Please excerpt out any parts of these that you find to be relevant to your point. 'Cause I don’t believe they support your position, and so reading them would be a waste of time, and I am not so bored as to need you to find ways of spending my time purposelessly.
I view a number as a descriptor of a fixed value relating in some way to quantity. By this standard, -1, sqrt(-1) are numbers, and infinity by explicit definition is not one, and there is no possible way to interpret it as one while staying compatible with any of its definitions.
Feel free to propose a definition that works with your little theory. And don’t try “A number bigger than every other number”, because by explicit definition of all number systems that is either a specific finite number or no such number exists.
Brief argument: There is no such thing as an infinite quantity. Some amount of time has already passed. All possible amounts of time are finite. So, some finite amount of time has passed. If a finite amount of time has passed, then that amount of time prior to now, time started. Thus, there was a beginning of time.
This argues that nobody should believe in infinite history; this is admittedly not going against the grain, because anybody who believes in (and understands) the big bang doesn’t believe in infinite history. Admittedly this doesn’t comment at all on how this relates to God’s existence…but nothing in the OP did either - in fact it erroneously assumed that atheists were presumed to believe in infinite history…for no visibly stated reason.
Admittedly there are (finitely) numerous other, simpler, and more direct ways to eviscerate the argument presented in the OP, but I felt that nonetheless this was on-topic, as it seemed quite relevant to the tangential discussions at least.
All any of those cites show is that particular properties of particular number systems lacking infinity differ from those of other particular number systems applied in particular ways to the infinite. The third cite isn’t very credible at all (The Flat Earth Society?) and the first is really disappointingly egregious in saying “In other words, does there exist any number system which, as well as including the familiar numbers we are used to, also includes an ‘infinity’ concept? The answer is no”, when, in fact, the first cite itself actually gives a number system containing infinite numbers (it just happens to contain more than one of them); to wit, the ordered ring of polynomials.
Basically, the first cite notes that infinity has no additive inverse in the arithmetic of the real projective line, and thus dismisses the idea of calling infinity a number in any context. The second cite notes that some infinite quantities satisfy the equation X + X = X in cardinal arithmetic, and thus dismisses the idea of calling anything infinite a number in any context. These are both really misbegotten objections. I could just as well object to the complex numbers, because they contain solutions to X * X = -1, which no real numbers satisfy.
The point is, there are many contexts in which professional mathematicians would simultaneously describe a value as “infinite” and “a number”. Do you disagree with this assertion of mine?
What is the quantity described by sqrt(-1)? And how are “the amount of integers” or “the slope of a vertical line” not also fixed values relating in some way to quantity?
Um, ok; let’s look at some particular little theories. Like “number”, “diagram”, or “game”, there are many different but interrelated notions of “infinity”, the most useful one depending on the particular context. Within the cardinal numbers (which measure the quantity of things in a set), one formal definition of “finite” would be “The size of a set which is inductively generable starting with the empty set and using only the operation of adding a single element”; the size of the integers would not be finite. Within the projective real line, one formal definition of “finite” would be the similar “A quantity bounded by those inductively generable starting from 0 and using only the operations of +1 and -1”; the slope of a vertical line would not be finite.
Are you really eviscerating the OP’s argument, as concerns what is logically necessary in temporal structure? You seem to be agreeing with him.
Actually, incredible as it is, the messageboard discussion in Telemark’s third cite contains numerous people pointing out examples of number systems containing infinity and infinite quantities. It hardly speaks with one unified voice.
Anyway, it doesn’t matter whether we apply the word “number” or reserve it. The idea that we can “prove” time has a beginning simply by saying “Infinity is not a number. There must be a number to describe the number of seconds which have passed. Ergo, time began some finite number of seconds ago. Q.E.D.” is silly. I can prove everything to be finite by this same line of reasoning, except where you step in and say “Nuh-uh. I didn’t mean for it to apply there. Time is different from other things. The past is different from the future. Those differences are key.” Can you spell out these differences in a way which anyone not already believing in a finite past will accept? If you cannot, the argument is of no merit.
