## Sunday, September 23, 2007

### Benford's Law and number 11

Sigh .

Accountants should know better .

I refer you to Benford's Law (Google it) .Wikipedia has a good reference .

The frequency distribution of the first digit of numbers to base 10 (not labels , so no use in lotto) is
1 2 3 4 5 6 7 8 9
30.1 17.6 12.5 9.7 7.9 6.7 5.8 5.1 4.6

This has been rigorously proven as a property of numbers , not just a statistical effect . It is also scale and base invariant .

The number 11

So , 11(base 10) = 10(base 11) , and the frequency of the first digit will have nearly the same distribution as base 10 .

The frequency distribution of the first digit of numbers to base 11 is
1 2 3 4 5 6 7 8 9 10
28.9 16.9 12.0 9.3 7.6 6.4 5.6 4.9 4.4 4.0

Why base 11 ?
Because of the hidden assumption in the sampling . No what the mapping is , the sum of the digits are kept smaller or equal to 11 .

This is the same as defining a base 11 .

This is typically Human procrustean sampling . Chop and stretch .

So , on these axioms ,the number 11 will appear about 29% of the time , regardless of the mapping used . Any significance can only lie in a divergence from this expected frequency .

There are numerous scams and faulty analyses based on this property of numbers .
Numerology is one . Elliot waves to a certain extent .
Of special note is the"Bible Code" , which appears impressive . On analysis , it is simply trawling through a large but finite set of human grammar- organised numbers using different bases and finding higher probabilities of some sequences . This is like saying that one horse will run faster than another . True , but of very limited use .
Vibrations , which is merely numerology in another guise .
Quantum physics , the latest human fad of how many true angels can dance on the head of a pin .

Andre

Start Post scriptum.
---
I Quote from the Wikipedia article :
Even more astonishing are the effects of Benford's Law on number sequences. Intuitively, most people assume that in a string of numbers sampled randomly from some body of data, the first non-zero digit could be any number from 1 through 9. All nine numbers would be regarded as equally probable.
But, as Dr. Benford discovered, in a huge assortment of number sequences -- random samples from a day's stock quotations, a tournament's tennis scores, the numbers on the front page of The New York Times, the populations of towns, electricity bills in the Solomon Islands, the molecular weights of compounds the half-lives of radioactive atoms and much more -- this is not so.
Given a string of at least four numbers sampled from one or more of these sets of data, the chance that the first digit will be 1 is not one in nine, as many people would imagine; according to Benford's Law, it is 30.1 percent, or nearly one in three. The chance that the first number in the string will be 2 is only 17.6 percent, and the probabilities that successive numbers will be the first digit decline smoothly up to 9, which has only a 4.6 percent chance.
A strange feature of these probabilities is that they are "scale invariant" and "base invariant." For example, it doesn't matter whether the numbers are based on the dollar prices of stocks or their prices in yen or marks, nor does it matter if the numbers are in terms of stocks per dollar; provided there are enough numbers in the sample, the first digit of the sequence is more likely to be 1 than any other.
The larger and more varied the sampling of numbers from different data sets, mathematicians have found, the more closely the distribution of numbers approaches what Benford's Law predicted.
One of the experts putting this discovery to practical use is Dr. Mark J. Nigrini, an accounting consultant affiliated with the University of Kansas who this month joins the faculty of Southern Methodist University in Dallas.
Dr. Nigrini gained recognition a few years ago by applying a system he devised based on Benford's Law to some fraud cases in Brooklyn. The idea underlying his system is that if the numbers in a set of data like a tax return more or less match the frequencies and ratios predicted by Benford's Law, the data are probably honest. But if a graph of such numbers is markedly different from the one predicted by Benford's Law, he said, "I think I'd call someone in for a detailed audit."
End Post scriptum.

-----------

-----Original Message-----From: Botha, Aniki [mailto:abotha@kpmg.com.au] Sent: 20 September 2007 06:02 AMTo: jade chilvers; Bradley, Angie; Lappin, Renae; Simon O'Malley; Imogen; Craig.Taylor@det.nsw.edu.au; niki.schneider@sasol.com; janebotha@hotmail.com; Kleyn, Johan (JM); karienconradie@hotmail.com; Johnston, Andrew; andre.w@absamail.co.za; 2004007858@student.uovs.ac.za; mpbotha@hotmail.com; Michael.Reid@dpi.vic.gov.au; Ului.Latu@dhs.vic.gov.au; Zubko, Inna; coopster2012@yahoo.caSubject: FW: The number 11
The Secret behind the number 11

Pretty Chilling - read to the bottom. Try it out.
If you are a sceptical person - still read on as it's actually very interesting!!
This is actually really freaky!! (Mainly the end part, but read it all first)
1) New York City has 11 letters2) Afghanistan has 11 letters.3) Ramsin Yuseb has 11 letters. (The terrorist who threatened to destroy the Twin Towers in 1993) 4) George W Bush has 11 letters.

This could be a mere coincidence, but this gets interesting: 1) New York is the 11th state.2) The first plane crashing against the Twin Towers was flight number 11. 3) Flight 11 was carrying 92 passengers. 9 + 2 = 114) Flight 77 which also hit Twin Towers, was carrying 65 passengers. 6 + 5 = 115) The tragedy was on September 11, or 9/11 as it is now known. 9 + 1+ 1 =116) The date is equal to the US emergency services telephone number 911.

Sheer coincidence..?

1) The total number of victims inside all the hi-jacked planes was 254.
2 + 5 + 4 = 11
2) September 11 is day number 254 of the calendar year.
3) The Madrid bombing took place on 3/11/2004. 3 + 1 + 1 + 2 + 4 = 11. 4) The tragedy of Madrid happened 911 days after the Twin Towers incident.
Now this is where things get totally eerie:

The most recognized symbol for the US, after the Stars & Stripes, is the Eagle. The following verse is taken from the Koran, the Islamic holy book:
"For it is written that a son of Arabia would awaken a fearsome Eagle. The wrath of the Eagle would be felt throughout the lands of Allah while some of the people trembled in despair still more rejoiced: for the wrath of the Eagle cleansed the lands of Allah and there was peace."
That verse is number 9.11 of the Koran.

Unconvinced about all of this still ..?

Try this and see how you feel afterwards, it made my hair stand on end: