Flatlander 3D: Hypersphere to Flat Space

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There are previous posts regarding the Flatlander illustration: How a 2D flat person would perceive a 3d object passing through a 2D flatlander plain. This post applies the same principle to the interpretation of 3D Flatlanders viewing a 4D universe. The Hypersphere and its 3D space (the surface) are described in a previous post.

A diagram would be best to explain our (my asserted) reality but that will need to wait til I have time. Briefly,
  • Take the circumference of a hemisphere:-
  • The radius (drawn vertically) represents the time since BB.
  • The circumference is hyperspherical 3d space.
  • The distance from the top to the base ( from time now to t=0) along the circumference is the space through which light (minus a bit) has travelled since t=0.
  • Mark dots to represent events on the circumference.
  • Project the events to the base (the horizontal part of the hemisphere)

The result is a flatlander view of 4D hyperspherical space. Notice, that the further you look from the origin (on the 3D horizontal base) the events crowd together.

If the vertical is tilted (rotated) slightly, the view will extend further around the hypersphere and increase the space between previously recorded events as projected to the horizontal base. This may provide evidence of this projection that we are 3D Flatlanders in a Hyperspherical Universe. Hints already exist from the discovery of 'anomalous' galaxies.

Some clever Astronomers may be able to calculate our relative speed in one direction compared to another. If they can discern a difference distant events should reveal character differences depending on their 'angle of separation'.
 
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To add a more friendly description -

We can not picture a 4D spatial environment but we can still understand the situation by use of mathematics or by drawing using one dimension less. For example, a cross-section of a hypersphere is an everyday sphere. A circle is a cross-section of a 3D sphere.

We can use a circle to illustrate a hypersphere (limited to circumference but still useful). As the 3D space of a hypersphere is its surface, any distance travelled in a hypersphere 3D space is along the circumference of our drawn circle. As our perception of 4D space is limited to its effect on our 3D perception we view events occurring in our hypersphere reality as a flat 3D space.

We can illustrate this 3D interpretation by projecting from the circle (hyperspherical 4D space) to a baseline representing the diameter of the hypersphere. This provides us with a 3D view of what is 'going on'. It is worth noting (if you have bothered to draw it yourself) that at what appears to be t=0 (an origin of the BB) is in fact the event horizon of our observable universe

As we look to the event horizon the curvature of the hypersphere appears to us as if distances were shorter between events. Similarly nearby, where the hypersphere curvature appears to us as flatter. the distance between events is interpreted (on our flat baseline) as larger. This might be interpreted by us as the universe expanding faster (when this is not the case).

In addition, the belief that when 'looking out into space' we are looking back in time to the Big Bang is an error - we are looking back to the event horizon of our observable universe. The BB occurred at the origin of the hypersphere which does not exist (even back in time) in our 3D space. However, because we think the universe is flat 3D we assume that the BB is expanded to 'everywhere' but in FLAT space and then it follows that if we could see t=0 it would show the original state (or nearly). This is wrong.

The explanation is that time expands the hypersphere. The increase in radius (of the hypersphere) is felt by us as time NB you can illustrate this yourself by calculating the Hubble constant which corresponds closely to the current value.

This hypothesis even if incorrect does illustrate the importance of considering the actual SHAPE of our universe before we make assumptions about reality and 'how things work'. Also, it shows that mathematics alone needs an 'everyday' interpretation to enable easy progress. I may well have it all wrong but it shows how 'Flatlander thinking' can clear away fog and once again that the world may not be as simple as we might hope.

I hope I have not appeared too arrogant but very many years ago on similar sites to this I was 'trolled' relentlessly and I gave in trying to get the idea across. I am so grateful for the tolerance here which lets me get most of it "off my chest". Thank you.
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
I suppose we really need to differentiate between flat and 2D (excluding time). The surface of a sphere is 2D, but not flat.

There is also the issue here of semantics, which I have raised elsewhere.


The flatlander's universe (observable universe) is only a very small part of a 3D's universe (observable universe).

