Of Time, Space, and Other Things
Part II Of Other Things 11. Forget It!
The other day I was looking through a new textbook on biology (Biological Science: An Inquiry into Life, written by a number of contributing authors and published by Har court, Brace amp; World, Inc. in 1963). 1 found it fascinating.
Unfortunately, though, I read the Foreword first (yes, I'm one of that kind) and was instantly plunged into the deepest gloom. Let me quote from;the first two paragraphs:
"With each new generation our fund of scientific knowl edge increases fivefold... At the current rate of s.cien tific advance, there is about four times as much'significant biological knowledge today as in 1930, and about sixteen times as much as in 1900. By the year 2000, at this rate of increase, there will be a hundred times as much biology to dcover' in the introductory course as at the beginning of the century."
Imagine how this affects me. I am a professional "keeper upper" with science and in my more manic, ebullient, and carefree moments, I even think I succeed fairly well.
Then I read something like the above-quoted passage and the world falls about my ears. I don't keep up with science. Worse, I can't keep tip with it. Still worse, I'm falling farther behind every day.
And finally, when I'm all through sorrowing for myself, I devote a few moments to worrying about the world generally. What is going to become of Homo sapiens?
We're going to smarten ourselves to death. After a while, we will all die of pernicious education, with our brain cells crammed to indigestion with facts and concepts, and with blasts of information exploding out of our ears.
But then, as luck would have it, the very day after I read the Foreword to Biological Science I came across an old, old book entitled Pike's Arithmetic. At least that is the name on the spine. On the title page it spreads itself a bit better, for in those days titles were titles. It goes "A New and Complete System of Arithmetic Composed for the Use of the Citizens of the United States," by Nicolas Pike, A.M.
It was first published in 1785, but the copy I have is only the "Second Edition, Enlarged," published in 1797.
It is a large book of over 500 pages, crammed full of small print and with no relief whatever in the way of illustrations or diagrams. It is a solid slab of arithmetic except for small sections at the very end that introduce algebra and geometry.
I was amazed. I have two children in grade school (and once I was in grade school myself), and I know what arith metic books are like these days. They are nowhere near as large. They can't possibly have even one-fifth the wordage of Pike.
Can it be that we are leaving anything out?
So I went through Pike and, you know, we are leaving something out. And there's nothing wrong with that. The trouble is we're not leaving enough out.
On page 19, for instance, Pike devotes half a page to a listing of numbers as expressed in Roman numerals, ex tending the list to numbers as high as five hundred thou sand.
Now Arabic numerals reached Europe in the High Middle Ages, and once they came on the scene the Roman numerals were completely outmoded. They lost all pos sible use, so infinitely superior was the new Arabic nota tion. Until then who knows how many reams of paper were required to explain methods for calculating with Roman numerals. Afterward the same calculations could be performed with a hundredth of the explanation. No knowledge was lost only inefficient rules.
And yet five hundred years after the deserved death of the Roman numerals, Pike still included them and ex pected his readers to be able to translate them into Arabic numerals and vice versa even though he gave no instruc tions for how to manipulate them. In fact, nearly two hun 138 dred years after Pike, the Roman numerals are still being taught. My little daughter is learning them now.
But why? Where's the need? To be sure, you will find Roman numerals on cornerstones and gravestones, on clockfaces and on some public buildings and documents, but it isn't used for any need at all. It is used for show, for status, for antique flavor, for a craving for some kind of phony classicism.
I dare say there are some sentimental fellows who feel that knowledge of the Roman numerals is a kind of gate way to history and culture; that scrapping them would be like knocking over what is left of the Parthenon, but I have no patience with such mawkishness. We might as well suggest that everyone who learns to drive a car be required to spend some time at the wheel of a Model-T Ford so he could get the flavor of early cardom.
Roman numerals? Forget iti-And make room instead for new and valuable material.
But do we dare forget things? Why not? We've forgot ten much; more than you imagine. Our troubles stem not from the fact that we've forgotten, but that we remember too well; we don't forget enough.
A great deal of Pike's book consists of material we have imperfectly forgotten. That is why the modern arithmetic book is shorter than Pike. And if we could but perfectly forget, the modern arithmetic book could grow still shorter.
For instance, Pike devotes many pages to tables-pre sumably important tables that he thought the reader ought to be familiar with. His fifth table is labeled "cloth meas ure.29 Did you know that 2% inches make a "nail"? Well, they do. And 16 nails make a yard; while 12 nails make an ell.
No, wait a while. Those 12 nails (27 inches) make a Flemish ell. It takes 20 nails (45 inches) to make an English ell, and 24 nails (54 inches) to make a French ell. Then, 16 nails plus 1% inches (371/5 inches) make a Scotch ell.
