Calculating Stop Combinations, Part III
(con't from Part III)
What if the instrument was supplied with 84 stops? ... (click photo to read drawstops)
X = 2 to the 84th power minus 1 = 2,048,990,435,833,474,145,058,816 - 1
= 2, 048,990,435,833,474,145,058,815
This staggering number (rounded off to 2.049 x 10 to the 24th power) is, for all intents and purposes, beyond human comprehension. It exceeds the radius of our own Milky Way galaxy measured in hundredths of an inch. It's 300 times heavier than the entire Earth measured in tons. At a rate of 1 per second it would take 31 quadrillion years (over 200 times the estimated Age of the universe) to work through all of them. Presuming that only 1 possible combo in a million sounded good enough to be worth storing on piston memory, the capacity required for storage would still have to be large enough to accomodate over 2 pentillion combos (2.049 x 10 to the 18th power). The magnitude of THIS number still boggles the mind. It's over 2 billion times larger than a billion.
The finite human mind can kind of comprehend a hundred thousand. When it gets up into the tens of millions it starts to get a little fuzzy. To get an idea of what a billion is ... the one dollar bill is 6-1/8 inches long. One billion of them taped end to end would stretch nearly 97,000 miles, enough to wrap around the entire Earth nearly 4 times. A billion seconds ago takes one backward in time nearly 32 years to the Gulf War. A billion minutes ago leads backward in time over 1,900 years to the Roman Empire. A billion hours ago leads backward into the dim past 114,000 years ago. And on and on.
The combos available using the couplers of the organ are subject to the same formula. A mere 15 couplers provides some 32,767 possibilities. Add those to the equation too, and you see where that would lead -- to the 99th power in the formula.
The point is this: all the piston memory on all the organ consoles ever built in recorded human history would hold only a tiny percentage of the useful stop groupings offered on an organ supplied with 84 stops. Fully shaking and studying the tree of possibilities here would be quite impossible. The time involved simply to draw each useful stop combo, even by conservative estimate (2 x 10 to the 18th power), when clocked at the ridiculously fast pace of 1 per second, would require a thousand trillion human lifetimes (1 lifetime = 70 yrs.).
Astounding, but true.