Why is, “How much time passed prior to this point, a point preceded by an infinite past?” an unanswerable question? It’s not. The answer is, “an infinite amount of time.”
So… there isn’t a concrete answer. All I proved is that, within an enormous class of systems of measurement, you can come up with a finite number of seconds. All of the following (and many more) would have worked:
x(t)=e^-t
x(t)=e^-c*t for any positive real number c
x(t)=e^-(t^2)
x(t)=sin(t) / t
x(t) = 1/t^2
x(t) = 1/t^n for any positive real n greater than 2
and so on.
Every one of those functions will give you a different concrete answer. I don’t know which one is right - that would presumably be constrained by observation, but maybe by more serious thought as well. But it doesn’t matter: all that was asked is “is it logically possible?” and the answer is yes.
Understandable. If you are interested in understanding the proofs, these are improper integrals. That’s all this is. But either way, it’s alright. I’ll rest comfortably knowing that you are at least mathematically wrong.
A big caveat - even though the semifinite interval may be finitely measurable, that doesn’t necessarily make it physically meaningful, for the reasons given above in the previous post. It just makes it logically consistent
Yep, that silly math that says that any finite amount of time will be less than an infinite amount of time. I’m a heretic that way. One day the world will celebrate my genius, mark my words!
Because there is no interval to measure. If you insist on knowing “how much time has passed prior to now”, then I would answer “undefined” rather than “infinite”, since what you are asking doesn’t really make sense.
Yes, that’s why it’s logically impossible. But it’s not “undefined,” it’s “infinite,” by definition. Remember the premise? “Is an infinite past logically impossible?” My response was to that premise.
You’re not alone. There are plenty (well, okay, not plenty) of finitists in the world. Just know that you are sort of in this guy’s camp, though.
OK. Do you also believe that it is logically impossible for time to have no beginning?
Your problem here is that your equation [Finite < Infinite] assumes “Infinite” is a “number”. It’s not. “Finite” is, “Infinite” is not. Your math is wrong. Mathematics does not correspond to the real world, except by chance. It’s all about logical reasoning from definitions. This problem, by definition, assumed an infinite universe has always existed, and so an infinite amount of time has already passed, bringing us up to the present, which we currently experience. No logical problem. It may not correspond to the real universe, but there is no logical flaw given the definitions already stated by the OP.
BTW, the calculus the earlier poster gave you checks out. Look for the “infinity” terms cancelling. That’s all you need to follow the math. Forget calculus. Think algebra.
An infinite amount of time can’t have already passed. A universe that comes into being with an already existing “infinite past” tortures the meaning of “past” into meaninglessness–how can something emerge with a past attached to it that stretches before the point of emergence? Conversely, how can something “always exist,” possessing an infinite past, except by arbitrary definition? The past is the ongoing “exhaust” of the present. The only infinite past that can exist is a past that defies any meaning–it’s something we call the past, but it has not, in fact, actually “passed.” It’s time that exists as a concept only, without the “clock ticks” that make any discussion of time meaningful. It’s a universe simultaneously bound by time and not bound by time. Or so it seems to me.
Strato, I think you’re assuming some kind of motion through time as being inherent to the nature of time. This is not necessarily the case. General Relativity, empirically verified in our own Universe, tells us that motion through time is relative, and therefore neither absolute nor universal. There is no universal Now through which every moment must “pass”. What I and some of the others in this thread are driving at is the so-called block interpretation of GR, wherein every point in time and space exists equally, and our perception of motion through or progression of time is an illusion. This interpretation, as far as my graduate education in physics has led me to understand, is a logically consistent possibility, and it does allow for a block of infinite temporal length.
There is a “now” through which everything passes relative to a given position in space, which would amount to the same thing. Rather, relativity doesn’t destroy the flow of time, it just changes the rate of the flow (as compared between two different vantage points). All the same events occurred, in the same sequence. They just may have unfolded at a different pace, from my vantage point on my rocket ship. The “illusion” you describe is not one that changes the properties of the flow of time in a way that permits the infinite past–from any given position you might measure it, time would flow forward in a linear fashion, the present is preceded by the past, etc.
