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Philosophy and Fun of Algebra-Mary Everest Boole · Ethan Frome

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  Speaker 1: This is LibriVox recording. All LibriVox recordings are in the
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  Speaker 1: public domain. For more information and to find out how
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  Speaker 1: you can volunteer, please visit LibriVox dot org. Philosophy and
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  Speaker 1: Fun of Algebra by Mary Everest Pool read by Patricia Oakley,
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  Speaker 1: dedication and chapter one to Basil and Margaret, My dear children.
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  Speaker 1: A young monkey named Genius picked up a green walnut
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  Speaker 1: and bit threw a bitter rind down into a hard shell.
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  Speaker 1: He then threw the walnut away, saying, how stupid people
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  Speaker 1: are they told me walnuts were good to eat. His grandmother,
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  Speaker 1: whose name was Wisdom, picked up the walnut, peeled off
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  Speaker 1: the rind with her fingers, cracked the shell, and shared
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  Speaker 1: the colonel with her grandson, saying those get on best
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  Speaker 1: in life who do not trust to first impressions. In
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  Speaker 1: some old books the story is told differently. The grandmother
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  Speaker 1: is called Missus Cunning Greed, and she eats all the
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  Speaker 1: kernel herself. Fables about the Cunning Greed family are written
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  Speaker 1: to make children laugh. It is good for you to laugh.
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  Speaker 1: It makes you grow strong and give you the habit
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  Speaker 1: of understanding jokes and not being made miserable by them.
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  Speaker 1: But take care not to believe such fables, because if
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  Speaker 1: you believe them, they give you bad dreams. Mary Everestpool,
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  Speaker 1: January nineteen o nine, Chapter one, From arithmetic to algebra.
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  Speaker 1: Arithmetic means dealing logically with facts which we know about
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  Speaker 1: questions of number logically, that is to say, in accordance
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  Speaker 1: with the logos or hidden wisdom, i e. The laws
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  Speaker 1: of normal action of the human mind. For instance, you
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  Speaker 1: are asked what will have to be paid for six
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  Speaker 1: pounds of sugar at threepennies a pound. You multiplied the
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  Speaker 1: six by the three. That is not because of any
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  Speaker 1: property of sugar or of the copper of which the
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  Speaker 1: pennies are made. You would have done the same if
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  Speaker 1: the thing bought had been starch or apples, you would
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  Speaker 1: have done just the same if the material had been
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  Speaker 1: tea at three shillings a pound. Moreover, you would have
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  Speaker 1: done just the same kind of action if you had
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  Speaker 1: been asked the price of seven pounds of tea at
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  Speaker 1: two shillings a pound. You do what you do under
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  Speaker 1: the direction of the logos or hidden wisdom. And this
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  Speaker 1: law of the logos is not made by any king
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  Speaker 1: or parliament, but by whoever or whatever created the human mind.
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  Speaker 1: Suppose that any parliament passed an act that all the
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  Speaker 1: children in the kingdom were to divide the price by
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  Speaker 1: the number of pounds. The parliament could not make the
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  Speaker 1: answer come right. The only result of a foolish act
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  Speaker 1: of parliament like that would be that everybody's sums would
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  Speaker 1: come wrong, and everybody's accounts would be in confusion, and
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  Speaker 1: everybody would wonder why the trade of the country was
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  Speaker 1: going to the bad. In former times, there were kings
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  Speaker 1: and emperors quite stupid enough to pass acts like that.
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  Speaker 1: But governments have grown wiser by experience and found out
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  Speaker 1: that as far as arithmetic goes, there is no use
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  Speaker 1: in ordering people to go contrary to the laws of
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  Speaker 1: the logos, because the logos has the whip hand and
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  Speaker 1: knows its own business and is master of the situation. Therefore,
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  Speaker 1: children now are allowed to study the laws of the
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  Speaker 1: logos whenever the business on hand is finding out how
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  Speaker 1: much they are to pay in a shop. Sometimes your
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  Speaker 1: teachers set you more complicated problems than what is the
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  Speaker 1: price of six pounds of sugar? For instance, in what
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  Speaker 1: proportion must one mix ta bought at one shilling four
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  Speaker 1: pennies a pound with tea bought at one shilling tenpennies
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  Speaker 1: a pound, so as to make five percent profit by
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  Speaker 1: selling the mixture at one shilling nine pennies a pound.
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  Speaker 1: Arithmetic then means dealing logically with certain facts that we
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  Speaker 1: know about number, with a view to arriving at knowledge
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  Speaker 1: which as yet we do not possess. When people had
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  Speaker 1: only arithmetic and not algebra, they found out a surprising
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  Speaker 1: amount of things about numbers and quantities. But there remained
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  Speaker 1: problems which they very much needed to solve and could not.
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  Speaker 1: They had to guess the answer, and of course they
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  Speaker 1: usually guessed wrong, and I am inclined to think they disagreed.
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  Speaker 1: Each person, of course, thought his own guess was nearest
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  Speaker 1: to the truth. Probably they quarreled and got nervous and
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  Speaker 1: overstrained and miserable, and said things which hurt the feelings
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  Speaker 1: of their friends, and which they saw afterwards they had
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  Speaker 1: better not have said things which threw no light on
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  Speaker 1: the problem, and only upset everybody's mind more than ever.
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  Speaker 1: I was not there, so I cannot tell you exactly
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  Speaker 1: what happened. But quarreling and disagreeing and nerve strain always
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  Speaker 1: do go on in such cases. At last, At least
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  Speaker 1: I suppose this is what happened. Some man or perhaps
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  Speaker 1: some woman suddenly said, how stupid we've all been. We
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  Speaker 1: have been dealing logically with all the facts we know
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  Speaker 1: about this problem, except the most important fact of all,
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  Speaker 1: the fact of our own ignorance. Let us include that
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  Speaker 1: among the facts which we have to be logical about,
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  Speaker 1: and see where we get to. Then in this problem,
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  Speaker 1: besides the numbers which we do know, there is one
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  Speaker 1: which we do not no, and which we want to know.
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  Speaker 1: Instead of guessing whether we are to call it nine
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  Speaker 1: or seven, or one hundred and twenty or one thousand
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  Speaker 1: and fifty, let us agree to call it X, and
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  Speaker 1: let us always remember that X stands for the unknown.
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  Speaker 1: Let us write X in among all our other numbers,
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  Speaker 1: and deal logically with it according to exactly the same
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  Speaker 1: laws as we deal with six or nine, or one
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  Speaker 1: hundred or a thousand. As soon as this method was adopted,
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  Speaker 1: many difficulties which had been puzzling everybody fell to pieces,
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  Speaker 1: like a rupert's drop when you nip its tail or
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  Speaker 1: disappeared like bats when the sun rises. Nobody knew where
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  Speaker 1: they had gone to. And I should think that nobody cared.
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  Speaker 1: The main fact was that they were no longer there
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  Speaker 1: to puzzle people. A little girl was once saying the
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  Speaker 1: evening hymn to me, May no ill dreams disturb my rest,
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  Speaker 1: No powers of darkness mean molested. I asked if she
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  Speaker 1: knew what powers of darkness meant. She said, the wolves,
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  Speaker 1: which I cannot help fancying, are under my bed, when
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  Speaker 1: all the time I know that they are not there.
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  Speaker 1: They must be the powers of darkness, because they go
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  Speaker 1: away when the light comes. Now, that is exactly what
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  Speaker 1: happened when people left off disputing about what they did
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  Speaker 1: not know and began to deal logically with the fact
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  Speaker 1: of their own ignorance. This method of solving problems by
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  Speaker 1: honest confession of one's ignorance is called algebra. The name
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  Speaker 1: algebra is made up of two Arabic words. The science
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  Speaker 1: of algebra came into Europe through Arabs, and therefore is
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  Speaker 1: called by its Arabic name, but it is believed to
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  Speaker 1: have been known in India before the Arabs got hold
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  Speaker 1: of it. Any fact which we know or have been
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  Speaker 1: told about our problem is called a datum. The number
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  Speaker 1: of pounds of sugar we are to buy is one datum.
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  Speaker 1: The price per pound is another. The plural of datum
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  Speaker 1: is data. It is a good plan to write all
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  Speaker 1: one's data on one column or page of the paper
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  Speaker 1: and work one sum on the other. This leaves a
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  Speaker 1: first column clear for adding to one's data if one
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  Speaker 1: finds out any fresh one. End of chapter one, Philosophy
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  Speaker 1: and Fun of Algebra by Mary Everest Boule read for
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  Speaker 1: Librevox dot Org by Patricia Oakley, Chapter two, The Making
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  Speaker 1: of Algebras. The Arabs had some cousins who lived not
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  Speaker 1: far off from Arabia, and who called themselves Hebrews. A
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  Speaker 1: taste for algebra seems to have run in the family.
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  Speaker 1: Three algebras grew up among the Hebrews. I should think
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  Speaker 1: they are the grandest and most useful that ever were
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  Speaker 1: heard of or dreamed of on Earth. One of them
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  Speaker 1: has been worked into the roots of all our science.
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  Speaker 1: The second is much discussed among persons who have leisure
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  Speaker 1: to be very learned. The third has hardly yet begun
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  Speaker 1: to be used or understood. In Europe. Learned men are
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  Speaker 1: only just beginning to think about what it really means.
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  Speaker 1: All children ought to know about at least the first
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  Speaker 1: of these. But before we begin to talk about the
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  Speaker 1: Hebrew algebras, there are two or three things that we
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  Speaker 1: must be quite clear about. Many people think that it
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  Speaker 1: is impossible to make algebra about anything except number. This
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  Speaker 1: is a complete mistake. We make an algebra whenever we
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  Speaker 1: arrange facts that we know round a center, which is
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  Speaker 1: a statement of what it is that we want to
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  Speaker 1: know and do not know, and then proceed to deal
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  Speaker 1: logically with all the statements, including the statement of our
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  Speaker 1: own ignorance. Algebra can be made about anything which any
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  Speaker 1: human being wants to know about. Everybody ought to be
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  Speaker 1: able to make algebras, and the sooner we begin, the better.
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  Speaker 1: It is best to begin before we can talk, because
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  Speaker 1: until we can talk, no one can get us into
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  Speaker 1: illogical habits. And it is advisable that good logic should
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  Speaker 1: get the start of bad. If you have a baby brother,
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  Speaker 1: it would be a nice amusement for you to teach
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  Speaker 1: him to make algebra when he is about ten months
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  Speaker 1: or a year old, and I will tell you how
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  Speaker 1: to do it. Sometimes a baby, when it sees a
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  Speaker 1: bright metal teapot, laughs and crows and wants to play
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  Speaker 1: with the baby. Reflected in the metal. It has learned,
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  Speaker 1: by what is called empirical experience, that teapots are nice,
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  Speaker 1: cool things to handle. Another baby, when it sees a
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  Speaker 1: bright teapot, turns its head away and screams, and will
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  Speaker 1: not be pacified while the teapot is near. It has
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  Speaker 1: learned by empirical experience that teapots are nasty, boiling hot
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  Speaker 1: things which burn one's fingers. Now you will observe that
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  Speaker 1: both these babies have learnt by experience. Some people say
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  Speaker 1: that experience is the mother of wisdom. But you see
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  Speaker 1: that both babies cannot be right, and as a matter
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  Speaker 1: of fact, both are wrong. If they could talk, they
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  Speaker 1: might argue and quarrel for years, and vote and write
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  Speaker 1: in the newspapers, and waste their own time and other
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  Speaker 1: people's money, each trying to prove he was right. But
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  Speaker 1: there is no wisdom to be gotten that way. What
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  Speaker 1: a wise baby knows is that he cannot tell by
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  Speaker 1: the mere look of a teapot whether it is hot
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  Speaker 1: or cold. The fact that is most prominent in his
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  Speaker 1: mind when he sees a teapot is the fact that
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  Speaker 1: he does not know whether it is hot or cold.
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  Speaker 1: He puts that fact along with the other fact that
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  Speaker 1: he would very much like to play with the picture
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  Speaker 1: in the teapot, supposing it would not burn his fingers.
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  Speaker 1: And he deals logically with both these facts, and comes
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  Speaker 1: to the wise conclusion that it would be best to
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  Speaker 1: go very cautiously and find out whether the teapot is
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  Speaker 1: hot by putting his fingers near, but not too near.
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  Speaker 1: That baby has begun his mathematical studies, and begun them
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  Speaker 1: at the right end. He has made an algebra for himself,
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  Speaker 1: and the best wish one can make for his future
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  Speaker 1: is that he will go on doing the same for
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  Speaker 1: the rest of his life. Perhaps the best way of
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  Speaker 1: teaching a baby algebra would be to get him thoroughly
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  Speaker 1: accustomed to playing with a bright vessel of some kind
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  Speaker 1: when cold. Then put it and another just like it
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  Speaker 1: on the table in front of him, one being filled
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  Speaker 1: with hot water. Let him play with the cold one,
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  Speaker 1: and show him that you do not wish him to
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  Speaker 1: play with the other. When he persists, as he probably will,
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  Speaker 1: let him find out for himself that the two things
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  Speaker 1: which look so alike have not exactly the same properties.
