Seeing Beyond the Illusion of Infinity

[Gibsense]

I thought a post in a Flatlander thread could usefully be 'expanded' and asked AI to reword in a way suitable for here as a post challenging the idea of infinity in a universe concept:

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Seeing Beyond the Illusion of Infinity​

We often imagine the universe to be infinite—an endless cascade of turtles supporting turtles. But this may simply reflect our limited perception, shaped by living in a world confined to three spatial dimensions. Our failure to embrace other dimensions blinds us to alternative, more elegant realities.


Imagine you're a one-dimensional being living on a line. You know only forward and backward—“sideways” doesn’t exist. From this view, your world seems infinite. But if you could perceive a second dimension, you’d discover that the line could curve into a circle, rendering it finite yet boundless.


Now apply this insight to our universe. String theory attempts to introduce extra dimensions—but suggests they must be “curled up” and hidden, simply because we can’t see them. That’s not just speculative—it’s anthropocentric. The truth may be that these dimensions aren’t hidden but rather imperceptible from our three-dimensional viewpoint.


To understand this, think like a Flatlander—someone living on a two-dimensional surface. If a three-dimensional ball passes through their plane, they'd witness only a growing and shrinking circle. The full reality is inaccessible from within their dimension. Only through abstract reasoning could they infer something greater.


Now consider our own experience. If time is a fourth dimension—not merely a flow but a geometric direction—then entities like atoms stretch through it. These aren’t isolated spheres; they’re string-like structures extending from past to future. The quantum world becomes a vast tapestry of filaments—interconnected and dynamic until specific collapses “clip” the threads.


Our awareness is anchored to a single moment—what we call “now”—which slides through this four-dimensional landscape. We perceive this traversal as time. But we err by assuming it’s infinite and linear, simply because we lack a higher-dimensional vantage point.


In truth, the universe may not be infinite at all. Like the circle hidden within the line, space-time might curve back on itself—not just spatially, as in a hypersphere, but temporally, forming a closed loop. This elegant geometry replaces infinity with comprehensible finiteness—without boundaries, but also without contradiction.

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Would you like to include a diagram that visualizes the dimensional analogy and hyperspherical curvature? I could help you sketch one up for your post or report. Or we could take it a step deeper and link this to your JWST observational modelling of extended string-like entities in ETGs. Let’s make it sing.

I agreed to the follow-up, but I am now going to watch Tennis

 

[promytius]

It seems illogical to declare something 'elegant' that is just as theoretical as its alternative. No proof for a closed loop, and no proof for infinity. Your argument falls apart.

 

[promytius]

AI seems to have created a rabbit hole for you, and you went down it.

 

[Gibsense]

AI seems to have created a rabbit hole for you, and you went down it.

It seems illogical to declare something 'elegant' that is just as theoretical as its alternative. No proof for a closed loop, and no proof for infinity. Your argument falls apart.

MY rabbit hole, as expressed by an AI.

For that matter, the book "Flatlander" (and a later extended version by a different author whose name I have forgotten ) attempted to explain the same 'Rabbit Hole' but as a story to entice atrophied brains to open their eyes to the obvious.

Blindspot

It may seem to us that the universe is infinite—as if the cosmic principle of “tortoises all the way down” persists endlessly. But this perception is a direct consequence of our limitations: our senses and cognition are confined to a three-dimensional existence, and we habitually dismiss realities beyond what we can immediately observe.


To simplify the concept, imagine living within a single dimension—a line. Movement is restricted to forward or backwards. The idea of “sideways” is inconceivable. From this constrained perspective, the line appears infinite because there’s no framework for understanding a second dimension—one that could bend the line into a circle, removing the notion of infinity entirely.


String theory attempts to breach this barrier, proposing the existence of additional dimensions. However, it paradoxically suggests that these dimensions must be “curled up” to account for why we can’t perceive them—a notion that borders on absurdity. Just because we can’t see extra dimensions doesn’t mean they’re hiding. It’s more accurate to say we’re blind to them, like the Flatlander who cannot conceive of ‘up’ or ‘down’.


