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Sexy maths
Oct 23, 2008, 04:54 AM
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Oct 23, 2008, 04:54 AM
What goes around comes around as they say and I was interested to see that today’s Times is covering a story (‘Sexy maths’ and, yes, Moira Stewart is mentioned) that was covered when I was editor of Tolley’s Practical Tax Newsletter many moons ago; happy days.
I know you are going to be interested so those articles were ‘Vital Statistics’ (13 Dec 2000), ‘The Numbers Game’ (3 Jan 2001) and ‘Benford is Back in Town’ (18 Jul 2001).
Well, if a story is good, it's worth covering in detail - and you may now have guessed that the subject in question is Benford’s Law.
In fact, it should probably be called Newcomb’s Law after its previous discoverer in 1881, but he didn’t back up the theory with a detailed analysis like Frank Benford, who rediscovered the phenomenon in 1938.
Back to the story...
My understanding is that both Newcomb and Benford noticed that the front pages of their logarithm tables were more well-thumbed than the back pages.
For the more junior readers among you, these tables assisted in complex calculations - for example, multiplying large numbers - before the introduction of calculators.
Benford realised that the fact that the front pages, showing the ‘logs’ of numbers starting with lower digits such as 1, 2, 3, etc, were grubbier than the latter ones (starting with 7, 8, 9, etc), could only mean that he was using these pages more often and was thus dealing with lower numbers more often than higher ones.
Now, one might think that if one was presented with a set of numbers (a set rather than a random sequence, mind) that numbers starting with a digit 1 to 9 would feature evenly. Not so: numbers starting with lower digits are more common than those starting with the higher ones.
As an example, those starting with a number 1 appear about 30% of the time, 2 about 18%, and so on until those starting with a 9 only feature about 5% of the time.
I won’t go into why, as I can sense a couple of you yawning at the back (and here’s a link for those interested – which actually should be all of you), but why is this important to tax?
Because sets of figures, such as lists of business expenses, will follow Benford’s Law, HMRC have been known to check these against the law. Discrepancies are likely to show that fraudulent figures have been used or inserted.
As the article in The Times says: ‘Remember, when filling out your tax returns, the Inland Revenue too is looking out for number 1’.
Get numerical with Taxation.co.uk.
I know you are going to be interested so those articles were ‘Vital Statistics’ (13 Dec 2000), ‘The Numbers Game’ (3 Jan 2001) and ‘Benford is Back in Town’ (18 Jul 2001).
Well, if a story is good, it's worth covering in detail - and you may now have guessed that the subject in question is Benford’s Law.
In fact, it should probably be called Newcomb’s Law after its previous discoverer in 1881, but he didn’t back up the theory with a detailed analysis like Frank Benford, who rediscovered the phenomenon in 1938.
Back to the story...
My understanding is that both Newcomb and Benford noticed that the front pages of their logarithm tables were more well-thumbed than the back pages.
For the more junior readers among you, these tables assisted in complex calculations - for example, multiplying large numbers - before the introduction of calculators.
Benford realised that the fact that the front pages, showing the ‘logs’ of numbers starting with lower digits such as 1, 2, 3, etc, were grubbier than the latter ones (starting with 7, 8, 9, etc), could only mean that he was using these pages more often and was thus dealing with lower numbers more often than higher ones.
Now, one might think that if one was presented with a set of numbers (a set rather than a random sequence, mind) that numbers starting with a digit 1 to 9 would feature evenly. Not so: numbers starting with lower digits are more common than those starting with the higher ones.
As an example, those starting with a number 1 appear about 30% of the time, 2 about 18%, and so on until those starting with a 9 only feature about 5% of the time.
I won’t go into why, as I can sense a couple of you yawning at the back (and here’s a link for those interested – which actually should be all of you), but why is this important to tax?
Because sets of figures, such as lists of business expenses, will follow Benford’s Law, HMRC have been known to check these against the law. Discrepancies are likely to show that fraudulent figures have been used or inserted.
As the article in The Times says: ‘Remember, when filling out your tax returns, the Inland Revenue too is looking out for number 1’.
Get numerical with Taxation.co.uk.
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