A Question For Mathemeticians Only

[thomaq]

from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?

[ComestibleVenom]

Originally posted by thomaq
from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?

Obviously you could define such a system. So yes. I'm no mathematician but it's a very simple question.

[Demosthenes]

Depends on what system you're specifying. If you're talking about our universe's past, then the answer is no. The physical theories' mathematics say that any line that extend into the past must end at the singularity.

[Normal]

Logically, if time extended infinitely into the past, we would not be here yet.

[Clutch]

Yes, you could, no problem.

If one individuates the events in a series coarsely enough to make this true:

Before each event there is exactly one immediately preceding event.

...then one gets an infinite past modelled by the natural numbers.

And there is no general problem of "getting to the present", since, from any point P in the past, there are only finitely many events between P and now (for any "now"). Just as no two natural numbers are more than finitely separated.

Finally, this is all a matter of logical or mathematical possibility. Our best empirical theories do indeed tell us that space-time begins with a singularity or something equally strange.

But I'm no mathematician -- just a guy who knows how to spell it. ;)

[Hawkingfan]

Originally posted by thomaq
from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?
No. Because the initial state of the universe was a singularity whose very definition means the breakdown of mathematics!

[Dominus Paradoxum]

Logically, if time extended infinitely into the past, we would not be here yet.

That's only true on an A series view of time. On a B series view, the present doesn't "progress", since every time is 'the present' to someone located at that time. So for those of us who actually so exist now, we would indeed be here "yet". For the B series, every time is on a par with every other time past and future, so there's nothing special about the now.

[Normal]

Originally posted by Clutch
And there is no general problem of "getting to the present", since, from any point P in the past, there are only finitely many events between P and now (for any "now"). Just as no two natural numbers are more than finitely separated.

If you relate this logic to time, then there is no event P, which does not have an event P-1 that preceded it, extending infintely, (ie no event B=P-1, that was not preceded by B-1), without a starting point, to talk of time like this is nonsense because the present P would never exist.

[Normal]

Originally posted by Dominus Paradoxum
That's only true on an A series view of time. On a B series view, the present doesn't "progress", since every time is 'the present' to someone located at that time. So for those of us who actually so exist now, we would indeed be here "yet". For the B series, every time is on a par with every other time past and future, so there's nothing special about the now.

Could you explain A series and B series? If in "B series" time is equal to all who are in the "present", then time seems to lack a chronological flow, and loses it's very definition.

[Hawkingfan]

Originally posted by Normal
Could you explain A series and B series? If in "B series" time is equal to all who are in the "present", then time seems to lack a chronological flow, and loses it's very definition.
Please define "time". Because it certainly does not mean "chronological flow".

[Normal]

Originally posted by Hawkingfan
Please define "time". Because it certainly does not mean "chronological flow".

I'm not even sure of the definition of time. I assume it's an axis for space of some sort.

[Clutch]

Originally posted by Normal
If you relate this logic to time, then there is no event P, which does not have an event P-1 that preceded it, extending infintely, (ie no event B=P-1, that was not preceded by B-1), without a starting point, to talk of time like this is nonsense because the present P would never exist. I'm afraid I can't understand this very well -- the problem being grammatical and not philosophical.

I'll try breaking it down, though.

If you relate this logic to time, then there is no event P, which does not have an event P-1 that preceded it, extending infintelyRight so far. This is a rephrasing of my point: if the past is infinite, then there is no event lacking an immediate predecessor.(ie no event B=P-1, that was not preceded by B-1)An unhelpful epicycle of formalization, but yes, that seems accurate.without a starting point, to talk of time like this is nonsense because the present P would never exist.But this is simply the repeated assertion of your initial claim, plus some serious confusion. Just what starting point are you talking about?

Notice that the IP model does NOT say: There was a starting point, then infinitely many successive events of fixed duration occurred, and now here we are. That would be incoherent.

But -- obviously -- the whole point of the IP model is the denial of a starting point. So there is no infinite series to be completed, in order to "reach the present", because there was no infinite series that got started. The question, "But how did we get to Now?" is ill-formed; the counter-question must be "From when?" For any specific point in the past you care to name, the answer is straightforwardly finite.

What's lurking in the background of your confusion, it seems, is an implicit assumption that would answer the counter-question with "From the beginning, of course! How did we get to Now from the beginning, if infinitely many events are interposed?" And this is just to miss the point altogether. On the IP model, there is no beginning. That's what the infinity of the past means.

[thomaq]

Originally posted by Clutch
But I'm no mathematician -- just a guy who knows how to spell it. ;)

DANG!! i spelled it right, and then i second guessed myself because it looked wrong. woops.

[ex-xian]

I'm not a mathematician yet (and I can spell it too), but I'm taking degrees in math and physics, with grad school focus yet to be determined. There is nothing mathematically of philosophically troubling about time extending infinitly in the past, just as there is nothing wrong with assuming that time will extend infinitly in the future. But I don't think that this is a purely mathematical question. There are empirical observations that seem to indicate that time doesn not extend infinitly in the past.

