No past infinity? But what about a minus past infinity?
|April 23, 2014||Posted by News under Mathematics, Cosmology, News|
And we just happen to be on the other side of the zero! end, no less. Further to “There cannot be an infinite past, since we would not reach our ‘here-and-now,’” Kirk Durston responds to this argument from Sean Carroll’s idea that there could be a negative past infinity of time.
Just as it is impossible to count down through the negative integers from minus infinity to zero, so it is impossible in real time, for time t to run from minus infinity to plus infinity. The real past, therefore, must have a beginning, and a key proposition in the cosmological argument still stands.
Now let us try out the idea of time t running from zero to plus infinity, 0, 1, 2, 3, … No problem here. This is what is known in mathematics as a potential infinity. You never actually reach infinity, but you are going in that direction.
Now let us try out the idea of the past being infinite. 0, -1, -2, -3, … No problem here either but, what a minute, real time does not run backward from the present. For an eternal universe, according to Carroll, time runs from minus infinity to zero.
Imagine walking into a room and observing an ageless-looking person sitting on a chair counting, ‘…, -3, -2, -1, zero!’ She then triumphantly looks up and tells you that she just finished counting down, one integer at a time, from minus infinity to zero, taking one second for each integer. I trust that we can all agree that it is impossible to count through the entire set of negative integers, from minus infinity to zero, one integer at a time. Counting down through the seconds of past history is no different. More.
So what happened to all the stuff that must have existed negatively then? Did it just disappear at zero, leaving no trace?
See also: The Science Fictions series at your fingertips (cosmology) on how what started as astronomy and the space race ended up in these kinds of discussions.
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