I consider it not irrelevant to suggest that a 4D's (4D person's) universe (observable universe) would view ours correspondingly.

Cat :)
 
Cat,
Your idea of higher dimensional being, or more advanced being, tends to a Utopian being (a Star Trek "Organian" being), a monolithic or monopolar, or cyclopian, whatever like a naked singularity of a singled celled creature, not even an all encompassing geometrically expandingly pyramidical being that keeps its shape and form, its advancing complexity and chaos and "Tree of Life" fissions and branching in roots and branches, throughout its increase in the "infinity of the mind." Conservation of energies, don't you know.

Think more broadly and deeply into an expanding frontier universe cosmopolis expanding the frontier cosmopolis of the mind, the mass mind to be exact, never the survivalist "scattering" individuality physics of individuals' individual minds.... Higher dimensionalities do not spike, they go universally multi-dimensional multiversal pyramidical in keeping!

You want Utopian mental spiking, think in terms of the lowest protoplasmic forms of life, not the highest (always complex and chaotic, bound to reaching for frontier and freeing (including the mind))!


Remember one little item about them, though, Cat. The lowest protoplasmic forms of life can physically "shape shift!" The highest forms of life can mentally, mindfully, infinitely "shape shift!"
 
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And the light we see took some portion of the escalator ride on the expanding hypersphere (through time) to get to us. (interesting curves to imagine)

And does a simple linear increase in the radius of the hypersphere create an accelerating expansion of space? (DE)
 
And if space on the hypersphere frame hanger started contradicting how might that work?

So the now decreasing hypersphere radius would be a new vector for time, but there would have to be an additional vector of time to displace us from going directly backwards in time.

Would that create intersections bands (rings?) between the present and the/some past, perhaps a different location in space as well as time?
(as previous hypersphere radii slide sideways)

Then the hypersphere's center point would be sliding on its own vector.
But if that were the case [in the first place] rings (spheres?) of the hypersphere would already have been intersecting with the past because the expansions wouldn't be neatly concentric/nested.*

* Citation from,
"God's Instruction Manual on How to Construct a Working Universe:
and Pitfalls to Avoid."
Chapter 7
Time Foibles
page 634,729; 3rd paragraph.
 

Catastrophe

"Science begets knowledge, opinion ignorance.
As a general comment, I abide by general semantics as proposed in Science and Sanity by Korzybski.

For this reason, I try to avoid a superfluity of map burying a modicum of territory. More words only complicate. This is a general comment.

This is a simple expression of my standpoint. Anyone is entitled to their own opinion, and, with due consideration, I will adhere to mine.

Cat :)
 

Catastrophe

"Science begets knowledge, opinion ignorance.
Atlan,

Cat,
Your idea of higher dimensional being, or more advanced being, tends to a Utopian being (a Star Trek "Organian" being), a monolithic or monopolar, or cyclopian, whatever like a naked singularity of a singled celled creature, not even an all encompassing geometrically expandingly pyramidical being that keeps its shape and form, its advancing complexity and chaos and "Tree of Life" fissions and branching in roots and branches, throughout its increase in the "infinity of the mind." Conservation of energies, don't you know.

Think more broadly and deeply into an expanding frontier universe cosmopolis expanding the frontier cosmopolis of the mind, the mass mind to be exact, never the survivalist "scattering" individuality physics of individuals' individual minds.... Higher dimensionalities do not spike, they go universally multi-dimensional multiversal pyramidical in keeping!

You want Utopian mental spiking, think in terms of the lowest protoplasmic forms of life, not the highest (always complex and chaotic, bound to reaching for frontier and freeing (including the mind))!


Remember one little item about them, though, Cat. The lowest protoplasmic forms of life can physically "shape shift!" The highest forms of life can mentally, mindfully, infinitely "shape shift!"

Atlan0001,
Thank you for your comments.

According to Google:

The Organians were a race of powerful incorporeal beings, composed of pure energy and thought, native to the planet Organia.

