Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 05/11/2017 16:35:58

What follows may have an ominous look of familiarity about it, but please be patient. As I said in another thread, it is a last attempt to get my ideas straight.
Acknowledging that any necessary modification or explanation can come later; could I ask to start with yes/no answers to a couple of questions? I’ll set a good example by giving my own answers, and, of course, being prepared to defend them later.
1. In our perceived 4+1 dimensional Universe, is it possible to formulate a “working” concept of infinity/eternity beyond a mathematical infinity? Yes.
2. Given that there is something, can there ever have been (absolutely) nothing? No.

Already I see a possible sticking point. What do I mean by a “working” concept?
I mean no more than a concept which can be used in a rational way, without recourse to philosophy or theology.

1. Don't know.
2. Don't know.

Too much Heisenberg makes you uncertain  I think. :)

This is the kind of argument that makes mathematicians and philosophers pull their hair out, but from the standpoint of a mere physicistcumengineer, there are as many kinds of infinity as you need to do the job or explain why it can't be done.
AFAIK the most distant observable object is about 13.5 Gly away, roughly the Schwarzchild radius of all the mass inside that sphere, but I can't think of any reason why there shouldn't be stuff outside the event horizon, nor why there should be a limit to the amount or radius of stuff we can't observe. Now the gravitational sucking of this infinite exauniverse neatly describes the expansion of the observable one, and if bits from the edge of the observable universe disappear over the horizon, there's no reason why they shouldn't coalesce in the exaverse to form new galaxies etc.
At the other end of the scale we can leap from practical infinitesimals to quantum finities depending on whether we are trying to describe the motion of ambient air over a wing or the speed of a single molecule in a "vacuum" chamber.

Thanks Alan. I have difficulty imagining you as a "mere" anything.
That's the sort of post I was hoping would come a bit later. It neatly sidesteps answers to the questions, which are, I think, essential to any promise of progress, especially Q2.

I think the implication is that there was never nothing. IIRC, Hawking's "Black Holes And Baby Universes" hinted at the same notion of pseudocyclic local creation and extinction within a much bigger space than can be observed from any point within it.
"Mere"  Old English (that's me)  a stagnant bog. Ipsi dixit.

Still not committing yourself, Alan. How about sticking your neck out (of the mere) and saying what you think?
Seriously, I'm just looking for opinions, at this stage. I may not always agree with you, but I value your opinion, especially as I know you will defend it.
There are others whose opinions I value, and I hope they will contribute soon.

We won't ever know if there was ever nothing. We can assume that there wasn't ever nothing but that is by choice.
I have no idea what a working concept of infinity would be. Define working.

We won't ever know if there was ever nothing. We can assume that there wasn't ever nothing but that is by choice.
Has anyone demonstrated a mechanism by which something can emerge from nothing?
I have no idea what a working concept of infinity would be. Define working.
It may not be a definition, as such, but I did say what I meant, at this stage.
I mean no more than a concept which can be used in a rational way, without recourse to philosophy or theology.

Position and momentum are continuous functions. A displacement in coordinates is not thought to be quantised. Yet Zeno's paradox suggests that this may not be true at the Planck scale. Is this where nothing exists? In quantum jumps?

Infinity and nothingness inhabit the same space. We can theoretically define both but conceive of neither.
So what is infinity plus 1, or nothingness 1?

Infinity and nothingness inhabit the same space. We can theoretically define both but conceive of neither.
So what is infinity plus 1, or nothingness 1?
If we represent nothingness by zero then minus one is actually something. Since you have moved away from nothing. If we define everything in terms of energy then there may be nothing in the universe.

Is this where nothing exists? In quantum jumps?
To resurrect the famous McEnroe quote: "You cannot be serious!"
In order to have quantum jumps, you have to have something jumping.

If we represent nothingness by zero then minus one is actually something. Since you have moved away from nothing.
This is an example of how mathematics can sometimes be unhelpful if not used with care. Mathematically, zero may be defined as nothing, but in order to make that definition, or even to conceive of zero, a mind has to exist; and that is something. Must there not be a difference between mathematical "nothing" and physical "nothing"?
If we define everything in terms of energy then there may be nothing in the universe.
Is that because the net energy may be zero?
Doesn't that require that +ve and ve energy be present in order to achieve the net balance?

1. In our perceived 4+1 dimensional Universe, is it possible to formulate a “working” concept of infinity/eternity beyond a mathematical infinity? Yes.
2. Given that there is something, can there ever have been (absolutely) nothing? No
No and No.

Infinite is an idea related to measurement.
Infinity is not a number since it has no value. It is a relation about numbers stating there is no limit to a magnitude. A common example is the set of integers. The set has a beginning but is 'open ended/without limit/unbounded', but NOT infinite.
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!
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.
So much for rigorous or precise definitions.
Since mathematics is a language, it’s subject to the same limitations as any language. The terms are by definition, and those definitions are in terms of other definitions, etc. The ultimate reality is, there are no fundamental independent definitions. They are circular or accepted without proof, i.e. postulates/axioms.
Couple this with the fact that human experience has no provable examples of anything without end. Despite the mind being one of the most complex organisms known, it has a tendency to naively conceptualize and oversimplify to obtain a first approximation or preliminary grasp of an idea.
How many times have we heard, “it’s more complicated than we originally thought”, when experience doesn't agree with prediction.

Is this where nothing exists? In quantum jumps?
To resurrect the famous McEnroe quote: "You cannot be serious!"
In order to have quantum jumps, you have to have something jumping.
I saw chalk dust! Damn it!

I saw chalk dust! Damn it!
And chalk dust is something. Mc is with me, I shall not want, or should that be "found wanting"?

Infinity and nothingness inhabit the same space.
This is an example of how our language makes it difficult to talk about infinity or nothingness without letting in the pedants, who say things like “space is something, and we know of no infinite space”.
We can theoretically define both but conceive of neither.
Are you going to go for a definition of either?

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

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 counterexample:
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 secondprevious 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

Mathematics is full of surprises.

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

Say we start with the concept of spacetime. At the speed of light reference, the fabric of spacetime, to use a metaphor, unravels into separated threads of space and separated threads of time.
(https://i.pinimg.com/236x/ec/e3/5a/ece35aea9df66076d0a24912a4aff9dafabricart.jpg)
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 pointinstant. As a pointinstant there is a perception of simultaneity, in space and time due to the pointinstant 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 spacetime, 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 spacetime; dt, plus some extra time threads; t. The extra time threads are woven into the fabric of spacetime, to create pucker; bend of spacespace. 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.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.laurelleaffarm.com%2Fitemphotos%2FvintagecrinklepuckertexturelightweightpolysilkfabricgreenblueyellowfloralLaurelLeafFarmitemnont220431.jpg&hash=596fd58b279f285494af8830b5c2403b)

Say we start with the concept of spacetime. At the speed of light reference, the fabric of spacetime, 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 spacetime, 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?

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

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.

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.

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 (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.

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.

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. :)

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?

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.

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

….. one boundless, eternal, contiguous space, that has always existed….
Is change possible within this “space”, or is it timeless, like Barbour’s “Platonia”?

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

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.

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.

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 goingson around us.

