# Finite space in infinite time

Sauwelios
Lectori salutem.

Can anyone refute the finite space/energy/matter in infinite time theory?

Finite space/energy/matter implies that the universe is not something endlessly extended, but set in a definite space as a definite force.

Infinite time implies that it will never reach a final state of equilibrium.

This means that the universe consist of a finite amount of energy (in whatever manifestation) that flows on in an infinite stream - not infinitely deep or wide, but infinitely long.

I will welcome any serious thoughts on the subject.

Sauw

heusdens
Originally posted by Sauwelios
Lectori salutem.

Can anyone refute the finite space/energy/matter in infinite time theory?

Finite space/energy/matter implies that the universe is not something endlessly extended, but set in a definite space as a definite force.

Infinite time implies that it will never reach a final state of equilibrium.

This means that the universe consist of a finite amount of energy (in whatever manifestation) that flows on in an infinite stream - not infinitely deep or wide, but infinitely long.

I will welcome any serious thoughts on the subject.

Sauw

From what perspective, reason, or observation, you conjecture that space is finite in extend.

All we know or assume is that space has no edges or boundaries. Which does not imply it being infinite, but neither disables that option.

I really doubt that space or matter are finite in extend, in more or less the same way as I doubt that time is finite in extend.

If space would be finite in extend, and have no boundaries or edges, this means that space is not flat, but curved. If space is sufficiently large, we might not observe that fact on small distance scales.

Current astronomical observations indicate however that space seems perfectly flat. It is not a proof, but just an indication that space can be infinitely large. And if not, it would need to be very large indeed. Most atronomers assume that we only see a small fraction of all of space.

Infinite space is a real candidate, and not just a theoretical model for the universe.

Sauwelios
All I need is the POSSIBILITY of finite space; and that possibility exists until it is refuted - i.e. until the infinite-space theory is proven PRACTICE.

heusdens
Originally posted by Sauwelios
All I need is the POSSIBILITY of finite space; and that possibility exists until it is refuted - i.e. until the infinite-space theory is proven PRACTICE.

Why do you 'need' finite space?

What is your motivation for assuming that space is finite in extend?

Sauwelios
If space were infinite it could not expand. This is contrary to the big-bang theory.

Simply put, if the universe is a finite force in infinite time, this means that all possible conditions will exhaust themselves and sooner or later the same condition shall come about. From which it follows...

heusdens
Originally posted by Sauwelios
If space were infinite it could not expand. This is contrary to the big-bang theory.

Why do you think that? The assumption is false.

Take for instance the infinite number set. You can add to it an infinite amount of numbers, without problem. Also you can subtract from it an infinite amount of numbers, while it sill maintains being infinite.

You have to look at space expansion as an expansion of the metrics.
An infinite space that expands still remains infinite.

However, it can be stated that the Big Bang is the expansion of an initial region as small as a infinitesimal small part of the size of a proton. However, in the embedding theory of inflation, this is just one region, and the surrounding space is still infinite space.
Inflation indeed talks about a small region of space that expands, which means that that region, no matter how large and how fast it expands, always will be finite in size.

Simply put, if the universe is a finite force in infinite time, this means that all possible conditions will exhaust themselves and sooner or later the same condition shall come about. From which it follows...

That everything would repeat itself? every moment is an eternal moment? well it explains my feelings of deja-vue... LOL

The situation is however not very different in an infinite space, cause then it could be said that there must be infinite many planets exactly like earth, with the same inhabitants, etc.

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Originally posted by Sauwelios
Finite space/energy/matter implies that the universe is not something endlessly extended, but set in a definite space as a definite force.
And what would this finite existence be residing within? Nothing? Impossible.
Infinite time implies that it will never reach a final state of equilibrium.
Which implies that all things within the universe have always been effects. No cause. That doesn't make sense either.

heusdens

Originally posted by Lifegazer
And what would this finite existence be residing within? Nothing? Impossible.

The model of a 2D sphere curved in 3D space, is a good model for a finite, yet unbounded space. For 3D space it must mean it is curved in 4D space. But all astronomical observations conclude that space is almost perfectly flat. From observation we thus concldue that space is indeed very large, possibly infinite.

Which implies that all things within the universe have always been effects. No cause. That doesn't make sense either.

Not realy. All effects are at the same time causes for the next effect. Which doesn't mean that I conclude that a circular chain of cause-and-effect, based on the finitiness of space, makes any sense to me...

Originally posted by heusdens
The model of a 2D sphere curved in 3D space, is a good model for a finite, yet unbounded space.
Sure. But what is this "model" residing within? Certainly not 'nothing'. That's a logical impossibility.
Something must have boundless existence. This is clear. But this thing cannot reside within 'nothing'. Therefore, existence itself is not finite.
But infinite-existence imposes singularity upon existence itself. The position of any thing within such an existence is thus subjective.
Not realy. All effects are at the same time causes for the next effect.
No effect can lay-claim to being the true cause of any event.
To say that I (lifegazer) am the absolute-cause of this post, for example, is utterly incorrect.

heusdens

Originally posted by Lifegazer
Sure. But what is this "model" residing within? Certainly not 'nothing'. That's a logical impossibility.
Something must have boundless existence. This is clear. But this thing cannot reside within 'nothing'. Therefore, existence itself is not finite.
But infinite-existence imposes singularity upon existence itself. The position of any thing within such an existence is thus subjective.

While I agree on the conclusion that space is infinite, this does not mean that your argument against finite space is correct. What is against a 3D sphere curved onto itself as a 4D hypersphere? (except that it implies that time had a beginning)

No effect can lay-claim to being the true cause of any event.
To say that I (lifegazer) am the absolute-cause of this post, for example, is utterly incorrect.

We come here again on the point which you argued against, namely that the chain of cause-and-effect is infinite indeed, that means: it has neither a begin nor an end. A finite circular cause-and-effect chain has neither a begin or end, but this means that everything happened already an infinite number of times.
(hmmmm. it appear to me I already say that many times before? lol)

BTW: Did you change your mind on the beginning-of-time thing?

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Sauwelios
Originally posted by heusdens
You have to look at space expansion as an expansion of the metrics.
An infinite space that expands still remains infinite.

That is a mathematical abstraction. "An infinite space that expands" is an oxymoron: it implies that the space have bounds which expand. However, the word infinite means "without bounds"...

[B}The situation is however not very different in an infinite space, cause then it could be said that there must be infinite many planets exactly like earth, with the same inhabitants, etc. [/B]

That is very interesting. Thank you for submitting your views.

Sauwelios

heusdens
Originally posted by Sauwelios
That is a mathematical abstraction. "An infinite space that expands" is an oxymoron: it implies that the space have bounds which expand. However, the word infinite means "without bounds"...

That is a incorrect view. Model all of space as a flat sheet, infinite in extend, and draw a grid on that sheet.
The expansion of that infinite sheet can now be visualized as a change in the metrics of that grid. It gets larger.
And the only way we can know about that, is because the objects on the grid (the atoms, and material objects) do not expand themselves.

In fact this situation is similar to the grid not expanding, and all material things on the grid, contracting.
However, I never heard a physical explenation to that, although it must be the same thing, we only changed the definition of our length unit... Physical laws are absolute the same and not dependend on our choise of the length units...

Can anyone explain me this, cause this aspect of "space expansion" I still don't get?

That is very interesting. Thank you for submitting your views.

The fact that either time and/or space is infinite, seems both lead to many contradictionary implications. Either "this moment" happened an infinite number of times already, or "this moment" happens at infinitely many places at once...

Originally posted by heusdens
While I agree on the argument that space is infinite, this does not mean that your argument against finite space is correct.
I said that existence was infinite. Not space.
... and why do you disagree with my argument about finite-existence?
We come here again on the point which you argued against, namely that the chain of cause-and-effect is infinite indeed, that means: it has neither a begin nor an end.
A finite circular cause-and-effect chain has neither a begin or end, but this means that everything happened already an infinite number of times.
(hmmmm. it appear to me I already say that many times before? lol)
Yep. A stumbling-block of communication, is this.
My position remains unaltered. If all effects are the product of causality, and causality is infinite in regress, then there cannot be a 'product'. Nothing you have posted has ever convinced me otherwise. Sorry.

Sauwelios

Originally posted by Lifegazer
And what would this finite existence be residing within? Nothing? Impossible.

Nothingness, ye-e-es. But the idea of something within nothing is a rational impossibility: for, to envision this, one should be able to imagine "The Nothing"... Utter darkness? But that is still something. No, "space enclosed by nothingness" means there is only space, not within something but in itself.

