Big Bang or Big Dud? A study of Cosmology and Cosmogony - Origins

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iow, without using magical numbers how is it we find ourselves here and now if an infinite sequence of past events can be traversed?

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I'm not sure that I fully understand your question (what do you mean by magical nimbers?) - but I'm pretty sure that no-one's talking about traversing an infinite sequence of past events. After all, time (more correctly spacetime) began at the Big Bang. This isn't a boundary you can traverse.PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell[This message has been edited by Primordial Egg, 11-24-2002]

I'm still not getting this...

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ok, let's assume time began (as you say above) with bb... from that very moment, time began... each subsequent moment resulted in an event... using just our history, for example, we know the gettysburg address was written in a certain time, magna carta an earlier time, etc, etc

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now we can see a sequence of past events, correct? and theoretically, given your statement that time 'began to exist', we should be able to traverse these past events (after all, if you can cross them coming forward you can do the same going backwards)

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I'm with you in principle up to here.

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*but*.. if the universe (which includes this very time of which we speak) is infinite, it's impossible to traverse the series of past events unless we use make believe numbers

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Consider the set of positive integers (1,2,3,4,5...) and lets say we're sitting on the number line at 5. The set of integers is infinite but we can only go back as far as 1. So infinite and bounded by one side - have you allowed for this possibility?

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... and if we can't traverse a series of events going backwards, they can't be traversed coming forward... that means we'd never have reached this present event, the one we're obviously at

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I was with you in principle above because I thought you were talking about a thought experiment in which you could go backwards in time. To do so in reality would violate (clears throat) the Second Law of Thermodynamics would it not? I'm pretty confused here about what you mean by traversing backwards in time - not sure what you're getting at at all.

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so my comment was meant to show that an infinite universe can't exist (without those imaginary numbers)

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Are you referring to the mathematical use of i? Its certainly a tool that would be very difficult to do without - even Feynman said that it was impossible to do quantum mechanics without their use - but the final measurements, results and predictions all involve the real - I mean, you wouldn't say that John Doe was 6 ft (4+3i)in would you? You may as well chastise physicists for using "angles".PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

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i'm not sure it is a possibility... but by so assuming you seem to be saying that you can increase the number of infinite things by subsequent addition... if a set of "things" can be increased by addition, the set is potentially infinite but not actually so... see the difference? also i'm not quite clear on how a set can be infinite in one direction only, maybe you can explain this to me

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I think I sort of see - but under this regime the universe is only potentially infinite, no (as we could always, in principle add more to it)? I don't want to turn this into a semantic discussion (unless I've missed the point) - so can you give me an example of an actual infinite (ie an infinite which cannot be added to)? Can they exist in the universe?

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take an infinite number of boxes containing playing cards... each box contains, in order, 52 cards containing all 4 suits, 52 spades, 52 hearts, 52 diamonds, 52 clubs... now let's continue this series and keep the boxes in the same relative order... if the sum total of those boxes is actually infinite, each containing hearts only would equal each containing clubs which in turn equal the sum total of ALL of the boxes...

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Took me a while to follow this example. If I've understood correctly, are you saying that exactly a quarter of the (infinite) boxes contain hearts, a quarter contain spades etc? I don't know what you mean by having an infinity number of boxes - infinity isn't a number.Mathematically, let's define (actual) infinity by 1/0, so 1/4 of this would be: 1/(4*0) = 1/0 = infinity. I'm afraid I don't follow the notion of divided infinity into quarters and then summing, this shows the dangers of treating infinity as a number.

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i think one of the best examples i've seen concerns an infinite set of dominoes, one of which has a big red 'X' painted on it... all are standing on end... some cause (dare we call it a first cause?) started the dominoes falling... if the set is actually infinite, there would never be a time when the one with the 'X' would be struck... in the same vein, if the universe is actually infinite, we would never be here.. *this* point in space/time would not have been traversed

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You've just described my own number line example here haven't you? Nobody's saying you're at the infinitieth domino (not that one could exist, see above) - you're on the fifth (say) - easy to see how you got there, and reachable. Time does not extend an infinite direction backwards.