#12
If we represent nothingness by zero then minus one is actually something.
Minus one represents a vector in the complex plane.
#14Must there not be a difference between mathematical "nothing" and physical "nothing"?
Think of the symbol '0' as the empty container, i.e. containing nothing, and serving as a place holder for any number system. A minus integer now has no meaning, since there are no elements to remove. This assumes the symbol '' denotes the operation of subtraction, whereas in #12 it denotes direction, a 2nd attribute of a vector. Integers do not have direction.
#20If that is the case, it must be very loosely related, as infinity is not measurable
It began with counting, with the natural/whole numbers, for purposes of expressing multiplicity, family, livestock, commerce, etc., which is the simplest form of measurement. After someone demonstrated there couldn't be a largest integer, 'thinkers' speculated on determining a size for an 'infinite' set, as is done with finite sets. This is typical deduction, conceptualizing new things in terms of things currently understood *, a direct violation of the anonymous proverb, 'a brick is not made of smaller bricks'. If they continued adding more elements to the set, eventually (when?) it would become infinite. This introduces time as a factor. If a calculation algorithym requires an interval of time for each step, then ‘without limit’ translates to ‘always incomplete’,or impossible.
Consider Dedekinds’ method of forming an irrational number. If you pause at step n, you always have more cuts to make than the n you have done.. You are not making any progress to a final answer.
*A plumber could explain electric circuits in terms of fluid dynamics, but that doesn't mean electricity is water.
#21The 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.
To count is to quantify, typically for the purpose of finding a value that represents the size or extent of something.
Finite and measurable are synonyms for quantifiable. So we have another contradiction in terms. From the definition of 'infinite', infinite number equates to immeasurable number. Is it really a '1 to 1' correspondence?
My conclusion is, the mind lacks the ability to conceptualize the idea of something with a beginning and no end.
Assignment for today:
How do you measure a stick with only one end?

The stick is not infinite in length since it terminates at one end. The is no such thing as half of infinity so there is a dilemma here. This is always the problems with human conceptions of infinity.

From the definition of 'infinite', infinite number equates to immeasurable number. Is it really a '1 to 1' correspondence?
My conclusion is, the mind lacks the ability to conceptualize the idea of something with a beginning and no end.
Assignment for today:
How do you measure a stick with only one end?
Ok, I'll bite.... ;)
Lets take the integers (positive and negative whole numbers): 0, ±1, ±2, ±3, ±4..... etc
This could be considered a "ruler with two ends".
How do you put this in 11 correspondence with the nonnegative integers: 0, 1, 2, 3, 4....etc? (which you could consider to be a "ruler with one end")
There are many ways to do it, but a simple one is:
 0 (in nonnegative integers) corresponds to 0 (in integers)
 even number n (in nonnegative integers) corresponds to n/2 (in integers), eg 54 corresponds with 27
 odd number n+1 (in nonnegative integers) corresponds to n/2 (in integers), eg 55 corresponds with 27
By using a pronumeral "n", or the abbreviation "etc", I can make an infinite number of true statements in a single statement, and so I can prove 11 correspondence for an infinite number of cases  without consuming all the electrons in the universe (and still failing).

In my view, change is constant, and the product of the forces that govern the interaction between matter and energy in said space.
OK with that; but you still have divisions of infinity. If you remove one such division, what are you left with? Infinity 1?

The stick is not infinite in length since it terminates at one end. The is no such thing as half of infinity so there is a dilemma here. This is always the problems with human conceptions of infinity.
It will be fascinating to see what responses you get to this. I have been saying this in various guises for several years, in this and other forums. Someone always comes up with a mathematical “answer” that doesn’t really address the issue.

OK with that; but you still have divisions of infinity. If you remove one such division, what are you left with? Infinity 1?
I didn’t include “divisions” of infinity in my definition. I think that if you have an infinite universe, there are no divisions of it, that I know of. Give me an example.

I can make an infinite number of true statements......
Let's make a bid for clarity: Is infinity a number? What is "an infinite number of" anything?

I think that if you have an infinite Universe, there are no divisions of it, that I know of.
Agreed. However, if you admit change, then you have the universe before, and after, each change; thus you have divisions. I would argue that in infinity there can be no change.
If the cosmos is infinite, there can be no change within the cosmos. You may ask how I equate that with the idea that the Universe is "part" of the cosmos, and the Universe, manifestly, changes. Hopefully we'll get there. but res unum post alium

Agreed. However, if you admit change, then you have the universe before, and after, each change; thus you have divisions. I would argue that in infinity there can be no change.
If the cosmos is infinite, there can be no change within the cosmos. You may ask how I equate that with the idea that the Universe is "part" of the cosmos, and the Universe, manifestly, changes. Hopefully we'll get there. but res unum post alium
My definition of infinity, in regard to the universe, does have language that can avoid such an inconvenient interpretation. It is in the last phrase, when talking about the invariant natural laws … “that also restrain the possibilities of what is and what can be.” According to my interpretation, your interpretation that, "there can be no change" within the cosmos, could be a violation of the set of invariant natural laws.
For example, since it is in accord with the natural laws that when there is the presence of matter and energy, there is going to be continual change, then it is natural that there would be change within the “one boundless, eternal, contiguous space”.

According to my interpretation, your interpretation that, "there can be no change" within the cosmos, could be a violation of the set of invariant natural laws.
It could also be a violation of some unknown divine edict, but unless we know what that invariant natural law, or divine edict might be, how can we base a scientific argument on either?
For example, since it is in accord with the natural laws that when there is the presence of matter and energy, there is going to be continual change, then it is natural that there would be change within the “one boundless, eternal, contiguous space”.
Let’s consider a single change in “the one boundless, eternal, contiguous space”. This space has always existed in a specific state. Then comes change; after which its state is different.
Is this not like Jeffrey’s stick; it “is not infinite in length since it terminates at one end”?

It could also be a violation of some unknown divine edict, but unless we know what that invariant natural law, or divine edict might be, how can we base a scientific argument on either?
A divine edict is not science because the supernatural is not recognized by the scientific method. Anything that seems Supernatural, has natural causes that we don’t yet understand.
Let’s consider a single change in “the one boundless, eternal, contiguous space”. This space has always existed in a specific state. Then comes change; after which its state is different.
Where does the idea that the contiguous space has always existed “in a specific state”, come from? It has always existed and has always encompassed all there is, all matter, energy, everything, in one boundless, eternal, contiguous space, and the straight forward interpretation is that such a universe would be in more than one state, and would probably encompass all of the possible states permitted by the invariant natural laws.
Is this not like Jeffrey’s stick; it “is not infinite in length since it terminates at one end”?
Infinite and eternal, no beginning, no end, (and nothing Supernatural), is my interpretation of the stated definition of a working concept of Infinity/eternity.
There must be better definitions out there; someone will post one if they want to improve on mine.
Edit: Let me know if this line of discussion goes beyond the intended scope of this subforum.

Bogie_smiles, I'm not ignoring your post, but am finding breathing (and thinking :) ) a bit difficult today, and want to be able to do justice to your points.
I might look for some "reprise" points as an easy option, and to try to stop them from slipping into oblivion.

“It’s reprise time folks” Yes, that was Hughie Green, but who’s old enough to remember that?
We won't ever know if there was ever nothing. We can assume that there wasn't ever nothing but that is by choice.
Has anyone demonstrated a mechanism by which something can emerge from nothing?
I know books have been written about it, but doesn't the "nothing" always turn out to be "something"?