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  Speaker 1: Of course, you must take care that he does not
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  Speaker 1: hurt himself. Seriously end of chapter two, Philosophy and fun
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  Speaker 1: of Algebra by Mary Everes Bool read for librovox dot
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  Speaker 1: org by Patricia Oakley, Chapter three, Simultaneous problems. It often
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  Speaker 1: happens that two or three problems are so entangled up
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  Speaker 1: together that it seems impossible to solve any one of
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  Speaker 1: them until the others have been solved. For instance, we
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  Speaker 1: might get out three answers of this kind. X equals
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  Speaker 1: half of y, y equals twice x, z equals x
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  Speaker 1: multiplied by y. The value of each depends on the
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  Speaker 1: value of the others. When we get into a predicament
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  Speaker 1: of this kind, three courses are open to us. We
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  Speaker 1: can begin to make slap dash guesses, and each argue
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  Speaker 1: to prove that his guess is the right one, and
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  Speaker 1: go on quarreling and so on, as I describe people
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  Speaker 1: doing about arithmetic before algebra was invented. Or we might
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  Speaker 1: write down something of this kind. The values cannot be known,
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  Speaker 1: there is no answer to our problem. We might write
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  Speaker 1: X is the unknowable, why is nonexistent, Z is imaginary,
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  Speaker 1: and accept those as answers and give them forth to
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  Speaker 1: the world with all the authority which is given by
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  Speaker 1: big print wide margins, a handsome binding and a publisher
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  Speaker 1: in a large way of business, and so make a
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  Speaker 1: great Many foolish people believe we are very wise. Some
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  Speaker 1: people call this way of settling things philosophy. Others call
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  Speaker 1: it arrogant conceit. Whatever it is, it is not algebra.
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  Speaker 1: The algebra way of managing this, we say, suppose that
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  Speaker 1: X were unity one, what would become of y and z?
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  Speaker 1: Then we write out our problem as before, only that
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  Speaker 1: whenever there was x, we now write one. If the
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  Speaker 1: result of doing so is to bring out some ridiculous
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  Speaker 1: answer as two and three make seven, we then know
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  Speaker 1: that x cannot be one. We now add to our
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  Speaker 1: column of data X cannot be one. But if we
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  Speaker 1: come to a truism such as two and three make five,
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  Speaker 1: we add to our column of data x may be one.
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  Speaker 1: Some people add to their column of data x is one,
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  Speaker 1: But that again is not algebra. Next we try the
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  Speaker 1: experiment of supposing x to be equal to zero and
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  Speaker 1: go over the ground again. Then we go over the
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  Speaker 1: same ground, trying hy as one and as zero, and
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  Speaker 1: then we try the same with z. Some people think
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  Speaker 1: that it is a waste of time to go over
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  Speaker 1: all this ground so carefully. When all you get by
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  Speaker 1: it is either nonsense such as two and three are seven,
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  Speaker 1: or truisms such as two and three are five. But
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  Speaker 1: it is not waste of time, for even if we
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  Speaker 1: never arrive at finding out the value of x or
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  Speaker 1: y or z, every conscientious attempt such as I have described,
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  Speaker 1: adds to our knowledge of the structure of algebra and
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  Speaker 1: assists us in solving other problems. Such suggestions, as suppose
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  Speaker 1: x were unity, are called working hypotheses or hypothetical data.
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  Speaker 1: In algebra. We are very careful to distinguish clearly between
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  Speaker 1: actual data and hypothetical data. This is only part of
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  Speaker 1: the essence of algebra, which, as I told you, consists
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  Speaker 1: in preserving a constant, reverent, and conscientious awareness of our
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  Speaker 1: own ignorance. When we have exhausted all the possible hypotheses
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  Speaker 1: connected with unity and zero, we next begin to experiment
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  Speaker 1: with other values of x e g. Suppose x word two.
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  Speaker 1: Suppose x wor three. Suppose it were four, Then suppose
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  Speaker 1: it were one half or one and a half, and
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  Speaker 1: so on, registering among our data each time either x
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  Speaker 1: may be so and so, or x cannot be so
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  Speaker 1: and so. The method of finding out what X cannot
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  Speaker 1: be by showing that certain suppositions or hypotheses lead to
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  Speaker 1: ridiculous statement is called the method of reductio ad absurdum.
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  Speaker 1: It is largely used by Euclid. End of chapter three
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  Speaker 1: Philosophy and fun of Algebra by Mary everest Bule read
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  Speaker 1: for librovox dot org by Patricia Oakley, Chapter four Partial
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  Speaker 1: Solutions and the Provisional Elimination of Elements of complexity. Suppose
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  Speaker 1: that we never find out for certain whether X is
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  Speaker 1: unity or zero or something else. We then begin to
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  Speaker 1: experiment in a different direction. We try to find out
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  Speaker 1: which of the hypothetical values of X throw most light
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  Speaker 1: on other questions. And if we find that some particular
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  Speaker 1: value of X, for instance, unity, makes it easier than
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  Speaker 1: does any other value to understand things about Y and Z,
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  Speaker 1: we have to be very careful not to slip into
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  Speaker 1: asserting that X is unity. But the teacher would be
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  Speaker 1: quite right in saying to the class for the present,
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  Speaker 1: we will leave alone thinking about what would happen if
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  Speaker 1: X were something different from unity, and attend only to
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  Speaker 1: such questions as can be solved on the supposition that
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  Speaker 1: X is unity. This is what is called in algebra
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  Speaker 1: provisional elimination of some elements of com perplexity. It might
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  Speaker 1: happen that one of the older pupils, specially clever at
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  Speaker 1: mathematics but not very well disciplined, should start some point
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  Speaker 1: connected with the supposition that X is something different than unity.
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  Speaker 1: It would be the teacher's business to remind her, at
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  Speaker 1: present we are dealing with the supposition that X is unity.
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  Speaker 1: When we have exhausted that subject, we will investigate your question.
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  Speaker 1: But till then, please do not distract the attention of
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  Speaker 1: the class by talking about what is not the business
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  Speaker 1: on hand at present. If the girl forgot, the teacher
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  Speaker 1: might say, I should very much like you to try
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  Speaker 1: your own suggestion in private, but please do not talk
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  Speaker 1: about it in class till I give you leave. If
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  Speaker 1: she forgot again, the teacher might say, I think I
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  Speaker 1: should be inclined to say, if you cannot remember not
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  Speaker 1: to distract the class by talking about what is irrelevant
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  Speaker 1: to the business on hand, I shall have to request
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  Speaker 1: you to keep outside my classroom till you can. In
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  Speaker 1: an orderly school, the teachers have time to be polite,
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  Speaker 1: and it is their business to set the example of
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  Speaker 1: being so in history, especially such history as that of
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  Speaker 1: half civilized countries three thousand years ago, teachers were under
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  Speaker 1: too much strain to cultivate either a polite manner of
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  Speaker 1: saying things, or what is of far more consequence, that
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  Speaker 1: genuine intellectual courtesy, which is the absolute necessary condition for
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  Speaker 1: the development of any really perfect mathematical system. The Great
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  Speaker 1: Hebrew algebra therefore never became quite perfect. It was only
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  Speaker 1: rough hewn, so to speak, and its manners and customs
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  Speaker 1: were rough too. The teachers had ways of saying hold
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  Speaker 1: your tongue or get out of my classroom, which perhaps
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  Speaker 1: we should now call bigoted and brutal. But what I
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  Speaker 1: want you to notice is that hold your tongue or
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  Speaker 1: get out of my classroom is not the same thing
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  Speaker 1: as my hypothesis is right, and yours ought not to
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  Speaker 1: be tried anywhere. This latter is contrary to the essential
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  Speaker 1: basis of algebra. This a recognition of one's own ignorance.
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  Speaker 1: The other, a rough way of saying, get out of
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  Speaker 1: my classroom, is only contrary to that fine intellectual courtesy
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  Speaker 1: which is essential to the perfection of any mathematical method.
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  Speaker 1: End of Chapter four. Velosophy and fun of algebra by
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  Speaker 1: Mary Everest Boole. Read for LibriVox dot org by Patricia Oakley,
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  Speaker 1: Chapter five, Mathematical certainty and reductio ad absurdum. It is
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  Speaker 1: very often said that we cannot have mathematical certainty about
• 23:02
  Speaker 1: anything except a few special subjects, such as number or
• 23:07
  Speaker 1: quantity or dimensions. Mathematical certainty depends not on the subject
• 23:13
  Speaker 1: matter of our investigation, but upon three conditions. The first
• 23:18
  Speaker 1: is a constant recognition of the limits of our own
• 23:21
  Speaker 1: knowledge and the fact of our own ignorance. The second
• 23:25
  Speaker 1: is reverence for the as yet unknown. The third is
• 23:30
  Speaker 1: absolute fearlessness in meeting the reductio ad absurdum. In mathematics,
• 23:36
  Speaker 1: we are always delighted when we come to any such
• 23:39
  Speaker 1: conclusion as two plus three equals seven. We feel that
• 23:44
  Speaker 1: we have absolutely cleared out of the way one among
• 23:48
  Speaker 1: the several possible hypotheses, and are ready to try another.
• 23:53
  Speaker 1: We may be still groping in the dark, but we
• 23:56
  Speaker 1: know that one stumbling block has been cleared out of
• 23:58
  Speaker 1: our path, and that we are one step forwarder on
• 24:02
  Speaker 1: the right road. We wish to arrive at truth about
• 24:06
  Speaker 1: the state of our balance sheet, the number of acres
• 24:09
  Speaker 1: in our farm, the time it will take us to
• 24:12
  Speaker 1: get from London to Liverpool, the height of Snowden, the
• 24:17
  Speaker 1: distance of the moon, and the weight of the sun.
• 24:20
  Speaker 1: We have no desire to deceive ourselves upon any of
• 24:24
  Speaker 1: these points, and therefore we have no superstitious shrinking from
• 24:29
  Speaker 1: the rigid reductio ad absurdum. On some other subjects, people
• 24:35
  Speaker 1: do wish to be deceived. They dislike the operation of
• 24:39
  Speaker 1: correcting the hypothetical data which they have taken as basis. Therefore,
• 24:45
  Speaker 1: when they begin to see looming ahead some such ridiculous
• 24:50
  Speaker 1: result as two plus three equals seven, they shrink into
• 24:55
  Speaker 1: themselves and try to find some process of twisting the
• 24:58
  Speaker 1: logic and tinkering the equation which will make the answer
• 25:03
  Speaker 1: come out as a truism instead of an absurdity. And
• 25:07
  Speaker 1: then they say, our hypothetical premise is most likely true,
• 25:11
  Speaker 1: because the conclusion to which it brings us is obviously
• 25:15
  Speaker 1: and indisputably true. If anyone points out that there seems
• 25:22
  Speaker 1: to be a flaw in the argument, they say, you
• 25:26
  Speaker 1: cannot expect to get mathematical certainty in this world, or
• 25:31
  Speaker 1: you must not push logic too far, or everything is
• 25:36
  Speaker 1: more or less compromise, and so on. Of course, there
• 25:42
  Speaker 1: is no mathematical certainty to be had on those terms.
• 25:46
  Speaker 1: You could have no mathematical certainty about the amount you
• 25:50
  Speaker 1: owed your grosser if you tinker the process of adding
• 25:53
  Speaker 1: up his bill. I wish to call your attention to
• 25:56
  Speaker 1: the fact that even in this world, there is a
• 26:00
  Speaker 1: good deal of mathematical certainty to be had by whosoever
• 26:04
  Speaker 1: has endless patience, scrupulous accuracy in stating his own ignorance,
• 26:10
  Speaker 1: reverence for the as yet unknown, and perfect fearlessness in
• 26:15
  Speaker 1: meeting the reductio ad absurdum end of chapter five. Philosophy
• 26:25
  Speaker 1: and fun of Algebra by Mary Everest Bull read for
• 26:29
  Speaker 1: Libravox dot org by Patricia Oakley, Chapter six. The First
• 26:35
  Speaker 1: Hebrew algebra. The first Hebrew algebra is called Moeism, from
• 26:42
  Speaker 1: the name of Moses, the Liberator, who was its great
• 26:45
  Speaker 1: incarnation or singular solution. It ought hardly to be called
• 26:51
  Speaker 1: an algebra. It is the master key of all algebras,
• 26:56
  Speaker 1: the great central director for all who wished to learn
• 26:59
  Speaker 1: how to get in right relations to the unknown, so
• 27:02
  Speaker 1: that they can make algebras for themselves. Its great keynotes
• 27:08
  Speaker 1: are these, when you do not know something and wish
• 27:13
  Speaker 1: to know it, state that you do not know it,
• 27:16
  Speaker 1: and keep that fact well in front of you. When
• 27:21
  Speaker 1: you make a provisional hypothesis, state that it is so,
• 27:25
  Speaker 1: and keep that fact well in front of you while
• 27:30
  Speaker 1: you are trying out that provisional hypothesis. Do not allow
• 27:35
  Speaker 1: yourself to think or other people to talk to you
• 27:39
  Speaker 1: about any other hypothesis. Always remember that the use of
• 27:46
  Speaker 1: algebra is to free people from bondage. For instance, in
• 27:51
  Speaker 1: the case of number, children do their numeration, they're carrying
• 27:58
  Speaker 1: intens because as primitive man had nothing to do sums
• 28:02
  Speaker 1: with but his ten fingers. Many children grow superstitious and
• 28:08
  Speaker 1: think that you cannot carry except intents, or that it
• 28:12
  Speaker 1: is wrong to carry in anything but tens. The use
• 28:17
  Speaker 1: of algebra is to free them from bondage to all
• 28:20
  Speaker 1: this superstitious nonsense, and to help them to see that
• 28:25
  Speaker 1: the numbers would come just as right if we carried
• 28:29
  Speaker 1: in eights or twelves or twenties. It is a little
• 28:34
  Speaker 1: difficult to do this at first, because we are not
• 28:37
  Speaker 1: accustomed to it, but algebra helps to get over our
• 28:41
  Speaker 1: stiffness and set habits and to do numeration on any
• 28:45
  Speaker 1: basis that suits the matter we are dealing with. Of course,
• 28:51
  Speaker 1: we have to be careful not to mix two numerations.
• 28:55
  Speaker 1: If we are working a sum intens we must go
• 28:58
  Speaker 1: on working intens to the end of that sum. Never
• 29:03
  Speaker 1: let yourself get fixed ideas that numbers or anything else
• 29:07
  Speaker 1: that you are working at will not come right unless
• 29:11
  Speaker 1: your sum is set or shaped in a particular way.
