How does one find True Knowledge?

[BigBango]

We can measure a finite line, but without the paper (that the line is drawn on) there is no finite line to measure.

If I start from place A and go along a straight line, measuring the distance, and then arrive at the same place A, I have measured the size of a finite universe. It has a curved non-euclidean geometry. It is logically possible. I do not know if it is physically possible or real.

I do not think you have measured the size of a finite universe. You may have simply followed the path of a light stream as it travels near to a large mass. Light passing near to stars follows a non Euclidean path, or geodesic described by Riemann geometry. To call the line "straight" is to imagine that Euclidean geometry is the operative math of reality. However if we use "light" as the generator of lines in space then the SPACE that those lines follow is non Euclidean. Generally speaking these lines are just bent when they pass by massive objects. Having it bend all the way around a large mass could result in the line intersecting the starting point A. But that does not form a circumference of a finite universe.

I think you may be referring to the fact that a light beam seemingly traveling outside of the known world does bend back toward the world we know and has been the empirical evidence that the "space time continuum" is closed rather than open in any sense of "infinite".

[Tamminen]

If I start from place A and go along a straight line, measuring the distance, and then arrive at the same place A, I have measured the size of a finite universe. It has a curved non-euclidean geometry. It is logically possible. I do not know if it is physically possible or real.

I do not think you have measured the size of a finite universe. You may have simply followed the path of a light stream as it travels near to a large mass. Light passing near to stars follows a non Euclidean path, or geodesic described by Riemann geometry. To call the line "straight" is to imagine that Euclidean geometry is the operative math of reality. However if we use "light" as the generator of lines in space then the SPACE that those lines follow is non Euclidean. Generally speaking these lines are just bent when they pass by massive objects. Having it bend all the way around a large mass could result in the line intersecting the starting point A. But that does not form a circumference of a finite universe.

I think you may be referring to the fact that a light beam seemingly traveling outside of the known world does bend back toward the world we know and has been the empirical evidence that the "space time continuum" is closed rather than open in any sense of "infinite".

I am not an expert on this, but I have read that there are at least 3 possible geometries describing the universe: flat, spherical and the "saddle" form. Only the spherical makes a finite universe. So I am not speaking of massive objects, that is another story, but the geometry as a result of the whole mass of the universe. But my main point is that measuring the size of a finite universe is logically possible from within the universe.

[BigBango]

I am not an expert on this, but I have read that there are at least 3 possible geometries describing the universe: flat, spherical and the "saddle" form. Only the spherical makes a finite universe. So I am not speaking of massive objects, that is another story, but the geometry as a result of the whole mass of the universe. But my main point is that measuring the size of a finite universe is logically possible from within the universe.

I am not an expert on these subjects either but I try.

I think the evidence suggests that the universe we are in is spherical but very flat.

As to your main point, "that measuring the size of a finite universe is logically possible from within the universe" is questionable. We can never know that our empirical conclusions based on local measurements will be true of the entire universe we are in. In fact if the space/time continuum that we are in keeps expanding at an accelerating rate then any evidence about the greater universe and the galaxies that are now observable will just disappear.

[Tamminen]

I am not an expert on this, but I have read that there are at least 3 possible geometries describing the universe: flat, spherical and the "saddle" form. Only the spherical makes a finite universe. So I am not speaking of massive objects, that is another story, but the geometry as a result of the whole mass of the universe. But my main point is that measuring the size of a finite universe is logically possible from within the universe.

I am not an expert on these subjects either but I try.

I think the evidence suggests that the universe we are in is spherical but very flat.

As to your main point, "that measuring the size of a finite universe is logically possible from within the universe" is questionable. We can never know that our empirical conclusions based on local measurements will be true of the entire universe we are in. In fact if the space/time continuum that we are in keeps expanding at an accelerating rate then any evidence about the greater universe and the galaxies that are now observable will just disappear.

Yes, we have the measurement problem, and as I said cosmologists have not succeeded to determine whether the universe is finite or infinite, but logically it can be one or the other if the standard cosmological theories are correct, I mean GR and its application to the whole universe.

[BigBango]

In RJG's favor I think we can accept Euclidean Geometry as a priori true as Kant insisted. What we cannot conclude is that "light" does not bend around massive objects. My point is that physical things like how "light" travels do not have to conform to Euclidean Geometry. However we can use the logic of Euclidean Geometry to describe how light acts differently from Euclidean tenants and is therefore something physical which does not have to adhere to those pure concepts of Euclidean Geometry.

In summary, the way light behaves can be described in Euclidean terms as not conforming to Euclidean geometry, but why should the way "light" acts deter us from a logical "mental" way of measuring the behavior of light in the world by assessing its differences from our natural conceptual way of thinking about the world?