What I actually posted was:

However, unbeknownst to our flatlander, there is a superior being who appreciates that the flatlander's observed universe is simply the surface of a sphere which is really quite an insignificant part of "superbeing"s perceived universe. This superbeing sees that the flatlander's observed universe is simply his little playground, and does not merit the term "Universe". The flatlander's two dimensional surface still has no boundary to its surface area, which, nevertheless is increasing in area as the radius increases, and still (in the flatlander's mind) has nowhere to expand into. Problem solved. We just have to see such problems from the standpoint of beings with the ability to perceive higher dimensions.

My emphasis.

From:

Goodbye infinity and all that infinite singularity and infinite density descriptions | Space.com Forums

As you will notice, the first part of this, rendered bold, simply states that the superior being sees the flatlander's observed universe as really quite an insignificant part of "superbeing"s perceived universe. Thus, in this context, we would qualify as superbeing, and please note that I have put superbeing in quotes to emphasize this.

From the second part, rendered bold, We just have to see such problems from the standpoint of beings with the ability to perceive higher dimensions you will see that this further emphasises the point by substituting "beings with the ability to perceive higher dimensions" (we being one such) in place of superbeing.

Would you not agree that this is a perfectly acceptable use of the term "superbeing" in this context, making a comparison, as it does, with a "flatlander"?

Whilst I would thank you again for your extensive comment on this point, I do feel that it was slightly excessive suggesting this,

The Organians were a race of powerful incorporeal beings, composed of pure energy and thought, native to the planet Organia.

where mere humans were clearly what I described in parentheses as "superbeings".

I do further stand by this latter comment as possibly relevant to any "higher beings", even when we are describing rabbits to amoebae.

I hope that you will take this reply in the friendly and constructive manner as I intend it.

Cat :)
 
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And if space on the hypersphere frame hanger started contradicting how might that work?

So the now decreasing hypersphere radius would be a new vector for time, but there would have to be an additional vector of time to displace us from going directly backwards in time.
Time is always positive (even when running in the opposite direction).
A contracting radius would still be 'time passing' ie the process of moving the circumference (of a hypersphere). Whether moving outward or inward it would be 'fresh' moving and new.
The contracting universe would not be reversing into previous time (would not be going back to the past) it would be treading a new future just as it was when expanding.

Time is the process of moving our 3d space in a 4th spatial direction (I suggest). It matters not that it has changed direction. It doesn't stop and then run the past backwards. Note that in a sphere the opposite time would appear to be negative.
The " negative time" is relative. If our time runs one way and another runs the opposite way, we would call the other time 'negative' but each process is positive. Gee, I hope that's clear lol.
 
Cat,
The super being we are going to create, evolve, if we manage it first before closed systemic extinction, will be an open systemic space faring 'Frontier Civilization' and its overall mass genius (NOT including but plus to it, always, the one in a million, one in a billion, one in a trillion.... for which the million, billion, and trillion are the absolutely necessary fertile ground)! Either create or join, which ever comes first. And remember, there will always be the other side of the coin, the down side of the coin, the hard wild bark of the tree, called by many, sometimes too many, the "noble savage."

Aldous Huxley called the basic man of the primal primordial 'Wild' named "Savage" absolutely necessary to any possible continuance of the perfection of 'A Brave New World'. "Savage", the basic man-weed of the primal primordial 'Frontier Wild' stood, and stands, and will always stand, in superposition to the perfect lawn of 'A Brave New World'.
 
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As historian Will Durant said, among many others, history is always repeating (thus always going backward . . . thus time always going backward) in its large aspect, though rarely, if ever, in its fine details. Think 'Schrodinger' functionality . . . and possibly, probably, 'Dirac' as well.
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
Atlan, I am really sorry that I ever involved the term superbeing.
What I intended was only sufficient difference for "beings with the ability to perceive higher dimensions" as I explained in #8.

I really have no wish to involve superbeings in the sense of:
The Organians were a race of powerful incorporeal beings, composed of pure energy and thought, native to the planet Organia.

