On The Nature Of Infinity

[Pargat Perrer]

A while back, before ChessTalk was split into chess forum and non-chess forum, I started a thread about infinity. I can't remember what prompted me to do so. But it was well responded to, and I particularly remember Fred Harvey saying it was the most interesting thread he had seen on ChessTalk in a long time.

I think that thread has disappeared here, along with many other non-chess topic threads. So what the hey, let's get it started again! For the sake of those who love chess AND love philosophy!

So here are my newest thoughts on infinity....

Trying to concisely (lol) define it ..... (concise being almost the opposite of infinity) ....

Here's what I now think of as concisely defining infinity:


INFINITY IS....

(1) not able to be measured or quantified
(2) ever-increasing

and the newest thoughts....

(3) ever-increasing at an ever-increasing rate R(1)
(4) R(1) is ever-increasing at an infinite rate R(2)
(5) R(2) is ever-increasing at an infinite rate R(3)
(6) infinitely repeating, such that R(N) is ever-increasing at an ever-increasing rate R(N+1) and N goes on to infinity

Note that this definition of infinity is infinitely recursive. There is no termination condition. In (6), we define infinity in TERMS OF INFINITY.

I thought of (3) to (6) because if infinity was only increasing at some constant rate R, then that rate could be at some instant of time 1/R measured and quantized into a specific rate .... meaning that when you add 1 to that time period T, infinity increases by exactly some measureable, quantizable amount. No matter how small time T is, it is not infinitely small because it is 1/R and R is quantizable, meaning time T could be POTENTIALLY realizable as a "snapshot" and ... that would mean infinity COULD POTENTIALLY BE MEASURED OR QUANTIZED. In other words, a "snapshot" of infinity could be taken, hypothetically speaking.

Thus (3) to (6) are necessary to correctly define infinity, so that any snapshot time T can never be measured or quantized.

Which perhaps means something many people who have had a Near Death Experience (NDE) have tried to tell us .....

Time does not exist.

The concept of "everything" does not exist.

There is always MORE than EVERYTHING.

By this definition, I believe infinity is self-proving. By this definition, infinity proves that infinity exists.

If it is imaginable, it exists. Infinity is imaginable in the human mind. Not measurable, not quantifiable, but imaginable.

Our universe has been observed by latest measurements to be increasing in size AT AN INCREASING RATE. A microcosm of infinity???

[Brad Thomson]

Time does not exist.

I speak only as a philosopher, having no training in physics or mathematics. I am of the opinion that in the final analysis, ONLY Time exists. I contend that Time and Substance are ultimately the same concept, as is Space, Being, Existence and so on. But I think that Time defines what IS more accurately and completely than any of the other terms. What comes from Nothing and returns to Nothing? Time. What do you have left if you remove consideration of all particulars and leave only what never goes away? Time. What is the one thing humans intuit absolutely purely, without any input from the senses, emotions or thoughts? Time (otherwise music would be impossible because we would have no comprehension of a beat, no ability to KEEP time). Metaphorically, what is another name for God? Father Time. If Substance is that which does not change, and the expression, "The only thing permanent is change" is true, then Substance is Change, in other words, Time.

It is important to note that there is no such thing in reality as a "point" in Time that does not contain within itself duration. We are speaking only figuratively when we make such a statement or suggestion. I elaborate this in a paper I wrote on Hegel's comments upon music, it can be found here, among other works, if anyone is interested: Brad Thomson (University of Ottawa) - PhilPeople

How all of this relates to infinity, I do not know. :)

[Bob Armstrong]

Time is a human mental construct that assists us in organization. There is no "time" (No past, present or future; no NOW even).

What there is is BEING, or Existence.

It is Being that is always changing.........this is a tough concept because our mind depends on logic - our mind immediately says that if something changes, there is a "before" and an "after"; so......there must be "Time". I think we Non-Timers, though, are reduced to having to use the concept of "present" to get across the idea that "something is changing before our eyes" and that is the only reality.....we have to say the change is taking place always in the "present" or the "now"...........it is our feeble attempt to get across that there is no longitudinal time, by saying there is only the "present" (One of the time concepts/constructs).

So, Pargat, the concept of "infinity" is another time-based concept. If time does not exist, then neither can "infinity". There is only the ever-changing now.

So the really critical statements in life are:

1. There only one Being, and "everything" we perceive to be "out there", and ourselves, are merely individuations of this One Absolute!!