Which implies that all things within the universe have always been effects. No cause. That doesn't make sense either.
It is indeed a vicious circle. But is a circular argument neccesarily a false argument? Or must you really infer a "Creator" as a primary cause. Who, then, invented the Creator? Did He invent Himself? Or has He always been there? - But this is merely a repetition of the question...

Sauwelios
Originally posted by heusdens
The fact that either time and/or space is infinite, seems both lead to many contradictionary implications. Either "this moment" happened an infinite number of times already, or "this moment" happens at infinitely many places at once...

Or Both?

Originally posted by Sauwelios
But the idea of something within nothing is a rational impossibility: for, to envision this, one should be able to imagine "The Nothing"... Utter darkness?
Absolute-nothing is utter nothingness. Not utter colour or colourlessness or any other thing which you'd care to mention.
You cannot have something residing within such a state. It's rationally impossible.
But that is still something.
Then it is not 'nothing', is it? And if you want to put 'something' beyond universal-existence, you just extend existence beyond our material-domain. Hence, existence is boundless and non-finite.
No, "space enclosed by nothingness" means there is only space, not within something but in itself.
Sorry, but this is no longer a rational discussion. You cannot have a finite-entity residing within nothing other than itself. The very-fact that the entity is finite means that it must be embraced by another entity - which cannot be 'nothing'.
It is indeed a vicious circle. But is a circular argument neccesarily a false argument?
Not if the circular argument makes sense.
Or must you really infer a "Creator" as a primary cause.
Personally, I think so. Most here will side with you though.
Who, then, invented the Creator? Did He invent Himself? Or has He always been there? - But this is merely a repetition of the question...
Existence itself is eternal (note: by existence, I do not automatically infer that the material-universe is eternal). This is obviously-apparent when one realizes that something cannot emanate from absolute-nothingness. And since something does exist now (whatever that thing may be), then we can be sure that this thing has always existed, and always shall - since 'nothingness' cannot come of something.
Thus, existence is eternal, and the question about its own causality is shown to be meaningless.

Like other members here, you seem to want to use the term 'nothing' so that it actually is 'something'. This is your base-error, imo.
By the way, welcome to the forums.

Sauwelios
Originally posted by Lifegazer
Absolute-nothing is utter nothingness. Not utter colour or colourlessness or any other thing which you'd care to mention.
You cannot have something residing within such a state. It's rationally impossible.

Then it is not 'nothing', is it? And if you want to put 'something' beyond universal-existence, you just extend existence beyond our material-domain.

I made the mistake of assuming you could fill in the blanks I intentionally left in this part of my argument. You have, but at the cost of thinking that I could not do so myself. Then you gave the same impression to other readers by cutting my argument into pieces.

Hence, existence is boundless and non-finite.

This conclusion does not follow from the premises. It rather seems to be some kind of idée-fixe you have.

Sorry, but this is no longer a rational discussion. You cannot have a finite-entity residing within nothing other than itself. The very-fact that the entity is finite means that it must be embraced by another entity - which cannot be 'nothing'.

These are all personal opinions, not facts. Why must something be enveloped by something else?

When asked whether you think there is a Creator, you said: "Personally, I think so." That is not very scientific. What makes you think there is one?

Existence itself is eternal (note: by existence, I do not automatically infer that the material-universe is eternal). This is obviously-apparent when one realizes that something cannot emanate from absolute-nothingness. And since something does exist now (whatever that thing may be), then we can be sure that this thing has always existed, and always shall - since 'nothingness' cannot come of something.
Thus, existence is eternal, and the question about its own causality is shown to be meaningless.

This has been my point from the beginning - with the incorporated notion that the essence of existence is to all eternity flux.

Thank you for making me feel at home.

Sauwelios

Sauwelios
Originally posted by heusdens
Model all of space as a flat sheet, infinite in extend

One can never model all of space if it is infinite...!

heusdens

Originally posted by Lifegazer
I said that existence was infinite. Not space.
... and why do you disagree with my argument about finite-existence?

Yep. A stumbling-block of communication, is this.
My position remains unaltered. If all effects are the product of causality, and causality is infinite in regress, then there cannot be a 'product'. Nothing you have posted has ever convinced me otherwise. Sorry.