As for the definition of time, I have a few possibilities.

Time the dimension of time/space wherein cause and effect phenomena happen.
Time is the scalar quantity and space is the vector quantity to a mathematical description of the universe.
Time is what we measure with a clock. - Einstien


But there is another possibility. Time could have a beginning, but still extend infinitly into the past. If time never took on the value of t=0, but was infinitly close to that value.

___0(___________>

where time started at the paranthesis. I posted this on another thread, but I thought it was cool enough to repeat here. I read about this concept in a book called Infinity and the Mind. I've not finished the chapter, so I'm not sure what consequences the author sees, and I'm not sure what consequences I see either. But I thought I'd throw it out there and see what happens. :)

[Normal]

Originally posted by Clutch
But -- obviously -- the whole point of the IP model is the denial of a starting point. So there is no infinite series to be completed, in order to "reach the present", because there was no infinite series that got started. The question, "But how did we get to Now?" is ill-formed; the counter-question must be "From when?" For any specific point in the past you care to name, the answer is straightforwardly finite.

What's lurking in the background of your confusion, it seems, is an implicit assumption that would answer the counter-question with "From the beginning, of course! How did we get to Now from the beginning, if infinitely many events are interposed?" And this is just to miss the point altogether. On the IP model, there is no beginning. That's what the infinity of the past means.

Thanks, your post helped cleared up a lot of my confusion, although I still don't completely understand the logic behind it.

If there is an infinite past, you claim there was no beginning, fine, but it still means we can take any point in the past, and it's possible to take a point FURTHER in the past then that, and do that over and over and over again, ad infinitum. I simply cannot make sense of this being the case where we have now reached the present, and have not gone through an infinite amount of cases, since, by the very definition of infinite, an infinite amount of cases is inexhaustible.

[ex-xian]

Originally posted by Normal
Thanks, your post helped cleared up a lot of my confusion, although I still don't completely understand the logic behind it.
I'm not sure I follow it either, but I'll assume that I do and try to make a meaningful post.

Since time is a scalar quantity, we can imagine it as a line. Assuming that time is infinite in both directions, we can apply any arbitrary coordinate system that we want to it. So, pick a point and call it zero. If you choose any other point, say, t=42, then there are infinite values of time before and after 42. You can always go one after and or one before. But that doesn't change that 42 is a legitimate point in time.

...now why did i choose 42? is there some cosmic signigicance to this number that i was previously unaware of? no, probably not...think i'll pop off to milliways for a bite to eat....

edited to correct tags

[ComestibleVenom]

Originally posted by Normal
Logically, if time extended infinitely into the past, we would not be here yet.

Nonsense, we could be here and an infinity could be there. We don't travel through the infinity to reach the point at which we are, we exist locally.

That argument is entirely specious.

[ComestibleVenom]

Originally posted by Normal
I simply cannot make sense of this being the case where we have now reached the present, and have not gone through an infinite amount of cases...


Obviously you can't, and that's exactly what you're confused about. Having an infinite amount of time in the past is no more a problem then an infinite amount of time in the future. We neither travel through the past nor through the future. Our existence is a purely local phenomenon in what logically could be an infinite domain.

[thomaq]

the real issue here is which theory of time is correct. A-theory or B-theory. if A theory is correct then Normal would be correct, if B-theory is correct, then the others are correct. this is the way i see it. to me it seems like the A-theory of time is the more common sense approach. but i'm in the process of studying it more. i started a thread to start a discussion of the two theories of time so we could hash this out. in some of the other threads (Naturalism Irrational? etc.) it seems like the issues are breaking down to which theory of time is correct.

[soulofdarwin]

Your intuition that only a mathematician, specifically one who can interpret the field equations of general relativity, can bring any definitive insight to your question seems well-founded. Not being a mathematician, I can only offer a few observations regarding what has been said thus far in the discussion of this matter. The field equations predict the existence of singularities, discontinuities of the space-time continuum wherein local regions of the continuum are infinitely compressed, manifested only by their immense gravitational fields. From my reading on the subject, it is my understanding (I am certain that someone will correct me if I am wrong) that the space-time continuum does not cease to exist at these points of discontinuity, it only becomes "infinitely immeasurable". While the consensus view of astronomical physicists is that the most probable origen of the present incarnation of the universe (the one that we now perceive) was a singularity (presumably one of incomprehensible proportion), I am unaware that anyone to date has offered proof beyond doubt for that idea. Still, if the origen of this universe was in fact a singularity, I suppose that you could argue, based on the continued existence of space-time, for the idea of an infinite regression of time. That might only beg the question, however, regression relative to what?

[Dominus Paradoxum]

Well, we can't yet be sure if there was a true singularity or not, because we don't have a theory of quantum gravity. If string theory is correct, then there was no singularity, though there was something very close to it.

[Witt]

thomaq :
from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?

IMHO, Yes. We do attribute 'real number' qualities to space-time.
That there is no smallest distance nor smallest duration, is granted.
That there are an indefinite number of intervals between any two, is presumed. There is no next in space-time at all.

Endlessness seems self-evident.
There cannot be a happening without time.
The creation of time is absurd, by any god.
Atomicity is a convenient fiction.

Witt

[Clutch]

Originally posted by Normal
Thanks, your post helped cleared up a lot of my confusion, although I still don't completely understand the logic behind it.Hey, thanks for hanging in there! I'll see if I can do better.If there is an infinite past, you claim there was no beginning, fine, but it still means we can take any point in the past, and it's possible to take a point FURTHER in the past then that, and do that over and over and over again, ad infinitum.Right -- those are all three different ways of saying the same thing, in this context. I simply cannot make sense of this being the case where we have now reached the present,Er... well, weren't you just counting backwards from a given point a second ago? Of course we don't "reach the present" that way. But never mind; suppose we pick a given event and work forwards. Do you see that from any event in the series -- and that's absolutely any event, remember -- it's a finite distance to any other event? And hence only a finite distance from any event to any "now". Putting it in the negative: There exists no event in the series more than finitely separated from any other event. And "there exists no such event" means there exists no such event.

That is, on the IP model, there is no infinity of events to be completed in arriving at the present as an endpoint, because the series by its mathematical definition contains no point that can serve as the starting point of such an series....and have not gone through an infinite amount of cases, since, by the very definition of infinite, an infinite amount of cases is inexhaustible. Again, we haven't "gone through" an infinity because we never began one.

To be fair, if at any point we ask, "How many events have already occurred?" the answer might be given as "Indefinitely many." Not very helpful, I know. But the innocent nature of this answer should be evident from the fact that it can be paraphrased as: "One for every instant that has passed", and does not amount to "A completed infinite series worth."

I don't pretend that this is intuitive. It isn't. But that's not a problem with the notion of an infinite past -- it's a fact about infinities more generally. As soon as we start dealing with, e.g., sets that are the same size as proper subsets of themselves, our pre-theoretic intuitions are not going to be very reliable guides. But the structure of the natural numbers is mathematically very basic and well-understood, so the original question is easily, if counter-intuitively, answered.

[Demosthenes]

I'm thinking about the whole thing in another way. Since assuming that time extends infinitely in the past then there has been an infinite amount of time to reach present hence we exist today because it was possible for time to have an infinite amount of time to arrive at this point.

That's how I'm approaching the problem. Does it make any sense?

[ComestibleVenom]

Originally posted by Witt

Endlessness seems self-evident.

Not to me, it's very far from self-evident. It's a scientific question and those are not the sort of questions that lazy "self-evidence" cannot alone solve.


Atomicity is a convenient fiction.


Strictly speaking, that's true. It is convenient to think of the world in atomistic terms. That's because it's true. The world is of, in fact, sharply varying densities in the structure of the universe at definable scales.

It's convenient to assume the truth. It's markedly inconvenient to ignore it as the truth. We have no choice but to acknowledge atoms because they are part of our world.

[metacristi]

thomaq

from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?

Yes.In spite of the fact that our Universe has a beginning,if we define time as a function of movement,this is still possible.Even if we cannot prove scientifically that the hypothesis regarding the existence of 'something' is more probable than the creation ex nihilo (natural or artificial) it is at least an equal logical possibility.Indeed a regression ad infinitum of causes and effects is logically possible therefore is also logically possible to define a metatime that extends ad infinitum.Only if we could prove somehow that there was no movement at the moment of Big Bang (that state of the universe being also uncaused) or that the universe appeared ex nihilo are we entitled to discard the above possibility.

[wiploc]

Originally posted by Demosthenes
I'm thinking about the whole thing in another way. Since assuming that time extends infinitely in the past then there has been an infinite amount of time to reach present hence we exist today because it was possible for time to have an infinite amount of time to arrive at this point.

That's how I'm approaching the problem. Does it make any sense?


Makes perfect sense to me. There's no reason to think that it isn't now just because an infinite amount of time has passed.
crc

[wiploc]

Originally posted by ex-xian
But there is another possibility. Time could have a beginning, but still extend infinitly into the past. If time never took on the value of t=0, but was infinitly close to that value.

___0(___________>

where time started at the paranthesis.

Could you have gotten that backwards? It looks to me as if your example is of a finite line with no beginning point. (This assumes that the zero point is only a finite distance away.)
crc

[ex-xian]

Could you have gotten that backwards? It looks to me as if your example is of a finite line with no beginning point. (This assumes that the zero point is only a finite distance away.)
crc
No, the paranthesis implies an open interval.

[Normal]

Originally posted by ex-xian
No, the paranthesis implies an open interval.

With 0 as an asymptote?

[ex-xian]

Originally posted by Normal
With 0 as an asymptote?
No, since is regarded as the scalar component to time/space, it doesn't have two dimensions. The zero is the earliest possible state of the universe. In this example, time goes extends infinitely into the past and approaches t=0 as a limit.

[Witt]

Witt: Endlessness seems self-evident.

ComestibleVenom:
Not to me, it's very far from self-evident. It's a scientific question and those are not the sort of questions that lazy "self-evidence" cannot alone solve.

What can be more trivial than that: if you add one to x it is larger, and so on and so on.

Witt: Atomicity is a convenient fiction.

ComestibleVenom: Strictly speaking, that's true. It is convenient to think of the world in atomistic terms. That's because it's true.

Could you try to convince me?
Why do you believe there are atomic instances of space-time, or, mass-energy?

ComestibleVenom: The world is of, in fact, sharply varying densities in the structure of the universe at definable scales.

In what scale? What scales?

The very concept of density implies compactness, ie. infinite things!

How dense is the ' ' between things?
How many 'other things' exist betweeen them?

Surely, if we use real numbers to represent reality, we must acknowledge 'real number qualities of things'.

ComestibleVenom: It's convenient to assume the truth. It's markedly inconvenient to ignore it as the truth.

"We have no choice but to acknowledge atoms because they are part of our world."

That's a hell-of-a-leap, from 'convenient truth' to 'necessary atomism'.

Could you expand?

Witt

[paul30]

I don't think time exists.

Time is a fiction we use to describe our perception of change and recurrence.

So I don't think time is quantifiable except tautologically--that is, except in the same way the points on a number line are quantifiable. Time, like the number line, is an artificial construct.

In math, an infinite set is one that can have any number of its members taken away and still not be reduced.

I'm not sure that can be said of time.

It seems to me that time, like space, is not a thing or a stream but a relation.

[AdamWho]

from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?

not a mathematical question

[Clutch]

not a mathematical questionI thought it was.

Consider a set of events or times closed under a two-place "earlier than" relation whose properties are supposed to be familiar. Is there a consistent mathematical model of this?

Answer: Plausibly, yes -- the natural numbers, closed under the successor function.

[AdamWho]

The reason that I say it is not a mathematical question is because it is based on a physical phenomea (time) rather than mathematical concepts. I think the "real" mathematical answer was given already:
from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?
Yes, if you define it that way

[soulofdarwin]

Originally posted by paul30
I don't think time exists.

Time is a fiction we use to describe our perception of change and recurrence.

Feels right to me!

[ComestibleVenom]

Originally posted by paul30
I don't think time exists.

Time is a fiction we use to describe our perception of change and recurrence.

So I don't think time is quantifiable except tautologically--that is, except in the same way the points on a number line are quantifiable. Time, like the number line, is an artificial construct.

Time is as real as space and atoms. The fact that it might be a localized pheomenon, (for instance, at the event horizon of a black hole, space takes on the aspect of time in the sense that it is one-directional but local and finite) does not mean it's not in a very important sense REAL and quantifiable.

But paul30, if you have invented a complete system of physics without a temporal dimension, I urge you to revolutionize all of physics with it. Come on now, let's see your theoy, start a new thread. Contact the Nobel Prize committee!

[PJPSYCO]

Current theories tend to say that time started at a point, but existance was nul and mute before that. Ther problem is that matter is energy, and energy is not very easily put into terms with matter as a basis. To know where space came from one must know what non-space is like. That is where we use energy. Time however seems to only exist in space as a concequent or controller of gravitation. So, the answer would be no it does not go in two directions.

And to note the answer was not mathmatical it was scientific(specifically quantum physics). The mathmatical answer would be - go talk to a physicist or at least me. I'm working on PhD as an inorganic synthesis chemist (aka energy manipulation specialist).

[Nowhere357]

Originally posted by ComestibleVenom
Time is as real as space and atoms.
Atoms have physical existence. Space has three dimensions, and can be freely moved around in.

Time has neither of those qualities. Time is what we call the fact that things (atoms in space) change. Every tool that measures time, actually measures change - a pendulum swings back and forth, the hands on a clock go around, an atomic clock counts atomic ocsillations.

So actually, time does not exist. What does exist is the fact that we can measure cyclic changes of matter through space. The reason time has no meaning before the initial singularity is simply because there was no matter in space to change!

Time can be thought of as a fourth dimension, and that is useful in mathematics. However, it is NOT a dimension - if it were, we could move around in it freely, and of course we cannot. We only can move forward one moment at a time(!).

Iow, time is not a fundamental quality of reality along with space and matter/energy - but it is a fundamental quality OF space and matter/energy.

That is my lay opinion, deconstruct it if you will, but please don't harsh on me too much. :)

[ex-xian]

Originally posted by Nowhere357
Atoms have physical existence. Space has three dimensions, and can be freely moved around in.

Time has neither of those qualities. Time is what we call the fact that things (atoms in space) change. Every tool that measures time, actually measures change - a pendulum swings back and forth, the hands on a clock go around, an atomic clock counts atomic ocsillations.

-snip-
Time can be thought of as a fourth dimension, and that is useful in mathematics. However, it is NOT a dimension - if it were, we could move around in it freely, and of course we cannot. We only can move forward one moment at a time(!).

Iow, time is not a fundamental quality of reality along with space and matter/energy - but it is a fundamental quality OF space and matter/energy.