In other words, it plays with part of itself, reshaping itself, for example into a rational person, and wipes the knowledge of the Absolute from that part of itself. So the life goal of mankind becomes re-discovering that it does not exist as a separate entity, but that it is, and always has been, one with the Absolute.

2. There a "Separate Supra-Natural" that IS. And it "creates a creation (E.g. Mankind) with an existence, "based on" its own always "S-N" Existence, but with an entirely separate, free, rational existence of its own - what we call "Human Nature"!! And what was created did not always exist, as does the S-N Her/Him/Itself. And it may go out of existence at some point (Subject to our going into the whole murky theological area of the "Non-Material Spirit" - e.g. as when a person claims to have a spiritual "soul" - but surely that topic requires its own thread!)

The Million Dollar Question: Is it a "zero sum game" between these two statements?

Simply put: one statement is true and fact; the other statement is false and merely a conceptualization.

What do CT'ers think?

~ Bob A (T-S/P)

P.S. I will be the first to admit that this stuff is heavy..........

[Neil Frarey]

So, Pargat, the concept of "infinity" is another time-based concept.

Nope.

'Infinity' is not time based.

Infinity is Life based ... NOT time based.

[Pargat Perrer]

I speak only as a philosopher, having no training in physics or mathematics. I am of the opinion that in the final analysis, ONLY Time exists. I contend that Time and Substance are ultimately the same concept, as is Space, Being, Existence and so on. But I think that Time defines what IS more accurately and completely than any of the other terms. What comes from Nothing and returns to Nothing? Time. What do you have left if you remove consideration of all particulars and leave only what never goes away? Time. What is the one thing humans intuit absolutely purely, without any input from the senses, emotions or thoughts? Time (otherwise music would be impossible because we would have no comprehension of a beat, no ability to KEEP time). Metaphorically, what is another name for God? Father Time. If Substance is that which does not change, and the expression, "The only thing permanent is change" is true, then Substance is Change, in other words, Time.

It is important to note that there is no such thing in reality as a "point" in Time that does not contain within itself duration. We are speaking only figuratively when we make such a statement or suggestion. I elaborate this in a paper I wrote on Hegel's comments upon music, it can be found here, among other works, if anyone is interested: Brad Thomson (University of Ottawa) - PhilPeople

How all of this relates to infinity, I do not know. :)

Of course, infinity cannot be discussed without discussing time. Can one exist without the other? That makes these possibilities:
(1) There is only infinity and no time
(2) There is only time and no infinity
(3) Both exist simultaneously
(4) all of the above
(5) none of the above

LOL had to add those last 2 items!!!

In my attempt to define infinity, I used the phrase "ever-increasing". This seems to mandate the concept that time exists. However, when you come to the last item of the definition, you discover that "ever-increasing" is itself infinite. This seems to indicate that as you wrote Brad, there is no "snapshot" of time that doesn't contain duration. There is no "quantum" or "particle" or "photon" of time. This agrees with our comcept of space, in which we learn in mathematics class that a "point" in space is infinitely small. And so it makes sense what Einstein discovered, that space and time are interwoven together as spacetime. To which we can add "with absolutely no irreducible quantum possible".

Even the Planck time shows us this. It is defined mathematically as the "time it takes for a photon of light travelling at the speed of light TO TRAVERSE a Planck length." Therefore it is NOT an irreducible quantum, and it is this described in language as the smallest possible time that we in this physical universe could ever MEASURE. But it contains within it this concept of time, i.e. a traversal that is not instantaneous.

This ties in with Zeno's paradox. Apparently, an arrow speeding towards a target can never arrive. And that ties also into our concept of the beginning of our universe, i.e. "The Big Bang" -- not the TV show, but apparently a precise and irreducible instant of time, a "shapshot" that cannot contain duration. This all introduces us to the concept of Limits, the ideas of "before" and "after" and "approaching".

Why is it that we are able in this universe to observe limits being reached? Even going to the subatomic level, we can precisely START nuclear fission leading to the explosion of a nuclear bomb. At what "instant" of time is such an explosion triggered and unstoppable?

Why is there a "before" and an "after"?

Is the universe a hologram? And if so, does that somehow introduce an "illusion" of limits being reached?

[Brad Thomson]

Pargat, I can respond only as a philosopher.

First, I am not sure about infinity, I suppose this depends upon how one chooses to define the word, but if there is no time then there can be no change, but there is change, therefore there is time.