Your reasoning is obviously wrong. Because your reasoning assumes at a certain point there is a begin to the infinite chain of cause-and-effect. From there on you reason that if such a begin is an infinite time from the present, you cannot get from there to the present, and hence there can not be a product.
We been on this point now many times, and the error in your argument is that you put in the conclusion of your argument (time must have a beginning) in the premise to your argument.
Infinity, namely, implies there is no begin to the time line. So, wherever you place your 'begin point' where you start your count, you always leave behind you an infinite amount of time.

So, your reasoning is circular. Your basic (implicit) assumption is that time had a begin. Then you state that if time is infinite, that an infinite amount of time must have been passed since that beginning. You then conclude: that is impossible, so time could not be infinite, hence time must have had a beginning. But that was just the start of your reasoning, the premise you implicitly smuggled into the argument!

Your error: you have assumed that there was a begin (else, where do you start counting?), while in fact, infinity of time in both directions (past and future) means that there is no begin or end to time at either side of the timeline.

The fact is, your conclusion is wrong, cause the 'product' (the here and now) exist (that is for sure). Further we now that all things of the present must be the effects of previous causes, which themselves are also effects of previous causes. Hence it follows that time had no beginning. Otherwise, there would have been effects without causes.

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heusdens
Originally posted by Lifegazer
Absolute-nothing is utter nothingness. Not utter colour or colourlessness or any other thing which you'd care to mention.
You cannot have something residing within such a state. It's rationally impossible.

Then it is not 'nothing', is it? And if you want to put 'something' beyond universal-existence, you just extend existence beyond our material-domain. Hence, existence is boundless and non-finite.

Sorry, but this is no longer a rational discussion. You cannot have a finite-entity residing within nothing other than itself. The very-fact that the entity is finite means that it must be embraced by another entity - which cannot be 'nothing'.

Not if the circular argument makes sense.

Personally, I think so. Most here will side with you though.

Existence itself is eternal (note: by existence, I do not automatically infer that the material-universe is eternal). This is obviously-apparent when one realizes that something cannot emanate from absolute-nothingness. And since something does exist now (whatever that thing may be), then we can be sure that this thing has always existed, and always shall - since 'nothingness' cannot come of something.
Thus, existence is eternal, and the question about its own causality is shown to be meaningless.

Like other members here, you seem to want to use the term 'nothing' so that it actually is 'something'. This is your base-error, imo.
By the way, welcome to the forums.

You are very excellent in this reasoning. And for most part the reasoning is correct, except for the fact that you rob the material basis from existence. What can exist if no matter in whatever form (mass, energy, fields, whatever there is that can move/change in time and space) would exist?

Eh
Actually, the reasoning is crap. The claim that a finite manifold must be embedded in external space has been repeated often, but is not founded on logic or any reasoning at all. But maybe you missed that part.

heusdens
Originally posted by Eh
Actually, the reasoning is crap. The claim that a finite manifold must be embedded in external space has been repeated often, but is not founded on logic or any reasoning at all. But maybe you missed that part.

I already pointed that out. The 2D anology of space, modeled as the surface of a sphere, which is of course a finite size, but has no boundaries or edges; mathematically that is perfectly possible, and does not need 'outside' space.

Nevertheless, from observation and theory, I do not think that real space is finite.

Staff Emeritus
Gold Member
Originally posted by Sauwelios
I made the mistake of assuming you could fill in the blanks I intentionally left in this part of my argument. You have, but at the cost of thinking that I could not do so myself. Then you gave the same impression to other readers by cutting my argument into pieces.

Don't worry: He doesn't give that impression to any of the regular readers.

When asked whether you think there is a Creator, you said: "Personally, I think so." That is not very scientific. What makes you think there is one?

Ugh--Please, let's not. This was a big enough mess the first time. You can read about it here, if you are so inclined:

Eh
Originally posted by heusdens
I already pointed that out. The 2D anology of space, modeled as the surface of a sphere, which is of course a finite size, but has no boundaries or edges; mathematically that is perfectly possible, and does not need 'outside' space.

Nevertheless, from observation and theory, I do not think that real space is finite.

Edges aren't even the problem. The claim that finite space must be embedded in something external is where the argument falls apart. Even if some models of the expanding universe found by Georges Lemaître (with a center and edge) were correct, the claim is still wrong.

But I guess intuition takes priority over reason with some.

heusdens
Originally posted by Eh
Edges aren't even the problem. The claim that finite space must be embedded in something external is where the argument falls apart. Even if some models of the expanding universe found by Georges Lemaître (with a center and edge) were correct, the claim is still wrong.