Now if you're going to be in the business world and import and export cloth, you're going to have to know all those ells-unless you can figure some way of getting the ell out of business.
Furthermore, almost every piece of goods is measured in its own units. You speak of a firkin of butter, a punch of prunes, a fother of lead, a stone of butcher's meat, and so on. Each of these quantities weighs a certain number of pounds (avoirdupois pounds, but there are also troy pounds and apothecary pounds and so on), and Pike carefully gives all the equivalents.
Do you want to measure distances? Well, how about this: 7 92/100 inches make I link; 25 links make I pole; 4 poles make I chain; 10 chains make I furlong; and 8 furlongs make I mile.
Or do you want to measure ale or beer-a very com mon line of work in Colonial tim6s. You have to know the language, of course. Here it is: 2 pints make a quart and 4 quarts make a gallon. Well, we still know that much anyway.
In Colonial times, however, a mere gallon of beer or ale was but a starter. That was for infants. You had to know how to speak of man-sized quantities. Well, 8 gallons make a firkin-that is, it makes "a firkin,of ale in Lon don." It takes, however, 9 gallons to make "a firkin of beer in London." The intermediate quantity, 81/2 gallons, is marked down as "a firkin of ale or beer"-presumably outside of the environs of London where the provincial citizens were less finicky in distinguishing between the two.
But we go on: 2 firkins (I suppose the intermediate kind, but I'm not sure) make a kilderkin and 2 kilderkins make a barrel. Then ll/z barrels make I hogshead; 2 bar rels make a puncheon; and 3 barrels make a butt.
Have you got all that straight?
But let's try dry measure in case your appetite has been sharpened for something still better.
Here, 2 pints make a quart and 2 quarts make a pottle.
(No, not bottle, pottle. Don't tell me you've never heard of a pottle!) But let's proceed.
Next, 2 pottles make a gallon, 2 gallons make a peck, and 4 pecks make a bushel. (Long breath now.) Then 2 bushels make a strike, 2 strikes make a coom, 2 cooms make a quarter, 4 quarters make a chaldron (though in the demanding city of London, it takes 41/2 quarters to make a chaldron). Finally, 5 quarters make a wey and 2 weys make a last.
I'm not making this up. I'm copying it right out of Pike, page 48.
Were people who were studying arithmetic in 1797 ex pected to memorize all this? Apparently, yes, because Pike spends a lot of time on compound addition. That's right, compound addition. . You see, the addition you consider addition is just 44 simple addition." Compound addition is something stronger and I will now explain it to you.
Suppose you have 15 apples, your friend has 17 apples, and a passing stranger has 19 apples and you decide to make a pile of them. Having done so, you wonder bow many you have altogether. Preferring not to count, you draw upon your college education and prepare to add 15 + 17 + 19. You begin with the units column and find that 5 + 7 + 9 = 21.;You therefore divide 21 by 10 and find the quotient is 2 plus a remainder of I,. so you put down the remainder, 1, and carry the quotient 2 into the tens col- I seem to hear loud yells from the audience. "What is all this? comes the fevered demand. "Where does this 'divide by 10' jazz come from?"
Ah, Gentle Readers, but this is exactly what you do whenever you add. It is only that the kindly souls who devised our Arabic system of numeration based it on the number 10 in such a way that when any two-digit num ber is divided by 10, the first digit represents the quotient and the second the remainder.
For that reason, having the quotient and remainder in our hands without dividing, we can add automatically. If the units column adds up to 21, we put down I and carry 2; if it bad added up to 57, we would have put down 7 and carried 5, and so on.
The only reason this works, mind you, is that in adding a set of figures, each column of dicits (starting from the right and working leftward) represents a value ten times as great as the column before. The rightmost column is units, the one to its left is tens, the one to its left is hun dreds, and so on.
It is this combination of a number system based on ten and a value ratio from column to column of ten that makes addition very simple. It is for this reason that it is, as Pike calls it, "simple addition."
Now suppose you have I dozen and 8 apples, your friend has 1 dozen and 10 apples, and a passing stranger has I dozen and 9 apples. Make a pile of those and add them as follows:
I dozen 8 units
1 dozen 10 units
1 dozen 9 units
Since 8 + 10 + 9 = 27, do we put down 7 and carry 2? Not at all! The ratio of the "dozens" column to the (tunits" column is not 10 but 12, since there are 12 units to a dozen. And since the number system we are using is based on I 0 and not on 12, we can no longer let the dicits do our thinking for us. We have to go long way round.
If 8 + 10 + 9 - 27, we must divide that sum by the ratio of the value of the columns; in this case, 12. We find that 27 divided by 12 gives a quotient of 2 plus a remain der of 3, so we put down 3 and carry 2. In the dozens column we get I + I + 1 + 2 = 5. Our total therefore is 5 dozen and 3 apples.