Second, even "snapshots" contain duration in their creation, the shutter speed is measurable. Yes, a point in space must be extended in a measurable way or you will never have space. The same applies to time.

In my view the paradoxes of Zeno are interesting and serve as a good argument against the existence of extended substance, or space conceived of as a mind-independent void.

I cannot explain nukes.

There is a before and after because time comes from nothing and returns to nothing which renders its existence as a changing now, which now contains observable duration, in other words observable change.

The universe is a thought, a changing thought, being imagined by Nature/God. Nature/God is in time, or more precisely, IS time. We are smaller versions living inside the larger one. (Even intelligent Christians believe this, for the Apostle Paul refers to, "God, in whom we live and move and have our being.") Each of us senses a portion of the totality of what Nature/God is thinking while Nature/God senses the totality of what all of us and all other sentient beings are thinking. When we create a volition to move our bodies, we do not create the associated sensations that correspond to the volition, Nature/God does this by rethinking or reimagining the universe in response to our volition. Material substance does not exist, only minds and their contents exist. The contents of mind are imagined, and these visions, sounds and so forth are mistakenly deemed to be matter in space, but they are in reality only ideas in minds. (Consider dreams. You might dream that you are reading this. Is it out there in space? No, you are asleep, it can only be an idea in your mind. It is the same when you are awake.)

Almost anyone can keep time, though musicians train to do this and are often better at it. (The Rolling Stones are an exception and cannot even keep simple time let alone tune their instruments consistently.) A point in time in music is called a beat. Beats contain duration. Consider drummers. One drummer might play "on top of the beat" or at the "front end of it", while another might lag "at the back end of the beat" or "behind it". If you listen to a band with two drummers, one who plays the one way and one who plays the other, a band such as The Allman Brothers Band where Butch Trucks is on top of the beat while Jai Johanny Johanson is behind it, you will hear Butch striking his snare drum first, and Jai second, with observable time between the two, creating what is known as a flam, a tight flam in these cases, and yet neither drummer has missed the beat. To be sure if a third drummer, one such as John Bonham for example, who always seems to monotonously strike dead centre, were to join in then you would hear a fast triplet with all three strokes being distinct in time, yet with all of them being ON time. Thus, moments or points in time contain duration. Without time there can be nothing.

[Pargat Perrer]

Pargat, I can respond only as a philosopher.

First, I am not sure about infinity, I suppose this depends upon how one chooses to define the word, but if there is no time then there can be no change, but there is change, therefore there is time.

Second, even "snapshots" contain duration in their creation, the shutter speed is measurable. Yes, a point in space must be extended in a measurable way or you will never have space. The same applies to time.

In my view the paradoxes of Zeno are interesting and serve as a good argument against the existence of extended substance, or space conceived of as a mind-independent void.

I cannot explain nukes.

There is a before and after because time comes from nothing and returns to nothing which renders its existence as a changing now, which now contains observable duration, in other words observable change.

The universe is a thought, a changing thought, being imagined by Nature/God. Nature/God is in time, or more precisely, IS time. We are smaller versions living inside the larger one. (Even intelligent Christians believe this, for the Apostle Paul refers to, "God, in whom we live and move and have our being.") Each of us senses a portion of the totality of what Nature/God is thinking while Nature/God senses the totality of what all of us and all other sentient beings are thinking. When we create a volition to move our bodies, we do not create the associated sensations that correspond to the volition, Nature/God does this by rethinking or reimagining the universe in response to our volition. Material substance does not exist, only minds and their contents exist. The contents of mind are imagined, and these visions, sounds and so forth are mistakenly deemed to be matter in space, but they are in reality only ideas in minds. (Consider dreams. You might dream that you are reading this. Is it out there in space? No, you are asleep, it can only be an idea in your mind. It is the same when you are awake.)

Almost anyone can keep time, though musicians train to do this and are often better at it. (The Rolling Stones are an exception and cannot even keep simple time let alone tune their instruments consistently.) A point in time in music is called a beat. Beats contain duration. Consider drummers. One drummer might play "on top of the beat" or at the "front end of it", while another might lag "at the back end of the beat" or "behind it". If you listen to a band with two drummers, one who plays the one way and one who plays the other, a band such as The Allman Brothers Band where Butch Trucks is on top of the beat while Jai Johanny Johanson is behind it, you will hear Butch striking his snare drum first, and Jai second, with observable time between the two, creating what is known as a flam, a tight flam in these cases, and yet neither drummer has missed the beat. To be sure if a third drummer, one such as John Bonham for example, who always seems to monotonously strike dead centre, were to join in then you would hear a fast triplet with all three strokes being distinct in time, yet with all of them being ON time. Thus, moments or points in time contain duration. Without time there can be nothing.