Well, there are dimensions and there are dimensions. A one dimensional space is just as much a dimension as a three dimensional space. Time is more accurately described as a scalar. When I took modern physics, we learned an equation that described time/space. Space is the vector component, and time is the scalar component. So time, however you define is as integral to this universe as space.

You can call is a measure of change if you want, but there are changed in the way things happen as you approach the speed of light. Time, whatever it is, slows down. So something is happening; maybe the rate at which things change is slower, but that's more of a philosophical question than scientific, IMO.

I like Einstien's definition of time: time is what we measure with a clock.

[Nowhere357]

Originally posted by ex-xian
So time, however you define is as integral to this universe as space.

If we remove all matter/energy from space (thought experiment) then what exactly remains which can be called "time"?

Time is integral, because it describes a relationship between matter and space. My claim is that it does not exist as a thing unto itself.


I like Einstien's definition of time: time is what we measure with a clock.
Yes - we measure the change occuring in matter. The drip of water, the unwinding spring, the flowing electrons. These are what we measure with a clock.

Space exists, and matter exists. And they are not static - if they were, "time" would have no meaning! It is the changing of things which we measure, and we call that "time".

You can call is a measure of change if you want, but there are changed in the way things happen as you approach the speed of light. Time, whatever it is, slows down. So something is happening; maybe the rate at which things change is slower, but that's more of a philosophical question than scientific, IMO.
Can you explain please why the question becomes more philosophical than scientific? It seems to me to be a question of fact.

[ex-xian]

Originally posted by Nowhere357
Time is integral, because it describes a relationship between matter and space. My claim is that it does not exist as a thing unto itself.
That's what I think is a philosophical question, but of course, I could be wrong.

Consider this: You're probably familiar with the twin paradox. One twin gets into a space ship and travels at a significant portion of the speed of light to a star and then comes back. The twin on the ship is a lot younger than the twin on earth, because from the earth frame of reference, time slowed down on the space ship.

But from the ship's frame of reference, the dimension of length contracted. That is, if you look at the ship's "odometer" the distance traveled is significatnly less than what the observer on earth would say that it is. So neither time nor space is absolute, both vary with reference frame.

This makes me wonder what it is about the nature of "stuff" is such that "time" happens at different speeds depending on reference frame

Here's (http://www.fortunecity.com/emachines/e11/86/whattime.html) a great article on the nature of time by Lee Smolin, researcher in quantum gravity and friend of my physics teacher. He's written some really great popular works regarding quantum gravity.

[Nowhere357]

Originally posted by ex-xian

Thanks for the link - I'll definitely use it.

For now I just want to explain why I jumped in here: sci-fi's fascination with time travel has always annoyed me a little bit. I think part of the reason the idea is so prevalent is due to the notion of "space/time" which seems to give "time" a dimension just like the dimensions of space.

I am on board with the value of the space/time and matter/energy paradigm (shit I've never used that word before) but the past does not exist, so no-one will ever go there.

Think of some new ideas all you science fiction writers - please!

[spacer1]

I am neither a mathematician nor a philosopher but I would like to offer the suggestion that the concept of infinity may be based upon the concept of time, leading to some sort of paradox.

I'm unaware of the mathematical definition, but to the best of my understanding, infinity is founded upon the idea that for any given number, x, we can always determine a higher number, x + 1. However, the operation from x to the result of x + 1 involves change, which is what time measures.

The implications of this idea are:

(1) There can be no (static) number called infinity, in the sense that we know other numbers which signify a definite value. Whenever we try to define a "highest" (or lowest) limit, x', the concept of infinity steps in and changes the limit to x' + 1 (or x' - 1).

(2) Given (1), no fixed point can be determined in infinity.

If any of what I have said above happens to be true, then it seems that the answer to the opening question would be that time could not extend infinitely into the past, for the notion of infinity could not allow for the designation of any fixed point, which means we could not designate a "now". Once we do designate a fixed point of "now", we necessarily make our timeline finite.

[Rousseau_CHN]

A Question For Mathemeticians Only

of course, my only problem with this thread is the title itself.

like hell, I have a big problem with elitism?

"...from a mathematical perspective..."

do you mean to say only mathematicians have mathematical perspective?!?

[thomaq]

Originally posted by Rousseau_CHN
A Question For Mathemeticians Only

of course, my only problem with this thread is the title itself.

like hell, I have a big problem with elitism?

"...from a mathematical perspective..."

do you mean to say only mathematicians have mathematical perspective?!?

i started the thread, and i myself am not a mathematician. i meant no dis-respect to anyone, i just simply was interested in the view-point of a "specialist" in the field. and no, i do not think that only mathematicians have a mathematical perspective, however, maybe mathematicians have a "better" mathematical perspective.

[Ted Hoffman]

I was of the opinion that if an infinite amount of future is possible, then so is an infinite amount of past.
I am of the opinion that they are not only possible, but necessary.

Making them finite is convenient for first-cause hunters.