I can make an infinite number of true statements......
I do not claim that I can make an infinite number of statements that are particularly novel or profound.
 But it is useful in mathematics, where you can concisely make statements that are true for all numbers.
 eg a+a = 2*a is true for all real numbers.
Let's make a bid for clarity: Is infinity a number? What is "an infinite number of" anything?
I would say that "infinity is not a specific number; it is larger than any specific number.".
As Cantor showed, there are different kinds of infinity:
 There are an infinite number of integers. But you can count them. This is called ℵ_{0}
 Some kinds of infinity (eg the number of "real" numbers) is so much larger than the number of integers that you cannot count them. This is called ℵ_{1}
 There are even larger infinities.
See: https://en.wikipedia.org/wiki/Aleph_number
I would also say that we don't have any examples of an infinite number of real, physical things. So the physical world does not map directly onto mathematics.

Eh. Evan :)
If we had, wouldn't that change it into something finite?

For the infinite series of positive integers can we start counting from the highest and count downwards? Would we ever reach zero? Could we find a highest number to start from? If so isn't that a finite series?

For the infinite series of positive integers can we start counting from the highest and count downwards?
There is no highest, it is an infinite series to the high side.
Would we ever reach zero?
If you could find a starting point to count backwards from, you could reach zero, but the premise of staring from the highest number in an infinite series is flawed.
Could we find a highest number to start from? If so isn't that a finite series?
That is a no and a yes, :) .

For the infinite series of positive integers can we start counting from the highest and count downwards?
There is no highest, it is an infinite series to the high side.
Would we ever reach zero?
If you could find a starting point to count backwards from, you could reach zero, but the premise of staring from the highest number in an infinite series is flawed.
Could we find a highest number to start from? If so isn't that a finite series?
That is a no and a yes, :) .
Exactly! So how is an infinite series countable if you can't count from the highest to lowest?

For the infinite series of positive integers can we start counting from the highest and count downwards?
There is no highest, it is an infinite series to the high side.
Would we ever reach zero?
If you could find a starting point to count backwards from, you could reach zero, but the premise of staring from the highest number in an infinite series is flawed.
Could we find a highest number to start from? If so isn't that a finite series?
That is a no and a yes, :) .
Exactly! So how is an infinite series countable if you can't count from the highest to lowest?
Its not.
Edit to my working concept of infinity/eternity: That definition could be expanded to include an infinite mathematical series, as well … A mathematically infinite series is simply an ever increasing or ever decreasing series, or both. In the case of both, counting forward or backward from any selected starting point will never result in reaching the beginning or the end of the series.
Even if you count by tens, lol.

For the infinite series of positive integers can we start counting from the highest and count downwards?
Yes; the difference in the mathematical equation is as follows:
= 2 (Oops! :[ 2 is the answer if you start from n=0, not n=1 )
= 2
You basically reverse the upper & lower limits.
But the answer remains the same (2).
Would we ever reach zero?
Only by doing an infinite number of operations at once.
Mathematics has a number of ways of doing this, including the ∑ operator.
Could we find a highest number to start from? If so isn't that a finite series?
Yes (by approximation) and Yes.
For example, the standard mathematical infinite series for arctan converges fairly slowly, especially around π/4 radians.
But most people don't want their calculations done to infinite precision  most people are happy with 818 digits, most of the time (unless they are actually trying to break the record for generating the most digits for π).
There are various mathematical transformations that allow you to approximate an infinite series to a specific number of decimal places, using a finite series instead of an infinite series. That gives you a predictable execution time for your mathematical library, so your selfdriving car doesn't suddenly become unresponsive when the road swings around to bearing π/4.
See, for example: https://en.wikibooks.org/wiki/Trigonometry/For_Enthusiasts/Chebyshev_Polynomials
But approximation is more in the realm of applied mathematics, rather than pure mathematics.
The real world is so complicated (and not so well understood) that sometimes approximations are all we have.

jeffreyH #41
The stick is not infinite in length since it terminates at one end.
The set of integers has a beginning and no end, and is considered 'infinite'.
I think you are confusing 'infinite' with 'eternal', without beginning and end, with respect to time.
This is always the problems with human conceptions of infinity.
I agree. The mind only experiences finite things, whether natural or manmade. Some only appear to be permanent due to a long decay/transformation process.
The stick;
Keeping it simple, align the zero of the ruler to the end of the stick. How do you perform the 2nd alignment of the stick with the ruler, if you can't find the other end? If you say it's a distance x units from the 1st end, you are wrong (since there is no largest integer x). I.e., if it has no 2nd end, it has no measurement. This exposes the faulty extrapolation of applying mathematical operations for finite objects to nonfinite objects.
Cantor associated the idea of 'infinity' with God, and believed his thoughts concerning it were revelations from above. Given his chronic periods of depression, his concern with his standing in the mathematical community, and his assumed position as self appointed spokesman, his conclusions are not surprising.
This is just a continuation in human history of someone wanting to play god, but doesn't know how.

A divine edict is not science because the supernatural is not recognized by the scientific method. Anything that seems Supernatural, has natural causes that we don’t yet understand.
I’m not suggesting that we should try to introduce the supernatural to scientific thought. I was simply wondering about the extent to which a possible violation of a hypothetical set of invariant natural laws might be scientific, rather than philosophical.

I am not exactly confusing infinity with eternity since one could be considered spatial and the other temporal. We can't find an end to time since even vacuum fluctuations indicate changing states. So saying it's the big bang might be wrong.

Where does the idea that the contiguous space has always existed “in a specific state”, come from? It has always existed and has always encompassed all there is, all matter, energy, everything, in one boundless, eternal, contiguous space, and the straight forward interpretation is that such a universe would be in more than one state, and would probably encompass all of the possible states permitted by the invariant natural laws.
Possibly a bad choice of wording on my part. I was trying to look at infinity before and after a single change.
The states before and after that specific incident may have been states of continual change; but each would differ from the other as a result of the change we were considering. Does that make sense?

I would say that "infinity is not a specific number; it is larger than any specific number."
I’m reluctant to suggest you might be prevaricating, here, Evan; but the question was:
“Is infinity a number”. Does answering it by saying that is is not a specific number mean that you think it is a number of some sort? If so, what sort?
When you say: “it is larger than any specific number"; in what way is it larger? Are you saying it is not a number, but has some numerical value?

A divine edict is not science because the supernatural is not recognized by the scientific method. Anything that seems Supernatural, has natural causes that we don’t yet understand.
I’m not suggesting that we should try to introduce the supernatural to scientific thought. I was simply wondering about the extent to which a possible violation of a hypothetical set of invariant natural laws might be scientific, rather than philosophical.
Ok, I was just stating the obvious.
If a set of speculative and/or hypothetical invariant natural laws could be defined to make up a model, the premise would be that there can be no violation to that set. If any specific law identified as part of that model is violated, it falsifies the model.
My response is that the definition of a working concept of an infinite/eternal universe can be dissected by looking at individual natural laws, as I interpret you are suggesting, and showing that they can be violated.
For example, if the Universe could be shown to be finite spatially or temporally, it would violate the stated nature of the infinite/eternal universe in the definition, and would falsify the definition. The philosophy of the situation comes into play when the definition is not falsifiable, because there is no experiment to test it.