• 29:15
  Speaker 1: Have a way in which you usually do a particular
• 29:18
  Speaker 1: kind of sum, but do not let it haunt you.
• 29:22
  Speaker 1: You may someday become a teacher. If ever, you are
• 29:26
  Speaker 1: teaching a class how to set down a sum or
• 29:28
  Speaker 1: an equation, then say this is my way, or this
• 29:34
  Speaker 1: is the way which I think you will find most convenient,
• 29:37
  Speaker 1: or this is the way in which the government inspector
• 29:41
  Speaker 1: requires you to do sums at present, and therefore you
• 29:45
  Speaker 1: must learn it. But do not take in vain the
• 29:48
  Speaker 1: names of great unseen powers to back up either your
• 29:52
  Speaker 1: own limitations or your own authority or the inspector's authority.
• 29:57
  Speaker 1: Never say or imply a arithmetic requires you to do this.
• 30:02
  Speaker 1: Your sum will come wrong if you do it differently.
• 30:06
  Speaker 1: Remember that arithmetic requires nothing from you except absolute honesty
• 30:11
  Speaker 1: and patient work. You get no blessing from the unseen
• 30:15
  Speaker 1: powers of number by slipshod statements used to make your
• 30:18
  Speaker 1: own path easy. Be very accurate and plotting during your
• 30:25
  Speaker 1: hours of work, but take care not to go on
• 30:28
  Speaker 1: too long at a time doing mere drudgery. At certain times,
• 30:34
  Speaker 1: give yourself a full stretch of body and mind by
• 30:37
  Speaker 1: going to the boundless fairyland of your subject. Think how
• 30:42
  Speaker 1: the great mathematicians can weigh the earth and measure the stars,
• 30:46
  Speaker 1: and reveal the laws of the universe. And tell yourself
• 30:50
  Speaker 1: that it is all one science, and that you are
• 30:53
  Speaker 1: one of the servants of it, quite as much as
• 30:57
  Speaker 1: ever Pythagoras or Newton were. Never be satisfied with being
• 31:02
  Speaker 1: up to date. Think in your slack time of how
• 31:06
  Speaker 1: people before you did things. While you are at school,
• 31:10
  Speaker 1: my little book Logic of Arithmetic will help you to
• 31:14
  Speaker 1: find out many things about your ancestors which may amuse
• 31:18
  Speaker 1: and interest you. But as soon as you leave school
• 31:22
  Speaker 1: and choose your own reading, take care to read up
• 31:25
  Speaker 1: the histories of the struggles and difficulties of the people
• 31:28
  Speaker 1: who formerly dealt with your own subject, whatever that may be.
• 31:34
  Speaker 1: If you find the whole of the data too complicated
• 31:37
  Speaker 1: to deal with, and judge that it is necessary to
• 31:40
  Speaker 1: eliminate one or more of them in order to reduce
• 31:44
  Speaker 1: your material within the compass of your own power to manage.
• 31:48
  Speaker 1: Do it as a provisional necessity. Take care to register
• 31:53
  Speaker 1: the fact that you have done so, and to arrange
• 31:56
  Speaker 1: your mind from the first on the understanding that the
• 32:00
  Speaker 1: eliminated data will have to come back Forget them during
• 32:05
  Speaker 1: the working out of your experimental equation, but never give
• 32:09
  Speaker 1: way to the feeling that they are got rid of
• 32:11
  Speaker 1: and done with. Be very careful not to disturb other
• 32:16
  Speaker 1: people's relationships to each other. For instance, if a teacher
• 32:21
  Speaker 1: is explaining something to another pupil, never speak till she
• 32:25
  Speaker 1: has done. Beware of the sentimental craving to be in it.
• 32:31
  Speaker 1: Any studying group profits by right working relations being set
• 32:36
  Speaker 1: up between any two members, and ultimately each member profits.
• 32:41
  Speaker 1: The whole group suffers from any distraction between any two. Therefore,
• 32:47
  Speaker 1: listen and learn what you can, but never disturb or distract.
• 32:53
  Speaker 1: Take care not to become a parasite. Do not lazily
• 32:58
  Speaker 1: appropriate the results of other people's labor, but learn and
• 33:02
  Speaker 1: labor truly to get your own living. Take care that
• 33:07
  Speaker 1: everything you possess whether physical, mental, or spiritual, shall be
• 33:11
  Speaker 1: the result of your own toil as well as other peoples.
• 33:15
  Speaker 1: And remember that you are bound to pay in some
• 33:18
  Speaker 1: shape or way everyone who helps you. Do not make
• 33:24
  Speaker 1: things easy for yourself by speaking or thinking of data
• 33:27
  Speaker 1: as if they were different from what they are, And
• 33:31
  Speaker 1: do not go off from facing data as they are
• 33:35
  Speaker 1: to amuse your imagination by wishing they were different from
• 33:39
  Speaker 1: what they are. Such wishing is pure waste of nerve force,
• 33:44
  Speaker 1: weakens your intellectual power and gets you in habits of
• 33:48
  Speaker 1: mental confusion. When the time comes to stop grindwork, there
• 33:54
  Speaker 1: is no better rest than amusing your imagination by thinking
• 33:58
  Speaker 1: of nonexistent possibility. But do it on a free, generous scale.
• 34:05
  Speaker 1: Give yourself a perfectly free reign in the company of
• 34:08
  Speaker 1: the infinite. During such exercise of the imagination, remember that
• 34:14
  Speaker 1: you are in the company of the infinite and are
• 34:16
  Speaker 1: not dealing with or tinkering at the problem on your paper.
• 34:22
  Speaker 1: Keep always at hand, clearly written out a good standard
• 34:26
  Speaker 1: selection of the most important formulae arithmetical, algebraic, geometric, and trigonometrical,
• 34:35
  Speaker 1: and accustom yourself to test your results by referring to it.
• 34:39
  Speaker 1: These are the main laws of mathematical self guidance. Once
• 34:44
  Speaker 1: upon a time, Moses projected them on to the magic
• 34:47
  Speaker 1: lantern screen of legislation. In that form, they are known
• 34:52
  Speaker 1: as the Ten Commandments, or, to change the metaphors, we
• 34:56
  Speaker 1: might call the Ten Commandments the outer skin of the
• 34:59
  Speaker 1: mathematical body. A great many people seem to suppose that
• 35:04
  Speaker 1: though everyone ought to keep the Ten Commandments, it does
• 35:08
  Speaker 1: not matter what happens to one's mind. Just so, there
• 35:12
  Speaker 1: are people who live unhealthy lives and think they can
• 35:16
  Speaker 1: make all right by putting cosmetics on their skin. But
• 35:20
  Speaker 1: I hope you have learned in the hygiene class how
• 35:23
  Speaker 1: stupid and futile that all is. The way to have
• 35:26
  Speaker 1: a healthy skin is to grow it by leading a
• 35:29
  Speaker 1: hygienic life, on a moderate allowance of pure wholesome food,
• 35:33
  Speaker 1: and taking a proper amount of exercise in pure fresh air.
• 35:38
  Speaker 1: People who do that with their minds grow the Ten
• 35:41
  Speaker 1: Commandments naturally, just as Moses grew them. The world has
• 35:46
  Speaker 1: been trying the other plan, bad food and air inside
• 35:50
  Speaker 1: and cosmetics outside for at least four thousand years, and
• 35:54
  Speaker 1: not much seems to have come of it. Yet the
• 35:57
  Speaker 1: Ten Commandments have not yet succeeded in getting themselves kept.
• 36:02
  Speaker 1: Perhaps that is why some schoolmasters and mistresses think they
• 36:06
  Speaker 1: would like to try the other plan. Now. Still, it
• 36:10
  Speaker 1: is very good to have a normal model of what
• 36:13
  Speaker 1: a healthy human being ought to look like outside. It
• 36:17
  Speaker 1: is good to have a standard for reference. Therefore, do
• 36:21
  Speaker 1: not get too much immersed in the mere details of
• 36:25
  Speaker 1: your own problems. Learn the Ten Commandments and a few
• 36:29
  Speaker 1: other old standard formulas by heart, and repeat them every
• 36:33
  Speaker 1: now and then, And say to yourself, if I really
• 36:38
  Speaker 1: am doing my algebra quite rightly, This, the standard formularies,
• 36:44
  Speaker 1: is how I shall think and feel and wish I
• 36:48
  Speaker 1: shall wish to behave Thus, not because anybody ordered me
• 36:52
  Speaker 1: to do so, but from sheer liking and sense of
• 36:55
  Speaker 1: the general fitness of things. End of six. Philosophy and
• 37:03
  Speaker 1: fun of Algebra by Mary Everes Boole. Read for librovox
• 37:08
  Speaker 1: dot org by Patricia Oakley, Chapter seven, How to choose
• 37:14
  Speaker 1: our hypotheses. The faculties by means of which we get
• 37:19
  Speaker 1: our positive data are called the senses, sight, hearing, etc.
• 37:25
  Speaker 1: The faculty, by means of which we get our hypothetical
• 37:29
  Speaker 1: data is called the imagination. Some persons are prone to
• 37:35
  Speaker 1: warn young people against what they call an excessive exercise
• 37:39
  Speaker 1: of imagination. Of course, to say that excessive anything is
• 37:44
  Speaker 1: too much is a mere truism. But nobody knows yet
• 37:48
  Speaker 1: what is the proper amount of use for the imagination.
• 37:53
  Speaker 1: What we do know is that there is a good
• 37:55
  Speaker 1: deal of excessive misuse of the imagination, in which I
• 38:00
  Speaker 1: mean there is a frightful amount of using it contrary
• 38:04
  Speaker 1: to the laws of its normal action, a kind of
• 38:07
  Speaker 1: use of it, such as when we find a child
• 38:11
  Speaker 1: doing it with its eyes, we say, do not learn
• 38:14
  Speaker 1: the habit of squinting, Or if it does the analogous
• 38:18
  Speaker 1: thing with its legs, we say, go and run about,
• 38:21
  Speaker 1: or do some gymnastics. Do not stand there lolloping crooked
• 38:24
  Speaker 1: against the wall. Squinting and lolloping crooked are things that
• 38:30
  Speaker 1: it is best to avoid doing much of with any
• 38:33
  Speaker 1: part of one's self. Moreover, it is bad to spend
• 38:38
  Speaker 1: too many hours over either a microscope or a telescope,
• 38:42
  Speaker 1: or in gazing fixedly at some one distance range. The
• 38:47
  Speaker 1: eyes need change of focus, so does the imagination. There
• 38:52
  Speaker 1: has been in modern Europe a shocking riot in misuse
• 38:56
  Speaker 1: of the imagination. The remedy is to learn to use it.
• 39:01
  Speaker 1: But the same kind of people who would like to
• 39:03
  Speaker 1: bandage a child's eyes lest it learned to squint, like
• 39:08
  Speaker 1: to bandage the imagination lest it should wear itself out
• 39:11
  Speaker 1: by squinting. In a school which professes to be conducted
• 39:16
  Speaker 1: on hygienic principles, we have nothing to do with that
• 39:20
  Speaker 1: sort of pessimistic quackery. We use the imagination as freely
• 39:25
  Speaker 1: as the hands and eyes. But when we come to
• 39:30
  Speaker 1: the end of our arithmetic, we do not content ourselves
• 39:34
  Speaker 1: with guesses. We proceed to algebra, that is to say,
• 39:39
  Speaker 1: to dealing logically with the fact of our own ignorance.
• 39:44
  Speaker 1: One of the data that we do know is that
• 39:47
  Speaker 1: all great nerve centers affect each other. Misuse of any
• 39:52
  Speaker 1: one tends more or less to produce distorted action in
• 39:56
  Speaker 1: the others, And apart from that consideration, any energetic and
• 40:03
  Speaker 1: continued action of one tends more or less to suppress
• 40:07
  Speaker 1: the action of the others for the time being, by
• 40:11
  Speaker 1: drawing the blood from the organs which are the seat
• 40:14
  Speaker 1: of them. And then when normal circulation is restored, to
• 40:19
  Speaker 1: produce for a time and unusual sensitiveness in the others.
• 40:24
  Speaker 1: There is nothing abnormal or wrong in this provided that
• 40:27
  Speaker 1: we recognize the fact, and, as I said, are careful
• 40:32
  Speaker 1: to deologically with the fact of our own ignorance whenever
• 40:36
  Speaker 1: anything happens either to our eyes or to our imagination,
• 40:40
  Speaker 1: which we do not at the moment quite understand. If
• 40:46
  Speaker 1: you ever arrive at using your imagination strongly and rightly
• 40:50
  Speaker 1: in the construction of any sort of algebra, you may
• 40:54
  Speaker 1: find that it affects to some extent your sense organs.
• 40:59
  Speaker 1: It certainly will affect them more or less, whether you
• 41:02
  Speaker 1: know it or not. What I mean is that it
• 41:06
  Speaker 1: may affect them in a way that forces you to
• 41:08
  Speaker 1: be aware of the fact. If ever this should happen,
• 41:13
  Speaker 1: take it quite naturally, and as long as you are
• 41:16
  Speaker 1: too young to understand how it happens, just say to yourself,
• 41:21
  Speaker 1: this is x one of the things that I do
• 41:24
  Speaker 1: not know, and perhaps she'll know some day if I
• 41:28
  Speaker 1: go on quietly, acting in accordance with strict logic and
• 41:31
  Speaker 1: remembering my own ignorance. The ancient Hebrews use their imaginations
• 41:37
  Speaker 1: very freely, and sometimes really very logically, and sometimes the
• 41:42
  Speaker 1: free use of the imagination produces sensations in the eyes
• 41:45
  Speaker 1: and ears, as if of seeing and hearing. They considered
• 41:50
  Speaker 1: this quite natural, as it really was. Many great mathematicians
• 41:56
  Speaker 1: in modern Europe have had these sensations. The Hebrews call
• 42:01
  Speaker 1: these sensations by a Hebrew word, which is translated by
• 42:05
  Speaker 1: the English word angel, from the Greek angelos, a messenger.
