Sunday, November 30, 2014

Time Cannot Extend Infinitely Into The Past

I just finished reading this book and absolutely loved it.

As someone who once styled themselves as a theoretical mathematician, I was happily surprised and somewhat embarrassed to have learned the title of this blog post from this book. The concept had never occurred to me before.

The problem with a Universe of infinite age is that you can't reach any given point in time. That is, if time goes back infinitely through endless repetitions of Big Bangs and Collapses, you can't get to the November 30, 2014 and watch Southampton blow a perfect chance to at least draw with Manchester City after Man City went down to ten men because of a stupid challenge by Mangala near the box.

Where was I? Oh yes. Time.

Since time is sequential with one second following another, in order to reach the moment when Frank Lampard scores in ridiculous fashion for City, you need to cover the time between when you started counting and when the ball went into the back of the net. If you go back in time 90 minutes, the game hasn't started, but we know those 90 minutes have taken place. You can go back to the year 1066 and we know that time has happened. You can go back to any time you like and we know that time has gone by.

If the Universe was inifinitely old, no matter how far you went back, there would be moments older than that. Since time is sequential, those moments must have taken place. If that were the case, you could never wait long enough to get to Frank Lampard's goal. The current moment in time could never occur.

Ergo, the Universe had a beginning.

Way cool, no?


Ilíon said...

You'd never realized that before?

Another, prehaps simpler in the sense of being more concrete and less theoretical, way to explain that time had a beginning and why it is logically impossible for the past to have been infinite is this --

Presume that you, a person now alive in the year we call 2014 AD, are immortal (even if you don't yet realize it), and that you turn out to have a perfect memory (and a high tolerance for boredom, or the same thing over and over and over).

So, in 3014 AD, you're still alive; in 12014 AD, you're still alive; in 102014 AD; you're still alive; and so on. And you remember the count of every one of those years. By the time 1002014 AD rolls around, you think to yourself, "You know, it looks like I'm going to live forever" -- you can envision seeing New Years Day for *any* future year, except a year that we must call 'Infinity AD'. For, how many trillions of years you may happen live and experience, the count of the years you have lived will never reach 'infinity'. That is, no matter how vast the count of the years happens to become, it will always be possible to count off even more years: it is logically and arithmatically impossible to count to 'infinity'. There is no such thing/count as "infinity plus one".

So, there never will be a year 'Infinity AD', for such a year will never arrive. It is logically impossible.

Now, as it happens, the year 2014 AD stands in the same relation to the year 'Infinity BC' as the year 'Infinity AD' does to the year 2014 AD: an immortal alive in 'Infinity BC' would never see the year 2014 AD arrive -- nor would he see any other year to which we can count, such as 1002014 BC, arrive.

Ergo, just as 'Infinity AD' will never exist, likewise 'Infinity BC' never did exist. Ergo, the universe of time-and-space has a beginning.

K T Cat said...

You'd never realized that before?



K T Cat said...

That was an excellent, simplified description of the proof, by the way.

Trigger Warning said...

Infinities can be fun and profitable, but physicists generally hate infinities unless they can be substituted for God (cf., multiverse, aka Hilbert's Kahsmic Hotel). Then they're OK. Even necessary.

Ilíon said...

"That was an excellent, simplified description of the proof, by the way."

I think an infinite past often seems plausible to people because they are thinking of instances of time as being analogous to points on the number line. And since numbers can be counted off toward infinity in either direction, they incorrectly reason that time time can be likewise.

It seems they never stop to ask themselves either:
1) it it logically possible to count *to* infinity? (answer: no)
2) what would a "negative instant" be like? what would a time-span (of whatever unit is being used as the measurement) with a duration of less-than-zero be like? it such a thing even logically possible?

An irony of the situation, or so it seems to me, is that the whole idea of counting years in a "negative direction" from a fixed point-in-time of a universal calendar came from Christians in the first place.

Ilíon said...

... another way to express what I mean with 2) above is this --

* one can conceive/visualize what it is to have one apple, or ten thousand
* one can conceive/visualize what it is to have *no* apples
* no one can conceive/visualize what it is to have minus one apples; the very attempt at making such a statement is incoherent