I am not exactly confusing infinity with eternity since one could be considered spatial and the other temporal. We can't find an end to time since even vacuum fluctuations indicate changing states. So saying it's the big bang might be wrong.
“We can't find an end to time ”
This could be another of the difficulties that arise from the use of finite terminology in an attempt to discuss the infinite; but, just to clarify; are you saying that eternity is infinite time?

you might be prevaricating, here, Evan
Well, potentially, sometimes...
When you say: “it is larger than any specific number"; in what way is it larger?
For any specific, finite integer n, there exists a number n+1 which is larger than n.
Therefore n is less than infinity.
Mathematicians would write this as something like: ∀ n ∃ n+1: n+1 > n ∴ n < ∞
Where "∀" means "for all", and is another one of those mathematical tricks that allow you to make an infinite number of statements in a very small space.
Are you saying it is not a number, but has some numerical value?
It cannot have a specific numerical value (as proven above).
(Perhaps prevaricating again): It is not a specific number, but is more of a trend. This trend is contextspecific.
Mathematicians will say things like e^{x} = 0
This means that the Limit (or trend) of e^{x} is towards zero as x gets very large.
One of the reasons mathematicians avoid using ∞ as a number is that you can get yourself in trouble when you try to apply normal arithmetic/algebraic rules. For example, you could write: ∞ + ∞ = ∞
But when you reverse it and try to do ∞  ∞, is the answer 0, or ∞? Or somewhere inbetween?
Similarly, when you try and write ∞/∞, is the answer 0, 1, or ∞?
At times like these, you need to ask for more information.
In the example I gave earlier of Fibonnacci numbers,
F_{n} = ∞
You know this because for any finite integer y that you give me, there exists a finite value n whose Fibonnacci number F_{n} is greater than y.
∀ y ∃ n: F_{n} > y
Now, when you take the ratio of two successive Fibonnacci numbers:
F_{n+1}/F_{n}
It might look like ∞/∞, but that is only because you have thrown away most of the information.
In fact, when you consider all the information,
F_{n+1}/F_{n} = Φ ≈ 1.618033988749895...
“Is infinity a number”. Does answering it by saying that is is not a specific number mean that you think it is a number of some sort? If so, what sort?
I will probably get in trouble with real mathematicians here*, but provided you don't throw away all the information, you can sometimes come to some sort of answer. For example, if:
∞_{1} = the number of positive integers = (1, 2, 3, 4, 5, 6, ....)
where "..." is another of those mathematical tricks for doing an infinite number of things on a single line
∞_{2} = the number of positive even integers = (2, 4, 6, 8, ....)
You can show that ∞_{1} = ∞_{2}, as described above
But what about ∞_{1}  ∞_{2}? Is it 0, ∞, or somewhere inbetween?
If you remove the set of positive even integers from the set of positive integers, you end with the set of the positive odd integers (which is an infinite set).
I venture to suggest that in this case, provided you don't throw away all the available information, it looks like you are doing ∞  ∞ = ∞, but in reality you are subtracting infinite sets and counting the results, rather than subtracting infinite numbers and getting an answer.
However, different cases will produce different answers, because each individual case is different, when you consider all the information.
*I am only an imaginary mathematician (I only studied 3 years of maths at university level). ;)
If a set of speculative and/or hypothetical invariant natural laws could be defined to make up a model, the premise would be that there can be no violation to that set. If any specific law identified as part of that model is violated, it falsifies the model.
We have talked in this thread about Cantor's mindbending mathematical results.
Kurt Gödel also had some mindbending results. My simple interpretation is that in any sufficiently complex (mathematical) system, there will be true statements that you can't prove within that system, and/or there will be contradictions that you have to live with.
Mathematics does not map directly into the real world, but I think that your hypothetical natural invariant laws about the physical world may suffer the same fate.
See: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

Thanks for that very expansive answer, Evan. Please don’t think that I am unappreciative when I say that all you have done is confirm what I have said all along: namely, that mathematical infinities can be manipulated within the scope of mathematics. I am in no way qualified to criticise them or their use, even should I wish to do so. In fact, I have no wish to try.
What I am saying is that, as I see it, mathematical infinities and physical infinity are different things. There has been some fascinating stuff in this thread, but, as yet, nothing to convince me otherwise.

Cantor may have contributed to number theory, but his ideas about infinity were not accepted by all. The constructivist view rejects them.
The statement " there are as many even integers as integers",
is typically demonstrated using a 'one to one' correspondence as shown.
N: 1 2 3 4 5 6 ...
E: 2 4 6 8 10 12 ...
This is contradicted by:
1. Random sampling of integers results in an average of 50% even E, 50% odd D.
Statistics can be verified in the real world, and is useful in applications of probability.
2. In the above example, removing E from N leaves D, removing E form E leaves nothing, so where is the logic? An odd feature of this example is the appearance of the same integers in both sets.
The 'bijection' for example 1 defines y=2x, as a mapping from N to E. I see the results as not about the size of sets, but about the definition used for mapping.
Representing the first 'one to one/ correspondence above in a rectangular form, partitioned into subsets:
1 2 4 8...
3 6 12 24...
5 10 20 40...
...
The odd integers, all listed in column 1, are paired with the column of even integers to the right.
The remaining even integers in each column are paired with the column to the right.
The pairing is independent of direction. If a is paired with b, then b is paired with a.
The odd are paired 1 to 1 with an even.
The first subset of even (col 2) is paired with odd (col 1) and even (col 3).
The remaining even are paired with two columns.
Not all pairings are 1 to 1, and each integer appears only once.
A different correspondence can be formed with a subset of N as:
N: 2 4 6 8 10 12 ...
E: 2 4 6 8 10 12 ...
From this example, N is greater than E, since D in N has no corresponding members.
We can also map S the set of squares to N the set of naturals, without exhausting the set N.
N: 1 2 3 4 5 6 7 8 9 ...
S: 1 4 9 ...
N contains S, but S does not contain N.
N>S
A true example of a 11 correspondence, "there are as many even integers as odd integers "
D: 1 3 5 7 9 11 ...
E: 2 4 6 8 10 12 ...
A subset of N can always be paired/mapped to itself and remain less than N.
Maybe the first statement of the correspondence is a poor choice of words, similar to ‘approaching infinity’.

A stick can indeed be infinite. Having one end is not a problem: however long your stick may be, I can conceive of a longer one, without limit. We often use the term "semiinfinite" in physics and applied maths to denote a quantity or space with an origin and no positive limit. It's just one of several useful infinities, and AFAIK there is provably an infinity of infinities for which we have no conceivable use.
There is no contradiction in a countable or "denumerable" infinity. All it means is that you can in principle assign an ordinal number to every member of the set, but that doesn't mean you can predict the nth member

It's an interesting video by Vsauce showing different types of infinity.

infinite: adj
not measurable: without any limits that can be measured or realized
latin; not finite
It is an attribute modifying a noun, denoting a relationship to its surroundings, having no boundary.
infinity: noun
the property of (an unidentified) something being infinite.
Assume a substance s is infinite. Here is a volume of space with no s. If this space is filled with s, then the total volume of s is increased. This is a contradiction since by definition s is unlimited.
There cannot be an infinite amount of any substance.

A stick can indeed be infinite. Having one end is not a problem: however long your stick may be, I can conceive of a longer one, without limit.
How can you extend something without a limit?
(infinite: unmeasureable).
A dictionary is the best reference.