And if the definition of infinity has taught us anything, it’s that there is no such thing as an infinite quantity. Do you argue with that?
Some amount of time has passed - at least 32 years, according to my driver’s license. (Unless you want to argue that all of history, including our memories and sense of passage of time, is fake…in which case you’re not arguing for infinite time passing, you’re arguing for less time passing.) If some amount of time had passed before, say 8:00 this morning, then the amount of time that had passed before then is not an infinite or unfixed or growing or fluctuating amount of time; it’s a specific fixed amount of time. Which means a finite amount of time. Which means not an infinite amount of time. By definition.
Right?
Oh, it exists; I remember at least the last ten minutes of it quite specifically. Now, I admit we don’t know if it’s being created as we go, whether prior times persist in any form, whether it is in fact a ‘dimension’ upon which we’re sliding in one direction and cannot directly perceive either backwards or forwards - but it definitely exists.
And it’s definitely the medium where we track motion. Without it, motion and activity can’t even be conceptually described - you’re limited to a single state with only position to work with, and nothing’s position can ever change. This gives you giving you a perfectly static universal state. Nothing happens without time - regardless of what time actually it is.
If you want to believe in a static god that never does, has done, or will do anything, anything at all of any kind, ever, then…well, that’s your business, but I don’t see the appeal myself.
All the magic clocks I’ve seen emit a ticker tape that is one nanoangstram long for every second that they’ve shown the time for. How long is the ticker tape on yours?
The thing about bi-directional number lines is that they ‘grow’ in both directions. But if time ‘grew’ in both directions, then 1) there would still only be a finite amount of it total at any given, uh, metatime, even if we were adding years to the back of history as fast as we’re adding them to the front, and 2) reverse-growing time would sure bugger up causality, as far as I can figure. Doesn’t it seem like it would to you?
Let’s see some cites. I want to see if they’re using it as a verbal shorthand, like in 3 / 0 = Not A Number (and of course this sort of shorthand is the terms actual use in mathematics), or just making errors in phrasing as even mathematicians occasionally do.
It’s sqrt(-1), of course. Like -1, it only has meaning in context, but it nonetheless describes a specific fixed value relating to quantity.
The term infinity denotes situations things that do not reach fixed values, but rather cases where it just keeps going and going and going without ever reaching a final number. (And really, if you don’t know that by now, you should just bail out of the discussion because you don’t know what you’re talking about.)
There is no numerical ‘amount of integers’, and the way in which there is not a numerical amount of integers is precisely described by the term infinity, so that’s the answer given.
Similarity, in the only context where the slope of a vertical is infinity, rise over run, the situation is that you can keep rising and rising and rising and you’ll never finally reach a run of ‘1’. This matches the definition for infinity, so the term is used.
Why didn’t you use 3 / 0 = infinity as an example as well? Oh, right, because I already shot it down. You’re not making an argument; you’re just trying to find some sort of ‘trick question’ that I can’t handily answer.
Mm-hmm. And in all cases “infinity” means “doesn’t have a fixed quantity - it just keeps going and going and going without ever reaching the end.” I already know the definition. Do you?
How do you figure?
No, I cannot force “anyone” to comprehend. You can lead a horse to water, as they say…
Funny thing, I can never get to the end of that tape to measure how long it is.
But you’re assuming that the clock in fact did start. That is, there is a time X ago, that the ticker had zero length. Which would mean, at time (N-X-1), the clock was not displaying a number.
Of course, the problem with all this is that dealing with infinities is very difficult. It seems perfectly reasonable to think that the number of integers is greater than the number of even integers. But regardless of how reasonable it seems, it’s still wrong. (And as Indistinguishable keeps trying to tell you, there are contexts in which infinity does make sense, and contexts in which is a number.)
I don’t know. Maybe I’m wrong. Maybe I’m missing something. But your arguments haven’t convinced me yet.
But it has a length, right? Because every tape has a length. It has two ends after all, and some length of tape between them - which even if very long is still finite (by definition).
