Author Topic: Could the universe have no beginning? (i.e. Are actual infinities possible?)  (Read 2535 times)

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April 28, 2007, 03:40:36 PM
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Ephemeral

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Quite apart from its relevance to the cosmological argument for God's existence, does anyone have any thoughts on this? One the one hand, it seems perfectly coherent to say that for every moment, there was an earlier moment. On the other, Hilbert* believed that an actual infinity of anything was impossible because it led to 'paradox'. He illustrated the paradox with the example of 'Hilbert's Hotel': this hotel has infinitely many rooms, and is full (i.e. for every room n, there is exactly one occupant - this sounds to me like a perfectly acceptable definition of 'full' for an infinite hotel), but if a new customer arrives, the management can fit her in by moving each occupant of room n to room n + 1 and then moving her to room 1. Do you think this shows actual infinities to be impossible (which would be a very radical result, as it would not only imply that the universe had a beginning but also that space and time aren't 'dense', i.e. infinitely divisible)?

April 28, 2007, 10:22:19 PM
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kobok

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He illustrated the paradox with the example of 'Hilbert's Hotel': this hotel has infinitely many rooms, and is full (i.e. for every room n, there is exactly one occupant - this sounds to me like a perfectly acceptable definition of 'full' for an infinite hotel), but if a new customer arrives, the management can fit her in by moving each occupant of room n to room n + 1 and then moving her to room 1.

An even more interesting case shows up when a bus shows up with an infinite number of customers, all of which want a room.  How do you find them all rooms with one step?  (Hint:  There is a similar answer.)

Do you think this shows actual infinities to be impossible (which would be a very radical result, as it would not only imply that the universe had a beginning but also that space and time aren't 'dense', i.e. infinitely divisible)?

I don't believe this argument shows infinity to be impossible, as I do not believe this is a paradox.  I believe it only shows that our intuition of the finite does not apply to the infinite.  The reason your intuition is uncomfortable with the infinite hotel idea is because your mind keeps asking, "What about the person in the last room?"  This is equivalent to considering a universe with no beginning and asking, "But what about the first moment in time?"  To ask either of these is to ask an incorrect question, given the examples being considered.


With that said, I believe the universe did have a beginning, since the evidence indicating that it did seems reasonably strong.  I also do not believe time and space are infinitely divisible.  See the concepts of the Planck length and the Planck time.
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April 28, 2007, 10:22:56 PM
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Oriens Lvx Lucis

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Ah...

There is a very simple reason for why "no beginning and no end" can exist.  Looking at a situation from a strictly logical perspective, there can obviously be no true beginning.  One of Thomas Aquinas' truths for the existence of God is that all things must have a cause, essentially (all movement is imparted motion, as no thing can truly move itself without being moved beforehand).  The universe was started by a "Big Bang," but what began that big bang?  God?  Who cares, and what does it matter?  If we go back far enough, we find only two logical choices:

1.  There is an infinite progression backwards in time on motion (in other words, creation and vibration) being imparted from one being to the next, however grand those beings may be.

2.  There is one being who has no beginning and no end (one who has a truly infinite existence, having never been created).

Both of those choices involve infinity.  Infinity has to exist, in the form of an infinite being or an infinite creation.  Either their is an infinite chain of imparted motion, or there is an infinite being which imparts all motion, directly or indirectly.  Which is it?  That depends on what you believe, for the purposes of this post.

Now, is it not logical that there are some things which man can simply not understand?  Of course, to presume otherwise would be egotistical in my opinion.  Can mankind understand all things in the universe, and will mankind ever?  Dubious, to say the least.  Why should he be able to? 

As for understanding infinity fitting in with time, that solution is very simple indeed.  The human brain is programmed from birth to think of what we call time in three main stages: Present, Past, and Future.  Unfortunately, all of these are on a "linear time line" and if we imagine what humanity calls "time" as such a simple and "from backwards to forwards string" so to speak, then you can't understand it well.  Do not think of time in a linear sense, because that is like expecting a string you hold in your hand to end, and thus when you follow the string with your hand far enough, it ends.

Think of time as a circle.  Also, think of time as ONLY the present.  Every micro-second of the future which passes out of the present into the past no longer exists.  It is like driving a car around a cone (in a circle).  Is every single vibration the car makes stored?  No, once the present becomes the past, it no longer exists.  It can be recorded and remembered, but it no longer has any physical existence.  This is why we do not have as many copies of ourselves as we have seconds we have lived on the earth.  The only truly existing part of time is the present.  The future does not exist yet, but can be determined, but it still has no absolute existence, or any at all, until it becomes the present.  Think of a dot following the path of a circle.  The dot represents time, in the present.  It moves around an infinite loop.  The past does not exist, but it can be repeated and recorded with apparent accuracy, but it is no longer extant.  The future doesn't exist and will never exist until the present time does.  Then the "present time" dot can revolve around the circle infinitely while every motion it makes clears the path behind it (even though the past can be recorded).

Thinking of time that way makes it much easier to comprehend an infinite time scale.

April 29, 2007, 01:31:32 AM
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April 29, 2007, 06:04:15 AM
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April 30, 2007, 02:44:40 AM
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May 14, 2007, 03:06:12 PM
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Such questions are great food for thought, but aren't they ultimately pointless? Being merely human, we cannot possibly begin to comprehend infinity, and thus such a question is condemned to infest our brains in an endless spiral of conjecture and headaches (much like temporal logic puzzles). Am I missing something here? You all seem to comprehend it just fine.
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