And anyway, even if it were a complete illusion. I’ve already acknowledged that the one possibility that permits an infinite past is that which demonstrates that time does not operate as we perceive it to, it’s a mirage; therefore, there’s no “infinity” to overcome logically. But if time does have the properties we perceive it to, then an infinite past still seems a non sequitur.
How much time needs to have unfolded before we would reach the present point in time? “An infinite amount.” Then that sequence of time is still not completed, and yet, here we are in the present. “Ah, but that infinite span of time has already occurred. It’s done, by definition. An infinite series of events has occurred, and it did not require an infinite amount of time to take place. Or if it did, that infinite span is over, it’s already happened. By definition.” Oh. Well, there you go. The non sequitur is eliminated by decree.
It looks to me like your thought process goes something like “Suppose time is infinite. Now suppose that time is finite. But this is a contradiction! Therefore, time is not infinite.”. You’re saying that an infinite amount of time can’t have elapsed, because that would take an infinite amount of time. Well, yes. But that’s exactly what we have, by postulate.
How about this: Do you accept the logical possibility of a universe which has a beginning, but then lasts for an infinite amount of time after that? If so, we can work from there.
An infinite amount of time could have passed since a time infinitely long ago.
If we postulate an infinite past we can logically consistently infer a time infinitely long ago from which an infinite amount of time has passed to get us to the present. I’m not saying that that’s how the universe works. I’m just pointing out that there is nothing logically inconsistent with an infinite past.
I’m not saying I agree with an infinite past, but the complaint in this thread makes no sense.
An infinite amount of time cannot pass in a finite amount of time. Fine. From any point in time to now, there is only a finite amount of time.
An infinite amount of time CAN pass in an infinite amount of time. Also fine. There is an infinite past, and an infinite amount of time has passed to get to now.
No problems.
Yes, that’s what I meant by “the non sequitur is eliminated by decree.” I assumed the OP meant something more than that, or else the question answers itself. It would be a form of “Accept as a given that an infinite past already exists. Does an infinite past already exist?” That’s what I tried to clarify in my last post. We’re either torturing the definition of “past” into something unrecognizable, or we’re hand-waving away the impossibility (“No, just assume that that infinite span of time has already happened, somehow; that infinite past just somehow appeared, or it just always was, handily avoiding the need to actually deal with the passage of an infinite span of time”). Or that’s how it seems to me.
Well, that’s interesting. I think a never-ending future is possible in a way that an infinite past is not; the same non sequitur doesn’t exist here, I don’t think, in that there’s a starting point. We could (theoretically) be watching a time-line toward infinity unfold. That said, that future will never reach infinity, so I suppose it’s an impossibility simply because it’s self-evidently impossible. No matter how long our yet-to-end future extends itself, infinity is not within its view. I think…
Only that it begs the question, in the way I described to Chronos.
It’s quite possible to have a logically self-consistent model of time which regresses infinitely in to the past where the amount of time between any two events is finite. Infact I would say that all proposed models of a universe without a starting point fall in to this catergory.
There is no reason to assume that there must be an infinite amount of time between any two events just because time streches backwards infinitely.
If we wish to bring relativity in to we just need to make a few clarifications.
I’m not a mathematician, but I would argue that infinite is not an “amount”. It’s a descriptor. You can’t halve it, you can’t measure it, it has no size. Infinite is an adjective, meaning “without end”. As soon as you say “an infinite amount of”… you lose.
It’s for this reason that I reject the idea that the universe has existed “forever”. You can’t “add” to inifinite, because infinite is not a quantity. Yet, seconds are being “added” to time every second that ticks by.
I think it is intuitive, and logical, to believe that time had a beginning.
I think it’s a fair questionn i.e. does the term “infinite amount” mean anything? “Amount” is a term often used in mathematics, but it’s not rigorously defined. I think though most people will understand what is meant by for example “There are an infinite amount of real numbers between 1 and 0” i.e. the set described by the real interval (1,0) is bijective with some proper subset of itself.
It’s difficult to conceive of an infinite amount of time between events, but that doesn’t mean necessarily that it wouldn’t be possible to reasonably describe an interval of time between two events as “infinite” in a logically consistent way.
However I think that it’s a red herring anyway as the normal kind of model of a universe “without beiginning” doesn’t have such infinite intervals of time in it anyway.