Actually, I’m proving that the clock did in fact start. It’s impossible for a tape to have infinite length, by the definition of infinite. This reflects more concretely the perhaps harder to grasp fact that the timeline cannot reasonably be described as having infinite length either. Which proves that there must have been a time on your clock that did not have a preceding time. (Which, if you rigidly stick to its definition, proves that your “magic clock” doesn’t exist. Sadly, such is often the fate of ‘magic’ things…)
Hmm? Of course there are the “same number” of even integers as integers - not that either set has a number as its quantity, mind you. They can be mapped to each other 1:1 though.
I like dealing with infinities. They’re fun.
It makes sense in lots of contexts, but isn’t a number in any of them. Not that that’s stopped him from trying to prove otherwise, mind you, but he appears to have been ineffective so far.
The real kicker here is that the closest a quantity can get to being ‘infinite’ is to be ‘finite, but growing without limit’. Which seems to describe the future-facing end of the timeline reasonably enough to those of us who perceive time as passing…but can you reasonably say that you think the history-facing end of time is growing in the negative direction as well? What does that do to causality?
Well… ok. All the Wikipedia links I gave were examples. But if you’re unhappy with those, here, I’ll excerpt a statement from elsewhere for each one, quickly Googled:
Cardinal numbers: “Thus we call a cardinal number kappa ‘infinite’” or ‘transfinite’ iff kappa >= omega. … We write ICN for the class of infinite cardinal numbers. … Any infinite cardinal number which is uncountable and not a successor cardinal is called a limit cardinal."(source)
Ordinal numbers: “An infinite ordinal number is called an initial ordinal number of cardinality tau if it is the least among the ordinal numbers of cardinality tau…” (source)
Surreal numbers: “Surreal numbers are a field that contain both the reals as well as infinitely large and infinitely small numbers.” (source)
Supernatural numbers: “The other supernatural numbers are said to be infinite… It turns out that the pseudovarieties of abelian groups corresponding to natural numbers are locally finite, while those corresponding to infinite supernatural numbers are not locally finite.” (source)
Hyperreal numbers: “Using the ordered fields properties, it follows that the reciprocal of a positive infinite hyperreal number is positive infinitesimal.” (source)
Projectively extended real numbers: “For sake of simplicity we identify points on a line with the corresponding [projectively extended] real numbers on R (including the point Infinity for the point at infinity)… We now fix three distinct points on a line, and call them 0, 1, and Infinity… This construction allows us to equip the line with a scale that behaves ‘as if’ point 0 is the origin, 1 is a unit point, and point Infinity is infinitely far away.” (source)
Affinely extended real numbers: “If the set S does not contain the extended real number -Infinity, and if there exists some real number A such that s >= A for all s in S, then inf S > +Infinity… This function is discontinuous when p = + or -Infinity and q = 0, and when p = 0 and q = + or -Infinity. It is continuous for all other values of the extended real numbers p and q.” (source)
p-adic numbers: Eh, I’ll admit, this one was a stretch. But within the p-adic numbers, the sum of an infinite series of 1s converges, which I thought was worth something.
Super-real numbers: “Proposition 1: Any ordered field properly containing R contains an infinitely large number.” (source)
Aleph numbers: “The aleph numbers are infinite cardinal numbers defined by transfinite recursion, as described below.” (source)
Beth numbers: “Under the GCH, for all alpha, Beth_alpha = Aleph_alpha, and so the Beth numbers are just the infinite cardinals.” (source)
Jesus, guys, am I the only person who agrees with Indistiguishable?
Time doesn’t logically have to have a beginning. Period. All this talk about infinity and whatnot is beside the point. Either there was a beginning, and a finite amount of time between then and now, or else no beginning, and we can equivalently (and confusingly) say time ‘began’ infinitely long ago.
