,3,9).

So, here's his chart:





Notice the placement of the mirror opposites (directly across from each other), as well as 9's unique position at the top, so that if the chart were folded in half, the 'mirror reflections' would be facing each other and the single 'self-similar' number (the _one_ with no reflection) would be split by the crease.

Using multiplication of doubles starting at 1, Rodin further ascribes a mode of _directional travel_ in order to formulate aspects of the geometry within the circle (moving from 1 to 2, 2 to 4, 4 to 8, ...8 to 7, 7 to 5, and 5 to 1). How did he move from 8 to 7 by doubling 8? Well, 8x2=16, and 1+6=*7* (which is the single-digit AV, remember). Likewise, 7 doubled is 14 (1+4=5), and 5 doubled is 10 (1+0=1), closing the multi-directional loop right back where it started ...at 1. Absolutely beautiful.

Rodin then applies three symmetrical sets to 3-dimensionality, and this is where my comprehension begins to falter. I can fathom directional turns from height to width to depth/depth to width to height (and multiple variations of the 3), but as I try to visualize this, the demarcations between the dimensions themselves get blurred. Still, from what I've been able to gather thus far, it seems a very attractive approach for potential mathematical expressions of a monistic universe.

The mathematical justification for the dotted triangle (and the 3,6,9 correlation in general) is less clear to me, as moving in triplets wouldn't account for 6 (1 tripled is 3, 3 tripled is 9, 9 tripled is 9 (27, 2+7=9); so while 3 tripled could be viewed as the original formula for self-similarity, as to how it relates to the closed system of doubles ...is, at least for the moment, out of my reach. 

I suspect the deepest reason Marko Rodin's _Quantum Numerology_ appeals to me may be hidden in the relationships between twins, triplets, quadruplet's, ...and so on.

As always, any correction or instruction would be greatly appreciated.


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## Capstone (Jan 24, 2014)

In trying to incorporate Rodin's dotted triangle (and 3,6,9) into a multifaceted but fluid infinity loop (without disconnecting at any of the turning points), I could reconcile going from 1 to 3 and 3 to 9 (in triplets), but in order to move mathematically from 9 to 6 ...the impetus would have to be changed from multiplication of triples to either addition or division of 9's. 9+6=6 (15), just as 9 divided by 6=6 (1.5). Since a self-similar form of addition offered the only path I could see from 9 to 6 to 8 to 7 to 5 to 1, thereby retaining at least a semblance of mathematical/geometrical integrity in the process, addition seemed the way to go.

The integrated movement flows as follows:

 1,2,4,8,7,5,[1],3,[9],6,8,7,5,[1] ...repeating into infinity.

The bracketed numbers mark the points at which the impetuses change from multiplication of doubles to triples ...and then, from the point at which self-similarity has been attained via the formula 3x3=9, on to the less-restricted simple addition of 9 to 6,8,7,5, and 1 respectively.  

For the moment, let's refer to the turning points as 'axises'.

The math is as follows:

X-axis

1x2=2
2x2=4
4x2=8
8x2=7 (1+6)
7x2=5 (1+4) 
5x2=1 (1+0) 

Y-axis 

1x3=3
3x3=9 

Z-axis

 9+6=6 (1+5)
 9+8=8 (1+7)
9+7=7 (1+6)
 9+5=5 (1+4)
 9+1=1 (1+0)

It should be said: 9 is only obligated to follow and overlap the underlying geometry (6,8,7,5,1) for the sake of geometrical continuity, since 9 added to _any_ single-digit number (from any_where_ on the chart) would render an AV equivalent to that number. Therefore, Math alone couldn't justify _its decision_ to stay true to the loop. 

Here it is on the chart:




Note: the double lines denote overlapping movement _in opposite directions_, as 9's movement from 8 to 7 to 5 to 1 would be otherwise invisible.

Completely apart from the above, it seems that moving in fives renders a similar geometrical infinity loop as that created by moving in doubles. The differences would be in its approach to the crossing point (from above instead of below) and in its direction of travel. 

1x5=5
5x5=7 (2+5)
7x5=8 (3+5)
 8x5=4 (4+0)
4x5=2 (2+0)
2x5=1 (1+0)

1x2=2
2x2=4
4x2=8
8x2=7 (1+6)
7x2=5 (1+4)
5x2=1 (1+0)

So drawing two distinct lines from 1 to 5 to 7 to 8 to 4 to 2 to 1 ...and from 1 to 2 to 4 to 8 to 7 to 5 to 1 ...expresses a mirror symmetry between geometrically identical _twins_ (so to speak).

Similarly moving in sevens and fours (1 to 7 to 4 to 1 */* 1 to 4 to 7 to 1) -- also reveals a reverse directional symmetry with triangles.

Charted in order:




In all cases, the double lines denote overlapping/opposite directions of travel and thereby illustrate the mirror symmetry of the geometry.

This _geometrical_ symmetry between multiples of 2 and 5 & 7 and 4 seems to stand above and beyond the purely mathematical symmetry between multiples of 1 and 8, 2 and 7, 3 and 6, and 4 and 5.