Yes, I was agreeing that snapshots contain duration, even if the snapshot was precisely one Planck time duration. In that case, we could never measure the duration or break it into shorter duration, but it is still duration.

I am intrigued by your choice of language about time, i.e. "coming from" and "returning to" nothing. Speaking of that in purely physics terms, wouldn't both require duration? If time does exist, I prefer to think of it as homogeneous, woven into spacetime, with neither having any irreducible quantum. Yet even this contrasts with there being, in the case of ignition of a nuclear device, a precise instant time T at which the fission reaction is actually underway and cannot be stopped, with the idea that this instant was "instantly" preceded by a time T' at which the reaction is NOT underway yet. I wonder if we could be an observer in the subatomic realm and observe what actually happens to start the reaction, and could freeze-frame everything.... well, it goes against the whole idea of time always having duration. So the two concepts do not agree with each other, yet we do observe nuclear fission explosions that we bring into existence by pressing some figurative or literal button.

That's interesting what you wrote about music. I don't quite agree that being "behind the beat" is still being on time, and the reason I say that is because drum machines are so boring in comparison to human drummers.

In fact, it is miraculous that humans have such a precise intuition of musical time, and there is something to be explored in that area. Exactly how "precise" is our sense of musical time? If as you say a very price human drummer who is always right on the beat has his drum track recorded, has anyone ever measured how precise the durations between beats are? It would be fascinating if they were precise down to the microsecond level or even more precise than that!

[Pargat Perrer]

Time is a human mental construct that assists us in organization. There is no "time" (No past, present or future; no NOW even).

What there is is BEING, or Existence.

It is Being that is always changing.........this is a tough concept because our mind depends on logic - our mind immediately says that if something changes, there is a "before" and an "after"; so......there must be "Time". I think we Non-Timers, though, are reduced to having to use the concept of "present" to get across the idea that "something is changing before our eyes" and that is the only reality.....we have to say the change is taking place always in the "present" or the "now"...........it is our feeble attempt to get across that there is no longitudinal time, by saying there is only the "present" (One of the time concepts/constructs).

So, Pargat, the concept of "infinity" is another time-based concept. If time does not exist, then neither can "infinity". There is only the ever-changing now.

So the really critical statements in life are:

1. There only one Being, and "everything" we perceive to be "out there", and ourselves, are merely individuations of this One Absolute!!

In other words, it plays with part of itself, reshaping itself, for example into a rational person, and wipes the knowledge of the Absolute from that part of itself. So the life goal of mankind becomes re-discovering that it does not exist as a separate entity, but that it is, and always has been, one with the Absolute.

2. There a "Separate Supra-Natural" that IS. And it "creates a creation (E.g. Mankind) with an existence, "based on" its own always "S-N" Existence, but with an entirely separate, free, rational existence of its own - what we call "Human Nature"!! And what was created did not always exist, as does the S-N Her/Him/Itself. And it may go out of existence at some point (Subject to our going into the whole murky theological area of the "Non-Material Spirit" - e.g. as when a person claims to have a spiritual "soul" - but surely that topic requires its own thread!)

The Million Dollar Question: Is it a "zero sum game" between these two statements?

Simply put: one statement is true and fact; the other statement is false and merely a conceptualization.

What do CT'ers think?

~ Bob A (T-S/P)

P.S. I will be the first to admit that this stuff is heavy..........

Bob, I wonder if your statements 1. and 2. are mutually exclusive. I know that is the question you are asking. I tend to think both could be true in some way.

I like how you describe yourself as a "Non-Timer". Is that anything like an "Old-Timer"? LOL

In our physical universe, there is physical time because of the speed of light restriction. For there to be infinity in our universe, the speed of light should be infinite, it seems. But it isn't and so we have Planck length and Planck time, both defined in terms of the speed of light in a vacuum (and the term "vacuum" is even undefinable because apparently even in the smallest units of spacetime, there are subatomic particles, quarks etc., that are springing into and out of existence.)