I am also of the view that time is a measurement of change. Nothing more, nothing less. No universe, no change, no time.

[beowulf_king]

Here's my idiotic mathematical attempt to answer this:

I have formed my own definition of time using a "container" that represents any change per unit time. My definition is: Time is a relative measurement of duration in which entropy and ectropy (change) occur. My equation is H = C / T where C is the change and T is the conscious representation of the duration in which the change C occurred.

I will assume change is 1 for simplicity. First, say for one second, 1 unit of change has occurred.

H = 1 / 1 = 1

For two seconds, with one unit of change:

H = 1 / 2 = 0.5

Then for -infinity seconds, with one unit of change:

H = 1 / (-infinity) = - (1/infinity)

Since infinity gets extremely, extremly large, and then an infinitely limitless amount larger, the value of (1/infinity) goes to 0. Then, the negative value has no affect.

H = 0

We can intrepret this two ways. One way is that this says that no change has occurred, and yet one change was supposed to have occurred so there was a contraction showing that time can not be infinite. Another way is that since infinity can never be achieved, if we were to say that one change was supposed to have occurred over infinity, we could never reconstruct that event and measure to infinity which gives us another contradiction. Either way, infinity is unacheiveable. It would be required that a starting point (big bang) occurred.

[Another way though to look at this is that since both -infinity and +infiinity would result in H=0, then at the beginning and end, no change occurred (or nothing exists). This tells us that time is related to matter, and we started in a void and will end in a void.]

Anyway, enjoy my pointless rambling since I managed to create more questions than answers.

beowulf

[Satan Oscillate My Metallic Sonatas]

Thomaq,

Originally posted by thomaq
from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?

One of my degrees is in mathematics so I'll throw in my 2 cents here.


First off one of the most important discoveries of this past century was the idea of Relativity that Einstein popularized. While the Special Theory of Relativity is pretty easy to understand...the General Theory is quite a bit more difficult to chew. Regardless, an interesting artifact of General Relativity is that...


Math is subject to Physics.


If you were like me you are probably shaking your head right now. However, Einstein showed that Euclidian Geometery is a function of mass (or lack thereof). One bizzare upshot of this is that 'straight lines' are not necessarily straight.


So in a sense the 'mathematical perspective' is really going to be subject to the 'physics perspective' and the common 'physics perspective' currently is that time does not extend infinitely into the past. This is because time and space are the same thing and it's pretty damn obvious that space doesn't extend infinitely into the past, but that there was a Big Bang some time ago and space has been expanding ever since.




However, I would leave you with something to think about:

Suppose you were a 1 dimensional ant whose entire 'universe' was the function f(x)=1/(x(2-x)) over the interval (0, 2). Also suppose you live at X=1 and one day you start walking towards 0 (using our time analogy...this would be moving into the past).

Now from within your frame of reference...you can never get to 0 (ie you can never reach time = 0)...in fact your entire universe is undefined when x=0! Relative to you...your universe extends infinitely into the past.

Now suppose you started from you home at x=1 and started walking towards 2 (this would be analogous to moving into the future). Again from you frame of reference you can never reach 2 (time extends infinitely into the future). Also your universe is undefined at x=2.

However, from an outsiders perspective (a 2 dimensional outsider) your entire universe is completely contained within a very real, very concrete interval [0, 2].


Right about now the light should be going on that you and I could very well be the ants in such a universe (in our case however, it would be 4 dimensional). And while our universe may seem infinite (ie it doesn't make sense to talk about time at t=0) it is completely possible that our universe is contained within some closed higher dimensional structure.



Some food for thought.



-Satan Oscillate My Metallic Sonatas

[ex-xian]

Originally posted by Satan Oscillate My Metallic Sonatas
First off one of the most important discoveries of this past century was the idea of Relativity that Einstein popularized. While the Special Theory of Relativity is pretty easy to understand...the General Theory is quite a bit more difficult to chew. Regardless, an interesting artifact of General Relativity is that...


Math is subject to Physics.
I have to object to this. Math is only subject to the axioms that form the formal system in which you work.

If you were like me you are probably shaking your head right now. However, Einstein showed that Euclidian Geometery is a function of mass (or lack thereof). One bizzare upshot of this is that 'straight lines' are not necessarily straight.
Einstein showed that hyperbolic geometry, the geometry in which lines can have more than one parallel throught a given point, probably describes the actual universe. That doesn't mean that "straight lines" are not necessarily straight. Lines are undefined--in a Euclidean system, lines are straight. In hyperbolic or elliptic geometry, lines aren't straight.

Physics does decide which mathematical system may apply to the universe, but physics doesn't decide anything about math.

[Satan Oscillate My Metallic Sonatas]

Ex-xian,

Originally posted by ex-xian
I have to object to this. Math is only subject to the axioms that form the formal system in which you work.

Yeah I should have been more precise with this statement. Essentially Geometry is subject to physics. That is our concept of geometry is based upon an ideal (read completely massless) configuration of space. In the real world there common mathematical concepts are actually false for example...the shortest distance between two points is a straight line. As it turns out...really isn't the case.

