Old rocks and paradoxes
The oldest earth rocks are 4.2 billion years old; the piece of Oregon andesite on my desk is 40 million. How old is that in human terms?
We count a human artifact as an antique at 100 and as almost unbelievably old at 10,000, which is the age of some sandals that were found in an Oregon cave. So, how long is 10,000 years compared to 40 million? It is 1/4000th.
The human species only originated 150,000 years ago, which means that my rock was already 39,850,000 years old when homo sapiens first walked the earth, and 39,999,943 years old I was born—it is 701,754 times older than I, yet it is devoid of wrinkles and liver spots.
I wonder from time to time what would happen if I stored a rock in conditions that eliminated all external causes of alteration. How many years would pass before it looked any different than it does today? Surely, it would eventually assume a different form, but what number would represent the amount of years that this would take?
I have another puzzler. Numbers are said to be infinite, yet between each whole number and its successor, there is only one other whole number—as in 2+1=3. But how many fractions are between the numbers 2 and 3? An infinite number, right? But this would mean that the infinitude of fractions is larger than the infinitude of whole numbers!
Zeno posed a similar paradox. To wit: To cross a room, a person must first cross the one-half point. But to cross the one-half point, he (or she) must first cross the one-quarter point. Ah, but before the one-quarter point comes the one-eighth point. Because the number of points can be halved infinitely it is obviously impossible to cross a room.
Posted by Snowbrush