• 42:12
  Speaker 1: The Hebrews were quite right. The sensations are messengers from
• 42:17
  Speaker 1: the great unknown. They bring no information about outside facts.
• 42:23
  Speaker 1: No angel tells you how many petals there are in
• 42:26
  Speaker 1: a buttercup. If you want to know that, you are
• 42:29
  Speaker 1: supposed to ask the buttercup itself. No angel tells you
• 42:33
  Speaker 1: the price of sugar. You ought to ask your grocer.
• 42:38
  Speaker 1: No angel tells you how to invest your money. You
• 42:41
  Speaker 1: ought to ask your banker or your lawyer. There are
• 42:45
  Speaker 1: people foolish enough to ask angels about investments, or about
• 42:50
  Speaker 1: which horse will win a race, which is just as
• 42:53
  Speaker 1: foolish as asking your banker in town how many blossoms
• 42:56
  Speaker 1: there are on the rose tree in your country garden.
• 43:00
  Speaker 1: It is not his business, and if he made a guess,
• 43:04
  Speaker 1: it would most likely turn out a wrong one. All
• 43:08
  Speaker 1: that sort of thing is quackery and superstition. But the
• 43:13
  Speaker 1: angels do bring us very reliable information from a vast
• 43:17
  Speaker 1: region of valuable truth about which most of us know
• 43:21
  Speaker 1: very little as yet. They guide us how to frame
• 43:26
  Speaker 1: our next provisional working hypothesis, how to choose the particular
• 43:32
  Speaker 1: hypothesis which, at our present stage of knowledge and development,
• 43:37
  Speaker 1: will be most illuminating for us. Some of the angels
• 43:42
  Speaker 1: come during sleep, we call them dreams. Dreams sometimes suggest
• 43:47
  Speaker 1: the best working hypothesis to experiment on next. More often
• 43:53
  Speaker 1: they warn us against thinking upon some hypothetical basis which
• 43:57
  Speaker 1: for the present will not suit us. And here comes
• 44:02
  Speaker 1: in the value of such formulae such as attend commandments.
• 44:07
  Speaker 1: They are the laws of the normal working of the
• 44:10
  Speaker 1: brain machinery. The angel or imaginary messenger suggests to you
• 44:18
  Speaker 1: the one among possible working hypotheses on which your brain
• 44:23
  Speaker 1: will most readily work. Now, the formularies of which I
• 44:28
  Speaker 1: spoke give you the laws of healthy brain action. Therefore,
• 44:34
  Speaker 1: if the angel suggests something contrary to the registered formulas,
• 44:38
  Speaker 1: he is suggesting the hypothesis which you ought carefully to
• 44:42
  Speaker 1: avoid thinking out or using at that time. It is,
• 44:47
  Speaker 1: of all paths toward disease, the one which will lead you,
• 44:51
  Speaker 1: in your present condition, most rapidly toward disease. But if
• 44:57
  Speaker 1: the imaginary angel suggests no, nothing contrary to the formularies,
• 45:02
  Speaker 1: then the image or idea which he suggests is likely
• 45:06
  Speaker 1: to be one on which your mind, for the time
• 45:09
  Speaker 1: being can work safely, and the one along which it
• 45:14
  Speaker 1: can work most easily and profitably. When your imagination is
• 45:20
  Speaker 1: acting strongly in providing you with working hypotheses, there are
• 45:25
  Speaker 1: a few little precautions which you ought to observe. Do
• 45:30
  Speaker 1: not at such times take either very rapid or a
• 45:34
  Speaker 1: very much prolonged physical exercise. Be rather particular not to
• 45:40
  Speaker 1: eat anything either indigestible or highly flavored. Even if you
• 45:47
  Speaker 1: were in the habit of taking any kind of alcoholic stimulant,
• 45:51
  Speaker 1: which while you are young, I hope you will not do.
• 45:54
  Speaker 1: Avoid it during the process of framing hypotheses. Be extra
• 45:59
  Speaker 1: careful at such times to keep up any routine exercises
• 46:03
  Speaker 1: of slack muscles and slow breathing which you find suit you.
• 46:09
  Speaker 1: Take a little care at such times not to catch cold.
• 46:13
  Speaker 1: You are rather less liable than usual to take cold
• 46:17
  Speaker 1: at such times. But on the other hand, you are
• 46:20
  Speaker 1: less conscious than usual of ordinary physical sensations, and may
• 46:25
  Speaker 1: be very cold without knowing it. A chill may settle
• 46:29
  Speaker 1: locally and produce permanent mischief. Above all, be very careful
• 46:35
  Speaker 1: while the imaginative fit is on, to avoid letting the
• 46:39
  Speaker 1: subject as to which your imagination is stirred become the
• 46:43
  Speaker 1: object of either fun, vanity, or gossip. The vision which
• 46:49
  Speaker 1: you see may quite harmlessly and legitimately become a source
• 46:53
  Speaker 1: of fun to yourself and your friends at some future time,
• 46:57
  Speaker 1: but take care never to gossip or joke about it
• 47:01
  Speaker 1: until it has passed from the condition of imaginative vision
• 47:04
  Speaker 1: to that of working hypothesis. But the most important precaution
• 47:10
  Speaker 1: of all is incessant reverence for the great unknown, the
• 47:15
  Speaker 1: sacred X, or in other words, a constant awareness of
• 47:21
  Speaker 1: your own ignorance. Remember always that genius means conscientious, careful
• 47:28
  Speaker 1: work on suggestions of the imagination taken as provisional hypotheses.
• 47:35
  Speaker 1: To take suggestions of the imagination as fact is insanity.
• 47:40
  Speaker 1: When you hear of a man that he has unquestionable
• 47:44
  Speaker 1: genius but is a little mad, that means that he
• 47:47
  Speaker 1: sometimes takes the products of his imagination as working hypotheses,
• 47:52
  Speaker 1: but sometimes mistakes them for facts. All the above precautions
• 48:00
  Speaker 1: may be summed up in one sentence. Remember that the
• 48:04
  Speaker 1: more act of the imagination is, the less the physical
• 48:08
  Speaker 1: and moral instincts are on the alert. Therefore, conscious precaution
• 48:14
  Speaker 1: should supplement instinct at such times until self protection has
• 48:19
  Speaker 1: become so fixed by habit as to become in its
• 48:22
  Speaker 1: turn automatic and instinctive. If you observe these precautions, you
• 48:29
  Speaker 1: need not fear using your imagination freely. When you hear
• 48:34
  Speaker 1: of some brilliant, imaginative writer who has come to grief physically,
• 48:38
  Speaker 1: mentally or morally after a short and brilliant career, you
• 48:42
  Speaker 1: will find it advantageous to try to find out which
• 48:46
  Speaker 1: of the precautions he has been neglecting. In future letters,
• 48:52
  Speaker 1: I hope to point out to your notice some famous
• 48:55
  Speaker 1: cases of disaster due to such neglect. End of chapter seven.
• 49:06
  Speaker 1: Philosophy and fun of Algebra by Mary Everest Boole read
• 49:10
  Speaker 1: for LibriVox dot Org by Patricia Oakley, Chapter eight, The
• 49:16
  Speaker 1: Limits of the teacher's function. One of the greatest causes
• 49:22
  Speaker 1: of mental and moral confusion, as well as of absolute
• 49:26
  Speaker 1: insanity in modern Europe, is the fact that numbers of
• 49:30
  Speaker 1: people plunge into the second and third great Hebrew algebras
• 49:34
  Speaker 1: before they rightly understand the first even if they are
• 49:39
  Speaker 1: silent about their results. This distracts their own minds and
• 49:43
  Speaker 1: sows the seeds of bad habits and mental confusion in
• 49:46
  Speaker 1: their own constitutions. Many of these people give to the
• 49:51
  Speaker 1: world their own wild guesses about the second and third algebras,
• 49:55
  Speaker 1: and that puts the rest of the world into confusion.
• 49:59
  Speaker 1: We are there therefore, not going to enter on the
• 50:01
  Speaker 1: question of the second algebra till I have provided you
• 50:04
  Speaker 1: with the possibility of understanding and practicing the first. In
• 50:08
  Speaker 1: the next few chapters, I hope to give you a
• 50:10
  Speaker 1: series of stories of people who used and sometimes misused
• 50:13
  Speaker 1: the Algebra of Moses, in order that you may see
• 50:16
  Speaker 1: how to work the rules strictly and how mistakes might
• 50:20
  Speaker 1: creep in. But before we begin our stories, there is
• 50:25
  Speaker 1: one principle to which I must call your attention. It
• 50:29
  Speaker 1: is the business of your teachers at school to see
• 50:31
  Speaker 1: that you acquire skill in using certain implements or tools.
• 50:36
  Speaker 1: It is not their business nor mine to decide what
• 50:40
  Speaker 1: use you shall make when you are grown up of
• 50:42
  Speaker 1: the skill which you have acquired. It is their business
• 50:46
  Speaker 1: to see that you learn to read and to speak properly.
• 50:50
  Speaker 1: It is not their business to decide beforehand whether you
• 50:54
  Speaker 1: shall recite in public or only read to your own
• 50:57
  Speaker 1: family and your sick friends. It is their business to
• 51:01
  Speaker 1: see that you know how to sew, but not to
• 51:04
  Speaker 1: settle whether you shall in future make your own clothes
• 51:07
  Speaker 1: or work for the poor. So it is with the
• 51:11
  Speaker 1: tools of the mind, such as algebra and logic, it
• 51:15
  Speaker 1: is our business to see that you know how to
• 51:17
  Speaker 1: use algebraic and logical method accurately and skillfully. It is
• 51:23
  Speaker 1: not our business to decide whether in the future you
• 51:26
  Speaker 1: shall use your skill to deceive other people or to
• 51:30
  Speaker 1: show them the truth. It is our business to see
• 51:33
  Speaker 1: that you do not deceive yourself, because deceiving yourself distorts
• 51:38
  Speaker 1: your brain and ruins the possibility of using logical methods
• 51:42
  Speaker 1: skillfully to arrive at the knowledge of truths. When you
• 51:48
  Speaker 1: have found out a truth, then the question whether you
• 51:52
  Speaker 1: shall or shall not tell it to other people is
• 51:54
  Speaker 1: a matter of conscience. You will have to settle it
• 51:58
  Speaker 1: alone with the great power which no man knows self. Deception,
• 52:04
  Speaker 1: slipshod logic, and bad algebra are things which it is
• 52:08
  Speaker 1: the business of your elders to protect you from while
• 52:11
  Speaker 1: you are young, in order that you may not lose
• 52:15
  Speaker 1: the power of being honest in case you wish to
• 52:18
  Speaker 1: be so. My business is not to judge what is
• 52:22
  Speaker 1: good or bad conduct, but to see that you learn
• 52:26
  Speaker 1: how to be perfectly honest with yourself. I wish you
• 52:30
  Speaker 1: to notice this because in the books of the Hebrew
• 52:33
  Speaker 1: Algebra you will sometimes find good kind people spoken of
• 52:37
  Speaker 1: very harshly, and some of the most dishonest and selfish
• 52:41
  Speaker 1: people in the world praised and spoken of as blessed.
• 52:46
  Speaker 1: This puzzles many good people because they choose to fancy
• 52:50
  Speaker 1: that the Hebrew books are sermons about right and wrong feelings,
• 52:54
  Speaker 1: and do not like to recognize that they are really
• 52:57
  Speaker 1: about the algebra of logic. As I said before, people
• 53:04
  Speaker 1: who really conduct their minds strictly according to the algebra
• 53:07
  Speaker 1: of logic are very prone to grow kindness and honesty
• 53:12
  Speaker 1: towards other people without thinking about it as a matter
• 53:15
  Speaker 1: of taste of choice. They like being kind and honest
• 53:21
  Speaker 1: better than being selfish and dishonest, and they become kind
• 53:25
  Speaker 1: and honest without thinking much about it. But honesty to
• 53:30
  Speaker 1: other people and honesty to yourself are two different things
• 53:35
  Speaker 1: and must be kept apart in your mind. Just as
• 53:39
  Speaker 1: in physiology, class. You keep apart the flesh of an
• 53:42
  Speaker 1: animal and its skin. You believe that if the flesh
• 53:46
  Speaker 1: is thoroughly healthy, it will grow a good skin. But
• 53:50
  Speaker 1: while you are studying, you do not mix up statements
• 53:54
  Speaker 1: about the one with guesses about the other. If we
• 53:58
  Speaker 1: find that a man's logic was good and his conduct
• 54:02
  Speaker 1: what we should call bad, we must do what a
• 54:05
  Speaker 1: doctor would do if he found a spot on a
• 54:07
  Speaker 1: patient's skin which he could not account for by anything
• 54:11
  Speaker 1: wrong in his circulation or digestion. He ought not to say,
• 54:17
  Speaker 1: either that spot is not there, or I suppose it
• 54:21
  Speaker 1: is right that spots should be there, nor, on the
• 54:24
  Speaker 1: other hand, to jump to the conclusion that the patient
• 54:26
  Speaker 1: had been eating some particularly unwholesome thing. He ought to
• 54:31
  Speaker 1: register in his mind as one of his data. The
• 54:34
  Speaker 1: fact of his own ignorance of how that spot came there.
