Philosophy and Fun of Algebra

Excerpt:

When people had only arithmetic and not algebra, they found out a surprising amount of things about numbers and quantities. But there remained problems which they very much needed to solve and could not. They had to guess the answer; and, of course, they usually guessed wrong. And I am inclined to think they disagreed. Each person, of course, thought his own guess was nearest to the truth. Probably they quarreled, and got nervous and overstrained and miserable, and said things which hurt the feelings of their friends, and which they saw afterwards they had better not have said-things which threw no light on the problem, and only upset everybody's mind more than ever. I was not there, so I cannot tell you exactly what happened; but quarrelling and disagreeing and nerve-strain always do go on in such cases.

At last (at least I should suppose this is what happened) some man, or perhaps some woman, suddenly said: "How stupid we've all been! We have been dealing logically with all the facts we knew about this problem, except the most important fact of all, the fact of our own ignorance. Let us include that among the facts we have to be logical about, and see where we get to then. In this problem, besides the numbers which we do know, there is one which we do not know, and which we want to know. Instead of guessing whether we are to call it nine, or seven, or a hundred and twenty, or a thousand and fifty, let us agree to call it x, and let us always remember that x stands for the Unknown. Let us write x in among all our other numbers, and deal logically with it according to exactly the same laws as we deal with six, or nine, or a hundred, or a thousand."

As soon as this method was adopted, many difficulties which had been puzzling everybody fell to pieces like a Rupert's drop when you nip its tail, or disappeared like bats when the sun rises. Nobody knew where they had gone to, and I should think that nobody cared. The main fact was that they were no longer there to puzzle people. A little girl was once saying the Evening Hymn to me, "May no ill dreams disturb my rest, No powers of darkness me molest." I asked if she knew what Powers of Darkness meant. She said, "The wolves which I cannot help fancying are under my bed when all the time I know they are not there. They must be the Powers of Darkness, because they go away when the light comes."

Now that is exactly what happened when people left off disputing about what they did not know, and began to deal logically with the fact of their own ignorance. This method of solving problems by honest confession of one's ignorance is called Algebra. The name Algebra is made up of two Arabic words.

The science of Algebra came into Europe through Arabs, and therefore is called by its Arabic name. But it is believed to have been known in India before the Arabs got hold of it.

Any fact which we know or have been told about our problem is called a datum. The number of pounds of sugar we are to buy is one datum; the price per pound is another. The plural of datum is data. It is a good plan to write all one's data on one column or page of the paper and work one's sum on the other. This leaves the first column clear for adding to one's data if one finds out any fresh one.