Infinity

[Sputnick]

'Anything divided by infinity is 0' is a phrase I came across in 'Origins' by Neil de Grasse Tyson and Donald Goldsmith, published 2004. In the same book it says the currently accepted model of the universe says it will expand infinitely .. resulting in a cold, dark, dead void.

the first supposition I make is that time cannot be infinite, because time divided by infinity would be zero time .. but there is time .. and because time is not infinite, it will end.

the second supposition I make, since time is not infinite, with the universe expanding in time as well as space, is that the universe can not expand infinitely because time will end.

Any comments?

[makc]

there was a lot of related discussion here, notably with Dr. Skeptic participating

[apodman]

Lots of references to time in this topic, mostly starting a couple of pages in:

http://asterisk.apod.com/vie ... hp?t=14219

Two suppositions based on a phrase open a lot for me to imagine.

Imagination is about as far as I get.

I've tried to write something sensible on the subject three times now, but I didn't see anything I liked. Maybe later.

[bystander]

there was a lot of related discussion here, notably with Dr. Skeptic participating

split from Light Echoes from V838 Mon (APOD 03 Feb 2008)

Extent of space (APOD 23 Mar 2006)

[apodman]

'Anything divided by infinity is 0' is a phrase I came across in 'Origins' by Neil de Grasse Tyson and Donald Goldsmith, published 2004. In the same book it says the currently accepted model of the universe says it will expand infinitely .. resulting in a cold, dark, dead void.

the first supposition I make is that time cannot be infinite, because time divided by infinity would be zero time .. but there is time .. and because time is not infinite, it will end.

the second supposition I make, since time is not infinite, with the universe expanding in time as well as space, is that the universe can not expand infinitely because time will end.

Any comments?

We run into trouble constructing mathematics when we treat infinity like a number, so doing so is strictly avoided by mathematicians doing logic and proof. "Divided by" is arithmetic. Arithmetic only applies to numbers. "Infinity" is not a number. As a mathematician or a layman trying to think and talk as one, I must go no further.

Likewise, while a measure of time or a segment of time might be a number, "time" itself is not a number. So any use of "divided by" in this case is not in the usual mathematical sense.

So I'm not going to grant you any mathematical backup for the "cannot" in your phrase "time cannot be infinite". And I'm not going to grant your logic that uses the mathematical backup to conclude that "time cannot be infinite". But don't worry, I'll address the simpler question of whether time is infinite without the troublesome "cannot".

Is Time Infinite?

Sputnick presents the supposition that time is not infinite.

If time is not infinite, it will end, or so says Sputnick. Sounds possible to me. If a beginning of time sounds possible, why not an end? But what if it reverses? It wouldn't be infinite, but it wouldn't end either, or at least it wouldn't end going forward. Hey, it wasn't my idea. A bunch of noted physicists made it up.

If time is not infinite and will end, the expansion of the universe will end with it, or so says Sputnick. Sounds logical to me.

As far as I know, "we" still generally think the way they did in the 1930s that we don't know whether the universe will end (1) in a big crunch (reversal of expansion, time along with it according to a few), in (2) a big rip (continued expansion forever - the "cold, dark, dead void" you mention), or (3) a heat death (eventual dissolution of matter in place, localized or on a grand scale, irretrievably into energy - entropy death). I haven't heard anything about the "end of time" in (2) or (3), and I have only heard it in (1) with regard to the time reversal already mentioned.

But who knows?

I personally see time as infinite going forward, no matter what the fate of the contents of the universe. But that might just be my bias talking, based on my personal experience that time started when I first became aware and has continued ever since. There may be more things going on out there than an analogy to my personal experience can suggest.

[bystander]

We run into trouble constructing mathematics when we treat infinity like a number, so doing so is strictly avoided by mathematicians doing logic and proof. "Divided by" is arithmetic. Arithmetic only applies to numbers. "Infinity" is not a number. As a mathematician or a layman trying to think and talk as one, I must go no further.

Infinity and operations involving infinity are well defined in mathematics. Generally we're talking about limits. Division would be, the limit of 1/x, as x approaches infinity, equals zero. Division by zero can be defined similarly (although usually undefined), the limit of 1/x, as x approaches zero, equals infinity.

[apodman]

Infinity and operations involving infinity are well defined in mathematics.

http://www.physicsforums.com/showthread.php?t=132805

http://www.physicsforums.com/showthread.php?t=1438

[makc]

Infinity and operations involving infinity are well defined in mathematics.

http://www.physicsforums.com/showthread.php?t=132805

http://www.physicsforums.com/showthread.php?t=1438

What I said before.