Insisting that there can’t have been an infinite amount of time before now because we couldn’t have gotten here otherwise is automatically making the assumption that there was a beginning. In which case you’re right. There can’t have been an infinite amount of time between now and the beginning of the universe. But if there wasn’t a beginning… then it is perfectly possible, in fact necessary, that there was an infinite amount of time before now.
All this leaves aside the overwhelming empirical evidence that there was a beginning. All we’re arguing over is the logical possibility.
No real argument. Infinity means that something is boundless. Quantity implies finite (although this is probably arguable), so I’m ok with keeping those 2 words apart.
No, not necessarily right. It’s simple really: If you believe there is a beginning to time then you believe time that is already past is finite. If you do not believe there is a beginning to time then (I think) that means time that has already past is infinite.
You seem to be stating that there has to be a beginning of time. I personally don’t see the requirement for it.
Those are all assumptions you are making. There are a number of theories regarding time and no conclusions. What they do appear to have figured out is that our perception of time is far more limiting than the laws of physics appear to require.
I realize the OP was discussing god but I’m not. Although, if god was omnipotent, even without time couldn’t he/she still lift that burrito?
It looks like you’re mostly getting all excited about aleph numbers - an enumeration of the various ‘sizes’ of infinities. These of course aren’t numbers by my definition, or the common man’s definition; they are labels and certainly don’t correspond to usual numbers.
And then there are the various ‘surreal numbers’, etc, that are actually set theory formulations. Very creative - and I’ll grant you right now that these set theory guys seem to be very happy to call all sorts of things that aren’t actually numbers, numbers. Which doesn’t really have much to do with numbers as we’re talking about them here…
I admit I didn’t look at all the cites - I saw a trend and got bored. I suppose there might be some third and fourth and fifth ways things that are not numbers are called numbers in those cites; if so, good for you. Regardless, a set’s not a number, no matter what you name it. (Yes, you can model numbers with sets in various ways…but still, no sale.)
I think this tangent is boring. How about you go on thinking that infinity is a number, and that infinite years have passed before now, and that you have infinity miles on your odometer, and that you have infinity shoes in your closet, and as many other infinite amounts as you want to believe in, and I concede that there indeed are people out there who can’t be convinced out out their rock-hard preconceptions by any argument no matter how ironclad, and we both move on with life.
Right…except, no amount of time is infinite. (Any ‘amount’ is automatically less than ‘amount’+1, after all.) Which means that it’s in fact perfectly impossible for there to have been an infinite amount of time before now. Which, by your own logic, requires there to have been a beginning.
The argument starts with the definition of infinite, recognizing from that there’s no such thing as an ‘infinite amount’ of anything, from there recognizing that there can’t have been an infinite amount of time prior to now, and from there realizing that if there can’t have been an infinite amount of time prior to now, there must have been a start to time at some point in the past. The argument definitely does not base itself in any assumptions about the beginning of time; it is definitely not circular and doesn’t assume the conclusion. It simply, logically, proves that time logically has to have had a beginning. Period.
Right; it is convenient that the empirical evidence lines up neatly with my argument’s conclusion. It would be rather…distressing if it didn’t.
Not to repeat myself, but I have to wonder why I’m not getting across here. You concede that there’s no such thing as an infinite quantity. (Putting aside abstract set cardinalities of course; we’re talking about actualized quantities; items in a pile, inches of tape, rotations of the second hand, consecutive minutes gone by.)
If you accept that there are no infinite quantities, doesn’t it bug you just a little bit that you’re accepting as viable an option that, to be true, requires an infinite quantity of time to have passed? As you say, if you do not believe there is a beginning to time then that means that you believe that an infinite amount of time has already passed. But, it’s impossible for an infinite amount of time to have passed; because infinite amounts are impossible.
Logically speaking we’re looking at “If A is true, then B is true” and “B is false”. An equivalent argument form is “If it were raining, I’d be all wet” and “I’m not all wet”. The logical conclusion is “Then it’s not raining.”
Similarly, “If the universe had no beginning, then an infinite amount of time has passed.” “We know that an infinite amount of time cannot have passed”. So, the conclusion is “Then, it’s not the case that the universe had no beginning.”
