Heap, Zillion, and Bandwidth
Define the “Heap” as the first boring number; that is, the first number without features of any interest to you. Surely there must be a first such number, for you cannot be interested in every number, as there are infinitely many, and attention is finite.
But surely being the first boring number is interesting! Defining the Heap clearly would create paradox; for a number fitting any clear definition has at least one interesting property. The Heap is fuzzy; it’s where your mind slips a gear, so your mind can’t tell you where it is.
Now consider the “googol”, defined by young Milton Sirotta to be 10^100. He then defined the “googolplex” to be “10 ^ until your hand gets tired”. He and his mathematician uncle Edward Kasner decided to change that to 10^googol; but the original definition really is 10^Heap.
So define a Zillion as 10^Heap. But then Heap = 10^what? What to call the logarithm of a Heap? I propose the “Bandwidth”; meaning the number of digits needed to name every interesting number.
Zillion = 10^Heap.
Bandwidth = log Heap
A zillion is a number too big to accurately compute with, for it has too many digits to hold your interest; and the bandwidth is how many digits your system needs to process every number that interests you. A zillion is beyond the mind, the bandwidth is the size of the mind.