• 54:38
  Speaker 1: I shall have to tell you in another chapter the
• 54:40
  Speaker 1: story of one of the most selfish and deceitful persons
• 54:43
  Speaker 1: that ever lived, as to his conduct towards other people,
• 54:47
  Speaker 1: but who was said to be blessed, apparently for no
• 54:51
  Speaker 1: reason except that he was absolutely straight with his logic
• 54:54
  Speaker 1: and honest with himself. Besides, no one who consciously and
• 55:01
  Speaker 1: deliberately dishonest to serve his own selfish purposes can ever
• 55:05
  Speaker 1: do as much harm to other people as is done
• 55:09
  Speaker 1: every day by men and women who have muddled their
• 55:12
  Speaker 1: own brains with crooked logic. End of chapter eight. Philosophy
• 55:21
  Speaker 1: and Fun of Algebra by Mary Everest Bull read for
• 55:25
  Speaker 1: libravox dot org by Patricia Oakley, Chapter nine, The use
• 55:32
  Speaker 1: of sewing cards. When you go for holidays, perhaps your
• 55:39
  Speaker 1: friends will ask you what is the use of sewing
• 55:42
  Speaker 1: curves on cards? I should like you to know exactly
• 55:47
  Speaker 1: what to say. The use of the single sewing cards
• 55:53
  Speaker 1: is to provide children in the kindergarten with the means
• 55:56
  Speaker 1: of finding out the exact nature of the relation between
• 55:59
  Speaker 1: one dimension and two. There is another set of sewing
• 56:05
  Speaker 1: cards which is made by laying two cards side by
• 56:08
  Speaker 1: side on the table and pasting a tape over the
• 56:11
  Speaker 1: crack between them. This tape forms a hinge. You can
• 56:16
  Speaker 1: lay one card flat and stand the other edgewise upright
• 56:20
  Speaker 1: and lace patterns between them from one to the other.
• 56:25
  Speaker 1: The use of this part of the method is to
• 56:28
  Speaker 1: provide girls in the higher forms with a means of
• 56:31
  Speaker 1: learning the relation between two dimensions and three. There is
• 56:37
  Speaker 1: another set of models, the use of which is to
• 56:40
  Speaker 1: provide people who have left school with a means of
• 56:43
  Speaker 1: learning the relation between three dimensions and four. The use
• 56:48
  Speaker 1: of the books, which are signed George Boole or Mary Everstpool,
• 56:53
  Speaker 1: is to provide reasonable people who have learned the logic
• 56:57
  Speaker 1: of algebra conscientiously, with the means of teaching themselves the
• 57:01
  Speaker 1: relations between n dimensions and n plus one dimensions, whatever
• 57:07
  Speaker 1: number ND may be. The above is a quite accurate
• 57:11
  Speaker 1: account of the real Bull method. As much as there
• 57:15
  Speaker 1: is any need for you to know while you are
• 57:17
  Speaker 1: at school, I should feel grateful to you if you
• 57:21
  Speaker 1: will each copy it out in a clear handwriting, and
• 57:25
  Speaker 1: keep it by you and take it home whenever you
• 57:28
  Speaker 1: go away from school for the holidays. It would be
• 57:32
  Speaker 1: all the better if you learned it by heart. And
• 57:36
  Speaker 1: now I will tell you why I am so anxious
• 57:38
  Speaker 1: about this. The Bull method is a conveyance which will
• 57:44
  Speaker 1: take you safely to wherever the great Unknown directs you
• 57:47
  Speaker 1: to go. Some people mistake it for the carpet in
• 57:51
  Speaker 1: the Arabian Nights, which took whoever stepped on it wherever
• 57:55
  Speaker 1: he or she wished to go. Which is quite a
• 57:58
  Speaker 1: different thing. The true Bull method depends essentially on making
• 58:03
  Speaker 1: a right use of imaginary hypotheses. The magic carpet depends
• 58:09
  Speaker 1: for its efficacy on making a wrong use of imaginary hypotheses.
• 58:15
  Speaker 1: People get to very queer places on that carpet. I
• 58:19
  Speaker 1: have been for several excursions on it, so I know.
• 58:24
  Speaker 1: One of the places it can take you to is
• 58:26
  Speaker 1: a town where all the front doors open onto a
• 58:29
  Speaker 1: street very like Regent Street, with the most gorgeous millinery,
• 58:34
  Speaker 1: jewelry and fruits in shop windows, and all the back
• 58:38
  Speaker 1: doors open to wild country where blue roses, black tulips,
• 58:43
  Speaker 1: and the fattest double carnations of all colors, including green ones,
• 58:48
  Speaker 1: grow wild in the hedges and fields, and where all
• 58:51
  Speaker 1: the pigs have wings. Another place that it can take
• 58:55
  Speaker 1: you to is one where pigs can wallow in all
• 58:57
  Speaker 1: the filth they like without soiling their wings, and moths
• 59:01
  Speaker 1: fly into candles without singing theirs. The carpet will take
• 59:06
  Speaker 1: you straight to whatever place you wish to go. It
• 59:10
  Speaker 1: is by no means warranted to take you safely back
• 59:15
  Speaker 1: the advantage of Bull's method is that it is warranted
• 59:19
  Speaker 1: to bring you safe down somewhere on solid earth, not
• 59:23
  Speaker 1: always the exact place you started from, but a safe
• 59:26
  Speaker 1: and clean place of some kind. And to deposit you
• 59:30
  Speaker 1: study on your feet with a compass in your pocket,
• 59:32
  Speaker 1: which will show you a straight way home. End of
• 59:37
  Speaker 1: chapter nine. Philosophy and Fun of Algebra by Mary Everspool
• 59:47
  Speaker 1: read for LibriVox dot org by Patricia Oakley. Chapter ten
• 59:52
  Speaker 1: the story of a working hypothesis. In an old Hebrew book,
• 59:59
  Speaker 1: there is a story of a person named Jacob, which
• 1:00:02
  Speaker 1: means the supplanter. If you want to know why, you
• 1:00:06
  Speaker 1: had better read the story for yourself someday. It is
• 1:00:09
  Speaker 1: not entirely a pretty story, but it is very instructive.
• 1:00:14
  Speaker 1: Jacob had a dream in which he saw angels coming
• 1:00:18
  Speaker 1: down a ladder. It would be a very profitable exercise
• 1:00:23
  Speaker 1: of your imagination to ask yourselves why this particular patriarch
• 1:00:28
  Speaker 1: saw angels on a ladder, whereas so many other Hebrews
• 1:00:32
  Speaker 1: saw them in clouds, or flying down on wings, or
• 1:00:36
  Speaker 1: mixed up with flames and other romantic, pretty moving things.
• 1:00:42
  Speaker 1: Jacob had another dream and saw an angel who wrestled
• 1:00:46
  Speaker 1: with him and apparently left him with sciatica for life,
• 1:00:50
  Speaker 1: which is not surprising for he had been sleeping out
• 1:00:53
  Speaker 1: of doors on bare ground, just when he had been
• 1:00:56
  Speaker 1: wrestling with very serious difficulties caused by his own dishonor tricks.
• 1:01:02
  Speaker 1: At such times, as I told you before, people had
• 1:01:05
  Speaker 1: better be a little extra careful not to catch cold,
• 1:01:08
  Speaker 1: because colds caught under such conditions are rather prone to
• 1:01:12
  Speaker 1: leave unpleasant traces which last a long time, and sometimes
• 1:01:16
  Speaker 1: all one's life. Well, the angel who gave Jacob Sciatica
• 1:01:23
  Speaker 1: gave him something else, a new name. Why did he
• 1:01:27
  Speaker 1: give him a new name? Taking a new name was
• 1:01:30
  Speaker 1: an ancient ceremony which meant entering a new service. Sixty
• 1:01:35
  Speaker 1: years ago, servants in Devonshire were called by their employer's name.
• 1:01:40
  Speaker 1: A gardener would have two names, his own, which he
• 1:01:43
  Speaker 1: got from his father and his masters. I have even
• 1:01:48
  Speaker 1: heard dogs called by their master's names, for instance Toby
• 1:01:52
  Speaker 1: Smith or Ponto Jones. You will often notice in old
• 1:01:58
  Speaker 1: books that when people were converted, that is to say,
• 1:02:03
  Speaker 1: when they either took up a new religion or turned
• 1:02:06
  Speaker 1: from bad ways to good ones, the people who persuaded
• 1:02:09
  Speaker 1: them to be converted gave them a new name, very
• 1:02:13
  Speaker 1: often the teacher's own name. While the angel who wrestled
• 1:02:17
  Speaker 1: with Jacob appears to have converted him. He seems to
• 1:02:21
  Speaker 1: have persuaded Jacob that there are other ways of getting
• 1:02:24
  Speaker 1: on in the world and promoting the fortunes of one's
• 1:02:27
  Speaker 1: children and grandchildren, besides cheating everybody, including one's own nearest relations. Therefore,
• 1:02:35
  Speaker 1: Jacob was not to be called the supplanter anymore. His
• 1:02:39
  Speaker 1: new name was to be Israel. Jacob's descendants are called Hebrews,
• 1:02:46
  Speaker 1: and also the people of Israel. Israel was the new
• 1:02:51
  Speaker 1: name which Jacob got when he turned from cheating to
• 1:02:53
  Speaker 1: a better way of getting on in life. What was
• 1:02:58
  Speaker 1: that better way? That is our ex our first unknown?
• 1:03:04
  Speaker 1: What does the word Israel mean? That is our why?
• 1:03:09
  Speaker 1: Our second unknown? I may as well tell you at
• 1:03:13
  Speaker 1: once that, so far as I am concerned, why remains unknown.
• 1:03:19
  Speaker 1: I want you to take notice that I do not
• 1:03:22
  Speaker 1: know what the word Israel means. But some twenty years
• 1:03:26
  Speaker 1: ago my imagination supplied me with a working hypothesis. Suppose
• 1:03:32
  Speaker 1: Israel meant rhythm. Now, if I had gone telling people
• 1:03:38
  Speaker 1: that Israel means rhythm, I should have been contradicted and
• 1:03:42
  Speaker 1: laughed at and told that I had no proof of
• 1:03:45
  Speaker 1: what I said, and was talking of what I knew
• 1:03:47
  Speaker 1: nothing about, and whoever said so would have been perfectly right.
• 1:03:53
  Speaker 1: I should have been cheating myself and getting into bad,
• 1:03:55
  Speaker 1: slipshod habits. What I did was to post up inside
• 1:04:01
  Speaker 1: my brain as working hypothesis. Suppose Israel means rhythm. What
• 1:04:07
  Speaker 1: would be the consequence of that hypothesis? Then I read
• 1:04:13
  Speaker 1: through old books of the Hebrews, putting in my mind
• 1:04:16
  Speaker 1: the word rhythm whenever I found the word Israel and
• 1:04:21
  Speaker 1: the people of rhythm instead of the people of Israel.
• 1:04:26
  Speaker 1: In the stories that are told about Jacob and his
• 1:04:28
  Speaker 1: grandfather Abraham, the angels are represented as telling the two
• 1:04:33
  Speaker 1: men that if they would obey the angels, not only
• 1:04:37
  Speaker 1: they themselves would be blessed, but all their descendants would
• 1:04:40
  Speaker 1: be blessed too, and be made at last the means
• 1:04:44
  Speaker 1: of conferring a great blessing on all the world. Moses
• 1:04:50
  Speaker 1: warned them that if they did not obey their own
• 1:04:53
  Speaker 1: special angels, some special trouble would come to them. My
• 1:04:58
  Speaker 1: imaginations ad justed to me that perhaps getting into the
• 1:05:02
  Speaker 1: swing of rhythmic beats is good for all people, but
• 1:05:07
  Speaker 1: more good for the people of Israel than for anybody else,
• 1:05:11
  Speaker 1: and that wandering off into irregular, unrhythmic freaks is more
• 1:05:15
  Speaker 1: bad for the people of Israel than for anybody else. This, again,
• 1:05:21
  Speaker 1: you will observe, is purely imaginary hypothesis. I had not
• 1:05:27
  Speaker 1: the faintest warrant for saying anything of the kind. Therefore
• 1:05:31
  Speaker 1: I did not say it. But I experimented at treating
• 1:05:35
  Speaker 1: my Hebrew friends and acquaintances as if they were natural
• 1:05:40
  Speaker 1: born ministers or servants of the principle of rhythmic beat,
• 1:05:45
  Speaker 1: as if it was their business to introduce respect for
• 1:05:49
  Speaker 1: rhythm and an orderly arrangement of time into the general
• 1:05:53
  Speaker 1: morals of the world, and as if they would, of
• 1:05:57
  Speaker 1: course become degraded more than other people if they allowed
• 1:06:01
  Speaker 1: themselves to drift into being irregular and disorderly. Now you
• 1:06:06
  Speaker 1: will observe that though all this was purely imaginary hypothesis,
• 1:06:11
  Speaker 1: it was of a harmless kind. There is nothing contrary
• 1:06:15
  Speaker 1: to the Ten Commandments or to any other register of
• 1:06:18
  Speaker 1: safe rules in treating one's Hebrew acquaintance as if one
• 1:06:22
  Speaker 1: expected them to be more orderly as to time than
• 1:06:26
  Speaker 1: other people. The registered rules allowed me to consider this
• 1:06:31
  Speaker 1: a safe road, and my imagination showed me that it
• 1:06:34
  Speaker 1: was one along which I could travel quickly. Therefore I
• 1:06:38
  Speaker 1: started to go along it and waited to see where
• 1:06:41
  Speaker 1: I got to. One consequence which came was that some
• 1:06:45
  Speaker 1: of the people of Israel began telling me that I
• 1:06:48
  Speaker 1: seemed to know things about their old books, even some
• 1:06:52
  Speaker 1: old books that I had never read, which they themselves
• 1:06:55
  Speaker 1: had never observed before I had enabled them to get
• 1:07:00
  Speaker 1: at real values for the exes and ys of some
• 1:07:03
  Speaker 1: of their problems. Please notice that all this is pure
• 1:07:09
  Speaker 1: imaginary hypothesis. Ancient peoples made a hypothesis for which they
• 1:07:14
  Speaker 1: had no authority about angels, and I made one for
• 1:07:19
  Speaker 1: which I had no authority about some of those supposed angels.