The question is: how many square integers are there in the interval from 1 to 10?
If we count the squares, there are 10.
The one to one correspondence states there are as many squares as integers.
N: 1 2 3 4... 9 10
S: 1 4 9 16...81 100
What is it that results in that statement?
Yes, there are 10 integers in each row, but the integers are symbols representing sets.
There are 10 symbols in each row, so counting from '1' in the ordered set N, we arrive at the symbol that represents the set with the correct number of elements in the set S.
The 11 counts symbols, not sets.
The set of 10 squares S, ranges from 1 to 100, a density of 1/10, meaning there are 90 integers in N from 1 to 100 that are not squares.
Cantors interpretation is not acceptable.

A stick can indeed be infinite. Having one end is not a problem: however long your stick may be, I can conceive of a longer one, without limit.
How can you extend something without a limit?
(infinite: unmeasureable).
A dictionary is the best reference.
You don't have to extend the stick, but just consider the possibility of adding a bit at either end, to whatever stick the other guy is holding. Now you have a concept of a seminfinite body.
A dictionary is a poor reference for such a technical term as infinity.
Consider first the number of possible integers 1... N ... N+1 etc.However large you choose N, I can propose N+1 as a larger integer, so the number of possible integers is infinite, even by a dictionary definition.
But between any two integers there is an infinite number of rational numbers such as 2, 3/2, 4/3,.....(N + 1)/N....., 1 So the number of rationals is a greater infinity than the number of integers.
And between any pair of rational numbers there is an infinity of irrationals, so there is yet a greater infinity........
One question worth asking is whether the number of irrationals is a denumerable infinity. Now we are talking maths, not dictionaries. Fun, isn't it?

1. Random sampling of integers results in an average of 50% even E, 50% odd D.
Statistics can be verified in the real world, and is useful in applications of probability.
How often have you run into an infinite number of real objects in the real world?
Conventional Probability is of limited use when dealing with infinities.
50% of ∞ = ∞
1% of ∞ = ∞
Unless you get down to infinitesimal probabilities, which are numbers which are as small as ∞ is large; then you can come up with finite answers that start to follow conventional relationships like < and >. But you have to be careful not to throw away too much information, or you end up with statements like 0 x ∞, which you can't resolve.
Integration adds up an infinite quantity of infinitesimals to come up with a finite answer  at least, in the examples they give you in high school. Not all functions are so forgiving.
https://en.wikipedia.org/wiki/Infinitesimal
But between any two integers there is an infinite number of rational numbers such as 1/2, 3/2, 4/3,.....(N + 1)/N....., 1 So the number of rationals is a greater infinity than the number of integers.
Cantor showed a way of mapping the fractions onto the integers  this is shown nicely in the first couple of minutes of the video. So there is the same number of rationals as there are integers = .ℵ_{0}
Mindbending stuff!
Cantor showed that the number of real numbers (which includes irrationals) = ℵ_{1} is greater than the number of integers = ℵ_{0}. So the real numbers is not countable, since there are more of them than there are counting numbers.

In fact, random sampling of a set of integers won't give you 50% evens. If it did, you would suspect your sampling process of being selective, not random. It would be fairly clear as the sampling progressed that it was tending towards 50%, but if the sample is of an odd number of integers it cannot contain 50% of evens.
As an aside: We can use the χ^{2} "goodness of fit" parameter to determine whether we have a truly random sample of an experimental result. If we obtain an exact fit to the hypothesis at each measurement, it is more likely than not that the equipment is faulty and biased. Simplest case is where the expectation value is zero (a null experiment) and successive readings are exactly zero. The probability is that the equipment is not working at all. Not a joke: you can fly "perfectly straight and level" and spiral into the sea because the gyroscopic instruments are not switched on!

I'm just home from a short stay in Hosp. I'll be back in the thread as soon as I feel a bit better, and can catch up.
Don't let it die in the meantime. :) Looks as though there is some interesting content.

infinite: adj
not measurable: without any limits that can be measured or realized
latin; not finite
It is an attribute modifying a noun, denoting a relationship to its surroundings, having no boundary.
infinity: noun
(an unidentified) something being infinite.
Assume a substance s is infinite. Here is a volume of space with no s. If this space is filled with s, then the total volume of s is increased. This is a contradiction since by definition s is unlimited.
There cannot be an infinite amount of any substance.
The universe shows us just the opposite. Matter is discrete finite units at all levels, from astronomical to atomic. The closest candidate to qualify as infinite would be space.
Even that isn't necessary since physics at the local level is independent of remote mass (relativity).
That’s my basis for no usable/meaningful application of a physical ‘infinity’.

Gently back into the thread.
I’d like to go back to the content of #52.
We won't ever know if there was ever nothing. We can assume that there wasn't ever nothing but that is by choice.
Has anyone demonstrated a mechanism by which something can emerge from nothing?
Although the quote is Jeffrey’s, I would appreciate an example from anyone.

Assume a substance s is infinite. Here is a volume of space with no s. If this space is filled with s, then the total volume of s is increased. This is a contradiction since by definition s is unlimited.
I would anticipate a response from a mathematician along the lines:
Not necessarily, because the infinite amount of s might simply spread into the space where there was previously no s, with no increase in the amount of s. Of course, this is similar to “Hilbert’s Hotel” that works only because we can never reach infinity, in our physical world.
There cannot be an infinite amount of any substance.
That is, unless you accept the (dreaded) infinite sequence; or subscribe to the idea of an infinite, changeless cosmos.
The universe shows us just the opposite. Matter is discrete finite units at all levels, from astronomical to atomic. The closest candidate to qualify as infinite would be space.
I understand that experts are still arguing as to whether space is continuous or quantised. In any case, the only space of which we have any direct experience is our 3+1 D spacetime (Yes I did say 4+1 earlier but it was a typo.).
Unless/until we can establish a way in which something can come from nothing, it seems reasonable to suspect there might be more than that “out there”.

Has anyone demonstrated a mechanism by which something can emerge from nothing?
Brian Cox said that it is possible that there was nothing before the Big Bang.
I think he referred to quantum fluctuations as a possible source for something to appear from nothing.
Of course, that assumes that there is some potential energy somewhere that would produce the something, and allow it to continue to exist.
I'm just home from a short stay in Hosp.
Was that the inspiration for this thread on the infinite and eternity? ;)
I'm glad to see you back online!

Brian Cox said that it is possible that there was nothing before the Big Bang.
I think he referred to quantum fluctuations as a possible source for something to appear from nothing.
Of course, that assumes that there is some potential energy somewhere that would produce the something, and allow it to continue to exist.
It isn’t unusual to see well known science personalities talk about “before the Big Bang”. If Cox speculated about a quantum fluctuation “before” the Big Bang, I think someone should say, “Welcome to the world of infinite regress”, i.e., what caused the quantum fluctuation?
Is the Supernatural excluded from the scientific method? Would a quantum fluctuation with no cause qualify as the Supernatural?
I'm just home from a short stay in Hosp.
Hope all is well. Thanks for picking back up on the activity

Brian Cox said that it is possible that there was nothing before the Big Bang.
I think he referred to quantum fluctuations as a possible source for something to appear from nothing.
For an erstwhile onehitwonder Pop "Star", Brian Cox makes an interesting science presenter. His enthusiasm comes over as real, and I like (most) of his programs that I've seen. I've even bought some of his DVD to rewatch. However his comments about nothing and quantum fluctuations make no more sense now than when Stephen Hawking said the same thing.
Of course, that assumes that there is some potential energy somewhere that would produce the something, and allow it to continue to exist.
It's that very somethingy nothing again. It keeps appearing, but no one seems to explain it.
Was that the inspiration for this thread on the infinite and eternity? ;)
I'm glad to see you back online!
No, but the idea appeals. :)
Thanks for the sentiment.