The logic here is pretty solid, structurally; it’s the simplest sort of proof by contradiction (sometimes known as Modus Tolens, incidentally.) It eludes me how I could make clearer or simpler. I’m kinda at a loss, really.
It’s no assumption that in velocity equations, if there is a 0 span of time, there is 0 velocity. Thus: no time = no movement…by definition, pretty much.
I’m thinking that the act of ‘lifting’ requires there to be a change in state, which requires time to occur. The act of thinking about lifting would too, I’d think. So, if he was trapped inside a timeless state, that would essentially be complete stasis, with any action at all being a logical impossibility. (And I don’t grant even omnipotent gods logical impossibilities; that just gets silly.)
And “7” and “π” and “e” and “i”/“sqrt(-1)” aren’t labels?
The surreal numbers have nothing to do with set theory as such. Granted, one can construct them with set-theoretical methods, but then, one can construct the integers, real numbers, etc., with set-theoretical methods as well. Of my citations, only 4 had to do with set theory (cardinals, ordinals, aleph, and beth numbers), while the other 7 were just plain-vanilla systems of arithmetic like the standard real or complex numbers, having nothing to do with sets and motivated by mainly arithmetic concerns.
Even of the infinite cardinal numbers, though, I would think the quantities which answer “How many items is this?” are much closer to the common man’s notion of number than, say, sqrt(-1), and yet you accept the latter as a number but not the former, for some ungodly reason.
Yes. It’s a boring terminological hijack. It is of no great importance. You could refuse to call anything but odd squares greater than 90 “numbers” for all I care. Except, somehow, you think you can prove nontrivial facts about the universe by glibly saying “Well, obviously, infinite quantities can’t be numbers, and the answers to these questions must be numbers.”
Also, I admit, you got under my skin by accusing me of wallowing in ignorance.
But no one who doesn’t already agree with you from the outset would accept that there are no infinite quantities. Certainly, most would not consider it to be a logical fact that there are no infinite quantities; we would accept that some quantities could, in fact, be infinite, whether or not any actually are in this universe.
I mean, consider something like a meter. How many points are there within that interval? Well, there’s the point at distance 0, and the point at distance 1, and the point at distance 1/2, and one at distance 3/4, and one at distance pi/4, and so on. Now, one could talk about a universe in which everything is quantized in such a way as that there are only finitely many such points… but this isn’t logically mandated. It is logically possible that there are infinitely many points within that meter. All the analyses of classical mechanics were carried out in systems which had infinitely many points in a meter, and there was nothing inconsistent about it.
At how many possible angles can the clock’s hand point? Well, there are 12 obvious ones, and then there are the ones halfway between those, and then there are the ones halfway between those, and then… It sure looks like infinitely many. Certainly, we can mathematically model the situation where there are infinitely many. Whether or not it actually describes the universe we live in, it describes a universe which is logically possible; this model doesn’t fall apart in a puddle of its own incoherence.
For how many miles does space extend in the direction in which I am pointing? Well, it could be finite, or it could be infinite. Neither is logically mandated upon us; I can ask the question and the correct answer may well be “Well, it extends infinitely” rather than “I’d peg it at about 5 billion”.
“Everything which I have trouble thinking of as infinite is, in fact, finite” is not a logical proof of anything.
The terminology does not cause it to be true or false. If you say “an infinite quantity” of time, and that causes logical problems because infinite and quantity are in the same sentence, then it’s because of the assumptions you are making about those two words, it doesn’t actually change whether time is boundless or not.
This is all abstract and I imagine could go either way, but my intuition says that boundless time makes a little more sense than bounded time only because I then wonder “bounded by what?”
Either way, it doesn’t bother me to have something that is countable (e.g. time or rocks or space) and at the same time say “unfortunately there is no bound to these items and if you try, you will never finish counting”
You state, “We know that an infinite amount of time cannot have passed”, which really should be worded as “we know time is not boundless” (to use the meaning of infinity properly and get away from whether we can have an “infinite amount” or not, this is a more correct way to state the concept).
