Speaking of trivia...............

  Forum Editor 00:07 29 Jan 06
Locked

My son, who is a microbiologist, came for dinner on Friday, and over the meal the talk turned to statistics. He was explaining to my wife how he validates experimental results, and at one point he mentioned Benford's law. I had never heard of it, so I asked him to explain. What followed was quite fascinating, and I thought I would share it here - maybe some of you already know about it?

Dr. Benford was a physicist with GEC in the 1930's, and he conducted experiments on thousands of sets of random figures to see if there was a probability of any number turning up more often than others. He obtained the numbers from widely varied sources, such as the addresses of all the people on a certain page in a phone book, or the lengths of rivers, or the areas of counties - things like that. What he found was that the number 1 was the first digit in about a third of all cases, and that this was far in excess of the number of times any other digit was the first.

Intrigued by the results, he went further, and discovered that if you flip a coin say, 200 times the odds are huge that at some point in the sequence you'll get the same side of the coin appearing six times in a row. It will happen more often than not.

I found it all very fascinating, and I've done a bit of searching. I found this about Benford's law:-

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 this is not what happens. Dr. Benford discovered that 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 etc., the chance that the first digit will be 1 is not one in nine, as many people would imagine, but is actually 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.

Apparently, Benford's law is used by Tax authorities in America to help them detect fraud. People who fiddle figures don't understand the probabilities, so they try to start forged sets of figures with random numbers, not realising that certain figures would actually occur far more often, and so give themselves away.

I thought it was all pretty interesting, anyway.

  mco 00:41 29 Jan 06

I was always under the impression that the likelihood was random - ever since the first mr mco, a nuclear physicist, explained statistics to me...now I'm having to rethink the whole thing - fascinating! (I'm off to look up Benford's law and email ex!) But the most intriguing thing is....why? It doesn't make logical sense.

  Skyver 00:47 29 Jan 06

Very interesting - in a similar vein,Pi and The Golden Ratio (click here)...things that ought to be random and not `natural`, but appear to have an influence on things one would never have imagined.

  007al 00:48 29 Jan 06

Hmmm...lets see if my cheque for £1,111 slips through the TAX

  wolfie3000 01:41 29 Jan 06

Very interesting but Schrodinger's cat experiment
Makes Benfords law impossible.
Think about it if the number one comes up more than any other number its pre determined but Schrodinger's cat experiment says that nothing can be pre determined.

So in conclusion which is right?

Schrodinger's cat experiment
click here

  Chegs ®™ 02:21 29 Jan 06

Benford's Law and Zipf's Law click here The law was discovered by the American astronomer Simon Newcomb in 1881 who noticed that the first pages of books of logarithms were soiled much more than the remaining pages. In 1938, Frank Benford arrived at the same formula after a comprehensive investigation of listings of data covering a variety of natural phenomena. (Benford's original data table can be found on Eric Weisstein's Treasure Troves of Mathematics - Benford's Law page.) The law applies to budget, income tax or population figures as well as street addresses of people listed in the book American Men of Science. In the face of such universality of the law, it's quite astonishing that there exists a more general framework - Zipf's Law. Which, in turn, falls under a more general rubric of scaling phenomena.

All this is quite beyond my comprehension,I can generally cope with literacy problems but numerical stuff just floats over my head. ;-))

  Skyver 02:23 29 Jan 06

Schrodinger's cat experiment states that nothing is determinable if you go by the `laws` of quantum physics, but how do you explain probability in the face of such evidence? IE. How do you calculate how many times a slice of buttered toast will land face up , when everybody assumes it will `probably` land face down every time. There is a calculatable probability, worked out by people much more intelligent than I - I'm not discounting the theory at all, I'm very open to any new ideas or theories on such matters.

  Haol 10:06 29 Jan 06

Simply amazing.

  SG Atlantis® 10:21 29 Jan 06

Any chance of predicting the lottery numbers then?

  Sapins 10:24 29 Jan 06

Speaking of odds, what are the odds of posting a problem here that no one can solve?

  amonra 11:07 29 Jan 06

SG Atlantis

If you look elsewhere on this forum you will see that I was certain I had won the Euro lottery thanks to an absolutely guarranteed system. As with all infalible systems, there was a slight flaw. I think Schrodinger's cat p***sed on my winning ticket.

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