Is the Supernatural excluded from the scientific method? Would a quantum fluctuation with no cause qualify as the Supernatural?
IMO, "preternatural", perhaps; "supernatural", no. (Interesting to see what Alan says about that).
Hope all is well. Thanks for picking back up on the activity
Thanks. Good to be back.

We have been talking about infinities that occur after a seemingly unreachable infinity of steps.
But related problems can occur at finite levels, such as the "sinc" function: sinc(x) = sine(x)/x.
What happens to sinc(x) as x → 0? It looks like sinc(0) = 0/0.
 Is the answer 0, because the numerator is 0?
 Is the answer ∞, because the denominator is 0?
 Or is it somewhere inbetween?
Again it comes back to using all the information you have available.
L'Hopital's rule says differentiate the numerator and denominator, and see what you get.
sin(x)/x for x=0 = cos(0)/1 = 1/1 = 1
This has real commercial application in telecommunications, because sinc(0) comes up frequently.
See: https://en.wikipedia.org/wiki/Sinc_function

Without knowing much about the sinc function other than that I believe it is used in statistics, I would say we are still looking at maths, so, if infinity is not a number, are we looking in the right place for any sort of evaluation of anything other than its mathematical "approximations"?

Interestingly the opinions of those who answered the original questions directly enough to assess their actual position seemed to be divided roughly as follows.
Q1 Yes and Don’t Know where even, with no one giving a direct No. Although one poster gave a yes and no in the same post; #15.
Q2 No and Don’t Know where even, with no one giving a direct Yes.
Before trying to review explanations and reasons, I should check if there is anyone who felt that he/she gave a direct “No” to Q!, or “Yes to Q2, that I’ve missed?

Although one poster gave a yes and no in the same post; #15.
Look again, my reply was no and no.
I broke off the math debate, since it is another issue wandering away from the op.
I would ask, show me something that is in physical reality unbounded/immeasurable.

Thanks, Phyti. I looked several times, but the "Yes" seemed to go with Q1.
Clear now, though; it shall forever be recorded as "No and No".
So, #88 should read: Q1 "Don’t Know was slightly the favourite, with "No" and "Yes" coming joint second..

I would ask, show me something that is in physical reality unbounded/immeasurable
I certainly can't do that, but I suspect it is possible to construct a line of reasoning that .establishes that something "unbounded/immeasurable" must be a reality. I think you agree with that. Would I be right?

It may be silly to post more, while there are still unanswered points, but sometimes answers don't come, and I'm anxious not to let this slip, if possible.
Position and momentum are continuous functions. A displacement in coordinates is not thought to be quantised. Yet Zeno's paradox suggests that this may not be true at the Planck scale.
I'd be interested to know how you draw that conclusion from Zeno's paradox.
Vilenkin (“Many Worlds in One”) says: “The key observation was that the number of distinct configurations of matter that can possibly be realized in any Oregion [his term which doesn’t need explanation here] – or for that matter in any finite system – is finite. One might think that arbitrarily small changes could be made to the system, thus creating an infinite number of possibilities. But such is not the case.
If I move my chair by 1 centimerer, I change the state of our 0region. I could instead move it by 0.9, or 0.99, 0.999, etc., centimetre – an infinite sequence of possible displacements, which more and more closely approach the limit of 1 centimeter. The problem, however, is that displacements too close to one another cannot even in principle be distinguished, because of the quantummechanical uncertainty.”
If your observation is right, he and Zeno seem to be on the same page.

I too want to keep it going, so forgive me if I am hindering progress or stepping in.
It is true that particles are thought to be quantized, but in terms of the mechanics of how particles move, wouldn’t quanta continually be added and removed during motion?
I ask that because not only are particles considered quantized, but they also display waveparticle duality. Adding and removing quanta would then seem to have to be a wave process. Does a wave front move in continuous motion or is it incremental? If it is continuous, how do the invariant laws of nature enforce limits on how much wave motion equals a quantum?
How can we get answers to these kinds of questions without agreeing on the nature of particles themselves? Do you have that pinned down yet?

I too want to keep it going, so forgive me if I am hindering progress or stepping in.
You’re certainly not hindering things, and “stepping in” is, surely, what discussion threads are all about.
It is true that particles are thought to be quantized, but in terms of the mechanics of how particles move, wouldn’t quanta continually be added and removed during motion?
How would the addition of quanta influence the minimum distance Vilenkin could move his chair? I can see that it might influence the total distance, but not the minimum.
The wave/particle thing becomes difficult because we tend to think in terms of wave or particle; or wave and particle. Perhaps we should be thinking in terms of neither wave nor particle, but something different. Only our limited perception/knowledge/understanding/information obliges us to attach familiar labels like particle and wave.
How can we get answers to these kinds of questions without agreeing on the nature of particles themselves? Do you have that pinned down yet?
No way! I have nothing pinned down. (On second thoughts: I don't have "nothing" pinned down, either. :) )

How would the addition of quanta influence the minimum distance Vilenkin could move his chair? I can see that it might influence the total distance, but not the minimum.
If a particle has a particular number of quanta, and if motion is quantized in waves that carry a quantum of energy, motion might consist of quanta (waves) emitted and quanta (waves) absorbed in difference directions, quanta being added or absorbed in the direction of motion, and quanta being left behind or emitted, as the location of the particle gets redefined with each addition/subtraction.
The wave/particle thing becomes difficult because we tend to think in terms of wave or particle; or wave and particle. Perhaps we should be thinking in terms of neither wave nor particle, but something different. Only our limited perception/knowledge/understanding/information obliges us to attach familiar labels like particle and wave.
Particles contain energy, and the energy can be substantial, so there is some logic in the idea that the amount of energy contained in a particle influences the wave energy density within the particle. The more quanta you fit into the particle space, the denser the particle. How do you get more quanta within the particle space, you accelerate the particle. Nature does this all the time, and scientists have gotten pretty good at it too.
No way! I have nothing pinned down. (On second thoughts: I don't have "nothing" pinned down, either. :) )
If you believe there never was nothing, I think you have it pinned down; it is good logic, so there is no need to over analyze it. Just be alert to developments that might falsify your belief (your are on safe ground, lol). Then, as you confirm by answering “yes” to question #1 in the OP that you think there can be a working definition, did you post your working definition yet?

Bogie_smiles, you talk as though quanta as though they had an independent existence; is that my misinterpretation?
What would a quantum of nothing be like? :)
If you believe there never was nothing, I think you have it pinned down; it is good logic, so there is no need to over analyze it
The problem is not my over analysis; it's more the fact that it seemed to make perfect sense to me, before I started looking for the opinions of others. Once I had done that, and found that there were many who disagreed with me, I had to know why they thought as they did. Sometimes it is not easy to persuade even the most eloquent that they might need to back up their views.

