PHILOSOPHY AND FUN OF ALGEBRA WORKS BY MARY EVEREST BOOLE LOGIC TAUGHT BY LOVE. 35. 6d. net. MATHEMATICAL PSYCHOLOGY OF GRATRY AND BOOLE FOR MEDICAL STUDENTS. 35. 6d. net. BOOLES PSYCHOLOGY AS A FACTOR IN EDUCATION. 6d. net. THE MESSAGE OF PSYCHIC SCIENCE TO THE WORLD. 35. 6d. net. MISTLETOE AND OLIVE, is. 6d, net. Miss EDUCATION AND HER GARDEN. 6d net. PHILOSOPHY AND FUN OF ALGEBRA. 2s. net. C. W. DANIEL. THE PREPARATION OF THE CHILD FOR SCIENCE. 2s. THE LOGIC OF ARITHMETIC. 2s. CLARENDON PRESS. PHILOSOPHY FUN OF ALGEBRA BY MARY EVEREST BOOLE AUTHOR OF PREPARATION OP THE CHILD FOR SCIENCE, ETC. LONDON C. W. DANIEL, 1 1 CURSITOR STREET, B. C. 909 tco BASIL AND MARGARET MY DEAR CHILDREN, A young monkey named Genius picked a green walnut, and bit, through a bitter rind, down into a hard shell. He then threw the walnut away, saying u How stupid people are They told me walnuts are good to eat. His grandmother, whose name was Wisdom, picked up the walnut peeled off the rind with her fingers, cracked the shell, and shared the kernel with her grandson, saying Those get on best in life who do not trust to first impressions. In some old books the story is told differently the grand mother is called Mrs Cunning-Greed, and she eats all the kernel herself. Fables about the Cunning-Greed family are written to make children laugh. It is good for you to laugh it makes you grow strong, and gives you the habit of understanding jokes and not being made miserable by them. But take care not to believe such fables because, if you believe them, they give you bad dreams. MARY EVEREST BOOLE. January 1909. CONTENTS CHAP. p A GE 1. FROM ARITHMETIC TO ALGEBRA . . 9 2. THE MAKING OF ALGEBRAS . . . 15 3. SIMULTANEOUS PROBLEMS. . . . 1 9 4. PARTIAL SOLUTIONS AND THE PROVISIONAL ELIMINATION OF ELEMENTS OF COM PLEXITY ...... 23 5. MATHEMATICAL CERTAINTY AND REDUCTIO AD ABSURDUM ..... 26 6. THE FIRST HEBREW ALGEBRA ... 29 7. HOW TO CHOOSE OUR HYPOTHESES . . 37 8. THE LIMITS OF THE TEACHERS FUNCTION . 46 9. THE USE OF SEWING CARDS . . . 5 10. THE STORY OF A WORKING HYPOTHESIS . 55 11. MACBETHS MISTAKE . . . . 61 12. JACOBS LADDER ..... 67 CONTENTS CHAP. PAGE 13. THE GREAT X OF THE WORLD. . . 69 14. GO OUT OF MY CLASS-ROOM 73 15. N-I 77 1 6. INFINITY ...... 80 17. FROM BONDAGE TO FREEDOM ... 84 APPENDIX ...... 89 PHILOSOPHY AND FUN OF ALGEBRA CHAPTER I FROM ARITHMETIC TO ALGEBRA ARITHMETIC means dealing logically with facts which we know about questions of number. Logically that is to say, in accordance with the Logos or hidden wisdom, i. e., the laws of normal action of the human mind. For instance, you are asked what will have to be paid for six pounds of sugar at 3d. a pound. You multiply the six by the three. That is not because of any property of sugar, or of the copper of which the pennies are made. You would have done the same if the thing bought had been starch or apples. You wouM have done just the same 9 PHILOSOPHY AND FUN OF ALGEBRA if the material had been tea at 35. a pound. Moreover, you would have done just the same kind of action if you had been asked the price of seven pounds of tea at 2s. a pound. You do what you do under direction of the Logos or hidden wisdom. And this law of the Logos is made not by any King or Parliament, but by whoever or whatever created the human mind. Suppose that any Parliament passed an act that all the children in the kingdom were to divide the price by th number of pounds the Parliament could not make the answer come right. The only result of a foolish Act of Parliament like that would be that everybodys sums would come wrong, and everybodys accounts be in confusion, and every body would wonder why the trade of the country was going to the bad...