Whenever a ratio of other than 10 is used so that you have to make actual divisions in adding, you have "com pound addition." You must indulge in compound addition if you try to add 5 pounds 12 ounces and 6 pounds 8 ounces, for there are 16 ounces to a pound. You are stuck again if you add 3 yards 2 feet 6 inches to I yard 2 feet 8 inches, for there are 12 inches to a foot, and 3 feet to a yard.
You do the former if you care to; I'll do the latter.
First, 6 inches and 8 inches are 14 inches. Divide 14 by 12, getting 1 and a remainder of 2, so you put down 2 and carry 1. As for the feet, 2 + 2 + I = 5. Divide 5 by 3 and get I and a remainder of 2, put down 2 and carry 1. In the yards, you have 3 + 1 + 1 = 5. Your answer, then, is 5 yards 2 feet 2 inches.
Now why on Earth should our unitratios vary all over the lot, when our number system is so firmly based on 10?
There are many reasons (valid in their time) for the use of odd ratios like 2, 3, 4, 8, 12, 16, and 20, but surely we are now advanced and sophisticated enough to use 10 as the exclusive (or n arly exclusive) ratio. If we could do so, we could with such pleasure forget about compound addition-and compound subtraction, compound multipli cation, compound division, too. (They also exist, of course.)
To be sure, there are times when nature makes the uni versal ten impossible. In measuring time, the day and the year have their lengths fixed for us by astronomical condi tions and neither unit of time can be abandoned. Com pound addition and the rest will have to be retained for suchspecial cases, alas.
But who in blazes says we must measure things in firkins and pottles and Flemish ells? These are purely man made measurements, and we must remember that measures were made for man and not man for measures.
It so happens that there is a system of measurement based exclusively on ten in this world. It is called the metric system and it is used all over the civilized world except for certain English-speaking nations such as the United States and Great Britain.
By not adopting the metric system, we waste our time for we gain. nothing, not one thing, by learning- our own measurements. The loss in time (which is expensive in deed) is balanced by not one thing I can imagine. (To be sure, it would be expensive to convert existing instruments and tools but it would have been nowhere nearly as ex pensive if we had done it a century ago, as we should have.)
There are those, of course, who object to violating our long-used cherished measures. They have given up cooms and ehaldrons but imagine there is something about inches and feet and pints and quarts and pecks and bushels that is "simpler" or "more natural" than meters and liters.
There may even be people who find something danger ously foreign and radical (oh, for that vanished word of opprobrium, "Jacobin") in the metric system-yet it was the United Stettes that led the way.
In 1786, thirteen years before the wicked French revo lutionaries designed the metric system, Thomas Jefferson (a notorious "Jacobin," according to the Federalists, at least) saw a suggestion of his adopted by the infant, United States. The nation established a decimal currency.
What we had been using was British currency, and that is a fearsome and wonderful thing. Just to point out bow preposterous it is, let me say that the British people who, over the centuries, have, with monumental patience, taught themselves to endure anything at all provided it was "tra ditional"-are now sick and tired of their durrency and are debating converting it to the decimal system. (Tley can't agree on the exact details of the change.)
But consider the British currency as it has been. To begin with, 4 farthings make 1- penny; 12 pennies make I shilling, and 20 shillings make I pound. In addition, there is a virtual farrago of terms, if not always actual coins, such as ha'pennies and thruppences and sixpences and crowns and balf-crowns and florins and guineas and heaven knows what other devices with which to cripple the mental development of the British schoolchild and line the pockets of British tradesmen whenever tourists come to call and attempt to cope with the currency.
Needless to say, Pike gives careful instruction on how to manipulate pounds, shillings, and pence-and very special instructions they are. Try dividing 5 pounds, 13 shillings, 7 pence by 3. Quick now!
In the United States, the money system, as originally established, is as follows: 10 mills make I cent; 10 cents make I dime; 10 dimes make 1 dollar; 10 dollars make I eagle. Actually, modern Americans, in their calculations, stick to dollars and cents only.
The result? American money can be expressed in deci mal form and can be treated as can any other decimals. An American child who has learned decimals need only be taught to recognize the dollar sign and he is all set. In the time that he does, a British child has barely mastered the fact that thruppence ba'penny equals 14 farthings.
What a pity that when, thirteen years later, in 1799, the metric system came into being, our original anti-British, pro-French feelings had not lasted just long enough to allow us to adopt it. Had we done so, we would have been as happy to forget our foolish pecks and ounces, as we are now happy to have forgotten our pence and shillings.
(After all, would you like to go back to British currency in preference to our own?)
What I would like to see is one form of money do for all the world. Everywhere. Why not?
I appreciate the fact that I may be accused because of this of wanting to pour humanity into a mold, and of being a conformist. Of course, I am not a conformist (heavens!).
