Good Question: So to sum it all up - VII x VIII = LVI

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OUR regular Monday morning dose of erudition in reply to matters that are causing concern to readers.

Why does the Post Office charge less when it spends more time delivering your mail? What do they do with the second-class post in the meantime, and do they have to delay it deliberately to encourage you to pay the premium for first-class? (Roger Houghton)

The Post Office thought this a very interesting question and promised to get back to us. When they called back, they explained that post has to be collected, separated into first and second class, then sorted and despatched. The first-class mail is processed first, they said, 'because we couldn't handle everything that comes in on a single day', so the second-class is sorted and despatched on the following day.

We pointed out that handling all of today's first-class, and all of yesterday's second-class post in one day, is equivalent to handling all of today's post in total. So in fact they can handle everything that comes in on a single day. They agreed with this analysis and promised to get back to us.

The next explanation was more convincing: 'It's the time difference.' Many businesses post their mail late in the day, sending it first- class and expecting it to arrive the next morning. So the evenings are devoted to sorting and despatching first-class mail, while the mornings are reserved for second-class mail of the previous day.

This system currently results in 91.9 per cent of first-class mail arriving the next day, and 98.4 per cent of second-class mail arriving within three working days. Figures for second-class arrivals within two days were not available. Around 44 per cent of all mail is sent first-class.

Source: Post Office Press Office.

How did the Romans manage to do multiplication and division using Roman numerals? (M Donnelly, Birmingham - and variations from other readers)

According to Collier's Encyclopedia: 'The Romans, in general, were not strongly inclined toward mathematics, and they had little need for large numbers.' Nevertheless, their number system could cope with them, as an inscription dating back to the First Punic War of 260 BC proves: the symbol (((I))), indicating 100,000, appears 23 times on the columna rostrata to indicate 2,300,000.

Since computations were almost exclusively performed on an abacus, the Roman numbers worked well - as a means of writing down numbers rather than calculating. The system of Roman numerals considered standard today is a relatively recent development, particularly in the use of the subtractive principle. The ancient Romans would have used LXXXX and VIIII for 90 and 9, rather than adopt the shorthand of XC and IX. The latter form would certainly have made calculation more difficult.

In fact, modern methods of arithmetic were only introduced to Europe with a 12th-century translation of a treatise by the 9th-century Arab mathematician al-Khwarizmi. For the next 300 years, there was a heated controversy over whether the new system known after its author as 'algorism' was as good as the abacus. In 1542, Robert Recorde, in The Ground of Arts, explained how to use Arabic numerals to calculate, writing for an audience clearly expected to be well grounded in the Roman version.

Now here's one you can try at home: How the Roman schoolboy was taught to multiply together any two numbers between six and nine on his fingers (we shall take 7x8 as an example):

Hold both hands up with fingers extended; count out the first number on one hand, putting the fingers down until 5 is reached, then raising them again one by one; count out the other number on the other hand in similar fashion. (One hand will now have 2 up and 3 down, the other 3 up and 2 down.) Add together the raised fingers for the 'tens' figure of the answer (2+3=5); multiply together the numbers of unraised digits (3x2=6) for the 'units' figure. So the answer is 56, or LVI.

For the algebraically minded, this always works because 10(m+n) + (5-m)(5-n) = (m+5)(n+5).

But long division must have been a real pain in the abacus.

Sources: Encyclopaedia Britannica, Everyman's Encyclopaedia, Collier's Encyclopedia, BBC Schools Broadcasts (dimly remembered).

Perhaps you could find out who Riley (Reilly) was and what was the life he had.

The expression 'live the life of Riley' dates back to a 1919 music hall song, My Name is Kelly, written by H Pease:

'Faith, and my name is Kelly, Michael Kelly,

But I'm living the life of Reilly just the same.'

This in turn refers back to a popular song of 1882, Is that Mr Reilly which describes what Reilly would do if he became rich:

'Is that Mr Reilly that owns the hotel?

Well if that's Mr Reilly they speak of so highly

Upon my soul, Reilly, you're doing quite well.'

Sources: B A Phythian, A Concise Dictionary of Phrase and Fable; Nigel Rees, A Dictionary of Phrase and Allusion.

After much inquiry, I think I now have a vague idea what a 'spin doctor' is, but why this odd term? Could you elaborate on both the meaning and its origin, please? (S C Thomas, Bexleyheath, Kent).

The New Dictionary of American Slang, by Robert Chapman (1986), defines the term as meaning 'An advisor or agent, esp of a politician, who imparts a partisan analysis or slant to a story for the news media', giving the derivation from the notion of 'spin' on a baseball or pool ball, 'giving a deviant rather than straight tack'. The expression is said to be semantically related to 'throwing someone a curve'.

The Longman Register of New Words (1989) mentions that Donald Regan, the White House Chief of Staff from 1985-87, was informally known as the Director of Spin Control. It lists the equivalent terms 'spin-meister' and 'spin doctor', and gives a quotation from the Daily Telegraph of 11 December 1987, referring to 'Reagan Administration 'spin doctors' who will try to present the summit in a favourable light'.

The term was first satisfactorily defined in this country in the Economist of 26 December 1987:

'News coverage of the campaign can be influenced to a candidate's advantage by 'spin doctors' - professionals whose job it is to persuade political journalists to put the right spin on the story.'

FEEDBACK:

Apatosaurus or Brontosaurus?

P Skeldon of Warley, West Midlands, writes:

In 1877, O C Marsh found a few bones of a dinosaur which he names Apatosaurus. In 1879 he found 'one of the most complete skeletons ever' which he named Brontosaurus. The skeleton was displayed at Yale and pictures of Marsh's reconstruction were widely published. Thus Brontosaurus soon became everyone's typical dinosaur.

However, in 1903, Elmer Riggs of the Field Museum in Chicago realised that the Apatosaurus was a juvenile of the Brontosaurus genus. He wrote: 'As the term Apatosaurus has priority, Brontosaurus will be regarded as a synonym.'

When the US Post Office was criticised for issuing a stamp using the term 'Brontosaurus', they replied in Postal Bulletin 21744: 'Although now recognised by the scientific community as Apatosaurus, the name Brontosaurus was used because it was the more familiar to the general population.'

Mr Gould's information comes from Stephen Jay Gould's Bully for Brontosaurus, which he commends to all who seek diverting and illuminating tales of natural history.

Send your inquiries to Good Question, The Independent, 40 City Road, London EC1Y 2DB.

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