-Satan Oscillate My Metallic Sonatas

[Satan Oscillate My Metallic Sonatas]

Ex-xian,

Originally posted by ex-xian

Einstein showed that hyperbolic geometry, the geometry in which lines can have more than one parallel throught a given point, probably describes the actual universe. That doesn't mean that "straight lines" are not necessarily straight. Lines are undefined--in a Euclidean system, lines are straight. In hyperbolic or elliptic geometry, lines aren't straight.

Physics does decide which mathematical system may apply to the universe, but physics doesn't decide anything about math.

Not to seem confrontational, but I don't think that is totally correct.

General Relativity doesn't do away with straight lines it says that a straight line can actually be curved. More succintly, the curvature of space may produced straight lines that are curved.



-SOMMS

[ex-xian]

Originally posted by Satan Oscillate My Metallic Sonatas
Not to seem confrontational, but I don't think that is totally correct.
Yeah, well I'm offended! ;)


Yeah I should have been more precise with this statement. Essentially Geometry is subject to physics. That is our concept of geometry is based upon an ideal (read completely massless) configuration of space. In the real world there common mathematical concepts are actually false for example...the shortest distance between two points is a straight line. As it turns out...really isn't the case.
<snip>
General Relativity doesn't do away with straight lines it says that a straight line can actually be curved. More succintly, the curvature of space may produced straight lines that are curved.

The problem is that you're giving definiton to an undefined term. It's not that lines are straight and then not straight. It just that in Euclidean space, lines happen to turn out straight--because of the parallel postulate, and in hyperbolic space, they're not--again because of the analogous hyperbolic parallel postulate.

[JohannGoodflag]

Satan Oscillate My Metallic Sonatas
Math is subject to Physics.

Math is not subject to physics: physics is just the inspiration for math. Euclid was driven because of the idea that geometry defined the universe, and Newton was driven because of his interest in astronomy and gravity, but this does not mean that math is limited by physics; merely that it is driven (in part) by the study of physics.

Physics' role in limiting mathematics is only in that physics limits us (the beings which practise mathematics), and so indirectly controls some of the ideas we can formulate about mathematics. But just as we can imagine impossible objects (invisible pink unicorns) and uninstantiated objects (red elephants), we can have mathematical ideas which do not necessarily apply to this world.

Yeah I should have been more precise with this statement. Essentially Geometry is subject to physics. That is our concept of geometry is based upon an ideal (read completely massless) configuration of space. In the real world there common mathematical concepts are actually false for example...the shortest distance between two points is a straight line. As it turns out...really isn't the case.
Geometry is only subject to physics if you consider geometry as the subject of analyzing space as it actually exists.

Euclidean geometry is an approximation to reality, but this doesn't mean that it is 'false'. Euclidean space is not founded (since the later 1800s, anyway) on the idea "this is the way it must be": it's just founded on the axioms, which essentially define the concepts of line, point, and parallel. Saying "Euclidean goemetry is false" is a little like saying "5 is false" when you have three apples instead of five. It's more accurate to say, "Having understood what Euclidean space is, our space is not Euclidean".

General Relativity doesn't do away with straight lines it says that a straight line can actually be curved. More succintly, the curvature of space may produced straight lines that are curved.
:D It's at this point that most mathematicians start using 'geodesic' rather than 'striaght line' to avoid confusion. ('Geodesic' being the appropriate generalization of the concept of straight lines, for non-Euclidean spaces.)

spacer1
I am neither a mathematician nor a philosopher but I would like to offer the suggestion that the concept of infinity may be based upon the concept of time, leading to some sort of paradox.

I'm unaware of the mathematical definition, but to the best of my understanding, infinity is founded upon the idea that for any given number, x, we can always determine a higher number, x + 1. However, the operation from x to the result of x + 1 involves change, which is what time measures.

Please don't take offense, spacer1, but your lack of awareness of the accepted definition of infinity is despite the best efforts of some of the people on this board. I'm not claiming that you're ignorant or stupid, but only that you hold a philosophical position which is incompatible with the mainstream of mathematicians (including myself), which might make it difficult for you to accept the standard definition. Your position is tenable, but non-standard.

The definition of the natural numbers you use (common to the so-called constructionist position) depends on either (a) having an infinite set in the first place as the domain of the successor function, i.e. begging the question, or (b) having the successor function and its' properties act as an axiomatic concept, deliberately left with loose ends, precisely because that sort of incomplete definition is required to have an infinity through that method.

In more mainstream mathematics, you can certainly describe the natural numbers by this method, but that is not how it is defined. Essentially, one just assumes that the natural numbers as we understand them exist. Then, an infinite set is anything which is at least as large as the natural numbers. This definition requires no concept of time in mathematics itself, and so infinity does not rest upon any concept of time.