• 1:07:23
  Speaker 1: And by dealing logically with these imaginations, we got to
• 1:07:27
  Speaker 1: some very real knowledge. End of chapter ten. Philosophy and
• 1:07:37
  Speaker 1: Fun of Algebra by Mary Everest Bull read for librovox
• 1:07:41
  Speaker 1: dot Org by Patricia Oakley, Chapter eleven, Macbeth's mistake. The
• 1:07:50
  Speaker 1: whole question of choosing one's next working hypothesis has been
• 1:07:53
  Speaker 1: fogged owing to people's neglect of a very simple principle.
• 1:07:59
  Speaker 1: Suppose you are bicycling in a strange place. You come
• 1:08:03
  Speaker 1: to a bit of smooth, good road which is either
• 1:08:06
  Speaker 1: flat or goes very gently downhill, and presently curves in
• 1:08:10
  Speaker 1: a nice, big easy sweep round a bit of wood
• 1:08:14
  Speaker 1: or a cliff, so that you cannot see far along it.
• 1:08:18
  Speaker 1: What you know at once is that you can, if
• 1:08:22
  Speaker 1: you choose, get up great speed without over much exertion.
• 1:08:27
  Speaker 1: This is obvious and needs no discussion. The question you
• 1:08:32
  Speaker 1: have to settle is shall you choose to do it?
• 1:08:37
  Speaker 1: If you have heard the whole road spoken of in
• 1:08:40
  Speaker 1: general terms as a nice, safe one to go on,
• 1:08:44
  Speaker 1: you probably do choose to make use of the specially
• 1:08:47
  Speaker 1: easy bit of the road to get up a lively spin.
• 1:08:52
  Speaker 1: But supposing that at the beginning of the gentle slope
• 1:08:56
  Speaker 1: down you come upon a noticeboard with an inscription go
• 1:09:01
  Speaker 1: slowly or dangerous to cyclists, I hope you would have
• 1:09:07
  Speaker 1: sense enough not to think, what do these old fogies
• 1:09:11
  Speaker 1: know about the needs of the young generation. I have
• 1:09:14
  Speaker 1: a right to go fast if I choose, and I
• 1:09:16
  Speaker 1: shall have my jolly spin in spite of them. Nor
• 1:09:21
  Speaker 1: would you say I can't take care of myself, and
• 1:09:24
  Speaker 1: if I run into somebody else, that is his lookout.
• 1:09:29
  Speaker 1: If you are an experienced cyclist, you would keep on
• 1:09:32
  Speaker 1: your seat and go cautiously. If you are still a
• 1:09:36
  Speaker 1: very inexperienced one, it would be wise to get off
• 1:09:39
  Speaker 1: your cycle and not mount again till you have come
• 1:09:42
  Speaker 1: to the curve, gone round it, and seen what is beyond.
• 1:09:48
  Speaker 1: The notice board is not an actual prohibition to go
• 1:09:51
  Speaker 1: along the King's Highway if you choose. The people who
• 1:09:54
  Speaker 1: put up the board have no authority over you, but
• 1:09:58
  Speaker 1: your own instincts of self preservation, and I hope also
• 1:10:02
  Speaker 1: your instinct of loyalty and good comradeship with the possible
• 1:10:06
  Speaker 1: other cyclist who may be at the bottom of the
• 1:10:08
  Speaker 1: hill would suggest to you not to throw away the
• 1:10:11
  Speaker 1: guardianship of a caution from those who know more than
• 1:10:14
  Speaker 1: you do about the road. Having given you this general
• 1:10:18
  Speaker 1: indication of the principle which I am trying to explain,
• 1:10:21
  Speaker 1: we will go back to the question of an imaginary
• 1:10:24
  Speaker 1: working hypothesis. My imagination, as I told you, showed me
• 1:10:30
  Speaker 1: that my mind would travel quickly and easily along the
• 1:10:33
  Speaker 1: road opened up by supposing that Israel means rhythm. Looking
• 1:10:38
  Speaker 1: back in my memory, I could not find the smallest
• 1:10:41
  Speaker 1: indication that anybody had either come to grieve himself or
• 1:10:45
  Speaker 1: offended any Hebrew person by behaving as if the people
• 1:10:48
  Speaker 1: of Israel were the people of rhythm, and there is
• 1:10:51
  Speaker 1: nothing in the Ten Commandments to suggest that there is
• 1:10:54
  Speaker 1: any harm in doing so. So I started off on
• 1:10:57
  Speaker 1: a glorious, easy, rapid spin, and arrived without any mishap
• 1:11:02
  Speaker 1: at several very interesting bits of scenery. Now let us
• 1:11:06
  Speaker 1: take the case of the old Scotch legend of Macbeth.
• 1:11:10
  Speaker 1: As told by Shakespeare. Macbeth and his wife appear to
• 1:11:14
  Speaker 1: have been at first very well intentioned, good people, as
• 1:11:19
  Speaker 1: human beings go, better than most people, and enormously better
• 1:11:23
  Speaker 1: than Jacob, or his mother, or his uncle or most
• 1:11:27
  Speaker 1: of the people belonging to him. Macbeth was a brilliant
• 1:11:31
  Speaker 1: and successful soldier. His imagination suggested to him that he
• 1:11:36
  Speaker 1: had it in him to rise rapidly to fortune and power.
• 1:11:41
  Speaker 1: He might have become the Fane of Cowdor, and some
• 1:11:44
  Speaker 1: day even king of Scotland. His imagination was so vivid
• 1:11:49
  Speaker 1: that he pictured three old women going through some heathen
• 1:11:53
  Speaker 1: incantation and predicting to him that he would be the
• 1:11:57
  Speaker 1: Fiane of Cowdor and king. Here was a road open
• 1:12:02
  Speaker 1: along which it was quite sure that his mind would
• 1:12:05
  Speaker 1: travel easily if he would let it do so. The
• 1:12:09
  Speaker 1: question was should he let it go along that road?
• 1:12:14
  Speaker 1: Now there were living at the time a Thign of
• 1:12:17
  Speaker 1: Cowder and a King of Scotland. While they lived, he
• 1:12:22
  Speaker 1: could not be either. The commandments say thou shalt not
• 1:12:26
  Speaker 1: covet thy neighbor's goods. Here was a danger signal. If
• 1:12:31
  Speaker 1: Macbeth had known as much as Shakespeare knew about the
• 1:12:35
  Speaker 1: art of sound thinking, he would immediately have said to himself,
• 1:12:40
  Speaker 1: Howder and King are the roads that I have better
• 1:12:43
  Speaker 1: not travel along just now, for fear the wheels of
• 1:12:46
  Speaker 1: my mind should get too much way on and carry
• 1:12:49
  Speaker 1: me into danger. But Macbeth had either not learned algebra
• 1:12:55
  Speaker 1: at school, or if he had, he had crammed it
• 1:12:59
  Speaker 1: up for examination out of a textbook and not learned
• 1:13:02
  Speaker 1: it as the science of the laws of thought. Another day,
• 1:13:07
  Speaker 1: his imagination showed him a dagger. A dagger is a
• 1:13:11
  Speaker 1: thing to kill people with. As a soldier, he had
• 1:13:15
  Speaker 1: probably used a real one in war. But if he
• 1:13:20
  Speaker 1: had any proper nerve training, he would have known that.
• 1:13:24
  Speaker 1: When his imagination was so vivid that he did not
• 1:13:27
  Speaker 1: for the moment know an imaginary dagger from a real one,
• 1:13:31
  Speaker 1: he ought immediately to go slack and lie down and
• 1:13:35
  Speaker 1: think about the moors or the sky, or about anything
• 1:13:39
  Speaker 1: or anybody that was not connected with doing anything, in
• 1:13:42
  Speaker 1: particular with planning anything, with taking any resolution, and especially
• 1:13:47
  Speaker 1: with breaking any of the ten commandments. He had already
• 1:13:51
  Speaker 1: told his wife about the three old women. If she
• 1:13:55
  Speaker 1: had been a sensible woman, she would have told him
• 1:13:57
  Speaker 1: that she wanted to go away from home, and got
• 1:14:00
  Speaker 1: him to take her right away for a few weeks,
• 1:14:02
  Speaker 1: and kept him busy and amuse in thinking of other
• 1:14:05
  Speaker 1: things till he left off seeing things that were not there.
• 1:14:10
  Speaker 1: But neither Macbeth nor his wife knew as much as
• 1:14:13
  Speaker 1: Shakespeare did about the value of danger signals and the
• 1:14:17
  Speaker 1: conditions for making a safe working hypothesis. You had better
• 1:14:22
  Speaker 1: read the story of Macbeth and see for yourselves what
• 1:14:25
  Speaker 1: they did do. Next to the old Hebrew books, Shakespeare
• 1:14:30
  Speaker 1: is the best road map that I know of for
• 1:14:32
  Speaker 1: people who wish to travel safely about the country of
• 1:14:34
  Speaker 1: the imagination. End of chapter eleven. Philosophy and Fun of
• 1:14:43
  Speaker 1: Algebra by Mary Evers Boole read for LibriVox dot Org
• 1:14:47
  Speaker 1: by Patricia Oakley, Chapter twelve. Jacob's Ladder in chapter ten
• 1:14:55
  Speaker 1: I set you children a question, why did Jacob's angels
• 1:14:59
  Speaker 1: come down a ladder, whereas other Hebrews saw angels mixed
• 1:15:03
  Speaker 1: up with romantic pretty things such as wings and clouds.
• 1:15:08
  Speaker 1: I hope some of you have made a guess before now,
• 1:15:11
  Speaker 1: but some are not good at guessing. I will tell
• 1:15:15
  Speaker 1: you what may help you to find out. If a
• 1:15:19
  Speaker 1: bird wants to go up and down from the roof
• 1:15:22
  Speaker 1: to the garden, it trusts to its wings, A man
• 1:15:26
  Speaker 1: has to use a ladder step step step. If a
• 1:15:32
  Speaker 1: bird is not fully fledged or has a broken wing,
• 1:15:36
  Speaker 1: it has to find something more or less like a
• 1:15:38
  Speaker 1: ladder and go up and down bit by bit, hop
• 1:15:43
  Speaker 1: hop hop. If an artist wishes to draw parabola, he
• 1:15:50
  Speaker 1: does it freehand. That is to say, he just draws
• 1:15:53
  Speaker 1: the curve. He does not take all the trouble which
• 1:15:56
  Speaker 1: Missus Somerville's book makes little children take, getting the curve
• 1:16:00
  Speaker 1: step by step by the method of finite differences. Jacob
• 1:16:06
  Speaker 1: wished to be rich. Some angel, but a very bad
• 1:16:11
  Speaker 1: one inspired him with an idea of getting rich in
• 1:16:14
  Speaker 1: one big sweep by cheating his father and brother. By
• 1:16:19
  Speaker 1: wanting to do things in that sort of quick, easy way.
• 1:16:23
  Speaker 1: When he did not yet know how to do things
• 1:16:26
  Speaker 1: both quickly and rightly. He got into terrible trouble and
• 1:16:30
  Speaker 1: had to leave his country. Now I suppose that the
• 1:16:34
  Speaker 1: angels who converted him meant to say something like this.
• 1:16:39
  Speaker 1: It is all very well for good, holy god fearing
• 1:16:42
  Speaker 1: men like your father and grandfather to go where they
• 1:16:46
  Speaker 1: are taken by angels who can move about on wings.
• 1:16:50
  Speaker 1: But you are at present a stupid, clumsy person. Your
• 1:16:54
  Speaker 1: wings have not grown yet, or you have broken them
• 1:16:57
  Speaker 1: by being covetous. We are going to show you how
• 1:17:01
  Speaker 1: you should go about step step step, Have patience and
• 1:17:07
  Speaker 1: take pains, and don't go about on magic carpets. End
• 1:17:13
  Speaker 1: of chapter twelve. Philosophy and Fun of Algebra by Mary
• 1:17:19
  Speaker 1: Everspool Read for LibriVox dot org by Patricia Oakley, Chapter thirteen,
• 1:17:26
  Speaker 1: The Great ex of the World. A great question which
• 1:17:31
  Speaker 1: people like to quarrel about is who or what made
• 1:17:35
  Speaker 1: things be as they are. As soon as people grew
• 1:17:38
  Speaker 1: clever enough to think about anything except scrambling for food
• 1:17:42
  Speaker 1: and taking care of their own babies, they began quarreling
• 1:17:45
  Speaker 1: about who or what made things be. Nobody knew anything
• 1:17:49
  Speaker 1: about it, and most people had a great deal to
• 1:17:52
  Speaker 1: say about it. Moses saw that there was no hope
• 1:17:56
  Speaker 1: of getting a country orderly while all this confusion was
• 1:17:59
  Speaker 1: going on. So he said to the Hebrews, I must
• 1:18:03
  Speaker 1: not allow all this confusion to go on among a
• 1:18:06
  Speaker 1: people that I Am made responsible for. None of us
• 1:18:09
  Speaker 1: have ever seen the maker of things. We can see
• 1:18:12
  Speaker 1: things growing, but not the force that makes them. That
• 1:18:17
  Speaker 1: is our ex are unknown. We are going to begin
• 1:18:21
  Speaker 1: by stating that we don't know. We are going to
• 1:18:24
  Speaker 1: call the maker of things I Am, or that which is,
• 1:18:29
  Speaker 1: whatever it is, and we are going to make two
• 1:18:32
  Speaker 1: hypotheses to start with. We are going to try thinking
• 1:18:36
  Speaker 1: of I AM as unity one and not several or
• 1:18:40
  Speaker 1: a fraction. We will also try thinking of I AM
• 1:18:44
  Speaker 1: as no thing. We are not going to suppose at
• 1:18:48
  Speaker 1: present that any particular kind of thing made the rest.