I have no objection to local customs and local dialects and local dietaries. In fact, I insist on them for I constitute a locality all by myself. I just don't want to keep provin cialisms that were w 'ell enough in their time but that interfere with human well-being in a world which is now 90 minutes in circumference.
If you think provincialism is cute and gives humanity color and charm, let me quote to you once more from Pike.
"Federal Money" (dollars and cents) had been intro duced eleven years before Pike's second edition, and he gives the exact wording of the law that established it and discusses it in detail-under the decimal system and not under compound addition.
Naturally, since other systems than the Federal were still in use, rules had to be formulated and given for con verting (or "reducing") one system to another. Here is the list. I won't give you the actual rules, just the list of reductions that were necessary, exactly as he lists them:
I. To reduce New Hampshire, Massachusetts,, Rnode Island, Connecticut, and Virginia currency:
1. To Federal Money
2. To New York and North Carolina currency
3. To Pennsylvania, New Jersey, Delaware, and Maryland currency
4. To South Carolina and Georgia currency
5. To English money
6. To Irish money
7. To Canada and Nova Scotia currency
8. To Livres Toumois (French money)
9. To Spanish milled dollars
II. To reduce Federal Money to New England and Virginia currency.
III. To reduce New Jersey, Pennsylvania, Delaware, and Maryland currency:
1. To New Hampshire, Massachusetts, Rhode Island, Connecticut, and Virginia currency
2. To New York and...
Oh, the heck with it. You get the idea.
Can anyone possibly be sorry that all that cute provin cial flavor has vanished? Are you sorry that every time you travel out of state you don't have to throw yourself into fits of arithmetical discomfort whenever you want to make a purchase? Or into similar fits every time someone from another state invades yours and tries to dicker with you? What a pleasure to have forgotten all that.
Then tell me what's so wonderful about having fifty sets of marriage and divorce laws?
In 1752, Great Britain and her colonies (some two centuries later than Catholic Europe) abandoned the Julian calendar and adopted the astronomically more cor rect Gregorian calendar (see Chapter 1). Nearly half a century later, Pike was still giving rules for solving com plex calendar-based problems for the Julian calendar as well as for the Gregorian. Isn't it nice to have forgotten the Julian calendar?
Wouldn't it be nice if we could forget most of calendri cal complications by adopting a rational calendar that would tie the day of the month firmly to the day of the week and have a single three-month calendar serve as a perpetual one, repeating itself over and over every three months? There is a world calendar proposed which would do just this.
It would enable us to do a lot of useful forgetting.
I would like to see the English language come into worldwide use. Not necessarily as the only language or even as the major language. It would just be nice if every one-whatever his own language was-could also speak English fluently. It would help in communications and per haps, eventually, everyone would just choose to speak English.
That would save a lot of room for other things.
Why English? Well, for one thing more people speak English as either first or second language than any other language on Earth, so we have a head start. Secondly, far more science is reported in English than in any other lan guage and it is communication in science that is critical today and will be even more critical tomorrow.
To be sure, we ought to make it as easy as possible for people to speak English, which means we should rational ize its spelling and grammar.
English, as it is spelled today, is almost a set of Chinese ideograms. No one can be sure how a word is pronounced by looking at the letters that make it up. How do you pronounce: rough, through, though, cough, hiccough, and lough; and why is it so terribly necessary to spell all those sounds with the mad letter combination "ough"?
It looks funny, perhaps, to spell the words ruff, throo, thoh, cawf, hiccup, and lokh; but we already write hiccup and it doesn't look funny. We spell colour, color, and centre, center, and shew, show and grey, gray. The result looks funny to a Britisher but we are us 'ed to it. We can get used to the rest, too, and save a lot of wear and tear on the brain. We would all become more intelligent, if intelligence is measured by proficiency at spelling, and we'll not have lost one thing.
And grammar? Who needs the eternal hair-splitting arguments about "shall" and "will" or "which" and "that"?
The uselessness of it can be demonstrated by the fact that virtually no one gets it straight anyway. Aside from losing valuable time, blunting a child's reasoning faculties, and instilling him or her with a ravening dislike for the English language, what do you gain?
If there be some who think that such blurring of fine distinctions will ruin the language, I would like to point out that English, before the grammarians got hold of it, had managed to lose its gender and its declensions almost everywhere except among the pronouns. The fact that we have only one definite article (the) for all genders and cases and times instead of three, as in French (le, la, les) or six, as in German (der, die, das, dem, den, des) in no way blunts the English language, which remains an ad mirably flexible instrument. We cherish our follies only because we are used to them and not because they are not really follies.
We must make room for expanding knowledge, or at least make as much room as possible. Surely it is as im portant to forget the old and useless as it is to learn the new and important.