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## Delta4Embassy (Jan 25, 2014)

Wry Catcher said:


> Not to be glib, but how far is up?  If conventional theory is correct, and the universe is expanding, it boggles the mind that there is no end, or conversely, that the expansion will bend back upon itself _from every point on the non Euclidian compass_.



Think this is the 'if the universe is expanding, what's it expanding into?' Looking it up wondering about it myself, I found a good of kinda unsatisfactory answer (since the question was much more fun heh

Curious About Astronomy: What is the universe expanding into?

"The long explanation is below. However, if you just want a short answer, I'll say this: if the universe is infinitely big, then the answer is simply that it isn't expanding into anything; instead, what is happening is that every region of the universe, every distance between every pair of galaxies, is being "stretched", but the overall size of the universe was infinitely big to begin with and continues to remain infinitely big as time goes on, so the universe's size doesn't change, and therefore it doesn't expand into anything. If, on the other hand, the universe has a finite size, then it may be legitimate to claim that there is something "outside of the universe" that the universe is expanding into. However, because we are, by definition, stuck within the space that makes up our universe and have no way to observe anything outside of it, this ceases to be a question that can be answered scientifically. So the answer in that case is that we really don't know what, if anything, the universe is expanding into."

...That's the short answer.  Long one at link.


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## Capstone (Jan 26, 2014)

*Correction:*



Capstone said:


> Note: the double lines denote overlapping movement _in opposite directions_, as 9's movement from 8 to 7 to 5 to 1 would be otherwise invisible.



In this case, the overlapping movement of 9 would be in _the same direction_ as the underlying geometry.

If the goal were to produce overlapping flows in the opposite directions, the impetus for X-axis would have to be adjusted from multiplication by 2 to multiplication by 5 (the other axises would remain unchanged). 

Starting at 1, the resulting infinity loop would move as follows:

1, 5, 7, 8, 4, 2, [1], 3, [9], 6, 8, 7, 5, [1]

The illustration on the chart could apply either way, so long as the directional paths and the double lines were properly interpreted.

It has also occurred to me that these distinct infinity loops could be synthesized to propagate rotating layers of overlapping motion, with 9 moving in the same direction as the underlying geometry on one layer ...and then running in the opposite direction on the next layer.

1, 2, 4, 8, 7, 5, [1], 3, [9], 6, 8, 7, 5, [1], 5, 7, 8, 4, 2, [1], 3, [9], 6, 8, 7, 5, [1] ...oscillating back and forth into infinity.

Using this multi-layered formula, one could remain true to the geometry and mathematics of the illustration, and sketch it out into eternity ...without ever lifting the tip of the pencil from the paper.


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## Capstone (Jan 26, 2014)

Check this out: incorporating 1-9 into an infinity loop _with a single mathematical impetus_ can result in a nine-pointed star as follows:

1+4=5
5+4=9
9+4=4 (1+3)
4+4=8
8+4=3 (1+2=3)
3+4=7
7+4=2 (1+1)
2+4=6 
6+4=1 (1+0)

The movement: 1, 5, 9, 4, 8, 3, 7, 2, 6, 1







Sorry about my sloppiness, but I think careful measurement would result in an inverted nonagon in the center. 

Rodin's method is very cool.


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## Capstone (Jan 28, 2014)

It turns out that careful measurement not only results in a central inverted nonagon, it also reveals a total of 3 nine-pointed stars, which I've illustrated in black and white in the following image.





Look deeper to see 3 overlapping triangles (shown in grey, black, and blue as follows):





And deeper still for a dead-on corner-view of a four-sided (!) pyramid (in grey):





I realize, at the moment, all this math and geometry stuff might seem irrelevant to the topic of universal oneness, but I intend to tie it all together in this thread ...just as soon as I've sorted out the connections in my own mind.


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## Unkotare (Jan 28, 2014)

Classic example of a dimwitted buffoon taking himself too seriously.


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## Capstone (Jan 29, 2014)

I've invested more than my fair share in ridicule over the years (especially as a kid), so to see it returning to me _with interest_ as an adult ...feels as though some of the debt I've incurred in this life is being paid off a little bit at a time. That's a good feeling. Karma's only a bitch to those who fail to see her beauty.

That's not necessarily to say I'm not a dimwitted buffoon who takes himself too seriously, though. 
	

	
	
		
		

		
		
	


	




Anyway, getting back to Rodin's _Quantum Numerology_, while the nonagram in my previous post seems to illustrate width (via the 3 nine-pointed stars that appear to emanate from the center outward), depth (with the stacked-up triangles), and height (with the inferred 4-sided pyramid), what it doesn't represent is the overlapping cross-directional travel of the previous formula. 

The challenge then, is to create an opposing directional flow that remains true to the underlying geometry ...and, at least to some degree, to the movement by fours. 

For this, I think some restraints on the numerological reduction thing (without completely suspending it) may be in order.