• 1:18:53
  Speaker 1: We will suppose that I AM is not a thing.
• 1:18:57
  Speaker 1: When we find that any particular proceeding or be behavior
• 1:19:00
  Speaker 1: destroys men or makes them too sickly or weak, or
• 1:19:03
  Speaker 1: stupid or quarrelsome to manage other creatures and keep the
• 1:19:07
  Speaker 1: upper hand of the world, we will say, for short,
• 1:19:10
  Speaker 1: that I AM does not like or does not intend
• 1:19:14
  Speaker 1: the people of Israel to go on with that kind
• 1:19:17
  Speaker 1: of preceding or behavior. Now, these two hypotheses are as
• 1:19:23
  Speaker 1: much as we can deal with for the present. Anybody
• 1:19:26
  Speaker 1: who wants to think out other hypotheses than those will
• 1:19:30
  Speaker 1: have to think to himself or go out of the
• 1:19:32
  Speaker 1: country that I Am to manage. Now we will arrange
• 1:19:36
  Speaker 1: all the facts that we know round the statement of
• 1:19:39
  Speaker 1: our own ignorance, and then try our hypotheses on them.
• 1:19:44
  Speaker 1: We know that eating the flesh of certain uncleanly animals
• 1:19:47
  Speaker 1: gives people certain diseases. We will say for short, i
• 1:19:52
  Speaker 1: Am does not intend the Hebrews to eat the flesh
• 1:19:55
  Speaker 1: of these animals. We know that if people are dirty
• 1:19:59
  Speaker 1: in their house habits, and careless in preparing their food
• 1:20:02
  Speaker 1: and in washing their hands before they touch food, they
• 1:20:05
  Speaker 1: get fevers. We will suppose that i Am does not
• 1:20:09
  Speaker 1: intend the people of Israel to be dirty in their habits.
• 1:20:13
  Speaker 1: We know that if people burn things, the smoke of
• 1:20:16
  Speaker 1: which makes them drunk and silly, they manage their affairs
• 1:20:19
  Speaker 1: badly and make mistakes, and do not grow their crops properly,
• 1:20:23
  Speaker 1: and are not ready to fight when enemies attack them.
• 1:20:27
  Speaker 1: The people in neighboring countries say that the maker of
• 1:20:29
  Speaker 1: things likes or dislikes to smell the smoke of these drugs.
• 1:20:33
  Speaker 1: They know no more than we do what he likes
• 1:20:36
  Speaker 1: to smell. But we are going to suppose that I
• 1:20:39
  Speaker 1: Am does not like us to smell them. The Hebrews
• 1:20:44
  Speaker 1: never found out what I Am is. But those who
• 1:20:48
  Speaker 1: stuck loyally by the hypotheses of Moses and refuse to
• 1:20:52
  Speaker 1: be distracted from the matter in hand or to talk
• 1:20:55
  Speaker 1: about anything except the experiment which they were trying, found
• 1:20:59
  Speaker 1: out several things were very useful to them, for instance,
• 1:21:03
  Speaker 1: about weather and electricity of the atmosphere, or how to
• 1:21:06
  Speaker 1: take care of their health, and how to use their
• 1:21:08
  Speaker 1: imagination to supply them with working hypotheses for a variety
• 1:21:12
  Speaker 1: of sciences, and how to use their dreams to show
• 1:21:15
  Speaker 1: them where they had been making mistakes and spoiling their brains.
• 1:21:19
  Speaker 1: Whereas the people who would insist on shouting and arguing
• 1:21:23
  Speaker 1: and quarreling about things which were only wild guesses got
• 1:21:27
  Speaker 1: on very slowly with learning science. End of chapter thirteen.
• 1:21:35
  Speaker 1: Philosophy and Fun of Algebra by Mary Everspool read for
• 1:21:39
  Speaker 1: libravox dot Org by Patricia Oakley, Chapter fourteen, Go Out
• 1:21:46
  Speaker 1: of my classroom. A story is told of one of
• 1:21:51
  Speaker 1: the orderly pupils of Mosaism who got to know a
• 1:21:55
  Speaker 1: good deal about weather and electricity, And at last he
• 1:21:59
  Speaker 1: got out of patience with the people who wanted to
• 1:22:01
  Speaker 1: shout and argue, and he said to them, what is
• 1:22:06
  Speaker 1: the good of all this arguing backwards and forwards about
• 1:22:09
  Speaker 1: things that we do not know and cannot settle. Let
• 1:22:13
  Speaker 1: us try a fair experiment. You go on shouting and
• 1:22:16
  Speaker 1: doing whatever you think the unseen powers like, and I
• 1:22:20
  Speaker 1: will do what I think will get them to do
• 1:22:23
  Speaker 1: what I like. And let us agree that whichever of
• 1:22:27
  Speaker 1: us can draw a spark out of a thundercloud shall
• 1:22:30
  Speaker 1: be considered to know most about how to come to
• 1:22:32
  Speaker 1: an understanding with I am. So the other people shouted
• 1:22:37
  Speaker 1: and jumped about and cut themselves with knives, because they
• 1:22:40
  Speaker 1: had taken it into their heads to imagine that the
• 1:22:43
  Speaker 1: maker of things like to see that kind of behavior.
• 1:22:46
  Speaker 1: Why they thought so, I cannot conceive. But there is
• 1:22:49
  Speaker 1: no end to the rubbish that people get to think
• 1:22:52
  Speaker 1: when they argue about what X is. Instead of trying
• 1:22:55
  Speaker 1: hypotheses in an orderly manner, the unknown powers let them
• 1:23:01
  Speaker 1: shout all day long, and then Elijah got a spark
• 1:23:04
  Speaker 1: out of a thundercloud. The same sort of thing happened
• 1:23:08
  Speaker 1: again about one hundred and fifty years ago. Various sorts
• 1:23:12
  Speaker 1: of priests were shouting and arguing about what I AM
• 1:23:15
  Speaker 1: wished people to believe and to think. And then Benjamin
• 1:23:19
  Speaker 1: Franklin and his friends, who had not been mixing up
• 1:23:22
  Speaker 1: with the arguments or making wild guesses, but quildly experimenting
• 1:23:26
  Speaker 1: and dealing logically with the fact of their own ignorance,
• 1:23:29
  Speaker 1: sent up a kite into a thundercloud and got a
• 1:23:32
  Speaker 1: spark down. And the consequence of that is that all
• 1:23:35
  Speaker 1: kinds of people say what a wonderful man Benjamin Franklin was,
• 1:23:40
  Speaker 1: and all sorts of people are able to ride about
• 1:23:42
  Speaker 1: in electric trams. But the curious part of the matter
• 1:23:47
  Speaker 1: is that many people use electric trams to go to
• 1:23:49
  Speaker 1: meetings on purpose to shout and argue and make wild
• 1:23:54
  Speaker 1: guesses about things they know nothing about. However, what they
• 1:23:59
  Speaker 1: choose to do is not our business. You are living
• 1:24:03
  Speaker 1: in an orderly school, and of course you do not
• 1:24:06
  Speaker 1: argue about things you know nothing about. Let us go
• 1:24:10
  Speaker 1: back to our Hebrew electrician. He had shown the people
• 1:24:14
  Speaker 1: of Israel. What comes of sticking peaceably to one's working hypothesis.
• 1:24:21
  Speaker 1: If he had been thoroughly logical, he would have gone
• 1:24:24
  Speaker 1: on sticking to it. He would have said, to the
• 1:24:26
  Speaker 1: people of Israel, now you see that I can teach
• 1:24:30
  Speaker 1: you electricity. This land is going to be my classroom.
• 1:24:34
  Speaker 1: Make those shouting people hold their tongues or else go away,
• 1:24:38
  Speaker 1: so that we can go on with our lessons in peace.
• 1:24:41
  Speaker 1: When they want to learn electricity properly, they can come back.
• 1:24:47
  Speaker 1: But he was in too great a hurry to make
• 1:24:50
  Speaker 1: a complete and final settlement. A good teacher sends a noisy,
• 1:24:55
  Speaker 1: troublesome pupil out of his classroom for the time, but
• 1:25:00
  Speaker 1: does not expel her from the school merely for being troublesome.
• 1:25:04
  Speaker 1: The shouting people were among the facts which I Am
• 1:25:07
  Speaker 1: put before Elijah to deal with. He found it necessary
• 1:25:12
  Speaker 1: to eliminate them in order to reduce his data within
• 1:25:14
  Speaker 1: the compass of his power to manage. But he should
• 1:25:17
  Speaker 1: have done it as a provisional necessity. He should have
• 1:25:21
  Speaker 1: arranged his mind on the understanding that the eliminated data
• 1:25:24
  Speaker 1: would have to come back. Instead of that, he used
• 1:25:29
  Speaker 1: his power and signs to kill them and gave way
• 1:25:32
  Speaker 1: to the feeling that they were got rid of and
• 1:25:35
  Speaker 1: done with. And then his mind began to go wrong.
• 1:25:40
  Speaker 1: He lost his nerve, he began to talk nonsense about
• 1:25:44
  Speaker 1: things he knew nothing about, and led a great many
• 1:25:48
  Speaker 1: people into mistakes. End of chapter fourteen. Philosophy and Fun
• 1:25:56
  Speaker 1: of Algebra by Mary Everest Bull read for libravox dot
• 1:26:00
  Speaker 1: org by Patricia Oakley, Chapter fifteen, The square root of
• 1:26:07
  Speaker 1: negative one. When you come to quadratic equations, you will
• 1:26:12
  Speaker 1: be confronted with an entity or nonentity whose name is
• 1:26:16
  Speaker 1: written in this way the square root of negative one
• 1:26:21
  Speaker 1: and pronounced square root of minus one. Many people let
• 1:26:28
  Speaker 1: this nonentity persuade them to foolish courses. A story is
• 1:26:34
  Speaker 1: told of a man at Cambridge who was expected to
• 1:26:37
  Speaker 1: be senior wrangler, but he got thinking about the square
• 1:26:41
  Speaker 1: root of minus one as if it were a reality,
• 1:26:45
  Speaker 1: till he lost his sleep and dreamed that he was
• 1:26:48
  Speaker 1: the square root of minus one and could not extract himself,
• 1:26:52
  Speaker 1: And he became so ill that he could not go
• 1:26:55
  Speaker 1: to his examination at all. Angels and square roots of
• 1:26:59
  Speaker 1: no negative quantities, and the other things that have no
• 1:27:02
  Speaker 1: existence in three dimensions do not come to us to
• 1:27:06
  Speaker 1: gossip about themselves or the place they came from, or
• 1:27:10
  Speaker 1: where they are going to, or where we are going
• 1:27:12
  Speaker 1: to in the far future. They are messengers from the
• 1:27:17
  Speaker 1: as yet unknown, and come to tell us where we
• 1:27:20
  Speaker 1: are to go next, and the shortest road to get there,
• 1:27:24
  Speaker 1: and where we ought not to go. Just at present,
• 1:27:28
  Speaker 1: when square root of minus one comes to you, behave
• 1:27:31
  Speaker 1: reasonably about him. Treat him logically, exactly as if he
• 1:27:35
  Speaker 1: were six or nine. Only always remember to keep well
• 1:27:39
  Speaker 1: in front of you the fact of your own ignorance.
• 1:27:42
  Speaker 1: You may never find out any more about him than
• 1:27:45
  Speaker 1: you know now, But if you treat him sensibly, he
• 1:27:48
  Speaker 1: will tell you plenty of truths about your exes and
• 1:27:51
  Speaker 1: y's and other unknown things. Please don't suppose that I
• 1:27:55
  Speaker 1: have always behaved sensibly to angels. I have often made
• 1:27:59
  Speaker 1: serious mistakes in dealing with them. I have acted in haste,
• 1:28:04
  Speaker 1: and have had plenty of reason to repent at leisure.
• 1:28:08
  Speaker 1: But one thing they have taught me is that we
• 1:28:11
  Speaker 1: need never to be afraid of angels, whether white or black,
• 1:28:15
  Speaker 1: as long as we keep the laws of logic. Another
• 1:28:19
  Speaker 1: thing they have shown me is that angels never really gossip.
• 1:28:24
  Speaker 1: They have often pretended to gossip to me, but I
• 1:28:28
  Speaker 1: have found out afterwards that they have been talking clever
• 1:28:31
  Speaker 1: nonsense in order to test me and prove me, so
• 1:28:35
  Speaker 1: that I might see in what an illogical state of
• 1:28:38
  Speaker 1: mind I have met them. Angels leave real gossip to
• 1:28:42
  Speaker 1: old women who have done their life's work and have
• 1:28:45
  Speaker 1: time to sit at the chimney corner and tell tales
• 1:28:48
  Speaker 1: about their past experiences to their child friends. End of
• 1:28:54
  Speaker 1: chapter fifteen and Fun of Algebra by Mary Everest Boole
• 1:29:03
  Speaker 1: read for librovox dot Org by Patricia Oakley, Chapter sixteen. Infinity.
• 1:29:11
  Speaker 1: You remember the angel who looks like this square root
• 1:29:15
  Speaker 1: of minus one. Now I am going to introduce you
• 1:29:18
  Speaker 1: to another angel. It is called Infinity. When you come
• 1:29:23
  Speaker 1: to it, remember what I told you before. Angels are
• 1:29:28
  Speaker 1: messengers from the great world of the as yet unknown.
• 1:29:32
  Speaker 1: They never gossip about their private affairs or those of
• 1:29:35
  Speaker 1: other angels. They come to tell you either about what
• 1:29:39
  Speaker 1: you are to do next or about something you had
• 1:29:42
  Speaker 1: better not do next. And if you ask them impertinent
• 1:29:46
  Speaker 1: questions about things that do not concern you for the
• 1:29:48
  Speaker 1: time being, they will give you headaches and make your
• 1:29:51
  Speaker 1: head spin. Just to teach you to mind your own business.
