What If...

[RandomVariable]

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

 

[oldfart]

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.

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

 

[Capstone]

'....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".

"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.

 

[Capstone]

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.

 

[Unkotare]

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?

 

[Capstone]

...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'.

...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.

...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.

...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).

...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*

 

[midcan5]

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

 

[Capstone]

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.

 

[SmedlyButler]

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?

 

[Capstone]

[...]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.

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.

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.

 

[SmedlyButler]

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.

 

[SmedlyButler]

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.

 

[Capstone]

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...

 

[Unkotare]

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...

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

 

[Capstone]

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...

 

[Capstone]

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

1. position (along a common dimensional axis),
2. distance traveled (above a lower dimensional substrate which I'll call "available area")
3. 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.

 

[Capstone]

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.

 

[Capstone]

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 anywhere 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.

 

[Delta4Embassy]

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.

 

[Capstone]

Correction:

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.