[Brad Thomson]

Bob, you sound somewhat like both Spinoza and Kant.

For Spinoza, God exists outside of time, thus in the final analysis there is no time for Spinoza. The problem with this theory is that it leads to determinism. Kant believes that time is a form of sensible intuition imposed upon its objects by the mind, but that time has no relation to the objects, or noumena, themselves.

[Brad Thomson]

I am intrigued by your choice of language about time, i.e. "coming from" and "returning to" nothing.

That's interesting what you wrote about music. I don't quite agree that being "behind the beat" is still being on time, and the reason I say that is because drum machines are so boring in comparison to human drummers.

In fact, it is miraculous that humans have such a precise intuition of musical time, and there is something to be explored in that area. Exactly how "precise" is our sense of musical time? If as you say a very price human drummer who is always right on the beat has his drum track recorded, has anyone ever measured how precise the durations between beats are? It would be fascinating if they were precise down to the microsecond level or even more precise than that!

First, another way to put this is to say that time does not come from anything, and it does not go to anything. The now simply appears and then disappears.

Second, drum machines/metronomes do not keep musical time in any sense. They are at best crude approximations. Music that is performed with what is called a click-track where the musician tries to hit when the click happens, is very sluggish sounding. The same is true of drum machines that not only create the timing but also the sounds, in fact this is even worse because dynamics (how hard or soft the hit is) are either completely lost, or at best approximated. Much of today's "music" even has the voice played through a computer to smooth out the pitch so that even tone-deaf "singers" like Cheryl Crow (to name one of the most grotesque examples) sound on key. This is all a complete abomination. Music should be played by humans playing their own instruments and keeping their own time.

[Bob Armstrong]

Hi Pargat:

I am a Non-Timer. But the Timer's label me with their time concept: Old Timer.

I have not aged......there is no time.......

But I have "changed" - the fundamental characteristic of existence.........change is the one constant of the multiverse, and even of what exists in the other dimensions of creation.

~ Bob A (T-S/P)

[Sid Belzberg]

Hi Pargat:

I am a Non-Timer. But the Timer's label me with their time concept: Old Timer.

I have not aged......there is no time.......

But I have "changed" - the fundamental characteristic of existence.........change is the one constant of the multiverse, and even of what exists in the other dimensions of creation.

~ Bob A (T-S/P)

Well said, Bob; I agree!

[Bob Armstrong]

Hi Brad:

1. Not Spinoza:

Spinoza's most famous and provocative idea is that God is not the creator of the world, but that the world is part of God. This is often identified as pantheism, the doctrine that God and the world are the same thing – which conflicts with both Jewish and Christian teachings. In modern terms, this is the life view of "Wakefulness" - There is one Absolute; reality is in fact merely individuations of this Absolute, with its knowledge of it being part of the absolute, wiped clean.

It is my view that there IS a Supra-Natural existence. At some point it "changed" to create other separate, individual existences, some animate and spiritual, some inanimate, but able to become animate under the perfect storm conditions. The Creator and the created have separate existences. Though in Metaphysics it is stated that the Existence of the Supra-Natural is the "foundation" of all other existences. Without the Supra-Natural Existence, there is no other existence.

2. Not Kant

Next instalment when I get some CT time.

Bob A

[Brad Thomson]

It is my view that there IS a Supra-Natural existence. At some point it "changed" to create other separate, individual existences, some animate and spiritual, some inanimate, but able to become animate under the perfect storm conditions. The Creator and the created have separate existences. Though in Metaphysics it is stated that the Existence of the Supra-Natural is the "foundation" of all other existences. Without the Supra-Natural Existence, there is no other existence.

Maybe Hegel? Reason, for Hegel is the "Supra-Natural" that manifests in outward form, or changes, so as to actualize or come to know or be one with itself in and through human history? For Hegel, the Absolute Idea encompasses all. It is a permanently changing being unfolding according to its permanent logic.

[Bob Armstrong]

Hi Brad:

Some of Hegel seems right on - his dialectic (Picked up by Marx as "dialectic in human history")/

I was not that impressed with his philosophy/theology at the time I studied him (Under Emile Fackenheim - wrote Religious Dimension in Hegel's Thought - He gave me an "A" on my final essay for my Masters.............for my creativity..........his comment was: "Next time, would you please read some Hegel!").

Let me review my position - I hope my theology is not Hegelian!

Bob A