As always, starting the next axis where the previous one left off (at 1), but _parenthetically restricting_ the numerological reduction here on out, the addition of 1 to all of the numbers 4 times around the perimeter would come to a close at 37 (1+1=2, 2+1=3, 3+1=4, ...and so on to 36+1=37). Notice that 37 would correspond to 1's position on the chart, which makes perfect sense (since 3+7=10, and 1+0=1). The same would be true for all of the non-reduced numbers that had preceded it (36 would correspond to 9, 35 to 8, 34 to 7, all the way back to 1).

From 37 (and position 1), still refraining from numerological reduction _outside of the parentheses_, we could start the next axis by moving in fours via subtraction and travel backwards along the very path used during the initial addition phase.

37-4=33 (3+3=position 6)
33-4=29 (2+9=11, 1+1=position 2)
29-4=25 (2+5=position7)
25-4=21 (2+1=position 3)
21-4=17 (1+7=position 8)
17-4=13 (1+3=position 4)
13-4=9 (position 9)
9-4=5 (position 5)
5-4=1 (position 1)

So, the subtraction axis would move: [1], 6, 2, 7, 3, 8, 4, 9, 5, 1

The synthesized movement would then flow:

1, 5, 9, 4, 8, 3, 7, 2, 6, [1], 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, [1], 6, 2, 7, 3, 8, 4, 9, 5, 1.

Addition of 4, addition of 1 by 4x around the perimeter, and subtraction of 4 ...would be the respective impetuses. 

Notice the mirror symmetry between the first and third axises, despite the parenthetical restriction placed on the third.

This movement would result in 4 overlapping rotations in the same direction around the perimeter, as well as two perfectly overlapping nonagrams traveling in opposite directions.


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## Capstone (Jan 29, 2014)

...oh, and there would no longer be any need to _infer_ the other two sides of the pyramid.


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## Capstone (Feb 1, 2014)

The 4 laps around the perimeter and the restriction of numerological reduction to chart positions only could be circumvented by simply switching from addition of 4 to addition of 5 at the outset of the second axis. 

Addition of 5

1+5=6
6+5=2 (11, 1+1)
2+5=7
7+5=3 (12, 1+2)
3+5=8 
8+5=4 (13, 1+3)
4+5=9
9+5=5 (14, 1+4)
5+5=1 (10, 1+0)

Addition of 4 (notice the symmetry):

1+4=5
5+4=9
9+4=4 (13, 1+3)
4+4=8
8+4=3 (12, 1+2)
3+4=7
7+4=2 (11, 1+1)
2+4=6
6+4=1 (10, 1+0)

Since the simplest 'all-inclusive' (1-9, multi-dimensional, cross-directional, and perfectly symmetrical) formula should be preferred (per the principle of parsimony), the following movement seems the best one yet for an infinity-loop.

1, 5, 9, 4, 8, 3, 7, 2, 6, [1], 6, 2, 7, 3, 8, 4, 9, 5, [1]...back and forth forever.

The bracketed 1's mark the turning points from addition of 4 to addition of 5 (and back).

In addition to the above, accounting for the prospect of moving in increments smaller than whole numbers (mainly in order to promote more symmetry and geometrical inclusiveness), I've marked out the halfway points between all of the numbers on the chart as follows:





Rotating around the outer perimeter clockwise in increments of .5, the movement by addition of 4 and 5 _within the circle_ would result in an inverted nonagram stacked-up on top of the initial one.

This can be seen by moving from the close of the second axis at 1 to 1.5 ...and then running gamut inside the circle in 4's and 5's.

1.5+4=5.5
5.5+4=9.5
9.5+4=4.5 (13.5, 1+3.5)
4.5+4=8.5
8.5+4=3.5 (12.5, 1+2.5)
3.5+4=7.5
7.5+4=2.5 (11.5, 1+1.5)
2.5+4=6.5 
6.5+4=1.5 (10.5, 1+0.5)

1.5+5=6.5
6.5+5=2.5 (11.5, 1+1.5)
2.5+5=7.5
7.5+5=3.5 (12.5, 1+2.5)
3.5+5=8.5
8.5+5=4.5 (13.5, 1+3.5)
4.5+5=9.5
9.5+5=5.5 (14.5, 1+4.5)
5.5+5=1.5 (10.5, 1+0.5)

Continuing along the outer perimeter in increments of .5, we'd then move from 1.5 to 2 and run the gamut again...

2+4=6
6+4=1 (10, 1+0)
1+4=5
5+4=9
9+4=4 (13, 1+3)
4+4=8
8+4=3 (12, 1+3)
3+4=7
7+4=2 (11, 1+1)

2+5=7
7+5=3 (12, 1+2)
3+5=8
8+5=4 (13, 1+3)
4+5=9
9+5=5 (14, 1+4)
5+5=1 (10, 1+0)
1+5=6
6+5=2 (11, 1+1)

...then on to 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, all the way back around to 1.

The resulting multi-layered geometry:





Notice how many more formations now exist within the circle.









Even this:





...among others.

Considering that such formations couldn't otherwise be formed within a closed system of 9 whole numbers, an argument could be made that moving in halves would be _necessary_ in order to propagate those formations in the _simplest_ way possible.


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