[Tamminen]

In RJG's favor I think we can accept Euclidean Geometry as a priori true as Kant insisted. What we cannot conclude is that "light" does not bend around massive objects. My point is that physical things like how "light" travels do not have to conform to Euclidean Geometry. However we can use the logic of Euclidean Geometry to describe how light acts differently from Euclidean tenants and is therefore something physical which does not have to adhere to those pure concepts of Euclidean Geometry.

In summary, the way light behaves can be described in Euclidean terms as not conforming to Euclidean geometry, but why should the way "light" acts deter us from a logical "mental" way of measuring the behavior of light in the world by assessing its differences from our natural conceptual way of thinking about the world?

So you do not believe GR is true? If light proceeds along the shortest route near massive objects, it necessarily proceeds in curved space. That is what gravity is. And the universe can be seen as a massive object, from the standpoint of GR.

[BigBango]

In RJG's favor I think we can accept Euclidean Geometry as a priori true as Kant insisted. What we cannot conclude is that "light" does not bend around massive objects. My point is that physical things like how "light" travels do not have to conform to Euclidean Geometry. However we can use the logic of Euclidean Geometry to describe how light acts differently from Euclidean tenants and is therefore something physical which does not have to adhere to those pure concepts of Euclidean Geometry.

In summary, the way light behaves can be described in Euclidean terms as not conforming to Euclidean geometry, but why should the way "light" acts deter us from a logical "mental" way of measuring the behavior of light in the world by assessing its differences from our natural conceptual way of thinking about the world?

So you do not believe GR is true? If light proceeds along the shortest route near massive objects, it necessarily proceeds in curved space. That is what gravity is. And the universe can be seen as a massive object, from the standpoint of GR.

Yes I do believe in GR. I believe that GR can be understood as to how its physical entities can differ from a pure Euclidean account. The point is that we can understand GR in how it differs from Euclidean terms without committing to the idea that the way light travels commits us to the logic of non Euclidean Geometry. Light has physical properties in space but that does not deny our conceptual measure of those properties in pure logical Euclidean terms.

We can only assume that our local universe is it. We have no idea what the nature is of what cannot observe.

[Consul]

I am not an expert on this, but I have read that there are at least 3 possible geometries describing the universe: flat, spherical and the "saddle" form. Only the spherical makes a finite universe.

Not true:

"Contrary to a widespread opinion, the curvature of space dictates neither the time evolution of the Universe (unless the cosmological constant is zero), nor the finite or infinite extent of space (unless the topology is simply-connected)."

Cosmic Topology: http://www.scholarpedia.org/article/Cosmic_Topology

For example, space could be a 3D torus (hypertorus) with zero curvature (Euclidean geometry) and a finite volume, and without a boundary: viewtopic.php?p=340637#p340637

[Consul]

+++We're being hopelessly off-topic again!+++

[Tamminen]

I am not an expert on this, but I have read that there are at least 3 possible geometries describing the universe: flat, spherical and the "saddle" form. Only the spherical makes a finite universe.

Not true:

"Contrary to a widespread opinion, the curvature of space dictates neither the time evolution of the Universe (unless the cosmological constant is zero), nor the finite or infinite extent of space (unless the topology is simply-connected)."

Cosmic Topology: http://www.scholarpedia.org/article/Cosmic_Topology

For example, space could be a 3D torus (hypertorus) with zero curvature (Euclidean geometry) and a finite volume, and without a boundary: viewtopic.php?p=340637#p340637

Thanks for correction.

[RJG]

You are trying to make a claim of 'delineate-ation', with only one object. It takes TWO to 'delineate' anything. When you look at a line and say the line is 'finite' and it is 'all' that exists, you forget that without the paper that the line is drawn on, there can be no line! It takes TWO to tango. You can't delineate the universe as 'finite' without something to delineate it with!

As Tamminen said "only objects can occupy the space of the universe.

Yes. We can delineate 'objects' from 'space', because we have TWO to tango (delineate); we have "objects" and "space", therefore we can delineate one from the other.

We can "delineate the universe as 'finite'...

Yes we can "delineate it as finite" if there is something else out-there!

But if the universe is "everything", then there is nothing else out-there. And if there is nothing else out-there, then Tam's claim of the universe being "everything AND finite" is logically FALSE. "Everything" AND "finite" are mutually exclusive terms (contradictory), and therefore cannot refer to the same thing. In other words, to delineate something as 'finite' requires a dance partner. But if there is no dance partner, then there can be no "finite-ness".

"Everything and infinite" is logically coherent (sound).
"Everything and finite" is a logical contradiction.
"Not-everything and infinite" is logically coherent (sound).
"Not-everything and finite" is logically coherent (sound).

...if we delineate the SPACE time continuum as within an infinite space of nothing that has no properties…

Aah, so here you are adding a dance partner ("an infinite space of nothing"), so delineation is now possible! By adding this dance partner, you can now RATIONALLY claim the universe is "finite". Kudos to you BB! But this now means that the universe is "NOT-everything". For as you say, there is something 'else' out-there; there is also "an infinite space of nothing"! ...or so you claim.

