[Bill S (OP)]

  Infinite is an idea related to measurement.

If that is the case, it must be very loosely related, as infinity is not measurable.

Infinity is not a number since it has no value

Certainly not a number.  I assume you mean mathematical value?

A common example is the set of integers. The set has a beginning but is 'open ended/without limit/unbounded', but NOT infinite.

Agreed – absolutely.  Frustratingly, scientists/mathematicians who may agree with that tend, later, to argue as though they didn’t agree. 

Then there's the question of, how do you ‘approach infinity'?  At night, on your tip toes, or maybe while it's sleeping?
It's a contradiction in terms. You can't ‘approach infinity' anymore than you can approach the horizon, or the carrot on the stick.

We seem to be on the same page – a refreshing change.

How many times have we heard, “it’s more complicated than we originally thought”, when experience doesn't agree with prediction.

Everything is more complicated than I first thought!   

The rest of your post needs consideration, which, unfortunately I don't have time for at present.

[evan_au]

A common example is the set of integers. The set has a beginning but is 'open ended/without limit/unbounded', but NOT infinite.

Frustratingly, scientists/mathematicians who may agree with that tend, later, to argue as though they didn’t agree. 

Well, I don't agree with it - sorry to frustrate you, Bill!
The set of counting numbers is (countably) infinite.
ie you can count how many of them there are by drawing a 1 to 1 correspondence with the counting numbers (which is particularly easy to do, in this case).
There are an infinite number of numbers in this set.

Another instance of the meaningless term is found in the definition of a limit, such as:
the limit of (some sequence of n terms), as n approaches infinity, = u. By definition the sequence can never equal the limit u, because if it did, the statement would be false!

Let's take a simple counter-example:
Take the Fibonnacci numbers: F_n = 1,1,2,3,5,8,13....
Where you can generate the next number by adding the previous two numbers.

You can see that these are heading towards infinity, as each next one (after 2) is at least twice as large as the second-previous one. 

However, as Kepler discovered, if you take the ratio of two successive Fibonnacci numbers, this ratio approaches a finite number (by the time you get to a large number of them):
The Limit of F_n+1/F_n → 1.61803....(the Golden Ratio, φ), as n→∞
See: https://en.wikipedia.org/wiki/Fibonacci_number#Limit_of_consecutive_quotients

[jeffreyH]

Mathematics is full of surprises.

[Bill S (OP)]

Well, I don't agree with it - sorry to frustrate you, Bill!

That doesn't frustrate me at all.  I may not agree with some of the opinions of others, but I respect their right to hold them. The frustrating thing is when people say they agree, then act as though they did not.   

The set of counting numbers is (countably) infinite.

Of course it is.  Cantor demonstrated that; but this is a mathematical infinity.  Even cantor, having asserted that there was no "overarching" infinity, identified "absolute infinity" that could never be reached, and was not mathematically tractable.

The set of counting numbers is (countably) infinite.
ie you can count how many of them there are by drawing a 1 to 1 correspondence with the counting numbers

Only if you know how many counting numbers there are.

You can see that these are heading towards infinity, as each next one (after 2) is at least twice as large as the second-previous one.

So, how much nearer to infinity is, for example, 13 than 8?   Are they not both infinitely far away?

[puppypower]

Say we start with the concept of space-time. At the speed of light reference, the fabric of space-time, to use a metaphor, unravels into separated threads of space and separated threads of time.



This situation allows one to follow a space thread without the inertial constraints of time. This creates the condition, that has been historically called omnipresence.  Or one can follow a time thread without the inertial constraints of distance. This allows one to see the universe, simultaneously. This has been historically called omniscience. All I am doing i extrapolating the math concept.

This unique state of affairs is an artifact of traveling at the speed of light, where the inertial universe appears contracted to a point-instant. As a point-instant there is a perception of simultaneity, in space and time due to the point-instant overlap of everything. The separated threads is a way to magnify this without leaving the C reference.

Time threads and space threads, unwoven from the fabric of space-time, is where infinity can appear, since the C ground state represents a state of infinite entropy. All combinations are possible, at the same time and place.

The threads of time and space, since they are connected to infinite options within space and time, also have a connection to inertial references. For example, forces create accelerations, with acceleration d/t/t. If you  do a dimensional analysis and look at the units of acceleration, it is the same as space-time; d-t, plus some extra time threads; t. The extra time threads are woven into the fabric of space-time, to create pucker; bend of space-space. The extra time threads, since they allow one to move in time, without the constraints of space, allows the mass of the inertial universe, to act as an integrated universe.