P.S. my post № 1111 + 1

[Sputnick]

We run into trouble constructing mathematics when we treat infinity like a number, so doing so is strictly avoided by mathematicians doing logic and proof. "Divided by" is arithmetic. Arithmetic only applies to numbers. "Infinity" is not a number. As a mathematician or a layman trying to think and talk as one, I must go no further.

Likewise, while a measure of time or a segment of time might be a number, "time" itself is not a number. So any use of "divided by" in this case is not in the usual mathematical sense.

So I'm not going to grant you any mathematical backup for the "cannot" in your phrase "time cannot be infinite". And I'm not going to grant your logic that uses the mathematical backup to conclude that "time cannot be infinite". But don't worry, I'll address the simpler question of whether time is infinite without the troublesome "cannot".

Is Time Infinite?

Sputnick presents the supposition that time is not infinite.

If time is not infinite, it will end, or so says Sputnick. Sounds possible to me. If a beginning of time sounds possible, why not an end? But what if it reverses? It wouldn't be infinite, but it wouldn't end either, or at least it wouldn't end going forward. Hey, it wasn't my idea. A bunch of noted physicists made it up.

Thanks for your time, Apod. Time running backwards - it would probably do so in an anti-universe.

If time is not infinite and will end, the expansion of the universe will end with it, or so says Sputnick. Sounds logical to me.

Right. I must admit my main interest in cosmology and physics is to try to understand how the God of the bible does things (without being evangelistic) .. and a quote in Revelations says, 'there will no more time'.

=Apodman As far as I know, "we" still generally think the way they did in the 1930s that we don't know whether the universe will end (1) in a big crunch (reversal of expansion, time along with it according to a few), in (2) a big rip (continued expansion forever - the "cold, dark, dead void" you mention), or (3) a heat death (eventual dissolution of matter in place, localized or on a grand scale, irretrievably into energy - entropy death).

According to 'Origins" by Tyson and Goldsmith, 2004 - the end has been scientifically determined .. a constant expansion into cold nothingness. Of course I don't believe that as the biblical end seems to be a matter-antimatter explosion with all matter-anti matter destroyed .. spirit and personalities remaining.

[Sputnick]

Infinity and operations involving infinity are well defined in mathematics.

http://www.physicsforums.com/showthread.php?t=132805

http://www.physicsforums.com/showthread.php?t=1438

Very interesting stuff. Thanks Aman. I'm going to have to examine a dictionary to see if there are differences between infinity and eternity .. although I sense infinity is a measure of space while eternity measures time.

[bystander]

We run into trouble constructing mathematics when we treat infinity like a number, so doing so is strictly avoided by mathematicians doing logic and proof. "Divided by" is arithmetic. Arithmetic only applies to numbers. "Infinity" is not a number. As a mathematician or a layman trying to think and talk as one, I must go no further.

Infinity and operations involving infinity are well defined in mathematics. Generally we're talking about limits. Division would be, the limit of 1/x, as x approaches infinity, equals zero. Division by zero can be defined similarly (although usually undefined), the limit of 1/x, as x approaches zero, equals infinity.

Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts – usually linked to the idea of "without end" – which arise in philosophy, mathematics, and theology. In mathematics, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things: "an infinite number of terms") but it is a different type of "number" from the real numbers. Infinity is related to limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals, Russell's paradox, non-standard arithmetic, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite.

Arithmetic Operations:

• a + ∞ = +∞ + a = +∞ if a ≠ −∞
  a − ∞ = −∞ + a = −∞ if a ≠ +∞
  a × (±∞) = (±∞) × a = ±∞ if a > 0
  a × (±∞) = (±∞) × a = ∓∞ if a < 0
  a / ±∞ = 0 if −∞ < a < +∞
  ±∞ / a = ±∞ if 0 < a < +∞
  ±∞ / a = ∓∞ if −∞ < a < 0

Here, "a + ∞" means both "a + (+∞)" and "a − (−∞)", and "a − ∞" means both "a − (+∞)" and "a + (−∞)".

The expressions ∞ − ∞, 0 × (±∞) and ±∞ / ±∞ (called indeterminate forms) are usually left undefined. These rules are modeled on the laws for infinite limits. However, in the context of probability or measure theory, 0 × (±∞) is often defined as 0.