• 1:29:57
  Speaker 1: This particular angel always comes with a mess about a
• 1:30:00
  Speaker 1: broken link or a loosened chain. It comes when a
• 1:30:05
  Speaker 1: hypothesis has been fully worked out, to tell you that
• 1:30:09
  Speaker 1: you are now free from the bonds of that hypothesis
• 1:30:12
  Speaker 1: and at liberty to start experimenting on a fresh one.
• 1:30:16
  Speaker 1: But its message is never, you have got out of
• 1:30:19
  Speaker 1: that particular house of bondage, and therefore you may for
• 1:30:23
  Speaker 1: all the rest of your life run riot and eat
• 1:30:26
  Speaker 1: and drink and do whatever you please. Its message always
• 1:30:31
  Speaker 1: is you have outgrown that master. Now you may take
• 1:30:35
  Speaker 1: a holiday and have a fling before you to go
• 1:30:38
  Speaker 1: to a higher class. But just because you are set free,
• 1:30:42
  Speaker 1: look out for danger traps, and mind your ten commandments.
• 1:30:47
  Speaker 1: You will understand Infinity's messages better if you will read
• 1:30:51
  Speaker 1: carefully what is written about it. In chapter fifteen of
• 1:30:54
  Speaker 1: the Logic of Arithmetic, it brought the answer to the
• 1:30:58
  Speaker 1: question many eight children could pass through a schoolroom without
• 1:31:02
  Speaker 1: the apples all being eaten up? Supposing that none of
• 1:31:06
  Speaker 1: the children ate any let us go over that ground again.
• 1:31:12
  Speaker 1: Suppose there is cake on the table, How many children
• 1:31:16
  Speaker 1: can go through the room without the cake being all eaten? Up. Well,
• 1:31:21
  Speaker 1: that depends on two things, the size of the cake
• 1:31:24
  Speaker 1: and the share which each child eats. If the cake
• 1:31:29
  Speaker 1: weighs two pounds and each child eats two ounces, it
• 1:31:33
  Speaker 1: will be all eaten up when sixteen children have gone
• 1:31:36
  Speaker 1: through the room. If the cake weighs only one pound,
• 1:31:40
  Speaker 1: it will be eaten up when eight children have gone
• 1:31:42
  Speaker 1: through the room. But if each child eats only one ounce,
• 1:31:47
  Speaker 1: then again sixteen children will have to go through the
• 1:31:50
  Speaker 1: room before the cake is eaten up. And so on.
• 1:31:54
  Speaker 1: Many questions could be asked, all depending on the size
• 1:31:58
  Speaker 1: of the cake and the size of eating child's share.
• 1:32:02
  Speaker 1: All this time you are tied to a hypothesis that
• 1:32:05
  Speaker 1: the children eat cake more or less. But now suppose
• 1:32:10
  Speaker 1: we are freed from that hypothesis. Suppose no cake is
• 1:32:13
  Speaker 1: given to the children. How many can pass through the
• 1:32:17
  Speaker 1: room before it is all eaten up. The answer to
• 1:32:21
  Speaker 1: that is an infinite number. Infinity does not mean any
• 1:32:26
  Speaker 1: particular number or a very large number. It means a
• 1:32:31
  Speaker 1: loosened chain, a discarded hypothesis, escape from the rule we
• 1:32:36
  Speaker 1: were working under, something else. Not the size of the
• 1:32:40
  Speaker 1: cake determines the number of children. Infinity does not mean
• 1:32:45
  Speaker 1: that there are enough children in the world now to
• 1:32:48
  Speaker 1: go on passing through the room forever, but that the
• 1:32:51
  Speaker 1: number of children who pass through the room, now that
• 1:32:54
  Speaker 1: the share of each child is zero, will have to
• 1:32:57
  Speaker 1: be determined by the number of children that there are
• 1:33:00
  Speaker 1: in the school, or the parish, or wherever it is
• 1:33:03
  Speaker 1: that the children are supposed to come from, and not
• 1:33:07
  Speaker 1: by the size of the cake. The size of the
• 1:33:10
  Speaker 1: cake has no longer anything to do with answering the
• 1:33:13
  Speaker 1: question how many children can pass through the room before
• 1:33:17
  Speaker 1: the cake is all eaten? End of chapter sixteen. Philosophy
• 1:33:26
  Speaker 1: and Fun of Algebra by Mary Everes Bool read for
• 1:33:29
  Speaker 1: libravoxt dot org by Patricia Oakley, Chapter seventeen, From Bondage
• 1:33:36
  Speaker 1: to Freedom. Moses had said from the first that the
• 1:33:42
  Speaker 1: people of Israel would have to think of i Am
• 1:33:45
  Speaker 1: as the deliverer from bondage. But they were not at
• 1:33:49
  Speaker 1: the time when he said it, advanced enough in their
• 1:33:52
  Speaker 1: algebra to understand that idea properly. So he gave them
• 1:33:58
  Speaker 1: as a hypothesis to work on for the time being,
• 1:34:02
  Speaker 1: that i Am did not like the people of Israel
• 1:34:06
  Speaker 1: to eat and drink and smell unwholesome things. He wished
• 1:34:11
  Speaker 1: to make them attend to their own affairs and think
• 1:34:14
  Speaker 1: as little as possible about what was done and thought
• 1:34:18
  Speaker 1: outside of their own land. But after the time of
• 1:34:22
  Speaker 1: Elijah there came a change. A higher kind of algebra
• 1:34:26
  Speaker 1: came into use. Its incarnation was called Isaiah. The imagination
• 1:34:33
  Speaker 1: of the Hebrews broke loose from the hypothesis that I
• 1:34:36
  Speaker 1: Am had wishes and likes about the people of Israel
• 1:34:40
  Speaker 1: different from what was right for all the rest of
• 1:34:43
  Speaker 1: the world. When that hypothesis was taken away, the imagination
• 1:34:49
  Speaker 1: of such people as Isaiah took wings and flew to well,
• 1:34:53
  Speaker 1: we do not know where, but we call it infinity.
• 1:34:57
  Speaker 1: We know nothing about infinity except that it comes when
• 1:35:01
  Speaker 1: a chain is loosened. If you want to understand what
• 1:35:05
  Speaker 1: it was that happened to Isaiah and what infinity means
• 1:35:09
  Speaker 1: in algebra, this is how you can find out. Get
• 1:35:13
  Speaker 1: a bowl and dip up some of the water out
• 1:35:16
  Speaker 1: of a barrel in which a gnat has laid her eggs.
• 1:35:21
  Speaker 1: Little wigglers are born from those eggs. If you watch them,
• 1:35:26
  Speaker 1: you will see that they swim in different positions, some
• 1:35:30
  Speaker 1: with their tails uppermost, some with their heads uppermost. There
• 1:35:35
  Speaker 1: may also be some worms, which do not swim much,
• 1:35:38
  Speaker 1: but wriggle about at the bottom of the bowl. Perhaps
• 1:35:42
  Speaker 1: if we could hear them talking, we should hear them
• 1:35:44
  Speaker 1: quarreling about which was the right position. Some of them
• 1:35:49
  Speaker 1: might be disputing about what would happen to them in
• 1:35:51
  Speaker 1: the future. They might quarrel till the end of the
• 1:35:54
  Speaker 1: world and know no more about it at the end
• 1:35:58
  Speaker 1: than at the beginning. They are all tied by the
• 1:36:02
  Speaker 1: same hypothesis that everybody lives under water. It is a
• 1:36:07
  Speaker 1: very good working hypothesis for them, for if one of
• 1:36:10
  Speaker 1: them got out of the water, it would die. If
• 1:36:14
  Speaker 1: they knew algebra properly, they would understand that water is
• 1:36:18
  Speaker 1: only their present working hypothesis, and that it is quite
• 1:36:22
  Speaker 1: possible that there may be people who live out of it.
• 1:36:25
  Speaker 1: But it is not sure that they do know enough
• 1:36:28
  Speaker 1: algebra to be aware of their own ignorance. If you
• 1:36:32
  Speaker 1: watch them carefully, you will some day see a wiggler
• 1:36:35
  Speaker 1: come out of the water. It has got wings. The
• 1:36:40
  Speaker 1: water hypothesis no longer concerns him. Some link in the
• 1:36:45
  Speaker 1: chain that bound him down to water has opened. He
• 1:36:48
  Speaker 1: is set free. Infinity has come to him. That is
• 1:36:53
  Speaker 1: what happened to Isaiah when he got out of the
• 1:36:56
  Speaker 1: kind of mosaism by which such people such as Josh
• 1:37:00
  Speaker 1: and Samuel were tied down. That is what will happen
• 1:37:04
  Speaker 1: to you if you'll learn your algebra properly, when you
• 1:37:07
  Speaker 1: are no longer tied down to abc and the square
• 1:37:11
  Speaker 1: root of minus one as the values of X, and
• 1:37:15
  Speaker 1: learn to see that the answer to a problem may
• 1:37:18
  Speaker 1: sometimes be x equals infinity. Please notice that if a
• 1:37:24
  Speaker 1: winged gnat fell back into the water, he would die.
• 1:37:28
  Speaker 1: You will find this a good working rule. Whenever anything
• 1:37:32
  Speaker 1: comes near your imagination which calls itself either infinity or
• 1:37:38
  Speaker 1: the liberation from bondage, go slack for a few minutes,
• 1:37:43
  Speaker 1: say over the ten commandments and make a mind picture
• 1:37:46
  Speaker 1: of the gnat grub in the water. Tell yourself that
• 1:37:51
  Speaker 1: his best chance of growing strong wings and being able
• 1:37:54
  Speaker 1: to fly when Infinity comes and calls him to go
• 1:37:57
  Speaker 1: up higher is to stay in the water till the
• 1:38:00
  Speaker 1: wings have grown strong, and work out the water hypothesis
• 1:38:04
  Speaker 1: to its logical conclusion. Then make another mind picture. Then
• 1:38:10
  Speaker 1: nat who has got wings and therefore must not try
• 1:38:13
  Speaker 1: to amuse himself in the water. Please observe there is
• 1:38:19
  Speaker 1: nothing in this rule contrary to any commandment. Moreover, there
• 1:38:24
  Speaker 1: is nothing slavish or degrading in it, nothing in the
• 1:38:27
  Speaker 1: least like giving up your own liberty, or hampering your
• 1:38:30
  Speaker 1: own initiative, or being a slave to past ages, Nothing
• 1:38:35
  Speaker 1: which prevents your being up to date and fit for
• 1:38:38
  Speaker 1: the generation to which you belong. You are not asked
• 1:38:42
  Speaker 1: to have any opinions about it, or to think that
• 1:38:45
  Speaker 1: it is a duty in itself, or to think that
• 1:38:48
  Speaker 1: you are better than other people because you do it,
• 1:38:51
  Speaker 1: or that everyone is wrong who does not do it.
• 1:38:54
  Speaker 1: If you do it, it will be for no reason
• 1:38:57
  Speaker 1: that you know of, except that an old one who
• 1:39:00
  Speaker 1: has been trying to amuse you asks you to do
• 1:39:03
  Speaker 1: it as a token of friendly feeling towards her. End
• 1:39:08
  Speaker 1: of chapter seventeen. Philosophy and fun of Algebra by Mary
• 1:39:14
  Speaker 1: Evers Bool read for librovox dot org by Patricia Oakley,
• 1:39:19
  Speaker 1: Chapter eighteen Appendix. The essential element of algebra, the habitual
• 1:39:26
  Speaker 1: registration of the exact limits of one's knowledge, the incessant
• 1:39:31
  Speaker 1: calling into consciousness of the fact of one's own ignorance,
• 1:39:35
  Speaker 1: is the element which Bulls would be interpreters have left
• 1:39:39
  Speaker 1: out of his method. It is also the element which
• 1:39:43
  Speaker 1: modern theosophy omits in its interpretation of ancient oriental mind science.
• 1:39:49
  Speaker 1: Men who wish to exploit other men fear nothing in
• 1:39:53
  Speaker 1: logic or science accept this element. They fear nothing in earth, heaven,
• 1:39:59
  Speaker 1: or hell, so so much as a public accustomed to
• 1:40:02
  Speaker 1: realize exactly how much has been proved and where its
• 1:40:06
  Speaker 1: own ignorance begins. Exploiters fear this about equally, whether they
• 1:40:12
  Speaker 1: call themselves priests, schoolmasters, college dons, political leaders, or organizers
• 1:40:19
  Speaker 1: of syndicates and trusts. As long as general readers can
• 1:40:24
  Speaker 1: be kept from the habit of registering at every step
• 1:40:27
  Speaker 1: the fact of their own ignorance and the limits of
• 1:40:29
  Speaker 1: their own knowledge, a clever charlatan can deceive them about
• 1:40:33
  Speaker 1: anything he pleases, from pitch and toss to manslaughter, from
• 1:40:37
  Speaker 1: zero to infinity, from the contents of a meetin to
• 1:40:41
  Speaker 1: the contents of an engineer's report, from the interpretation of
• 1:40:44
  Speaker 1: a bill before Parliament to the interpretation of Isaiah. Once
• 1:40:49
  Speaker 1: get any fair proportion of the public into the steady
• 1:40:53
  Speaker 1: habit of algebraizing ignorance, and you will have done much
• 1:40:57
  Speaker 1: towards reducing all kinds of parasitic creeped to the alternative
• 1:41:01
  Speaker 1: of starvation, suicide, or earning their own living by rendering
• 1:41:06
  Speaker 1: some kind of real service to the organism which supports them.
• 1:41:12
  Speaker 1: End of Philosophy and fun of Algebra by Mary Everestpool