Forget it, I say, forget it more and more. Forget it!
But why am I getting so excited? No one is listening to a word I say.
Unfortunately, though, I read the Foreword first (yes, I'm one of that kind) and was instantly plunged into the deepest gloom. Let me quote from;the first two paragraphs:
"With each new generation our fund of scientific knowl edge increases fivefold... At the current rate of s.cien tific advance, there is about four times as much'significant biological knowledge today as in 1930, and about sixteen times as much as in 1900. By the year 2000, at this rate of increase, there will be a hundred times as much biology to dcover' in the introductory course as at the beginning of the century."
Imagine how this affects me. I am a professional "keeper upper" with science and in my more manic, ebullient, and carefree moments, I even think I succeed fairly well.
Then I read something like the above-quoted passage and the world falls about my ears. I don't keep up with science. Worse, I can't keep tip with it. Still worse, I'm falling farther behind every day.
And finally, when I'm all through sorrowing for myself, I devote a few moments to worrying about the world generally. What is going to become of Homo sapiens?
We're going to smarten ourselves to death. After a while, we will all die of pernicious education, with our brain cells crammed to indigestion with facts and concepts, and with blasts of information exploding out of our ears.
But then, as luck would have it, the very day after I read the Foreword to Biological Science I came across an old, old book entitled Pike's Arithmetic. At least that is the name on the spine. On the title page it spreads itself a bit better, for in those days titles were titles. It goes "A New and Complete System of Arithmetic Composed for the Use of the Citizens of the United States," by Nicolas Pike, A.M.
It was first published in 1785, but the copy I have is only the "Second Edition, Enlarged," published in 1797.
It is a large book of over 500 pages, crammed full of small print and with no relief whatever in the way of illustrations or diagrams. It is a solid slab of arithmetic except for small sections at the very end that introduce algebra and geometry.
I was amazed. I have two children in grade school (and once I was in grade school myself), and I know what arith metic books are like these days. They are nowhere near as large. They can't possibly have even one-fifth the wordage of Pike.
Can it be that we are leaving anything out?
So I went through Pike and, you know, we are leaving something out. And there's nothing wrong with that. The trouble is we're not leaving enough out.
On page 19, for instance, Pike devotes half a page to a listing of numbers as expressed in Roman numerals, ex tending the list to numbers as high as five hundred thou sand.
Now Arabic numerals reached Europe in the High Middle Ages, and once they came on the scene the Roman numerals were completely outmoded. They lost all pos sible use, so infinitely superior was the new Arabic nota tion. Until then who knows how many reams of paper were required to explain methods for calculating with Roman numerals. Afterward the same calculations could be performed with a hundredth of the explanation. No knowledge was lost only inefficient rules.
And yet five hundred years after the deserved death of the Roman numerals, Pike still included them and ex pected his readers to be able to translate them into Arabic numerals and vice versa even though he gave no instruc tions for how to manipulate them. In fact, nearly two hun 138 dred years after Pike, the Roman numerals are still being taught. My little daughter is learning them now.
But why? Where's the need? To be sure, you will find Roman numerals on cornerstones and gravestones, on clockfaces and on some public buildings and documents, but it isn't used for any need at all. It is used for show, for status, for antique flavor, for a craving for some kind of phony classicism.
I dare say there are some sentimental fellows who feel that knowledge of the Roman numerals is a kind of gate way to history and culture; that scrapping them would be like knocking over what is left of the Parthenon, but I have no patience with such mawkishness. We might as well suggest that everyone who learns to drive a car be required to spend some time at the wheel of a Model-T Ford so he could get the flavor of early cardom.
Roman numerals? Forget iti-And make room instead for new and valuable material.
But do we dare forget things? Why not? We've forgot ten much; more than you imagine. Our troubles stem not from the fact that we've forgotten, but that we remember too well; we don't forget enough.
A great deal of Pike's book consists of material we have imperfectly forgotten. That is why the modern arithmetic book is shorter than Pike. And if we could but perfectly forget, the modern arithmetic book could grow still shorter.
For instance, Pike devotes many pages to tables-pre sumably important tables that he thought the reader ought to be familiar with. His fifth table is labeled "cloth meas ure.29 Did you know that 2% inches make a "nail"? Well, they do. And 16 nails make a yard; while 12 nails make an ell.
No, wait a while. Those 12 nails (27 inches) make a Flemish ell. It takes 20 nails (45 inches) to make an English ell, and 24 nails (54 inches) to make a French ell. Then, 16 nails plus 1% inches (371/5 inches) make a Scotch ell.
Now if you're going to be in the business world and import and export cloth, you're going to have to know all those ells-unless you can figure some way of getting the ell out of business.