The expression 1/0 is not defined either as +∞ or −∞, because although it is true that whenever f(x) → 0 for a continuous function f(x) it must be the case that 1/f(x) is eventually contained in every neighborhood of the set {−∞, +∞}, it is not true that 1/f(x) must tend to one of these points. An example is f(x) = 1/(sin(1/x)). (Its modulus 1/| f(x) |, nevertheless, does approach +∞.)

[Orca]

.. although I sense infinity is a measure of space while eternity measures time.

The problem here is that you are separating time and space in your mind. This is easy to do; humans perceive time as a one-way arrow that never changes rate or direction. As it turns out time is just another dimension of our universe. Space and time are part of the same thing; the "fabric" of the universe is referred to as "spacetime."

[apodman]

Arithmetic Operations:

a + ∞ = +∞ + a = +∞ if a ≠ −∞

Lovely. I don't want to get into an extended discussion, but that starts to illustrate my point.

Add "infinity" to "a" and get "infinity".

So far, so good.

Now subtract "infinity" from the result and try to get your "a" back.

You can't.

If this were arithmetic on numbers, you could.

Further examples abound.

So just being able to perform arithmetic operations on "infinity" doesn't make it a number with respect to arithmetic, with all the properties to which numbers and the operations performed upon them are normally entitled.

I'm not saying that the mathematical concept of infinity is too slippery to handle; I'm just saying it should be handled with the special care it has earned over years of consideration and paradox.

[apodman]

Anything divided by infinity is 0

Arithmetic Operations:

a / ±∞ = 0 if −∞ < a < +∞

The bystander quote is in agreement with the Sputnick quote, with the additional requirement that the quantity to be divided must be finite for the equation to have a defined result.

This is an example of dealing with infinity on the terms it requires if we want to be sure we are using logic only where it applies.

[apodman]

P.S. my post № 1111 + 1

Yes, I noticed one post ago even if nobody else did. Congratulations. In some households, the first person to notice it's 11:11 p.m. "clocks" the others, so I can see numbers like that with my eyes closed. Sorry, that's a Tetris background burned into my retinas, so the eyelids are unavailable for screening. As long as I don't need the binomial theorem to read your posts, I'm happy. Personally, I shudder to watch my number of posts going up, fearing that the number of useful things I've said might not be going up as fast. Re: Infinity, huh?

[astrolabe]

Hello All,

This is kinda fun. If one doesn't have spacetime what does one have?

[apodman]

If one doesn't have spacetime what does one have?

I got plenty o'nothin' and nothin's plenty for me
I got no car, got no mule, I got no misery

Folks with plenty of plenty, they got a lock on the door
Afraid somebody's gonna rob 'em while they're out a'makin' more
What for?

I got no lock on the door, that's no way to be
They can steal the rug from the floor, that's OK with me
'cause the things that I prize, like the stars in the skies, are all free

Say, I got plenty o'nothin' and nothin's plenty for me
I got my gal, got my song, got heaven the whole day long
Got my gal, Got my love, Got my song

[astrolabe]

Hello apodman,

Good one!

[Sputnick]

"Look unto the stars to teach us
How the Master's thoughts can reach us
Each one follows Newton's math
Silently along its path."

Albert Einstein

[apodman]

"Look unto the stars to teach us
How the Master's thoughts can reach us
Each one follows Newton's math
Silently along its path."

Albert Einstein

I always wondered where Yoda learned to talk like that. Sounds like they adapted Einstein for Jedi nursery rhymes. Apodman's worst Jeopardy category is Poetry, and he is therefore unqualified to judge, but perhaps "poet" (like controversially "philosopher") should not be listed as Einstein's "day" job. I liked it, but I'm a nerd who's used to poetry that ends in phrases like "... and so on ad infinitum".

[Sputnick]

"Look unto the stars to teach us
How the Master's thoughts can reach us
Each one follows Newton's math
Silently along its path."

Albert Einstein

I always wondered where Yoda learned to talk like that. Sounds like they adapted Einstein for Jedi nursery rhymes. Apodman's worst Jeopardy category is Poetry, and he is therefore unqualified to judge, but perhaps "poet" (like controversially "philosopher") should not be listed as Einstein's "day" job. I liked it, but I'm a nerd who's used to poetry that ends in phrases like "... and so on ad infinitum".

In that same mindset I just opened a Cafe topic Planetary Formation.