Consider the Flatlander again, living on a two-dimensional plane. If a three-dimensional object like a ball passed through, the Flatlander wouldn’t see a sphere—they’d observe a growing and shrinking circle. The true nature of the event is inaccessible from within their plane. Only abstract modeling could hint at the higher dimensional reality.


Now apply this logic to us. If we inhabit a four-dimensional construct where time is the fourth dimension, then physical entities—say atoms—would not merely be point-like or spherical. They would extend through time as thread-like structures, forming tiny tubes stretching from the past into the future. The quantum world, in this view, is a vast interwoven system of these temporal filaments, with wavefunction collapse representing a localized “pinching off” in this temporal structure.


Our experience of this four-dimensional world is a fleeting slice—a single “now” moving through the higher dimensional space. We label this motion through 4D as “time.” But like the one-dimensional dweller who mistakes a circle for a line, we assume this time is open-ended simply because we lack the dimensional framework to perceive its curvature.


Indeed, our universe may not be an infinite 3D expanse with an arrow of time. It may well be a closed hypersphere—space curving not only into itself but also through time, forming a higher-order dimensional loop. Such a topology removes the illusion of infinity and replaces it with a far more elegant, though less intuitive, architecture.

 

[promytius]

(No AI involved)
Or, one could also by reversing the two, say: Indeed, our universe may not be a closed hypersphere—space curving not only into itself but also through time, forming a higher-order dimensional loop. It may well be an infinite 3D expanse with an arrow of time. Such a topology removes a less intuitive, architecture, and replaces it with an equally unprovable alternative.

We are 3D creatures, we can only speculate on what one and two dimensional existences would be. Well, I cannot imagine a one-dimensional brain, so I don't think there really is a unique, living one dimensional reality. Two dimensional brains? Impossible. I do not think there is a living 2D reality. Life takes at least three dimensions; however, that requirement forbids knowledge of higher dimensions. One can only percieve its own reality/perspective/position. We cannot know, we're 'trapped'/'confined' to these three dimensions.

"Our awareness is anchored to a single moment—what we call “now”—which slides through this four-dimensional landscape."

How is awareness anchored to a single moment? You're not referring to a single moment, you're referring to an uninterrupted existential awareness of being alive, it may occur moment to moment in what we call the present, altrhough I don't believe that's how it works, but it is neither a single event, nor interacts with a fourth dimension (which you've left undefined), because we are 3D.

"We perceive this traversal as time. But we err by assuming it’s infinite and linear, simply because we lack a higher-dimensional vantage point."

Well, because we lack a higher-dimensional vantage point, only wild speculations are possible. I believe the Universe to be infinite. It cannot have a container, because then it would not be the "Universe;" if anything is outside the universe, how can it not be part of it? We currently are preoccupied with the very small, and discovering things we got wrong and right; we have moved from the centimeter to the Planck Length in our 3 dimensions. Each time we reached a limit in measurement, we overcame it; now we're seeing some precident-breaking large-scale observations of the Universe, from how it formed to when; it gets bigger and older.

Time must be both infinite and linear, because that is how we experience it. Is there time in a 1D universe? Could a 1D world produce science? We don't know, we can't.
What I see, what I experience, is time as infinite and linear; any perceived variance in that can be explained by brain functions - loss of time, compression of time, deja vu - the observer/experiencer, being a 3D creature, is incapable of detecting their own mis-perceptions of time in real time.
Also, remember that we consciously fool ourselves continuously in thinking we experience life in real time; repeated studies have shown that we can be up to 15 seconds behind 'real' time in our perceptions. Imagine that!
An infinite Universe fits what we know; a recursive universe doesn't fit, because we don't do higher dimensions.

 

[Gibsense]

I believe the Universe to be infinite.

