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25 July 2009

It Doesn't Add Up

Tag(s): Pedantry

Mathematics

In my last blog I referred to the significant number of students entering University to study science today who cannot perform simple mathematical tasks. But this lack of numeracy is much more wide spread than that and is a real threat to our economy at large and to business. According to The Independent on Monday 20th July 2009

 “The economic pressure on the Treasury was further underlined when the National Audit Office (NAO) delivered an embarrassing rebuke to the department over its handling of the bailout of Britain's high street banks. It refused to sign off part of the Treasury's annual accounts, because a £24bn insurance scheme granted to Lloyds and Royal Bank of Scotland to cover toxic loans was not approved by Parliament. The refusal marked the first time in a decade that the Treasury's accounts were qualified.”
The credit crunch as a whole is largely down to mistakes in assessing risk and an inability to understand the complexity of the structured instruments that had been invented to re-package debt. An early example of this had been Long-Term Capital Management (LTCM) which was a US hedge fund which used trading strategies such as fixed income arbitrage combined with high leverage. It failed spectacularly in the late 1990s leading to a massive bailout by other major banks and investment houses which was supervised by the Federal Reserve.  Ironically its Board of directors included Myron Scholes and Robert C Merton who shared the Nobel Prize for Economics in 1997. Initially enormously successful with annualized returns of over 40% (after fees) in its first years, in 1998 it lost $4.6 billion in less than four months following the Russian financial crisis and became a prominent example of the risk potential in the hedge fund industry.
I have been both amused and disappointed to observe simple errors of mathematics reported in our national press. Back in March, 1998 a Labour MP, one Derek Wyatt, came up with a new millennium target: a computer in every home paid for by National Lottery funds. He claimed that this “would cost no more than the Millennium Dome - and would be a better use of the cash.” He said, “A typical home PC costs about £1,000, meaning it would take roughly £240m to provide every home with one. The funding for the Dome totals £700m.”
I was moved to write to The Independent who had reported this. “If funding was to be found to provide £1,000 PCs for 23.5 million homes, it would cost £23.5bn, not £240m, which clearly represents only a £10 unit cost for the PCs. Let’s hope the Millennium Dome does not make the same scale error in its forecasts.”
But it did and they still do.

Just recently The Week, an otherwise admirable summary of the week’s newspapers, reported on the problem of the loudness of the grunting of female tennis players at Wimbledon. They said that Michelle Larcher de Brito's grunting was measured at 109 decibels, "only 11 decibels quieter than the noise of a plane taking off.” To make this worse their caption for a photo of Ms Larcher de Brito read: "almost as loud as a plane taking off.” Perhaps it's complicated but the decibel scale is logarithmic which is useful mathematically because it means a huge range of outcomes can be measured on quite a tight scale, just as the Richter scale covers massive variation in earth tremors.
3db represents approximately a doubling of energy i.e. noise level, so moving from 109 to 112 would be a doubling of noise levels; then to 115 a doubling again; then to 118 a doubling again; then to 121 a doubling again. Thus the noise level of a plane taking off is about 16 times as loud as her grunts. Even if their reporters were ignorant of all this did not even a moment of reflection suggest that it was unlikely?

 

Copyright David C Pearson 2009 All rights reserved

 




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