Furthermore, almost every piece of goods is measured in its own units. You speak of a firkin of butter, a punch of prunes, a fother of lead, a stone of butcher's meat, and so on. Each of these quantities weighs a certain number of pounds (avoirdupois pounds, but there are also troy pounds and apothecary pounds and so on), and Pike carefully gives all the equivalents.
Do you want to measure distances? Well, how about this: 7 92/100 inches make I link; 25 links make I pole; 4 poles make I chain; 10 chains make I furlong; and 8 furlongs make I mile.
Or do you want to measure ale or beer-a very com mon line of work in Colonial tim6s. You have to know the language, of course. Here it is: 2 pints make a quart and 4 quarts make a gallon. Well, we still know that much anyway.
In Colonial times, however, a mere gallon of beer or ale was but a starter. That was for infants. You had to know how to speak of man-sized quantities. Well, 8 gallons make a firkin-that is, it makes "a firkin,of ale in Lon don." It takes, however, 9 gallons to make "a firkin of beer in London." The intermediate quantity, 81/2 gallons, is marked down as "a firkin of ale or beer"-presumably outside of the environs of London where the provincial citizens were less finicky in distinguishing between the two.
But we go on: 2 firkins (I suppose the intermediate kind, but I'm not sure) make a kilderkin and 2 kilderkins make a barrel. Then ll/z barrels make I hogshead; 2 bar rels make a puncheon; and 3 barrels make a butt.
Have you got all that straight?
But let's try dry measure in case your appetite has been sharpened for something still better.
Here, 2 pints make a quart and 2 quarts make a pottle.
(No, not bottle, pottle. Don't tell me you've never heard of a pottle!) But let's proceed.
Next, 2 pottles make a gallon, 2 gallons make a peck, and 4 pecks make a bushel. (Long breath now.) Then 2 bushels make a strike, 2 strikes make a coom, 2 cooms make a quarter, 4 quarters make a chaldron (though in the demanding city of London, it takes 41/2 quarters to make a chaldron). Finally, 5 quarters make a wey and 2 weys make a last.
I'm not making this up. I'm copying it right out of Pike, page 48.
Were people who were studying arithmetic in 1797 ex pected to memorize all this? Apparently, yes, because Pike spends a lot of time on compound addition. That's right, compound addition. . You see, the addition you consider addition is just 44 simple addition." Compound addition is something stronger and I will now explain it to you.
Suppose you have 15 apples, your friend has 17 apples, and a passing stranger has 19 apples and you decide to make a pile of them. Having done so, you wonder bow many you have altogether. Preferring not to count, you draw upon your college education and prepare to add 15 + 17 + 19. You begin with the units column and find that 5 + 7 + 9 = 21.;You therefore divide 21 by 10 and find the quotient is 2 plus a remainder of I,. so you put down the remainder, 1, and carry the quotient 2 into the tens col- I seem to hear loud yells from the audience. "What is all this? comes the fevered demand. "Where does this 'divide by 10' jazz come from?"
Ah, Gentle Readers, but this is exactly what you do whenever you add. It is only that the kindly souls who devised our Arabic system of numeration based it on the number 10 in such a way that when any two-digit num ber is divided by 10, the first digit represents the quotient and the second the remainder.
For that reason, having the quotient and remainder in our hands without dividing, we can add automatically. If the units column adds up to 21, we put down I and carry 2; if it bad added up to 57, we would have put down 7 and carried 5, and so on.
The only reason this works, mind you, is that in adding a set of figures, each column of dicits (starting from the right and working leftward) represents a value ten times as great as the column before. The rightmost column is units, the one to its left is tens, the one to its left is hun dreds, and so on.
It is this combination of a number system based on ten and a value ratio from column to column of ten that makes addition very simple. It is for this reason that it is, as Pike calls it, "simple addition."
Now suppose you have I dozen and 8 apples, your friend has 1 dozen and 10 apples, and a passing stranger has I dozen and 9 apples. Make a pile of those and add them as follows:
I dozen 8 units
1 dozen 10 units
1 dozen 9 units
Since 8 + 10 + 9 = 27, do we put down 7 and carry 2? Not at all! The ratio of the "dozens" column to the (tunits" column is not 10 but 12, since there are 12 units to a dozen. And since the number system we are using is based on I 0 and not on 12, we can no longer let the dicits do our thinking for us. We have to go long way round.
If 8 + 10 + 9 - 27, we must divide that sum by the ratio of the value of the columns; in this case, 12. We find that 27 divided by 12 gives a quotient of 2 plus a remain der of 3, so we put down 3 and carry 2. In the dozens column we get I + I + 1 + 2 = 5. Our total therefore is 5 dozen and 3 apples.