1. So then WHAT is an "infinite space of nothing"? ...this seems to be "double-speak" nonsense; it seems that you are trying to say "nothing is something" [X=~X] so as to then justify an indoctrinated belief in a 'finite' universe. It seems that you are trying to use ILLOGIC (non-sense!) [X=~X] to justify your point.

2. Also, now you seemingly believe that "infinite" is possible. If infinite is possible, then why not accept the universe itself as 'infinite'? Why kick-the-can-down-road, and claim something else as infinite, so as to then claim this universe is finite? Are you trying to justify, or support, an indoctrinated belief that the universe is supposed to be 'finite'?

...and don't get hung up on the logical contradictions…

YIKES!!! ...okay, well this explains everything now, ...sorry BB, but without 'logic' (sense-making) we only have "non-sense" making, so I'll leave this part of the "discussion" (...or should I say "fairy tale"?).

[Thomyum2]

Agreed, we can "measure" finite things. But finite things cannot logically be everything. If the universe (which includes all its measurement capabilities) is 'finite', then it can't be 'everything'.

A finite everything is an oxymoron. -- 'Finite' is not finite by itself. It takes another (separate) object to delineate 'finiteness'.

If a 'finite everything' is an oxymoron, then so must be an 'infinite something'. How can we profess to know or understand or say anything about an infinite universe? Any statement we can make about it is necessarily insufficient because there is always more there that we do not know or have not explored. There can never be a definitive fixed knowledge of it, no firm fact, if there is always the possibility of something else there that has not yet been measured, sensed, experienced.

[RJG]

Agreed, we can "measure" finite things. But finite things cannot logically be everything. If the universe (which includes all its measurement capabilities) is 'finite', then it can't be 'everything'.

A finite everything is an oxymoron. -- 'Finite' is not finite by itself. It takes another (separate) object to delineate 'finiteness'.

If a 'finite everything' is an oxymoron, then so must be an 'infinite something'.

Not so.

1. A "finite everything" is an oxymoron --- That which is 'finite' has a 'limit'; a point of 'delineation'. This delineation logically implies 'something else' from which to delineate its "finite-ness". Therefore --> "finite" logically implies something else, and "everything" logically implies nothing else. Therefore a "finite everything" is an oxymoron.

2. An "infinite something" is NOT an oxymoron. --- That which is 'infinite' has no limit; no delineation point, and therefore needs nothing else to delineate (establish) its "infinite-ness". Therefore an "infinite something" is not contradictory. Space, time, and matter are all examples of "infinite somethings".

How can we profess to know or understand or say anything about an infinite universe? Any statement we can make about it is necessarily insufficient because there is always more there that we do not know or have not explored.

We do know and understand that "infinite" means "no limit", and if we understand "universe" to mean "space-time-matter" then we also understand the universe is infinite.

[Tamminen]

If a 'finite everything' is an oxymoron, then so must be an 'infinite something'. How can we profess to know or understand or say anything about an infinite universe? Any statement we can make about it is necessarily insufficient because there is always more there that we do not know or have not explored. There can never be a definitive fixed knowledge of it, no firm fact, if there is always the possibility of something else there that has not yet been measured, sensed, experienced.

'Actual infinity' is a dubious concept, but we can try to scetch what finiteness and infinity mean applied to the universe. This is a hypothetical and simplified thought experiment, and essentially the same as what I presented before. I repeat it because there seems to be those who did not get the point, and therefore could not present any relevant counterarguments.

Let us take an arbitrary point in the universe. We go from that point along a straight line. It may happen that we come to where we started from. In that case, if this happens whatever direction we choose, we have gone through the whole universe, and made the conclusion that it is finite. There is no way "outside" of this finite universe and no reason to suppose that there is such an "outside". The distance from our starting point to the same point, along a non-euclidean "meridian" defines the finite size of the universe. Of course there is no limit, we can continue our trip ad infinitum, but the size of the circle remains the same. And if the size increases, the universe expands. This is what 'finite but unbounded' means.

It is also possible that we never come to our starting point, but in fact we can never know, because that can always happen some time in the future, and we do not live forever. So we can never know, in this example, if the universe is finite or infinite, until we come to our starting point, and then we know that it is finite.

[RJG]

The distance from our starting point to the same point, along a non-euclidean "meridian" defines the finite size of the universe. Of course there is no limit, we can continue our trip ad infinitum, but the size of the circle remains the same. And if the size increases, the universe expands. This is what 'finite but unbounded' means.

Tam, the flaw in this reasoning is that you are mixing apples-with-oranges. The "size of the circle" is one thing (; apples), and the "travel around it" is another thing (; oranges). The "size of the circle" is finite and bounded, and the "travel around it" is infinite and unbounded.

At no point does anything commit the logical impossibility of "finite but unbounded".