Below is a representation of too many time threads to create a very busy local universe. We would need to add some distance threads to organize this better using inertial constraints.

[Bill S (OP)]

Say we start with the concept of space-time. At the speed of light reference, the fabric of space-time, to use a metaphor, unravels into separated threads of space and separated threads of time.

I think I need to take this one "bite" at a time.

"At the speed of light reference"  What does this actually mean?

"...the fabric of space-time, to use a metaphor, unravels into separated threads of space and separated threads of time.

What form does this unravelling take?  How could we observe it?  What is a thread of space?

This situation allows one to follow a space thread without the inertial constraints of time.

Following involves change.  How can you have change without time?

[jeffreyH]

I wouldn't spend a lot of time on it Bill. It's thread hijacking and way off topic.

[Bill S (OP)]

Thanks, Jeffrey. 

The lack of depth of my scientific knowledge makes me reluctant to write something off as being "all my eye and Betty Martin" without some research (which I don't have much time for), or confirmation from someone with more knowledge.   

[jeffreyH]

Thanks, Jeffrey. 

The lack of depth of my scientific knowledge makes me reluctant to write something off as being "all my eye and Betty Martin" without some research (which I don't have much time for), or confirmation from someone with more knowledge.   

You are here to learn and debate which is far more than some are willing to do.

[Bogie_smiles]

Is it too late to get in?

1. Yes

2. No

A working concept of Infinity/eternity, not a mathematical infinity, in regard to the universe, encompasses all there is, all matter, energy, everything, in one boundless, eternal, contiguous space, that has always existed, and features a set of invariant natural laws, some known and some as yet unknown, that not only orchestrate all events, but that also restrain the possibilities of what is and what can be.


Edit: As per the question from Bill S in regard to my answer to #2, see reply #33
https://www.thenakedscientists.com/forum/index.php?topic=71765.msg527444#msg527444
My first version of the post was hastily typed and I simply responded yes to both questions without rereading the OP. Ten minutes later, before any responses, I noticed I had not answered question two according to my beliefs, but had made an error by typing "yes". I edited the first response to answer the second question as "no". Sorry for the confusion.

[Bill S (OP)]

Is it too late to get in?

No way!

A working concept of Infinity/eternity, not a mathematical infinity, in regard to the universe, encompasses all there is, all matter, energy, everything, in one boundless, eternal, contiguous space, that has always existed, and features a set of invariant natural laws, some known and some as yet unknown, that not only orchestrate all events, but that also restrain the possibilities of what is and what can be.

Wow!  That should stir up some +ve and -ve responses – I hope.

Duty calls, here, but I’ll be back. 

[Bill S (OP)]

You are here to learn and debate which is far more than some are willing to do.

When the subject is "infinity", I suspect there are some who think I'm here to try their patience.
Could be - not saying.

[Bill S (OP)]

Bogei_smiles, we need to clarify one point.

You answered “Yes” to Q2; ie there can have been a time when there was (absolutely) nothing.  Yet, you said of the universe that it “has always existed”

How do you equate the two?

[Bogie_smiles]

Bogei_smiles, we need to clarify one point.

You answered “Yes” to Q2; ie there can have been a time when there was (absolutely) nothing.  Yet, you said of the universe that it “has always existed”

How do you equate the two?

My first version of the post was hastily typed and I simply responded yes to both questions without rereading the OP. Ten minutes later, before any responses, I noticed I had not answered question two according to my beliefs, but had made an error by typing "yes". I edited the first response to answer the second question as "no". Sorry for the confusion.

[Bill S (OP)]

I thought that might be the case. Thanks for clarifying.

[Bill S (OP)]

….. one boundless, eternal, contiguous space, that has always existed….

Is change possible within this “space”, or is it timeless, like Barbour’s “Platonia”?

[Bogie_smiles]

In my view, change is constant, and the product of the forces that govern the interaction between matter and energy in said space.

[jeffreyH]

In an infinite expanse and over an eternal time interval it could be said that every possible combination of events must occur. Does this include a photon escaping the event horizon of a black hole? If not then some events will never occur.

[Bill S (OP)]

In my view, change is constant

As soon as you introduce change to infinity, you must run into all the inconsistencies that come with the infinite sequence. 

Does this include a photon escaping the event horizon of a black hole?

Only if that is physically possible.

[Bogie_smiles]

In my view, change is constant

As soon as you introduce change to infinity, you must run into all the inconsistencies that come with the infinite sequence. 

I refer to change as the simple observable goings-on around us.