Counting Sheep .
31 Oct 2009
Non-numerative counting plays an important part in predator-prey relationships in the physical , financial and intellectual worlds , as well as neurology and sleep .
Every sheep farmer knows this : herd the sheep in bunch , leave an opening and count them as they jump through in bunches . But the number in a bunch is not counted in a 1,2,3 etc fashion .
The mind is sort of uncoupled , and the primitive counting brain-mechanism does the job . This is hard to describe (our language does not have the detailed vocabulary ), but I have done it . Every sheep farmer has done it . Most of the people reading this has seen it done . It is a simple , learned skill , probably easily taught via computer screen. See previous posts on Primitive Counting and animal counting .
This process fatigues the neurotransmitter senders and receptor sites .
Famously , counting sheep will send you to sleep . It will , if you count the sheep in bunches . Until the system gets trained .
This leaves the problem of communicating the count .
See the excellent book "How Mathematics Happened: the first 50 000 years" by Peter S Rudman (ISBN 978-1-59102-477-4)
The bases usually used are 10 and 20 . The Babylonian base 60 is a combinations of abacus bases 10 and 6 in sequence . An intriguing hint at neurotransmitter fatigue before general schooling .
Arithmetic is more fatiguing than algebra . Neurotransmitter fatigue .
Click and neurotransmitter fatigue .
An initial one-to-one correspondence between the click and the counted item will quickly lead to fatigue of the tongue and neurotransmitters . Hence the grouping of numbers ( See Schmandt-Besserat on counting tokens in the early civilizations) .
As discussed in http://andreswhy.blogspot.com "Click , Lies , Hope and Sex" ,
Abstraction led to lies . As we secretly suspected , abstraction , and thus lies , only became possible on major scale with accountants . But hope as well .
What would you rather have : No hope and no lies , or hope and lies ? There is no middle way . In any case , any abacus-type counting (ie wealth) will immediately give rise to abstractions and thus lies . Poverty and honesty is, unfortunately , closely linked .
Hence accountants and lawyers .
A fascinating aside :
On page 123 of National Geographic of June 2009 is a photo of counters and a dice from the Belituck shipwreck of the Tang dynasty (Circa AD 826)
The dice can come from Las Vegas today , but the counters (chips) date back to Sumer . Gamblers are an extremely conservative lot . (Note Mongols , playing cards , printing and gambling. )
(See p92 and p93 of "How Mathematics Happened: the first 50 000 years" by Peter S Rudman (ISBN 978-1-59102-477-4) or Schmandt-Besserat on counting tokens in the early civilizations .)
The chips shown in the photo from the Belitung wreck (described as "ivory acorns") appear to be of 1 , 60 and 600 denominations according to the old Sumerian counters. High stakes .
Not many dice have survived , probably because there were not a large number to start with . It is quite difficult to get balanced (fair) dice when everybody is trying to cheat . The Chinese probably charged a premium for guaranteed fair dice , hence the very characteristic appearance and indented holes as numbers . A high-value trade item .
Which makes one wonder at the role gambling played . Remember , these were all civilizations with highly developed systems of Astrology (ie Luck masquerading as Destiny) . Hence the short half-life of fair dice .
Is there any record of lotteries?
A large city like Babylon could easily support at least three number rackets .
Gambling spreads literacy faster than any educational system .
To get back to Prey in large numbers:
They flash countable markers and flee (eg buck or sheep prancing . )
The optimum strategy for individual survival .
In small numbers they turn and confront the predator .
Quorum systems are applicable , and can be quite dangerous to even large predators .
The predator can be a bank , financial advisors , academic supremo's or political bigwigs . The systems can be exactly described and boundaries of behaviour ascribed
Music and counting .
Low neurotransmitter fatigue arithmetic and music are different sides of the same coin.
It is interesting to speculate that the latest financial instability was basically caused by iPod .
Quorum counting systems in the financial prey changed irrevocably .
Prey behaviour changed .
Predators who continue on the "business as usual" approach is headed for extinction .
This taps into this mechanism . Isolate into small groups and surround by natural predators . The quorum prey behaviour changes .
Mozart , anyone ?