Whenever a ratio of other than 10 is used so that you have to make actual divisions in adding, you have "com pound addition." You must indulge in compound addition if you try to add 5 pounds 12 ounces and 6 pounds 8 ounces, for there are 16 ounces to a pound. You are stuck again if you add 3 yards 2 feet 6 inches to I yard 2 feet 8 inches, for there are 12 inches to a foot, and 3 feet to a yard.
You do the former if you care to; I'll do the latter.
First, 6 inches and 8 inches are 14 inches. Divide 14 by 12, getting 1 and a remainder of 2, so you put down 2 and carry 1. As for the feet, 2 + 2 + I = 5. Divide 5 by 3 and get I and a remainder of 2, put down 2 and carry 1. In the yards, you have 3 + 1 + 1 = 5. Your answer, then, is 5 yards 2 feet 2 inches.
Now why on Earth should our unitratios vary all over the lot, when our number system is so firmly based on 10?
There are many reasons (valid in their time) for the use of odd ratios like 2, 3, 4, 8, 12, 16, and 20, but surely we are now advanced and sophisticated enough to use 10 as the exclusive (or n arly exclusive) ratio. If we could do so, we could with such pleasure forget about compound addition-and compound subtraction, compound multipli cation, compound division, too. (They also exist, of course.)
To be sure, there are times when nature makes the uni versal ten impossible. In measuring time, the day and the year have their lengths fixed for us by astronomical condi tions and neither unit of time can be abandoned. Com pound addition and the rest will have to be retained for suchspecial cases, alas.
But who in blazes says we must measure things in firkins and pottles and Flemish ells? These are purely man made measurements, and we must remember that measures were made for man and not man for measures.
It so happens that there is a system of measurement based exclusively on ten in this world. It is called the metric system and it is used all over the civilized world except for certain English-speaking nations such as the United States and Great Britain.
By not adopting the metric system, we waste our time for we gain. nothing, not one thing, by learning- our own measurements. The loss in time (which is expensive in deed) is balanced by not one thing I can imagine. (To be sure, it would be expensive to convert existing instruments and tools but it would have been nowhere nearly as ex pensive if we had done it a century ago, as we should have.)
There are those, of course, who object to violating our long-used cherished measures. They have given up cooms and ehaldrons but imagine there is something about inches and feet and pints and quarts and pecks and bushels that is "simpler" or "more natural" than meters and liters.
There may even be people who find something danger ously foreign and radical (oh, for that vanished word of opprobrium, "Jacobin") in the metric system-yet it was the United Stettes that led the way.
In 1786, thirteen years before the wicked French revo lutionaries designed the metric system, Thomas Jefferson (a notorious "Jacobin," according to the Federalists, at least) saw a suggestion of his adopted by the infant, United States. The nation established a decimal currency.
What we had been using was British currency, and that is a fearsome and wonderful thing. Just to point out bow preposterous it is, let me say that the British people who, over the centuries, have, with monumental patience, taught themselves to endure anything at all provided it was "tra ditional"-are now sick and tired of their durrency and are debating converting it to the decimal system. (Tley can't agree on the exact details of the change.)
But consider the British currency as it has been. To begin with, 4 farthings make 1- penny; 12 pennies make I shilling, and 20 shillings make I pound. In addition, there is a virtual farrago of terms, if not always actual coins, such as ha'pennies and thruppences and sixpences and crowns and balf-crowns and florins and guineas and heaven knows what other devices with which to cripple the mental development of the British schoolchild and line the pockets of British tradesmen whenever tourists come to call and attempt to cope with the currency.
Needless to say, Pike gives careful instruction on how to manipulate pounds, shillings, and pence-and very special instructions they are. Try dividing 5 pounds, 13 shillings, 7 pence by 3. Quick now!
In the United States, the money system, as originally established, is as follows: 10 mills make I cent; 10 cents make I dime; 10 dimes make 1 dollar; 10 dollars make I eagle. Actually, modern Americans, in their calculations, stick to dollars and cents only.
The result? American money can be expressed in deci mal form and can be treated as can any other decimals. An American child who has learned decimals need only be taught to recognize the dollar sign and he is all set. In the time that he does, a British child has barely mastered the fact that thruppence ba'penny equals 14 farthings.
What a pity that when, thirteen years later, in 1799, the metric system came into being, our original anti-British, pro-French feelings had not lasted just long enough to allow us to adopt it. Had we done so, we would have been as happy to forget our foolish pecks and ounces, as we are now happy to have forgotten our pence and shillings.
(After all, would you like to go back to British currency in preference to our own?)
What I would like to see is one form of money do for all the world. Everywhere. Why not?
I appreciate the fact that I may be accused because of this of wanting to pour humanity into a mold, and of being a conformist. Of course, I am not a conformist (heavens!).