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grant its usefulness, even its validity, ok? all i'm arguing against is using imaginary numbers to form imaginary time, because there's no basis in reality for assuming it solves any of the problems inherent in an actual infinite

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OK fair enough - I can't pretend that I fully understand what Hawking is getting at with his concept of imaginary time, so it would be dishonest of me to argue this point either for or against - I guess it all washes out in the maths PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

My last post didn't answer your question, which was:

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also i'm not quite clear on how a set can be infinite in one direction only, maybe you can explain this to me

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The set of an irrational numbers between 1 and 2 is bounded on two directions and is infinite. The set of points on a straight line is infinite.And I've also given more thought to:

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i grant its usefulness, even its validity, ok? all i'm arguing against is using imaginary numbers to form imaginary time, because there's no basis in reality for assuming it solves any of the problems inherent in an actual infinite

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All Hawking seems to be saying is that there may be more than one time dimension (substitute "orthogonal" for "imaginary") - I don't see anything particularly unreasonable about this. After all, its pretty staggering that Maxwell's equations pop out when you apply a fifth dimension to Einstein's theories, and I'm not aware of any requirement that the fifth dimension be spacelike.Why can't we have more than one time dimension?PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

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Originally posted by frank:
PE,

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I'm having some difficulty conceptualizing imaginary time, so am I correct in assuming that what you are saying is :

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If we we to chart time on a set of coordinates, the X axis running from left to right (time), then imaginary time is the Y axis, running from bottom to top. (and this is different from imaginary numbers - the square roots of negative numbers) ?

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thanks

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Frank

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Frank,I think so - its how I understood it anyway . Hawking's idea is that time is bounded and t=0 is an ordinary spactime point like any other. He invites us to think of spacetime like a globe and t=0 represents the North Pole, a point on Earth like any other. This gets us around having to start the universe off at a singularity - to ask what happened before the big bang is like saying what lies 10 miles North of the North pole.Here's his lecture on it:The page you were looking for doesn't exist (404)Although if you can persuade me that in this context, Hawking's use of imaginary is distinct from if he were to use orthogonal, I'm willing to stand corrected.PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

-whoops - that should be time is finite but unbounded in my last post.PE

duplicate deleted[This message has been edited by Primordial Egg, 11-24-2002]

Well, looks like I've got a bit of reading to do as regards potential vs actual infinities then! But I still don't see the relevance this distinction has to whether we can traverse backwards in time (especially as we're not even sure that actual infinities can exist in the physical world) - is this something you've already indicated?

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You've just described my own number line example here haven't you? Nobody's saying you're at the infinitieth domino (not that one could exist, see above) - you're on the fifth (say) - easy to see how you got there, and reachable. Time does not extend an infinite direction backwards.
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actually it isn't easy to see how that point was reached, or that it's even reachable... the moment we begin counting "1, 2, 3..." we're attempting to add to an infinite set, and such a point can't be reached by either subsequent addition or subtraction.. your examples are ones of potential infinities, and that exists in real time

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This part I spectacularly failed to understand. Maybe you can correct my understanding:-We have an infinite dominoes, the last of which(!) is marked with a "X", and the 5th with a "Y"
-we set the first domino off
- I grant you that we'll never reach X, but why should that have any bearing on whether or not we reach Y? Is there some property of the dominoes which I don't know about??PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

I'm with you now - you were talking about actual infinities (should have noticed). I do know about Hilbert's Hotel, but never come across potential vs actual before (prob. because I never had to ). Still a novel concept for me.But can't you use actual infinities to prove mathematically that ALL integers contain the number 3? If so, I'd be very mistrusting of any conclusions drawn from the properties of these beasts.PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

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i don't know... also, i'm not sure if proving the existence of the number 3 is the same time as *traversing* it... see what i mean? even if we can prove the existence of the domino with the red 'X' on it, we'd still have the problem of ever reaching it while playing some cosmic game of knock over the dominoes

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No my point is that I'd be very cautious of using infinities in proofs - its no different from dividing by zero. I'm still not clear on why you bring up actual infinities other than as a speculative tool btw.In your past events line of reasoning - is time a steady flowing river "happening" in the background or is it an active player, which is itself embedded in the events themselves? ie do you allow for time itself to be created?PE------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