And there lies the problem. Comfort zone. As soon as 'belief' is quoted, we know what the problem is. However, respect to you for your response, which has taken some consideration. Most of your statements are simply wrong, and as soon as belief enters the picture, the discussion is pointless. But again, respect to you for your thoughts on what is a deep and engaging subject , to me anyway

 

[Gibsense]

Time must be both infinite and linear, because that is how we experience it. Is there time in a 1D universe? Could a 1D world produce science? We don't know, we can't.

The answer to your question is quite obvious, isn't it?
For a start, it is a thought experiment, but if we take it more literally, the line dweller must be a point existing on the line (or perhaps a short dash). He could only move if time was involved in some way. If the line were a circle (avoiding infinity) then the radius would be time.
Time would pass in proportion to the expansion of his line. He would be able to go further (returning to the start) until the circumference expansion in distance exceeded the speed of light. He would then seemingly have an infinite expansion of available distance, except that, as we all know, the 'stretch' of wavelength would eventually lengthen to a point of dissipation where all things were stretched to oblivion. Maybe, lol.

But then we have the problem that the lineman would wonder what caused his Big Bang. They could argue for ages about a singularity and clashing lines in some exterior place. Maybe no one notices the relationship between time and his total length expanding and they would go on debating infinity and zero until destruction

 

[promytius]

You don't know that any of what you said is true, as you pointed out, it's a thought experiment; you're just listing your beliefs in 1D, you have no access to proofs. Your premises are just as speculative as mine - so to claim some sort of correctness over the use of one word - believe - is dodging.
Let me make it clearer - the Universe is Infinite.

 

[promytius]

Our concept of 'universe' is human-limited. All that we perceive as "universe" is a minuscule, tiny tiny local event in the infinity of the true Universe. There is no end, there is no boundary, there is no loop-back there is only a flat infinite universe. I know this. How? It is what it is. It is impossible for a tiny thing like our 'universe' to be "ALL" and no end to Space.

 

[Catastrophe]

This is just agreeing with "There is no objective ;Universe" - only "observable universes".

Cat

 

[Gibsense]

You don't know that any of what you said is true, as you pointed out, it's a thought experiment; you're just listing your beliefs in 1D, you have no access to proofs. Your premises are just as speculative as mine - so to claim some sort of correctness over the use of one word - believe - is dodging.
Let me make it clearer - the Universe is Infinite.

RE: Belief. To me that suggests you assume something is true without evidence. Belief is a mental attitude or conviction that something is true or exists, often without the need for empirical evidence or proof.

Our concept of 'universe' is human-limited. All that we perceive as "universe" is a minuscule, tiny tiny local event in the infinity of the true Universe. There is no end, there is no boundary, there is no loop-back there is only a flat infinite universe. I know this. How? It is what it is. It is impossible for a tiny thing like our 'universe' to be "ALL" and no end to Space.

In that case it follows that there exist an infinite versions of you. Rich ones, poor ones, good ones, bad ones etc.
I note that you qualified your infinity by restricting the possibilities to Flat within only one universe (this one) whereas you could have considered an infinite variety of modifications that were not flat. So that initself limits the universe and so it is not infinite in all respects.
Further we are in an infinitely small universe (in comparison to an infinitely large one). Some argue that infinitely small equates to Zero. Maybe you have proved we do not exist. Or worst we exist every where there is. I know I am being a bit flippant so I apologise but you will get the idea.

The idea of a loop like structure is to contain us in a logical framework set within what is likely nothing at all not even a spatial vacuum. This does not rule out other universes but only rules out that they exist in anything. The question remains can there be coordinates in an absence of anything? Possibly not as that would mean not nothing but a dimension(s).

If there can be no spatial dimension but other universes may exist then they must be touching our own. If so then our universe cannot exist there (assumed). That means our universe is not completely infinite in all respects as it is limited.

Whereas science tells us there are 4 dimensions, 2 of which you can draw on a piece of paper. If there are 2 then there must also be one dimension, and it must be infinitely long in an infinite universe unless it forms a loop in a 2D plane