But I guess intuition takes priority over reason with some.

Apart from the false argument against a finite extend of space, do you really think that space is finite, and for what reason?

To state that space is infinite is somehow difficult, because that aspect of space can not be observed directly. The only observational point is the "flatness" of space. But since we can not distinguish between an exactly flat space and space that is very near to flat (meaining: space is very big), how can we find out wether or not space is infinite?

Eh
It's not really something testible, though in theory a finite universe could be proven with the right technology. But in the mean time, I would say finite is more likely, if only because nature does not seem to contain infinities anywhere else. In the past, it was believed that space and time were infinite in extent, while matter and space were infinitely divisible. Quantum theory showed us matter is not continuous, modern cosmology gives difficulty to the idea of infinite time, and it is expected by many that a quantum theory of gravity will do away with the notion of continuous space-time. The only infinity left is that of space.

Is space an oddball, or does nature truly contain no infinities? I vote for the second.

heusdens
Originally posted by Eh
It's not really something testible, though in theory a finite universe could be proven with the right technology. But in the mean time, I would say finite is more likely, if only because nature does not seem to contain infinities anywhere else. In the past, it was believed that space and time were infinite in extent, while matter and space were infinitely divisible. Quantum theory showed us matter is not continuous, modern cosmology gives difficulty to the idea of infinite time, and it is expected by many that a quantum theory of gravity will do away with the notion of continuous space-time. The only infinity left is that of space.

Is space an oddball, or does nature truly contain no infinities? I vote for the second.

Cosmology does not model time as having a begin.
In fact there has been only one such hypothese (Hawking-Turok these) which modeled universe as having a begin in real time.
This hypothese however has been dropped. Alternative hypothesis are built on the assumptions that time had no beginning.

I suspect that time and space are closely linked together, and that either must be finite or infinite. As to my argument, I would therefore state that both are infinite.

Notice that a finite time and a finite space would not form a very consistent world. Because in the first place, it would not be possible to exist on it's own.

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Eh
Originally posted by heusdens
Cosmology does not model time as having a begin.
In fact there has been only one such hypothese (Hawking-Turok these) which modeled universe as having a begin in real time.
This hypothese however has been dropped. Alternative hypothesis are built on the assumptions that time had no beginning.

Actually, the standard model of cosmology predicts a beginning to the universe. Alternative models such as chaotic inflation build on that, but they still seem to require a beginning after all. For a while, it seemed that some self reproducing universes could be eternal, but now it seems even those must have a beginning. Perhaps theories based on extra dimensions may yield the possibility of an infinitely old universe, but the models based on 4D space-time do not seem to do the trick.

I suspect that time and space are closely linked together, and that either must be finite or infinite. As to my argument, I would therefore state that both are infinite.

Yes, that is why I would suspect finite.

Notice that a finite time and a finite space would not form a very consistent world. Because in the first place, it would not be possible to exist on it's own.

Not necessarily. You can model a beginning to the universe that does not have a before without suffering from any logical inconsistancy. The same applies to finite space. Of course this position goes against intuition, but that isn't a problem with logic.

Philosophical notions aside, modern cosmology does indeed give an infinite universe problems. Perhaps a cyclic model would work, but there is no guarantee such a universe did not have a first cycle.

wimms
Originally posted by Eh
Actually, the reasoning is crap. The claim that a finite manifold must be embedded in external space has been repeated often, but is not founded on logic or any reasoning at all. But maybe you missed that part.
Eh, this IS coming up often. Would you, as one of the pros care to explain it slow and understandably, why such reasoning is crap? Or if that has been beaten to death already, where's a link?

Eh
It's really just a matter of geometry. The volume of something has nothing to do with the space it is embedded in. And that's just it. The notion of area and volume are well defined geometric concepts that do not need reference to outside space for definition. So the claim that a finite universe must be embedded in some infinite space is founded on intuition and not any logic.

Originally posted by Eh
It's really just a matter of geometry.
Geometry is conceptual mathematics. It is formulated within the mind, for practical applications within space.
The difference between concepts of the mind and perceived-objects (finite objects), is that concepts are embraced by the mind, whereas 'objects' are embraced by perceived-space.
In either case, geometry is formulated within something.
It is not formulated within nothing. A finite-object cannot exist within nothing.