Unfortunately that is exactly what we are debating. You can’t just state “time is not boundless”, you have to provide a proof or some reasonable logic.
Do you believe anything can be boundless? Maybe the issue here is that you feel anything in our physical world has bounds, is this correct?
Yes, that’s true, but those are just equations that are useful for our brains to deal with our perception of the world around us. They don’t guarantee anything. All I’m saying is that it is a far more open question than you seem to realize.
Mainly because I have trouble seeing us causally influence a point infinitely far away, and thus would think that our causal future, and thus, also our light cones, are bound by infinity, though probably not finite themselves, if that makes sense; but you’re right in saying that the issue requires some more thought (also, I carelessly neglected to think about current cosmology, which does contain points possibly causally disconnected from us merely by continually expanding).
No.
Just to restate this, yes, that’s exactly where CalD’s and begbert2’s arguments beg the question and thus are fallacious. I don’t really know what the trouble in recognizing this is.
However, just for the sake of completeness, ‘infinite’ and ‘having a beginning’ aren’t actually the only options here; time may, for instance, well be finite, yet not have a beginning, but we probably shouldn’t get into this too deep, seeing how confused this thread has already gotten with only the two options.
I’ll sell you π apples for e dollar, i cent.
If any of those quantities can be called a number, there really isn’t anything prohibiting infinity to be one, to.
Doing quantum mechanics, one encounters so-called Hilbert spaces quite regularly; among their characteristics is that they are infinitely dimensional. That’s not a trend or limit or what have you, and neither is the number of points on a line, the number of lines in a plane, and the number of planes in a solid, for example.
That’s just the thing, though – nobody claims that infinite years have passed up to now if time has no beginning, since for them to have passed would imply that time has, in fact, a beginning.
Your demonstrated mastery of the subject doesn’t warrant that level of condescension, I’m afraid. Perhaps you should take a moment to familiarize yourself with the Dunning-Kruger effect.
That would be right, if the universe not having a beginning would actually imply that an infinite amount of time must have passed. Which it doesn’t, since the very notion would require a point in time from which on an infinite amount of time must have passed, i.e. a beginning. Consider a circle – it doesn’t have any beginning, yet no two points are infinitely far from each other. Now, how about a circle with an infinite radius?
There’s a host of constructs like that, which do not have a beginning and yet don’t have two points infinitely removed from each other; your assertion that time isn’t one of them is merely that, an assertion, and assumes what you are trying to prove.
Yeah, I’m afraid I basically settled for the same compromise of not confusing discussion too thoroughly yet. But, now that you’ve let the secret out of the bag, for anyone who’d care, consider, say, the open unit interval of numbers strictly between 0 and 1; finite in length, but with no beginning point.
Eh, I know what you’re saying, but careful with the wording here. I would (in the number-line model, etc.) make the claim “There are infinitely many years which lie in the past”, though of course I would not claim “There is a point in the past since which infinitely many years have currently elapsed”.
Incidentally, to begbert2, I am curious: do you believe units of time are infinitely divisible (e.g., there is such a thing as half a second, 1/3 of a second, 1/4 of a second, etc.)?
Actually, this argument doesn’t quite work that way, either; consider, for instance, photons: they experience no passage of time, yet, to us, seem to move at quite a zip, which is basically due to them moving only through the three spatial dimensions at light speed, while we (every massive particle) move through all four dimensions at the same speed, only when we’re at rest in the three dimensions of space, all our movement is through time.
I’m puzzled by this. Are you saying it is possible that there is an infinite amount of time between now and the end of time? Obviously, if an ‘infinite amount’ of time is impossible by definition, there must be an end, right?
You’ll have to explain why your argument applies in one direction, but leaves open the possibility of an infinite amount of time in the other direction.
Either infinite amounts of time are impossible, and from this we can prove time has a beginning and an end, or else it is possible that time had no beginning and/or will have no end.
