"LSD, Dirty Books and Accountancy Fraud"
Keith Tognetti
University of Wollongong
Thursday 05 February, 3:05-3:55PM
Carslaw 373

This talk attempts to describe what is going on in the "mind" of the 
computer when it carries out multiplications on long lists of numbers. 
It will be shown that in many cases the numbers coming out of the 
computer have a very fascinating pattern; instead of the probability 
of the LSD (leading significant digits) being evenly spread over
the integers p = 1, 2,...,9 and thus a first digit of one having a
probability of about 1/9 = 11%, it is more likely that this probability 
will be about 30%.  In fact for such numbers the probability of the 
LSD being equal to p will be shown to be equal about log(1+1/p). 
This is the Benford pattern and it has only recently been discovered 
by accountants as a basis for checking fraud.  If you use long lists 
of numbers, say from areas of lakes etc., check to see they have the 
Benford property and if so bring them along - if they don't, be 
suspicious of the source!  The seminar will explore the following 
- storing a number in the usual way on the computer into an
exponent and a mantissa, what is the mathematical representation of
these expressions using only the following, the fractional and
integral part operations and the logarithm?  From this the central
role of the fractional part of the logarithm of the numbers in a
sequence, in deciding the nature of the distribution of their LSD ,
will be demonstrated.  As an encore the speaker will prove
mathematically what we all know - socialism is more equitable than
capitalism.