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Author Topic:   Big Bang or Big Dud? A study of Cosmology and Cosmogony - Origins
forgiven
Inactive Member


Message 47 of 94 (24045)
11-24-2002 11:42 AM
Reply to: Message 46 by John
11-24-2002 10:48 AM


quote:
Originally posted by John:
quote:
Originally posted by forgiven:
unless we use make believe numbers...
Make-believe numbers? You mean imaginary numbers. It is a valid number system, not a child's game of pretend.

whew!! joz objects to imaginary numbers, preferring make believe, you object to make believe, preferring imaginary... sheesh... yes, the use of i as the square root of -1 has applications, i don't deny that... but in the actually existing universe, the one in which we find ourselves, we'd never be here if that universe is *actually* infinite, and it can be shown that it is actually infinite only by using make believe time resulting from make believe numbers... substitute imaginary if you want, that's fine with me

This message is a reply to:
 Message 46 by John, posted 11-24-2002 10:48 AM John has replied

Replies to this message:
 Message 48 by joz, posted 11-24-2002 11:50 AM forgiven has not replied
 Message 55 by John, posted 11-24-2002 3:17 PM forgiven has replied

  
joz
Inactive Member


Message 48 of 94 (24048)
11-24-2002 11:50 AM
Reply to: Message 47 by forgiven
11-24-2002 11:42 AM


No actually once again you are gleefully misrepresenting my opinion....
I do not want to call imaginary numbers make believe numbers, you already have....
But here we go just to clear things up for anyone not following the other thread....
quote:
Originally posted by forgiven:
i wasn't criticizing the mathmatics though, i was simply trying to show that an attempt to prove the existence of an actual infinite set of past events depended on imaginary time which in turn depended on imaginary numbers... and if joz prefers 'make believe' to 'imaginary', that's fine with me
Once again that sense of surreality creeps in....
Of course calling them make believe numbers wouldn`t bother you you have already done it....
But how on earth did you manage to twist this post
quote:
How about calling them make believe numbers? Sounds like he is taking the use of imaginary to be equivalent to its colloquial form, to me anyway.....
replying to Johns skepticism that you had misinterpreted the imaginary in imaginary numbers into a call from me to rename imaginary numbers make believe numbers? You, as you are won`t to do, ignored the context in which I posted....
And yes you do seem to have a problem with the use of i in mathmatics otherwise you wouldn`t be asserting that their utilisation makes a work unsatisfying....

This message is a reply to:
 Message 47 by forgiven, posted 11-24-2002 11:42 AM forgiven has not replied

  
Primordial Egg
Inactive Member


Message 49 of 94 (24052)
11-24-2002 12:08 PM
Reply to: Message 45 by forgiven
11-24-2002 10:09 AM


I'm still not getting this...
quote:
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
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)
I'm with you in principle up to here.
quote:
*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
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?
quote:
... 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
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.
quote:
so my comment was meant to show that an infinite universe can't exist (without those imaginary numbers)
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

This message is a reply to:
 Message 45 by forgiven, posted 11-24-2002 10:09 AM forgiven has replied

Replies to this message:
 Message 50 by forgiven, posted 11-24-2002 12:33 PM Primordial Egg has replied

  
forgiven
Inactive Member


Message 50 of 94 (24055)
11-24-2002 12:33 PM
Reply to: Message 49 by Primordial Egg
11-24-2002 12:08 PM


quote:
Originally posted by Primordial Egg:
quote:
*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
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?
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
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...
quote:
quote:
... 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
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.
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
quote:
quote:
so my comment was meant to show that an infinite universe can't exist (without those imaginary numbers)
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
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

This message is a reply to:
 Message 49 by Primordial Egg, posted 11-24-2002 12:08 PM Primordial Egg has replied

Replies to this message:
 Message 51 by Primordial Egg, posted 11-24-2002 12:55 PM forgiven has replied
 Message 52 by Primordial Egg, posted 11-24-2002 1:31 PM forgiven has not replied

  
Primordial Egg
Inactive Member


Message 51 of 94 (24058)
11-24-2002 12:55 PM
Reply to: Message 50 by forgiven
11-24-2002 12:33 PM


quote:
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
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?
quote:
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...
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.
quote:
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
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.
quote:
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
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

This message is a reply to:
 Message 50 by forgiven, posted 11-24-2002 12:33 PM forgiven has replied

Replies to this message:
 Message 54 by forgiven, posted 11-24-2002 3:12 PM Primordial Egg has replied

  
Primordial Egg
Inactive Member


Message 52 of 94 (24059)
11-24-2002 1:31 PM
Reply to: Message 50 by forgiven
11-24-2002 12:33 PM


My last post didn't answer your question, which was:
quote:
also i'm not quite clear on how a set can be infinite in one direction only, maybe you can explain this to me
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:
quote:
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
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

This message is a reply to:
 Message 50 by forgiven, posted 11-24-2002 12:33 PM forgiven has not replied

Replies to this message:
 Message 53 by frank, posted 11-24-2002 3:07 PM Primordial Egg has replied

  
frank
Inactive Member


Message 53 of 94 (24069)
11-24-2002 3:07 PM
Reply to: Message 52 by Primordial Egg
11-24-2002 1:31 PM


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

This message is a reply to:
 Message 52 by Primordial Egg, posted 11-24-2002 1:31 PM Primordial Egg has replied

Replies to this message:
 Message 56 by Primordial Egg, posted 11-24-2002 3:17 PM frank has replied

  
forgiven
Inactive Member


Message 54 of 94 (24071)
11-24-2002 3:12 PM
Reply to: Message 51 by Primordial Egg
11-24-2002 12:55 PM


quote:
Originally posted by Primordial Egg:
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?
right... potentially but not actually infinite... no, i've followed your posts and i know you don't play semantical games... neither do i, 'least not on purpose... as actual infinite would be something that has always existed, unbounded by space and time, and uncaused (not contingent) by definition... as to whether or such a thing can exist, we're looking at that now in 'one step at a time' thread
quote:
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.
ok, a set containing an infinite number of these boxes
quote:
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.
the point i was trying to make is, with a set of actually infinite "things," one in which both the individual things and the set itself are infinite, nothing can be added to or taken away... so the total of all individual things within the set would be the same as the total of all things collectively in the set... just an attempt to show that an actually infinite can't exist in space/time else no one event would be traversed
quote:
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.
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
quote:
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
lol who can? the man's a certifiable genius, so his concepts can't be dismissed out of hand by anyone, least of all me

This message is a reply to:
 Message 51 by Primordial Egg, posted 11-24-2002 12:55 PM Primordial Egg has replied

Replies to this message:
 Message 60 by Primordial Egg, posted 11-24-2002 3:38 PM forgiven has replied

  
John
Inactive Member


Message 55 of 94 (24072)
11-24-2002 3:17 PM
Reply to: Message 47 by forgiven
11-24-2002 11:42 AM


quote:
Originally posted by forgiven:
whew!! joz objects to imaginary numbers, preferring make believe, you object to make believe, preferring imaginary... sheesh...
I don't care what we call them, though the term 'imaginary' is the traditional term. Call them candy-stripe numbers, or alice-in-wumbers. Don't really care.
What I care about is that you posted a message indicating that imaginary numbers are unsatisfactory and thereby implying that you object to their use in building mathematical models of the early universe.
And then equivocate on that, like so:
[quote][b]yes, the use of i as the square root of -1 has applications, i don't deny that...[quote][b]
Then flip flop back the other way, like so:
quote:
but in the actually existing universe, the one in which we find ourselves, we'd never be here if that universe is *actually* infinite, and it can be shown that it is actually infinite only by using make believe time resulting from make believe numbers...
It is very confusing. I can't get a bead on what you are actually arguing. My best guess at the moment, taken from the above paragraph, is that you do not like the use of imaginary numbers because it leads to a description of the universe as an actual infinite, which is impossible in your view?
------------------
No webpage found at provided URL: www.hells-handmaiden.com