Oh, just noticed this:
Obviously, you’ve never taken freshman physics, because ‘instantaneous velocity’ is one of the first things they teach in that class. It is also one of the first things you learn in calculus when they introduce the derivative. Saying “if there is a 0 span of time, there is 0 velocity” is just flat out wrong.
No, you’re first taking as a premise that there was a beginning, and then you’re using that premise to prove that it could not have been infinitely long ago, i.e., there had to be a beginning. It’s a classic case of question-begging.
The problem is that, logically, there’s no reason that there must have been a beginning. So that yanks your premise out from under you, and your argument fails.
You seem to accept that time could extend infinitely far into the future, but for some reason are not able to wrap your mind around the idea of turning that around the other direction. Whatever argument you use to arrive at the conclusion that time logically could extend infinitely far into the future, can apply exactly the same in regard to the past.
I disagree that it matters whether the universe had a beginning when considering a deity’s existence
The OP is asking about the response to a “proof” of God’s existence. His “proof” may or may not be logically flawed, but it doesn’t matter. Despite the perceived flaws, he arrives at the same answer as modern scientists – the universe had a beginning.
Debating the validity of his argument for the beginning of time may be interesting, but it isn’t germane to the original question. Neither an eternal universe nor one that began 14 billion years ago is evidence for a Supreme Being like the FSM.
The term “infinitely divisible” does NOT mean that you can divide it into an infinite number of peices. It means that there is no maximum limit on the finite number of peices you can divide it into. And yes, units of time are infinitely divisible; this doesn’t do anything for your position though.
A unit of time can be divided into any finite number of subunits as you like, and the larger the number of (equally-sized) subunits you choose to divide it into, the smaller the size each of the subunits will be. That can be correctly written as “the limit of the size of the subunits as the quantity of subunits goes to infinity is 0”. This is another place where the term ‘infinity’ comes into play here, which also doesn’t do anything for your position, because the end point of a limit is explicitly not reached, as you surely know.
In real life, you cannot subdivide time or anything else into an infinite number of subunits at once, with each subunit having size 0. This should be obvious, because you end up with a pile of fragments of zero size, which of course have a total size of zero (because that’s how zeroes sum up), and which also sum up to the original non-zero unit size at the same time. This should be a clue to anybody that there is something wrong going on.
Also, it should be noted that everytime you try to ‘subdivide things infinitely’, the size of the resulting bits always “is” zero. (Acually it tends toward zero, if you’re correctly realizing that you can’t actually divide by infinity, but I’m playing along with you and tripping the light fantastic here.) So, the only way that you can even pretend to have infinite quantities of things in real life is if all those things have a size of zero. Seconds, however, do not have a size zero. So it’s erroneous and disingenuous to try and analogize infinite subdivision to the question of infinitely long pastward timespans.
Nope; I’m saying that there’s no apparent limit to the length the timeline can become. No matter how it grows, though, it will always be finite in length. “Trending towards infinity” is like “heading towards up”; you never get there, because there’s no “there” to get to. Infinity is not a destination, it’s a direction.
As noted, there is not and never will be an infinite quantity of time in any direction, so that part of my argument applies in both directions.
Now, you can reasonably call on me to defend why I think time is only growing in one direction. My answer to that is that I think that causality as it is observed implies that time can only grow in the forward direction. I would be willing to debate this, presuming that the opposing position is that the past is finite but growing backwards ‘infintely’ (as in, without limit) - not that an infinite amount of time has already occured in the past, which is impossible by definition.
I didn’t catch the misspeak until after the edit limit had passed - as should be obvious, I meant “if there is a 0 span of time, there is 0 change in position”, which I think you’ll find is consistent with your freshman physics text.
Dammit, WHERE? Where am I taking the existing of a beginning as a premise?! Show me! Quote it. Post it. Link it. Prove it!
Because I say that’s a damned dirty lie. Never in this thread have I taken it as a premise that there is a beginning, and never in this thread have I made a circular argument. It’s lies and slander and insulting and infuriating.