Bogie_smiles, you talk as though quanta as though they had an independent existence; is that my misinterpretation?
Gravitational waves carry energy. LIGO has confirmed Einstein’s prediction. Massive high energy events emit gravitational waves that carry a lot of energy across vast distances, but even an apple falling to the ground will emit gravitational waves. Logic supports the idea that space is filled with wave energy, coming and going in all directions, at the speed of light, form the gravitational wave emissions from nearby and distant particles and objects.
A quantum would be an amount of energy that is quantized in the exchange of energy between the particle and the gravitational wave energy coming and going at all points in space. When the particle emits a gravitational wave, it is logical to expect it to emit energy in quantum increments, if particles are quantized. That implies that the number of quantum increments is stable while the particle is at rest. If so, the logic is that the amount of energy that it absorbs will then equal the amount of energy it emits; a continual exchange of energy in quantum increments.
What would a quantum of nothing be like? :)
I’m tempted to try humor, but will resist, lol.
The problem is not my over analysis; it's more the fact that it seemed to make perfect sense to me, before I started looking for the opinions of others. Once I had done that, and found that there were many who disagreed with me, I had to know why they thought as they did. Sometimes it is not easy to persuade even the most eloquent that they might need to back up their views.
That is fine. I try to weigh the observational and test evidence presented, and in the lack of that, I consider the logic based on my own reasoning, make up my mind about it, and move on to asking about what causes it.

If the first part of your post answers the question about the possible independence of a quantum; I would interpret it as saying that matter/energy must be present for quanta to have any meaning. A quantum has in common with (eg) an inch the fact that each is a measure of something.
Would that be right?

Then, as you confirm by answering “yes” to question #1 in the OP that you think there can be a working definition, did you post your working definition yet?
Not yet; I tend to think of it as a work in progress, but I'll get there, and then will post it.

Where do we stand on: “can there ever have been nothing”?
There seems to be a fairly general feeling that there can never have been nothing, with some even saying so. However, there are some doubts, but efforts to discover any example of something coming from nothing have drawn a blank.
The nearest we have come so far is: “Brian Cox said that it is possible that there was nothing before the Big Bang.” (#82). Seemingly he does not say how this could be possible.
Or; (#83) “If Cox speculated about a quantum fluctuation “before” the Big Bang, I think someone should say, “Welcome to the world of infinite regress”, i.e., what caused the quantum fluctuation?” Of course, “infinite regress” is another form of the infinite sequence, with all its problems.
IMO, “nothing” and an infinite “something” are incompatible, so the question of whether or not there is an infinity that transcends maths is linked to the question of “nothing”; but let’s take one part at a time.

If the first part of your post answers the question about the possible independence of a quantum; I would interpret it as saying that matter/energy must be present for quanta to have any meaning. A quantum has in common with (eg) an inch the fact that each is a measure of something.
Would that be right?
A good place to start is to say that the space in our observable universe has always contained wave energy. One theory that supports that is Big Bang Theory; an instant after the implied Big Bang event, theory has it that a hot, dense, ball of energy emerged in a huge wave and expanded/inflated in volume. That would have been an extremely high energy plasma wave as the source of wave energy as it expanded and cooled.
Stable particles got their mass from exotic massive bosons (perhaps the Higgs boson or mechanism), that formed from the decay of the hot plasma, which is the logical source of the stable particles that exist today.
Expansion caused cooling, and the density of the expanding ball decreased, until those very massive bosons formed, and they continued to cool, separate form each other as expansion continued, and they also decayed due to their instability in the declining energy density environment, until stable particles formed.
The wave energy of the hot dense ball of energy was never destroyed, it became contained in the decay products and eventually in the stable particles, and in the space between them as the first atoms formed. Gravity in that young universe was the natural consequence of both particles and space being composed of wave energy, and so that process of absorption and emission of gravitational wave energy between particles and space began right from the start.
LIGO, and logic say it continues to function today, and is responsible for maintaining the presence of particles and objects, as well as the huge amount of energy that resides in and traverses space at the speed of light.
The amount of energy in the quantum would likely have evolved as the expansion, cooling, and particle decay occurred, until it is what it is today; a tiny quantum increment of which particles are composed.
This scenario closely follows theory, I think, but if it is bad science, I trust I will hear about it. Also, I know you are working on the issue of nothingness, and infinities, so I apologize if I am getting off track.

That's all good stuff as I see it.
Forgive me if I'm being extra dim, but I don't see an answer to the question: do you regard a quantum as something which has an independent existence, or is it just a measure of something?

That's all good stuff as I see it.
Forgive me if I'm being extra dim, but I don't see an answer to the question: do you regard a quantum as something which has an independent existence, …
No. (Edit)The quantum: At this point call this a thought experiment where the term “quantum”, as it pertains to the processes involving particles, mass, and energy that I am discussing is a way to equate wave energy in the sense that waveparticle duality might include wave energy in quantum increments, and quantum action would be a process of wave convergences related to particle interactions (not to be confused with the Quantum of Action, aka the Planck Constant; a photon is said to be one quantum of action that can have a range of energy, but the same photon particle will have numerous quanta of the sort that are found in the process of quantum action to account for the different energies that the photon can carry)(/edit)
or is it just a measure of something?
Hmm, this is all controversial (http://www.differencebetween.com/differencebetweenphotonandvsquantum/), but let me put it this way. A particular photon, say in the microwave energy range, might have a precise number of quanta in its given energy density environment, like in the CMB. If you know how many quanta there are in that low energy photon, then you have a measure of the energy of the photon in quanta. If you know the amount of energy in a quantum, relative to some appropriate standard unit of measure (a tiny fraction of a Newton maybe), then you have a measure that can be used to compare the energies of various particles.
However, if the universe continues to expand for another billion years, the energy density environment will decline. The same photon will occupy more space and have less density, so if the number of quanta remains the same, then the value of the energy in its quanta will be lower because of the lower energy density, I think. But this has to be off topic, and I’m not an authority on anything.

I certainly can't do that, but I suspect it is possible to construct a line of reasoning that .establishes that something "unbounded/immeasurable" must be a reality. I think you agree with that. Would I be right?
No.
There are discreteness of matter, ‘fundamental’ particles, composite objects, from extremely small to extremely large, and quantization of energy. None of these suggest ‘infinity’, and all are measurable.
What is questionble are fields, quantum, em, gravitational, as to composition. discrete or continuous. These also are measurable.
‘Infinity’ remains a mental abstract concept with no physical counterpart.

A particular photon, say in the microwave energy range, might have a precise number of quanta
We would normally say that a single photon has a precise number of quanta: 1.
The quantum of energy measured for that photon is dependent on the relative motion of source and observer.

The quantum of action is Planck's constant. The energy of a photon is this action multiplied by the frequency. Each wave represents one of these quanta. The number of waves or cycles per second produces the magnitude of the energy.

We would normally say that a single photon has a precise number of quanta: 1.
That would be my understanding.
Each wave represents one of these quanta.
I'm OK with the rest of your post, but this seems to suggest that a photon may = more than one quantum.