Joz (& John),What I believe forgiven is getting at is that its impossible to traverse an actual infinite rather than a potential one, both of which are defined terms.Potential infinity is the infinity we all know and love - thats the one you were talking about.Actual infinity is a strange creature - think of infinity as a number and you've pretty much got actual infinity, as far as I can make out. You can't add to it or traverse it, by definition. Its more of a metaphysical concept than anything else - certainly can't exist in the real world.What was puzzling me was why forgiven was making this distinction, and what this had to do with the price of fish. Do a google on "actual potential infinity" and you'll soon see why.Actual infinities are used in the Kalaam Cosmological Argument, as I suspect is favoured by forgiven (interestingly enough, devised by Islamic scholars). It goes something like this:1) The universe had to have had a beginning, else time would be an actual infinite, meaning it would be a philosophical impossibilty to be here now. (I'd like to see a proof of this btw, this guy thinks different http://www.qsmithwmu.com/infinity_and_the_past.htm).2)All things which begin to exist have a cause (you see where this is going now don't you?)3) Hence universe had first cause, hence God.Roughly Where the argument falls down is the second clause in (3), as you've no doubt spotted (oh, and there's also the problem of observational evidence). There's a non sequitur into a supernatural explanation.Also, the universe could have had many first causes - multiple demons coming together to create it.Also (2) fails as causation cannot be taken either as an a priori principle, or is even observed in everyday reality (well, quantum reality).Just wanted to avoid pointless debates about infinity. Of course, if I've got it all wrong, I'm sure forgiven will correct mePEPS forgiven - I agree with (1) anyway because it fits in with what is observed - is there a need to bring actual infinity into this?------------------
It's good to have an open mind, but not so open that your brains
fall out. - Bertrand Russell

Hi forgiven,Something just occurred to me while thinking about actual infinites. If heaven and hell are eternal, and eternity is an actual infinite, which cannot be traversed, then there will never be a point at which you can say "I am in heaven" or "ouch, that hurts!" Which seems to defeat the purpose.PE------------------
Skeptical scrutiny is the means, in both science and religion, by which deep thoughts can be winnowed from deep nonsense - Carl Sagan

hi forgiven

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hi p.e. i just saw this... i think you might not be far off... not sure if this makes sense, but let me give it a shot... my beliefs being as they are, i fully expect to spend eternity in God's heaven... now, to me that means when i die i'll "step" into eternity... but as i do so i believe i'll see (for example) the apolstle paul "stepping" in also... hmmm let's see if i can make it sound more understandable... i see eternity as one unfathomable "now"... imagine a milisecond stretched out into infinity in all directions... there is no time as we know it, tho the dimension of time exists within eternity... if that's even close to so, when we step out of time into eternity, it will simply be "now"

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If it is all one elongated "now" and yet one can never experience a "present" (tantamount to traversing an actual infinite - you can never say "I am feeling X", as it relates to the present), then how can you have the sensation of happiness in heaven / unhappiness in hell?PE

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i knew i wouldn't be able to put it into words... the "now" thingy is a new dimension... but all that is in *this* dimension is encompassed by "now" (eternity)... how things work in that dimension i don't know...

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How was it originally described to you?PE

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Originally posted by forgiven:

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Originally posted by Primordial Egg:

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i knew i wouldn't be able to put it into words... the "now" thingy is a new dimension... but all that is in *this* dimension is encompassed by "now" (eternity)... how things work in that dimension i don't know...

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How was it originally described to you?

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PE

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i'm not sure it ever was, p.e. ... i do know i've never had an original thought, so i don't claim that this is one... but it isn't so hard for me to imagine a place where time as we know it doesn't exist... do things have to be chronological in order to be logically sequential? i don't think so (thinking of God's thoughts for one thing), so if they don't then an eternal "now" is imagineable

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Well, if thats the case, you can't really argue that the universe can't be actually infinite as we could, in principle, be living in an extended now, with the illusion (Matrix-style!) of time and history.I'm afraid i can't really say I understood your description of heaven, the nearest thing it sounded like to me was the rush experienced by a heroin user, and you never drew any distinction between heaven and hell, and why you'd want to go to the one and not the other, if you can't experience sensation.On a wider scale, I suppose you could say that the two places are identical on a personal sensation basis, but for the fact that God is pleased with you if you're in one, and displeased if you're in the other, which makes about as much sense as any of religion as far as I'm concerned. Its a first for me I must admit,I've never been exposed to the view that heaven and hell are, on a physical basis at least, completely identical.PE------------------
Skeptical scrutiny is the means, in both science and religion, by which deep thoughts can be winnowed from deep nonsense - Carl Sagan