Robert J. Marks: The logical consequences of a literally infinite past are absurd, as a simple illustration will show:
The story starts with Slow Sam who is a very slow writer. Sam is writing his autobiography. But it takes Sam a week to write the account of a single day of his life. Poor Sam. He is falling further and further behind in his writing.
But in the world of infinities this need not be the case. If the universe has always been in existence and Slow Sam has been writing for this entire infinite time, then the number of days and number of weeks today — counting from an infinite time ago — are the same. The consequence of this is crazy. If he has been writing forever, Sam can have completed his autobiography if he dies today!
This conclusion is, of course, ludicrous. Although not a definitive mathematical proof that the universe was created a finite time ago, the observation is solid evidence that our universe had a beginning. Otherwise, we would have to deal with infinity weirdnesses like Slow Sam’s autobiography.
To avoid the ridiculousness of Slow Sam finishing his autobiography, we must conclude the universe had a beginning.
Robert J. Marks, “2. Infinity illustrates that the universe has a beginning” at Mind Matters News
Takehome: The absurdities that an infinite past time would create, while not a definitive mathematical proof, are solid evidence that our universe had a beginning.
Here’s Part 1: Why infinity does not exist in reality. A few examples will show the absurd results that come from assuming that infinity exists in the world around us as it does in math. In a series of five posts, I explain the difference between what infinity means — and doesn’t mean — as a concept.
You may also wish to read: Yes, you can manipulate infinity in math. The hyperreals are bigger (and smaller) than your average number — and better! (Jonathan Bartlett)