Getting to the OT:
thomaq
from a mathematical perspective, does it make sense to say that time could extend infinitely into the past?
I agree with several posters here in saying that this is not a mathematical question, so much as it is a cosmological/metaphysical question. The answer is that it depends on how you measure time. We take time for granted, but it's pretty damned slippery. In fact, the only definition for time which has any real acceptance in physics is the one that Einsteain implicitly used in formulating special relaitivity: time is that which is measured by clocks.

By 'clock', read any phenomenon which behaves very regularly (e.g. a grandfather clock, a swinging pendulum, the half-life of uranium, the vibration of quartz, etc). Each of these things have behaviour which is synchronized with all of the others: they evolve in a sort of lock-step, so that if you know the recent history of one of the systems, you can determine the recent past future of the others. We can take any of these objects to be a 'clock' suitable for defining time (although if you want precision over long timescales or short ones, you have to choose carefully).

In order to say whether time extends infinitely back into the past, you have to describe a set of things which could be used to measure time going back arbitrarily far into the past. Based on the current standard, you might ask for the vibrational period of certain molecules, or maybe half-life of certain nuclei. If you go back far enough, these things don't exist, even if the past is 'finite': we just have mostly hydrogen. It could be that we could find something else which can be used as a clock going even further back, but how far back does that closk reach?

If you are interested in how far back you can go with any clock of any sort, first you have to first find a Grand Unified Theory of physics, and give me a description of every possible kind of 'clock' under that theory, and then I can answer your question. All estimates of the age of the universe seem to be done this way: assuming that the speed of light is constant, that the universe is expanding in such-and-such a way, we then deduce the age. We don't have much problem with assuming the speed of light is constant, but guessing at whether the universes' expansion is accelerating or decelrating, and in what fashion, has turned out to be a big guessing game to judge from what I've read on the subject.

JohannGoodflag

[wiploc]

Originally posted by JohannGoodflag
In order to say whether time extends infinitely back into the past, you have to describe a set of things which could be used to measure time going back arbitrarily far into the past. Based on the current standard, you might ask for the vibrational period of certain molecules, or maybe half-life of certain nuclei. If you go back far enough, these things don't exist, even if the past is 'finite': we just have mostly hydrogen. It could be that we could find something else which can be used as a clock going even further back, but how far back does that closk reach?

Illuminating. Thank you.

crc

[spacer1]

Originally posted by Johann Goodflag
Please don't take offense, spacer1, but your lack of awareness of the accepted definition of infinity is despite the best efforts of some of the people on this board.
Actually, my comments on this thread were made well before our exchanges on the infinity threads. I think my post here was the first time I put forth any ideas regarding infinity on these boards. I do not reject set theory so vehemently anymore. However:
This definition requires no concept of time in mathematics itself, and so infinity does not rest upon any concept of time.
Yes, but the OP specifically asked whether time itself can extend infinitely.

[sophie]

When we define time we currently define it in terms of our existence. In short existence contributes to its own self-awareness (yes, this is true when the largest extent of the term existence is brought to bear on our thoughts). In short existence has a cohort called time.

Where we are NOW seems to have been contingent on the unfording of the universe within the realm of existence. If we say time as a miror of existence extends infinitely into the past then we necessarily mean the universe was continually unfolding and there is nothing we can substantially call the emergence of the universe.

If we wish to play tricks with the infinite division of an interval then there does not seem to be any matching physical reality which can support an infinity into the past.

If we claim time does not extend infinitely into the past all we are saying is there is a subtle point at which our universe became recognisable through the use of our current incarnation of physics.

If we claim time to be something else, something other than the mirroring of the passing of existence then it may just be possible for physical-time to extend infinitely into the past and psychological-time to have had a beginning, which means psychological-time cannot extend infinitely into the past.

[JohannGoodflag]

spacer1
Actually, my comments on this thread were made well before our exchanges on the infinity threads.
Ah. :o For some reason, I assumed the thread was more recent. Must check timestamps!

JohannGoodflag
This definition requires no concept of time in mathematics itself, and so infinity does not rest upon any concept of time.

spacer1
Yes, but the OP specifically asked whether time itself can extend infinitely.
Well, I'm probably just arguing with a past version of you on this, but anyway: it is precisely because time is not required to define infinity that makes it meaningful to ask whether time is infinite itself (i.e. no circular logic ensues).

sophie
When we define time we currently define it in terms of our existence. In short existence contributes to its own self-awareness (yes, this is true when the largest extent of the term existence is brought to bear on our thoughts). In short existence has a cohort called time.

Actually, when we define time, we define it not in terms of our self-awareness, but in terms of our awareness of events happening in our environment. If all there was was a disembodied mind contemplating it's own existence (à la the point in Flatland), it probably would not be able to recognise or conceive of the passage of time, because the only thing going on is itself.

I would guess that our concept of time arises from the awareness of changes (things are different from how we remember them being at one time), the presence of natural clocks (such as days, moon cycles, and seasons), and the fact that many of the changes in our lives take about the same amount of cycles of these natural clocks. Out emerges a concept that there is a global thing called 'time' which everything plays out in. A creature or device which is not self-aware would have problems articulating any idea of time, but that does not mean they cannot have any.