Each wave represents one of these quanta.
I'm OK with the rest of your post, but this seems to suggest that a photon may = more than one quantum.
The problem is with how you are interpreting ‘wave’.
Most textbooks show the electromagnetic wave as a series of peaks/troughs in the E and B fields, it almost looks like the sort of wave you see on the sea, but it isn’t. It is a time/distance graph of the variation of the E/B fields ie a single wave (or pulse maybe) travelling forward. It’s like flicking a rope and watching the wave travel along it. So the photon is that pulse of energy propagating through space, there is only one wave/pulse for each photon and the energy each one carries is 1 quantum.
I’ll leave Jeff and Evan to talk about the frequency of the photon :)

The problem is with how you are interpreting ‘wave’.
I've been looking again at EM waves, and I think I see what you mean, and where my confusion crept in.

https://www.thenakedscientists.com/forum/index.php?topic=68443.new#new
Relevant in this thread, but not quite yet.

I suspect it is possible to construct a line of reasoning that .establishes that something "unbounded/immeasurable" must be a reality. I think you agree with that. Would I be right?
‘Infinity’ remains a mental abstract concept with no physical counterpart.
To me, this says that you think there may have been nothing. If so, where did the something come from, and how?

A particular photon, say in the microwave energy range, might have a precise number of quanta
We would normally say that a single photon has a precise number of quanta: 1.
The quantum of energy measured for that photon is dependent on the relative motion of source and observer.
True. I got into some controversial usage of the term ”quantum” (http://www.differencebetween.com/differencebetweenphotonandvsquantum/) (not to be confused with the “quantum of action” or "Planck constant” ) when I was talking about thoughts on wave particle duality; in the sense that it might include wave energy in quantum increments. It might have been better if that part of the discussion had been posted to “New Theories”.

I’ve been pulling together some more of the content of this thread, there’s some really interesting stuff here.
My next task will be to try to integrate the relevant bits into my own, preexisting, notes.
Therein lies a range of questions:
1. The whole thing could come to about 8,000 words. Given that the number of people reading a post is inversely proportional to its length; would anyone read it? Is it worth posting?
2. Where to post? I thought new theories, but Bohm, Barbour and probably others were there way ahead of me. So, not new, and probably not a theory in the strict sense. So, where?
3. How would I post it? “Bitesized” chunks might seem best, but I think the whole will be such that splitting it up would lead to repetition and increased thread drift.
Anyway, it still needs some work, so in the meantime; suggestions welcome. Be brutal!

8000 words could come to over 40,000 characters, and there is a 20,000 character limit for posts (experience tells me, lol).
It matters more that you do it, and get it on the record for your own benefit, than if anyone reads it, though there are some troopers who will wade through it if they are interested.
It is just me, and you asked, but go to the "New Theories" subforum if there is material that you feel is quite alternative, unproven, untestable, etc. However, I find moderation to be lenient in this subforum, and if you acknowledge that it may not be generally accepted, but it is a result of an acceptable discussion that is open about the nature of the content, instead of saying you have some exceptional proof or insight, it could pass muster right here.
If it is 8000 words, I would organize it into smaller bits, like you suggest.

Thanks for the words of encouragement, Bogie_smiles. The thought of writing and posting something that no one would read, is a bit bleak; reminiscent of Father McKenzie's sermons. :)
I'm hoping for a comment from a Mod, even if its "go away!"

I’ve been pulling together some more of the content of this thread, there’s some really interesting stuff here.
My next task will be to try to integrate the relevant bits into my own, preexisting, notes.
Therein lies a range of questions:
1. The whole thing could come to about 8,000 words. Given that the number of people reading a post is inversely proportional to its length; would anyone read it? Is it worth posting?
2. Where to post? I thought new theories, but Bohm, Barbour and probably others were there way ahead of me. So, not new, and probably not a theory in the strict sense. So, where?
3. How would I post it? “Bitesized” chunks might seem best, but I think the whole will be such that splitting it up would lead to repetition and increased thread drift.
Anyway, it still needs some work, so in the meantime; suggestions welcome. Be brutal!
Save it as a pdf file and attach it.

Save it as a pdf file and attach it.
Thanks, Jeffrey. I'll get my son to show me how to do that when he recovers from the flu. He's improving. :)

I've not abandoned this thread. Just having health/caring/time problems at present.

Not sure if this has been mentioned as yet but I had heard an explanation to these regards recently. There are 2 kinds of infinity. Countable infinity and uncountable infinity. Where countable would refer to whole numbers and uncountable includes the infinite amount of numbers between each whole number as well

Hi Justin, welcome.
You are right, there are countable and uncountable infinities in mathematics. My (nonmathematical) understanding of that is that this works well because we can put things/concepts into onetoone relationships; or be unable to do so; in finite perception; then we imagine we can extrapolate that to infinity, which, of course, we cannot. Even Cantor could not do that.

I've not abandoned this thread. Some technical difficulties, plus nonrelated problems, combined with my not being entirely happy with my material, conspire to delay progress.

Where do we stand on: “can there ever have been nothing”?
There seems to be a fairly general feeling that there can never have been nothing, with some even saying so. However, there are some doubts, but efforts to discover any example of something coming from nothing have drawn a blank.
The nearest we have come so far is: “Brian Cox said that it is possible that there was nothing before the Big Bang.” (#82). Seemingly he does not say how this could be possible.
Or; (#83) “If Cox speculated about a quantum fluctuation “before” the Big Bang, I think someone should say, “Welcome to the world of infinite regress”, i.e., what caused the quantum fluctuation?” Of course, “infinite regress” is another form of the infinite sequence, with all its problems.
IMO, “nothing” and an infinite “something” are incompatible, so the question of whether or not there is an infinity that transcends maths is linked to the question of “nothing”; but let’s take one part at a time.
One way to create something from nothing is an artifact of waves. Say we had a wave tank, with wave generators on either side of the tank, each 180 degree out of phase with the other. Although energy is being pumped into the tank from both sides, the cancelling of the two waves creates stillness in the center of the tank. The energy is hidden due to wave addition. If we hid the wave generators and allowed the tank to reach steady state, and then had an audience look at the tan they will assume, no energy, since it is hidden.
We can makes this energy reappear, like magic, if we placed a partition in the stillness. Say we place a broad in the middle. One wave would rise on one side of the partition, and another wave will appear to sink on the other side. The audience would marvel since it appears like we have opened a worm hole.
In the case of the BB, the needed partition was the induction of particle matter. If we started with just waves without particles we can hide all the energy. Particles are different from waves, in the sense that particles cannot occupy the same space. Particles always need to add, whereas waves can add or subtract.
The question becomes how can you partition the stillness, to release the energy for the primordial particles? One such partition is the speed of light, which is distinct from slower inertial references; mass particles exist <C but cannot cross over into C. This can be done by introducing time and space to the universe; departure from the original C ground state of the hidden potential energy.
According to Special Relativity it would take infinite energy for a mass particle to cross over from inertial to C. If we go the other way, there is a lot of potential energy to release.

One way to create something from nothing is an artifact of waves. Say we had a wave tank, with wave generators on either side of the tank.....
I hesitate to believe you are really saying that waves, tanks generators etc are "nothing"; and even that "we" are nothing.
Something from nothing must require an initial "nothing".

According to Special Relativity it would take infinite energy for a mass particle to cross over from inertial to C. If we go the other way, there is a lot of potential energy to release.
This seems to say that a massive particle cannot accelerate from subluminal speed to c (agreed), but if a massive particle travelling at c were to decelerate to subluminal speed, it would release a lot of energy. (?)
Are you referring to tachyons?