Aug. 24, 2015

Calculating Stop Combinations, Part III

(con't from Part III)

What if the instrument was supplied with 84 stops? ...

         84

X = 2       - 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.

Even a billion is hard to comprehend.  One billion one dollar bills each 6-1/8 in. long laid end to end would stretch around the entire Earth nearly 4 times (96,760 miles).  A billion seconds backward in time from 2019 takes us back to 1988 (31 years 8-1/4 months ago) to when Ronald Reagan was U.S. President.  A billion minutes ago takes us back to 118 A.D. (1,901 years ago) to when Trajan was Caesar.  A billion hours backward in time takes us into the dim past 114,000 years ago to when great mammoth herds were roaming North America.

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 take us -- 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.