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Eh
No, you're wrong. The mathematical field of Geometry is a description of space, which is very real. Space-time does not need to be embedded in any external space, inspite of what intuitionists like yourself would claim.

Sauwelios
An end to the discussion?

I agree with Eh in this. However, I do not think that we can get much further in the discussion. We all disagree with others in some respects, while being in agreement with others. Therefore I propose to close this correspondence. I will unsubscribe myself from this thread. I want to thank all of you for participating in this discussion: some of your contributions have broadened my perspective, while others have adjusted it a bit. Most importantly, I feel I have discovered with this forum a resource from which I can tap valuable knowledge for the use, and even challenge the conclusions, of my personal investigations. Keep up the good work!

Sauwelios

heusdens
Originally posted by Eh
Actually, the standard model of cosmology predicts a beginning to the universe.

I don't think that the standard model describes that. The standard model is just the model of the observable universe (which extends beyond our obsevation) which was in the past more dense, smaller and more hot. In the standard model we can calculate back to perhaps the 10 to the minus 43 seconds, but then physical laws aren't able predicting anything. So the standard model can not make predictions about what was before.

Alternative models such as chaotic inflation build on that, but they still seem to require a beginning after all. For a while, it seemed that some self reproducing universes could be eternal, but now it seems even those must have a beginning. Perhaps theories based on extra dimensions may yield the possibility of an infinitely old universe, but the models based on 4D space-time do not seem to do the trick.

Eternal / open or chaotic inflation models are built in such a way that the Big Bang theory becomes part of the inflationary regime.
That what is stated in this theory is that once inflation starts, it can reproduce eternally, and therefore does not need a begin.
I have not seen the 'proof' that such a regime can't be eternal.
But if that is proven, it just means that also that theory can predict about reality in a limited way. It does not urge us however to state then that time must had a beginning, but that some other material form, which can not be described within inflation theory, preceded inflation.

Yes, that is why I would suspect finite.

But a beginning of time is a very weird concept. It would urge us to conclude that everything existing came out of nothing.
No physical law can ever describe that. Physical laws can not be built on 'nothing'.

Not necessarily. You can model a beginning to the universe that does not have a before without suffering from any logical inconsistancy. The same applies to finite space. Of course this position goes against intuition, but that isn't a problem with logic.

The logic inconsistency does occur however. When 'modelling' the state of the universe 'before' the begin of time, in fact we have to conclude that no model can describe it. Because a mere nothingness is either inexistent in time, or is just a concept of pure time, that is a concept of time without any foreign admixtures, without anything changing in time. The logic problem is that in such an eternal unchanging nothingness, a change did occur, 'causing' the material existence, time and space.

There is no logic that can work on that concept, if you ask me.

Philosophical notions aside, modern cosmology does indeed give an infinite universe problems. Perhaps a cyclic model would work, but there is no guarantee such a universe did not have a first cycle.

This is just an indication of how good our models are. If the model comes up with such inconceivable concepts as the 'begin of time' it would merely indicate that a new theory must emerge.

Philosophical note on Infinity of matter

The philosophical notion of the infinity of matter, does not reflect on a determined age or a detemined space. It denotes the eternal transformation of matter, the fact that matter can not be created or destroyed, but only can be transformed from one form, into another.
Infinity of matter means, that all finite development forms of matter in a finite spatial extent with a finite age transforms into another development form of matter, which also has a finite spatial extent and age.

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wimms
Originally posted by Eh
It's really just a matter of geometry. The volume of something has nothing to do with the space it is embedded in. And that's just it. The notion of area and volume are well defined geometric concepts that do not need reference to outside space for definition. So the claim that a finite universe must be embedded in some infinite space is founded on intuition and not any logic.
Sorry, that was too fast for me . Do I understand right, that because volume and area of brick can be well defined without any need for reference to outside space for definition, assumption that there must be something around the brick is plain stupid?

Isn't definition of finite manifold simply postulate that needs no further consideration? As such, isn't it just assumption that is forbidden to be questioned? For working model, no problem. But when suppressing other intellect 'from higher ground'? Patience please, some understanding doesn't come easy.

Logic doesn't reveal truth, it only checks consistency. Any theory is based on assumptions, intuitive or not.
Claim that a finite universe must be embedded in some infinite space may be unfortunate, but claim that universe cannot be finite comes from logical approach. I can't help but draw analogy with claim that set of _all_ integers can be finite.