Mary Everest Boole

“ I wish to call your attention to the fact that even in this world there is a good deal of mathematical certainty to be had by whosoever has endless patience, scrupulous accuracy in stating his own ignorance, reverence for the As-Yet-Unknown, and perfect fearlessness in meeting the reductio ad absurdum. ”

“ Above all, be very careful, while the imaginative fit is on, to avoid letting the subject as to which your imagination is stirred become the object of either fun, vanity, or gossip. The vision which you see may quite harmlessly and legitimately become a source of fun to yourself and your friends at some future time, but take care never to gossip or joke about it until it has passed from the condition of imaginative vision to that of working hypothesis. ”

“ What a wise baby knows is that he cannot tell, by the mere look of a tea-pot, whether it is hot or cold. The fact that is most prominent in his mind when he sees a tea-pot is the fact that he does not know whether it is hot or cold. ”

“ When square root of minus one comes to you, behave reasonably about him. Treat him logically, exactly as if he were six or nine; only always remember to keep well in front of you the fact of your own ignorance. ”

“ But Macbeth had either not learnt algebra at school, or, if he had, he had only crammed it up for examination out of a text-book, and not learned it as the Science of the Laws of Thought.
Another day his imagination showed him a dagger. A dagger is a thing to kill people with. As a soldier, he had probably used a real one in war. But, if he had had any proper nerve training, he would have known that when his imagination was so vivid that he did not, for the moment, know an imaginary dagger from a real one, he ought immediately to "go slack" ”

“ Always remember that the use of algebra is to free people from bondage. For instance, in the case of number: Children do their numeration, their "carrying," in tens, because primitive man had nothing to do sums with but his ten fingers.
Many children grow superstitious, and think that you cannot carry except in tens; or that it is wrong to carry in anything but tens. The use of algebra is to free them from bondage to all this superstitious nonsense, and help them to see that the numbers would come just as right if we carried in eights or twelves or twenties. ”

“ Some people think that it is waste of time to go over all this ground so carefully, when all you get by it is either nonsense, such as "2 and 3 are 7"; or truisms, such as "2 and 3 are 5." But it is not waste of time. For, even if we never arrive at finding out the value of x, or y, or z, every conscientious attempt such as I have described adds to our knowledge of the structure of Algebra, and assists us in solving other problems.
Such suggestions as "suppose x were Unity" are called "working hypotheses," or "hypothetical data." ”

“ Men who wish to exploit other men fear nothing in logic or science except this element. They fear nothing in earth, heaven, or hell, so much as a public accustomed to realise exactly how much has been proved and where its own ignorance begins. ”

“ As I said before, people who really conduct their minds strictly according to the algebra of logic are very prone to grow kindness and honesty towards other people, without thinking about it, as a matter of taste, of choice. ”

“ When the time comes to stop grind-work, there is no better rest than amusing your imagination by thinking of non-existent possibilities; but do it on a free, generous scale. Give yourself a perfectly free rein in the company of the Infinite. ”

“ The first Hebrew algebra is called Mosaism, from the name of Moses the Liberator, who was its great Incarnation, or Singular Solution. It ought hardly to be called an algebra: it is the master-key of all algebras, the great central director for all who wish to learn how to get into right relations to the unknown, so that they can make algebras for themselves. ”

“ Algebra can be made about anything which any human being wants to know about. Everybody ought to be able to make Algebras; and the sooner we begin the better. It is best to begin before we can talk; because, until we can talk, no one can get us into illogical habits; and it is advisable that good logic should get the start of bad.
If you have a baby brother, it would be a nice amusement for you to teach him to make Algebra when he is about ten months or a year old. ”

“ Perhaps the best way of teaching a baby Algebra would be to get him thoroughly accustomed to playing with a bright vessel of some kind when cold; then put it and another just like it on the table in front of him, one being filled with hot water. Let him play with the cold one; and show him that you do not wish him to play with the other. When he persists, as he probably will, let him find out for himself that the two things which look so alike have not exactly the same properties. Of course, you must take care that he does not hurt himself seriously. ”

“ We try to find out which of the hypothetical values of x throw most light on other questions, and if we find that some particular value of x—for instance, unity—makes it easier than does any other value to understand things about y and z we have to be very careful not to slip into asserting that x is unity. But the teacher would be quite right in saying to the class, "For the present we will leave alone thinking about what would happen if x were something different from unity, and attend only to such questions as can be solved on the supposition that x is unity." ”

