(2/48)(3/48)(4/48)(5/48)(6/48)(7/48)(8/48)(9/48... -

represents a dramatic mathematical "decay." While it begins with small fractions, the cumulative effect of multiplying 47 consecutive terms—most of which are significantly less than one—results in a number so small it effectively vanishes. The Mechanics of the Calculation This expression can be written using factorial notation as:

The graph above shows the "collapse" on a logarithmic scale. Even as the individual terms (like 47/48) approach 1, they are unable to reverse the momentum of the tiny fractions at the start of the chain. (2/48)(3/48)(4/48)(5/48)(6/48)(7/48)(8/48)(9/48...

This is roughly equivalent to one second compared to 26 billion years. Why It Matters represents a dramatic mathematical "decay