I have no objection to local customs and local dialects and local dietaries. In fact, I insist on them for I constitute a locality all by myself. I just don't want to keep provin cialisms that were w 'ell enough in their time but that interfere with human well-being in a world which is now 90 minutes in circumference.
If you think provincialism is cute and gives humanity color and charm, let me quote to you once more from Pike.
"Federal Money" (dollars and cents) had been intro duced eleven years before Pike's second edition, and he gives the exact wording of the law that established it and discusses it in detail-under the decimal system and not under compound addition.
Naturally, since other systems than the Federal were still in use, rules had to be formulated and given for con verting (or "reducing") one system to another. Here is the list. I won't give you the actual rules, just the list of reductions that were necessary, exactly as he lists them:
I. To reduce New Hampshire, Massachusetts,, Rnode Island, Connecticut, and Virginia currency:
1. To Federal Money
2. To New York and North Carolina currency
3. To Pennsylvania, New Jersey, Delaware, and Maryland currency
4. To South Carolina and Georgia currency
5. To English money
6. To Irish money
7. To Canada and Nova Scotia currency
8. To Livres Toumois (French money)
9. To Spanish milled dollars
II. To reduce Federal Money to New England and Virginia currency.
III. To reduce New Jersey, Pennsylvania, Delaware, and Maryland currency:
1. To New Hampshire, Massachusetts, Rhode Island, Connecticut, and Virginia currency
2. To New York and...
Oh, the heck with it. You get the idea.
Can anyone possibly be sorry that all that cute provin cial flavor has vanished? Are you sorry that every time you travel out of state you don't have to throw yourself into fits of arithmetical discomfort whenever you want to make a purchase? Or into similar fits every time someone from another state invades yours and tries to dicker with you? What a pleasure to have forgotten all that.
Then tell me what's so wonderful about having fifty sets of marriage and divorce laws?
In 1752, Great Britain and her colonies (some two centuries later than Catholic Europe) abandoned the Julian calendar and adopted the astronomically more cor rect Gregorian calendar (see Chapter 1). Nearly half a century later, Pike was still giving rules for solving com plex calendar-based problems for the Julian calendar as well as for the Gregorian. Isn't it nice to have forgotten the Julian calendar?
Wouldn't it be nice if we could forget most of calendri cal complications by adopting a rational calendar that would tie the day of the month firmly to the day of the week and have a single three-month calendar serve as a perpetual one, repeating itself over and over every three months? There is a world calendar proposed which would do just this.
It would enable us to do a lot of useful forgetting.
I would like to see the English language come into worldwide use. Not necessarily as the only language or even as the major language. It would just be nice if every one-whatever his own language was-could also speak English fluently. It would help in communications and per haps, eventually, everyone would just choose to speak English.
That would save a lot of room for other things.
Why English? Well, for one thing more people speak English as either first or second language than any other language on Earth, so we have a head start. Secondly, far more science is reported in English than in any other lan guage and it is communication in science that is critical today and will be even more critical tomorrow.
To be sure, we ought to make it as easy as possible for people to speak English, which means we should rational ize its spelling and grammar.
English, as it is spelled today, is almost a set of Chinese ideograms. No one can be sure how a word is pronounced by looking at the letters that make it up. How do you pronounce: rough, through, though, cough, hiccough, and lough; and why is it so terribly necessary to spell all those sounds with the mad letter combination "ough"?
It looks funny, perhaps, to spell the words ruff, throo, thoh, cawf, hiccup, and lokh; but we already write hiccup and it doesn't look funny. We spell colour, color, and centre, center, and shew, show and grey, gray. The result looks funny to a Britisher but we are us 'ed to it. We can get used to the rest, too, and save a lot of wear and tear on the brain. We would all become more intelligent, if intelligence is measured by proficiency at spelling, and we'll not have lost one thing.
And grammar? Who needs the eternal hair-splitting arguments about "shall" and "will" or "which" and "that"?
The uselessness of it can be demonstrated by the fact that virtually no one gets it straight anyway. Aside from losing valuable time, blunting a child's reasoning faculties, and instilling him or her with a ravening dislike for the English language, what do you gain?
If there be some who think that such blurring of fine distinctions will ruin the language, I would like to point out that English, before the grammarians got hold of it, had managed to lose its gender and its declensions almost everywhere except among the pronouns. The fact that we have only one definite article (the) for all genders and cases and times instead of three, as in French (le, la, les) or six, as in German (der, die, das, dem, den, des) in no way blunts the English language, which remains an ad mirably flexible instrument. We cherish our follies only because we are used to them and not because they are not really follies.
We must make room for expanding knowledge, or at least make as much room as possible. Surely it is as im portant to forget the old and useless as it is to learn the new and important.
Forget it, I say, forget it more and more. Forget it!
But why am I getting so excited? No one is listening to a word I say.
