## Tuesday, January 20, 2009

### The Sources of the Nile .

The Sources of the Nile .
Andre Willers
21 Jan 2009

Fashion , hot or cold, is master of them all . (AW)
The title is from a short story by Avram Davidson about the origin of fashions .

References are New Scientist 27 Dec 2008 p53 " I want what she wants"
and p43 " Magicology" .

Synopsis :
Fashion has a rational basis in probability maths via order of choice . This has major implications and applications .

Discussion :
Stage magic as discussed in "Magicology" is an entirely empirical system manipulating humans via four major ways"
1.Misdirection (limitations of attention span)
2.Illusion (visual limitations)
3.Humour (disengaging of attention)

4.Forcing .(The counting mechanism of the brain is manipulated)
I will use the example in the magazine (p45) given by Amlyn Amlani , a professional stage magician . He riffles a pack of 52 cards with 10 cards the being the same (say the 7 of spades) so the subject can see the faces briefly . He then asks the subject to nominate any card out of 52 . In 70% - 80% of cases the 7 of Spades will be chosen .

Why?

The argument is entirely logical .
Starting from the beginning , every fifth card (=10/52) is probably the 7 of Spades , but the distribution is unknown .
The critical thing to realize is that the number of wrong combinations in the partition of 5 numbers at the very start (first guess) is 5C4 = 5!/(4!*1!) = 5 .
The chance of an error is then 1/5 = 20% and of being right in choosing the 7 of Spades is then (100% – 20%) = 80% .
This seems counter-intuitive , but remember that you have to count the number of combinations of non-7Spades in positions 2,3,4,5 .

Generally ,
If there is a bias probability of P regarding a characteristic K , then the probability of choosing K in the first choice after doing the sample is = ( 1 – P) .

This is the basis of herd , flock , troop , stock market and other mass-behaviours .
Also Fashion .

This explains the Tributaries of the Nile .

But new sources of the Nile (ie new Fashions) continuously appear . This surfaces as hierarchies in social systems . Hierarchies and fashions are expressions of the same thing . Changes in the one are mirrored in the other . This drives continual improvement via the random-walk mechanism .
These can be identified by using descriptive mechanisms around discontinuities as set out in http://andreswhy.blogspot.com "Continuous fractions and quanta."

Now you too can be a fashion guru .

Andre .