COINAGE AND CALCULATION

Press, Volume CII, Issue 30146, 1 June 1963, Page 8

COINAGE AND CALCULATION

Implications Of Pending Currency Change

[Specially written for “The Press" by B. A. M. MOON. Senior Lecturer in Mathematics. University of Canterbury.] TJECIMAL currency in New Zealand! The . heresy that “It had to come” appears to have been right! At least we’ll be able to do money sums in the reckoning system we know most about—tens and hundreds—even if it is a third-rate system, onlv used so widely because we were taught nothing better at school So it will have to go, too; but in the meantime, since it is going to cost a bit, let us see where we really do have to spend money in changing to the decimal system. A change of currency has several effects. It affects:

(i) Our method of reckoning. (ii) The coinage. (iii) Our sense of monetary values. Let us consider them.

As long as we are taught only decimal arithmetic at school, sums in £ s d will always be unnecessarily cumbersome and those in decimals apparently simpler. But in these days more and more reckoning is done automatically by machines, ranging from the grocer's adding machine to electronic computers. How will they be affected?

The bigger a computer the more flexible it is; the currency change hardly affects it at all. In fact many computers, especially more powerful ones, including at least one in New Zealand and the Woomera rocket range machine in South Australia, do not work in decimals at all. They work in binary numbers which suit them much better, in which instead of tens, hundreds and co on, we have twos, fours and eights on one side of the point and halves, quarters and eighths on the other. This is a very simple system, because in any place in the number we have only to dec.de whether the amount represented by the place is to be included or not 1 . Thus 2 is .11 and I is 101 considering successively how many halves, quarters and •ighths are required to make up each number. Half quarter eighth i yes yes no i yes no yes

"Yes” becomes 1 and "no" becomes 0.

Smaller machines like bank accounting machines, cash register and adding machines are designed for special purposes, at present adding twelves then twenties then tens for whole numbers of pounds. This mixture is the real fault of our present system. Having several columns of tens, however, without any modification to a machine we could use the right hand one for cents instead of units of pounds, the next for tens of cents and the next for units of pounds instead of hundreds. This would mean that a five-column machine would add up to only 999 99 pounds or whatever the new units may be, instead of £99,999: and we would have to put the decimal point in afterwards instead of the comma. Few grocery bills and indeed not so very many bank cheques and deposits exceed £999 so the “overflow" problem is a modest one Inserting the decimal ppint afterwards is a common practice elreadv: engineers do it all the time with a slide rule and it is the invariable practice with automatic computers So we can manage with present machines to go on with.

Turning to coinage, let us remember.—

lai Out base metal coins are tokens; and within reason. w e can (by statute) make them tokens for any amounts we please.

(b) Whatever tts faults, dealings in sterling coinage have been the most widespread in history Strong practical considerations must therefore have shaped It.

Oddly, perhaps, but really because ot its simplicity, most successful coinage systems are based mainly on the binary system In it. any sum up to one unit less than twice the largest coin (or note) can be obtained with not more than one of each coin in the series. It is equally effective in getting an exact sum or making up change to a larger coin Mathematicians recognise this as an efficient way of getting to any number It is known as binary section Our' £1 and 10s notes crown and half-crown show this sequence (though nowadays two half-crowns are used for ss': florin, shilling sixpence threepence repeat it. so do penny, halfpenny, farthing It occurs in an even purer form in the system recently abolished by Pakistan and India, in a series of seven coins from 3 pice to 1 rupee <l2 pice: 1 anna. 16 annas: 1 rupee' It is unlikely that the new coinage in these countries is more efficient The Half-Crown The points where it does not apply in our system are of interest Hie half-crown is one of our most useful coins not because it is 21 shillings but because it is one-eighth of a pound Go to Australia where there is no half-crown and you will be «”rprised how vou miss it The awkward -atio 5: 4 between it and *llO florin and apparently trivial difference in value, is caused by having to flt the factor 5 into binary <vstem (a ’6-shilling pound •would solve this one' tn at one decimal system (the Dutch’ there *s at the other end of ’he scale, a 2» "ent coin, not because anvone wants cents but because ft f « • ouarter of ten cen’s The factor three between the lowest unit eo ; n and the next (three oence. three pice' baa more practical value One MOUirea ctwcew'vo batvine

mostly but occasionally one third. In pure binaries this is not possible without recurring fractions (as in decimals). This factor three permits division by three at any one point in the series without introducing fractions and doesn't interfere with the binary sequence elsewhere. One-third of every coin from threepence to £1 is an exact number of pence. This is one justification for a duodecimal system, based on reckoning in dozens, where one can divide twice by two for every once by three. To obtain a pure duodecimal system. Professor A. C. Aitken, F.R.S, of Edinburgh, has advocated a 12shjllang unit instead of a pound. Half-crowns would then become three shillings. Duodecimal addition and multiplication, like binary, is also easier than decimal, if only we were taught it properly. Roman Coinage Roman, the most widespread coinage of the ancient world reveals a similar story. Early Roman coinage based on the pound of copper or As, was divided almost exactly as our shilling, the twelfth part or uncia being the forerunner of our ounce (an ounce Troy is still one twelfth of a pound). Becoming more literate, the Romans (tried several decimal systems, in which coins of 2J units, notably the sestertius, kept appearing. At the founding of the Eastern Empire, one of remarkable culture on which the Renaissance of Western Europe was based, we find instead, a pound of gold divided into 6 dozen solidi (forerunner of our shillings) and a dozen gross of smaller units called siliquae, a return to pure duodecimals. Thus, all our coins from threepence up have earned their place. A half-crown is still an eighth of a pound or quarter of any new ten shilling unit, be it 30 pence, or 25 cents, even if cents are called pence.

The sixpence, becoming five cents, need not be withdrawn just because “sixpence” is written on it. It is merely a token and “sixpence” means five cents. Replacement may be gradual.

normal annual new issues having the new values upon them. That should save us something. That such a transition can work has been shown in the British West Indies, various members of which have changed from time to time since 1935 to a decimal system based on a dollar of 4s 2d. But British domestic coinage still circulates as normal tender. Sixpence is twelve cents, threepence six and a halfpenny one. Thus the coinage is duodecimal, but reckoning decimal That this cumbersome system works is a tribute, • not to the simplicity of decimals, but to the efficiency of the sterling coinage system. For the system proposed here the bronze coinage is more awkward. We /had better keep pennies: they fit our public telephones and many other coin-in-slot devices, but they had better be - revalued. Devaluation would be no problem since nobody would hoard depreciating coins. As appreciation by one fifth is required it will tend to stimulate hoarding.

Yet the problems are not insuperable. Our entire currency was appreciated by one-quarter not long ago. Hoarding of every penny in the country for the gain of one part in five, would probably not cost the Government as much as entire replacement with new coins. Orders to banks not to change coppers for more than say ten cents for some time after the change, would discourage more than trivial hording. Official adjustment of bank stocks could ensure fair measures there.

Not Iqng ago the company running ferries across Sydney Harbour to Manly wished to increase fares. Its tickets were tokens operating wharf barriers. Its whole stock of tokens was withdrawn, destroyed and replaced. Old tokens are now rare collectors’ items. Yet overnight revaluation, though a gift of a few pence to anybody holding old tokens, would have saved almost the whole cost of the new issue. So, fellow taxpayers, let our present coins remain. A gradual change will do. Readers of “The Press” are right--what to call them is the problem Can we conclude: a binary system for chimpanzees (“Press” 10/5/63) and the illiterate: duodecimals when we really want the simplest reckoning and most efficient coinage: decimals for the half-educated. "A little knowledge.” said the poet, “is a dangerous thing.”