“ It is of all paths towards disease the one which will lead you, in your present condition, most rapidly towards disease. But if the imaginary angel suggests nothing contrary to the formularies, then the image or idea which he suggests is likely to be one on which your mind for the time being can work safely, and the one along which it can work most easily and profitably.
When your imagination is acting strongly in providing you with working hypotheses, there are a few little precautions which you ought to observe. ”

“ Remember always that Genius means conscientious, careful work on suggestions of the imagination taken as provisional hypotheses.
To take suggestions of the Imagination as fact is Insanity. When you hear of a man that he has unquestionable genius but is a little mad, that means that he sometimes takes the products of his imagination as working hypotheses, but sometimes mistakes them for facts.
All the above precautions may be summed up in one sentence: Remember that the more active the imagination is, the less the physical and moral instincts are on the alert ”

“ We may be still groping in the dark, but we know that one stumbling-block has been cleared out of our path, and that we are one step "for-rader " on the right road. We wish to arrive at truth about the state of our balance sheet, the number of acres in our farm, the time it will take us to get from London to Liverpool, The height of Snowdon, the distance of the moon, and the weight of the sun. ”

“ For instance, about weather and the electricity of the atmosphere, and how to take care of their health, and how to use their imagination to supply them with working hypotheses for a variety of sciences, and how to use their dreams to show them where they had been making mistakes and spoiling their brains. Whereas the people who would insist on shouting and arguing and quarrelling about things which were only wild guesses got on very slowly with learning Science. ”

“ Some persons are prone to warn young people against what they call an excessive exercise of the imagination. Of course, to say that "excessive" anything is too much is a mere truism, but nobody knows yet what is the proper amount of use for the imagination. What we do know is that there is a good deal of excessive mis-use of the imagination, by which I mean that there is a frightful amount of using it contrary to the laws of its normal action. ”

“ Infinity does not mean that there are enough children in the world now to go on passing through the room for ever, but that the number of children who pass through the room, now that the share of each child is 0 (zero) , will have to be determined by the number of children that there are in the school, or the parish, or wherever it is that the children are supposed to come from; and not by the size of the cake. The size of the cake has no longer anything to do with answering the question: "How many children can pass through the room before the cake is all eaten?" ”

“ Sometimes your teachers set you more complicated problems than:—What is the price of six pounds of sugar? For instance:—In what proportion must one mix tea bought at 1s. 4d. a pound with tea bought at 1s. 10d. a pound so as to make 5 per cent. profit by selling the mixture at 1s. 9d. a pound?
Arithmetic, then, means dealing logically with certain facts that we know, about number, with a view to arriving at knowledge which as yet we do not possess.
When people had only arithmetic and not algebra, they found out a surprising amount of things about numbers and quantities. ”

“ They never gossip about their private affairs, or those of other angels. They come to tell you either about what you are to do next, or about something you had better not do next; and if you ask them impertinent questions about things that do not concern you for the time being, they will give you headaches and make your head spin: just to teach you to mind your own business. This particular angel always comes with a message about a broken link or a loosened chain. ”

“ They like being kind and honest better than being selfish and dishonest, and they become kind and honest without thinking much about it. But honesty to other people and honesty to yourself are two different things, and must be kept apart in your mind, just as, in physiology class, you keep apart the flesh of an animal and its skin. You believe that if the flesh is thoroughly healthy it will grow a good skin ”

“ As long as general readers can be kept from the habit of registering at every step the fact of their own ignorance and the limits if their own knowledge, a clever charlatan can deceive them about anything he pleases:—"from pitch-and-toss to manslaughter" ”

“ But the angels do bring us very reliable information from a vast region of valuable truth about which most of us know very little as yet. They guide us how to frame our next provisional working hypothesis, how to choose the particular hypothesis which at our present stage of knowledge and development will be most illuminating for us. ”

“ None of us have ever seen the Maker of things. We can see the things growing, but not the force that makes them. That is our X; our Unknown. We are going to begin by stating that we don't know. We are going to call the Maker of things 'I Am,' or 'That which is, whatever it is'; and we are going to make two hypotheses to start with. ”

“ Many people think that it is impossible to make Algebra about anything except number. This is a complete mistake. We make an Algebra whenever we arrange facts that we know round a centre which is a statement of what it is that we want to know and do not know ”

“ Take care not to become a parasite; do not lazily appropriate the results of other people's labour, but learn and labour truly to get your own living. Take care that everything you possess, whether physical, mental, or spiritual, shall be the result of your own toil as well as other people's; and remember that you are bound to pay, in some shape or way, everyone who helps you.
Do not make things easy for yourself by speaking or thinking of data as if they were different from what they are ”