Please can we agree on this to avoid unnecessary circumlocution?

Cat :)
 
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The structure of time always and probably only extends into the past.

I still vote for tachyons as time groomers (of the past).

Weird thought,
try to imagine a coherent deterministic future and an indeterminate fragmented past.
Not sure if or how that could/might work.
 
Atlan, I am really sorry that I ever involved the term superbeing.
What I intended was only sufficient difference for "beings with the ability to perceive higher dimensions" as I explained in #8.

I really have no wish to involve superbeings in the sense of:


Please can we agree on this to avoid unnecessary circumlocution?

Cat :)
I'm not sorry. I'm glad you did take the road you took. It gave us a chance to expound, to elaborate, upon certain aspects of the lookers visualizing and dealing in cosmology and cosmopolis. I "liked" it.
 
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I am stuck. Earlier we saw, in summary, that the BB (if the universe is a hypersphere) does not exist within the observable universe 3D + "NOW" and that, as a result, t=0 did not represent the BB but only (relative to our direction of time, the radius) a position at 90 degrees to the radius direction. This is simply the shape of space - similar to the space at a black hole; where approach (relative) tends to t=0 (time rotates because it is 90 degrees to the shape of space as a Black Hole is approached).

This is my problem:

The past is also (like the BB) not in the 'NOW' Observable Universe.

  • Light does not experience time (unlike mass)
  • Distance increasing stretches light wavelength as a consequence
  • IMO 'the speed of light' is a function of the radius increase (time) - it just sits there riding the 'timewave'.
Why do we think looking at something distant is looking back in time? Is it possible that looking at something distant is "Now"? That the James Webb Galaxies detected are contemporary to our own time - as is everything (except travelling through space where SR affects the issue)?
Clearly, I think that absolute space and absolute time do exist but the statement requires a caveat or two.
 

Catastrophe

"Science begets knowledge, opinion ignorance.
Gibsense,

Clearly, I think that absolute space and absolute time do exist but the statement requires a caveat or two.

Even if absolute space / time do exist, you are correct about caveat(s).

Consider four observers A, B, C and D standing in straight line, say each 100m from the next.

If A and C cause a loud noise "simultaneously", B will hear both at the same time.
However, D will hear the noise from C before the noise from A.
(This assumes nothing intervening changes the speed of sound)

This may be a simpler caveat than you had in mind, but it does show simply that "now" is different for different observers.

Another question. Does space exist at all if there are no objects present, by which you can measure it? If you are in totally empty space - no stars visible - you would be able to move a finger from shoulder to hand, but would this give you the impression of space which you could move through? If, over a long period, you spoke a number of random different words (say 100) would you know (remember) the order after, say, a year? You would have no need to know either. You would not need to invent words like before, after, nearer, further, since you would have no one to communicate with.

Coming back to the quote, why do you think that that absolute space and absolute time do exist?

Cat :)
 
Does going 'backwards in time' mean
1) inverse traversal of a fixed sequence or
2) unzipping/deconstructing the sequence or
3) both?

Space in this universe is literally a function of time-flow/speed, & in all likelihood not absolute but relative.

I think space may be literally the probability space of the superposition of EM photons.
 
You can't observe SPACE! Coordinate point SPACETIME "past-future" histories (as Cat described in #20), yes, and/or eventually (also in #20), but entangled, entangling, concurrent REALTIME NOW, and emergent SPACE, effectively "Flatland" (think a vertical wall of what must be a spontaneous instant of time (t=0), not a flat lay of surface, even surface of sphere, space), NO WAY!

I'm summoned! Definitely to be cont'd...!
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
It might be the case that going backwards in time goes with a contraction phase of the Universe, if a cyclic system operates. #21.

Please note that, as a cyclic phase contraction begins, there would not be a sudden dramatic reversal of entropy. I would suggest that eggs broken would not suddenly mend themselves, as so often seems suggested. I would suggest that, long before any such happening might be considered, there would be no intelligent life around to boil eggs.