This message is a reply to:
 Message 47 by forgiven, posted 11-24-2002 11:42 AM forgiven has replied

Replies to this message:
 Message 63 by forgiven, posted 11-24-2002 4:49 PM John has replied

  
Primordial Egg
Inactive Member


Message 56 of 94 (24073)
11-24-2002 3:17 PM
Reply to: Message 53 by frank
11-24-2002 3:07 PM


quote:
Originally posted by frank:
PE,
I'm having some difficulty conceptualizing imaginary time, so am I correct in assuming that what you are saying is :
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) ?
thanks
Frank

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

This message is a reply to:
 Message 53 by frank, posted 11-24-2002 3:07 PM frank has replied

Replies to this message:
 Message 57 by frank, posted 11-24-2002 3:26 PM Primordial Egg has not replied
 Message 58 by Primordial Egg, posted 11-24-2002 3:28 PM Primordial Egg has not replied
 Message 59 by Primordial Egg, posted 11-24-2002 3:29 PM Primordial Egg has not replied

  
frank
Inactive Member


Message 57 of 94 (24076)
11-24-2002 3:26 PM
Reply to: Message 56 by Primordial Egg
11-24-2002 3:17 PM


PE,
Thanks for the reply. Really interesting stuff. I'll read the link next.
Frank

This message is a reply to:
 Message 56 by Primordial Egg, posted 11-24-2002 3:17 PM Primordial Egg has not replied

  
Primordial Egg
Inactive Member


Message 58 of 94 (24078)
11-24-2002 3:28 PM
Reply to: Message 56 by Primordial Egg
11-24-2002 3:17 PM


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

This message is a reply to:
 Message 56 by Primordial Egg, posted 11-24-2002 3:17 PM Primordial Egg has not replied

  
Primordial Egg
Inactive Member


Message 59 of 94 (24079)
11-24-2002 3:29 PM
Reply to: Message 56 by Primordial Egg
11-24-2002 3:17 PM


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

This message is a reply to:
 Message 56 by Primordial Egg, posted 11-24-2002 3:17 PM Primordial Egg has not replied

  
Primordial Egg
Inactive Member


Message 60 of 94 (24081)
11-24-2002 3:38 PM
Reply to: Message 54 by forgiven
11-24-2002 3:12 PM


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?
quote:
quote:
--------------------------------------------------------------------------------
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.
--------------------------------------------------------------------------------
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
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

This message is a reply to:
 Message 54 by forgiven, posted 11-24-2002 3:12 PM forgiven has replied

Replies to this message:
 Message 61 by forgiven, posted 11-24-2002 4:41 PM Primordial Egg has replied

  
forgiven
Inactive Member


Message 61 of 94 (24096)
11-24-2002 4:41 PM
Reply to: Message 60 by Primordial Egg
11-24-2002 3:38 PM


quote:
Originally posted by Primordial Egg:
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
the reason is, there's an infinite number preceding 'Y' just as there is between 'Y' and 'X'... if any one domino (or deck of cards or universes or whatever) can't be reached, none can... an infinite number precede 'Y', an infinite number precede 'X'...
imagine alternating numbers '1' and '2' painted on the side of each... the total number of the dominoes with '1' on the side is exactly the same as the total number with '2' on the side... not only that, the total number of those with '1' on the side is *also* the total number of the ones with both '1' AND '2' on their sides...
hey, i just thought of this... do a search for 'hilbert's hotel' when you have time... shows the problem when dealing with an actual infinite better than i can

This message is a reply to:
 Message 60 by Primordial Egg, posted 11-24-2002 3:38 PM Primordial Egg has replied

Replies to this message:
 Message 62 by Primordial Egg, posted 11-24-2002 4:49 PM forgiven has replied

  
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