Of course, no one knows whether the Universe will continue expanding indefinitely, whether it will reverse, and, if so, any circumstances arising at and after expansion discontinues. It may be that expansion reaches a point where atoms are all separated, or some circumstance before or after that point. Anyway, no conscious material life would be there to boil eggs.

As stated, we do not know and we never will know (in all probability) what is going to happen.
This is all pure conjecture. But don't worry too much about broken eggs reassembling.


Cat :)

P.S. Just noticed #22. I don't understand where flatland or t = 0 come into #20.
 
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Physicists calculated the universe contracting reaching 0-point and started getting nervous about it, according to Stephen Hawking in my continuing favorite read of him, 'A Brief History of Time'. He told them not to let it bother them, the universe is already there and has always been, and always will be, there at 0-point! He continued on to his "Grand Central Station of the Universe" and that Universal Clock (clock time (t=0)) under which all travel travels, all change changes) overhanging the center, My favorite place and read of physics because it is where Einstein actually traveled to in his famous "mind's eye" trip to the speed of light! Hawking only mistakenly omitted the collapsed cosmological constant ((/\) (P/BB "T=1") which Einstein appeared to mistake for t=0. I've done it myself mixing up this particular fundamental binary base2, '0' and/or '1')).
 
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Gibsense,



Even if absolute space / time do exist, you are correct about caveat(s).

Consider four observers A, B, C and D standing in straight line, say each 100m from the next.

If A and C cause a loud noise "simultaneously", B will hear both at the same time.
However, D will hear the noise from C before the noise from A.
(This assumes nothing intervening changes the speed of sound)

This may be a simpler caveat than you had in mind, but it does show simply that "now" is different for different observers.

Another question. Does space exist at all if there are no objects present, by which you can measure it? If you are in totally empty space - no stars visible - you would be able to move a finger from shoulder to hand, but would this give you the impression of space which you could move through? If, over a long period, you spoke a number of random different words (say 100) would you know (remember) the order after, say, a year? You would have no need to know either. You would not need to invent words like before, after, nearer, further, since you would have no one to communicate with.

Coming back to the quote, why do you think that that absolute space and absolute time do exist?

Cat :)
I am not sure your analogy holds up in the context of what I have described as the cause of time (or rather what time is i.e. progress of our 3D space spherically - increasing radius - in a 4th spatial direction at 90 degrees to our 3D space).

Imagine a shockwave from some explosion. The 3D shockwave is our Observable Universe but in 4D embedding space.

The Radius Of the Observable Universe is proportionate to the 'Age of the Universe'. A fact that we have to accept although this was laughed at 20 years ago when I showed it was so.

So, given the above, (a thought experiment) if an object has spent the whole of time without any speed through space that is carried outward along the radius, then there will be no time dilation from speed through space with any other similar situation for some observer.

Mass objects would produce dilation so we have to imagine a situation where there is no mass or the observable universe is homogenous. All such imaginary objects can be plotted upon a circumference. The circle joining those points can be considered the absolute "Now" time. Similarly, all our objects are unmoving in 3D space but travel in time and can therefore be considered stationary reference points.

This is controversial but the usual objection involving special relativity is invalid for this thought experiment. So back to your initial 'loud noise' I suggest all observers exist on the circumference and do not move. They all have watches that read the same time but the one further from the source has to wait for time to pass (an extension of the radius) before they hear the noise.
All of the observers remain in 3D positions. They all experience the same addition of time (radius). They are at the same time; not looking into the past to any other one.

That's a thought experiment: how does that apply to our observable universe?

All the galaxies exist on the circumference but because they travel (have speed in space) special relativity takes its place in the issue but the effects are small as not many are travelling at close to 'c'. Observing galaxies near t=0 is not looking into the past (mostly - we have to accept some effects of speed). We observe galaxies almost 25% around the circumference when at extreme distances.

Have I made a logical error - it seems so.
 

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