Algebras. Specifically, as described in Philosophy and Fun of Algebra by Mary Everest Boole.
Hallo, and welcome to the Random Channel, where your host (me) lets you explore a few of the sad, dusty little cubbyholes of my mind. First stop: algebras, plural. Did you know there are more than one? There are, because Mary Everest Boole says there are. She writes,
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. Its great keynotes are these:—
When you do not know something, and wish to know it, state that you do not know it, and keep that fact well in front of you.
When you make a provisional hypothesis, state that it is so, and keep that fact well in front of you.
While you are trying out that provisional hypothesis, do not allow yourself to think, or other people to talk to you, about any other hypothesis.
….Do not make things easy for yourself by speaking or thinking of data as if they were different from what they are; and do not go off from facing data as they are, to amuse your imagination by wishing they were different from what they are. Such wishing is pure waste of nerve force, weakens your intellectual power, and gets you into habits of mental confusion.
So, that is one algebra. Oo, you disbelieve, don’t you? Think about it. That first keynote is x, the next one is x=y, the third one is x can’t equal y and y+1, and the last is “My equation is all wonky, I wish the problem were x=34 instead of 33, then I’d have it right.” But you wouldn’t, and you know it, and you’d feel all bad, and end up praying that you’d just figured it out the right way and now you’re stuck making sheep’s eyes at stupid guys instead of feeling good about yourself like you would if you’d listened to Mary Everest Boole.
And that’s just one algebra. She’s a very interesting lady, this Mrs. Boole. She warns us to be careful when formulating potential hypotheses not to stress ourselves with strange exercise and not to take cold, and to remember: “[T]he most important precaution of all is incessant reverence for the Great Unknown, the sacred x: or, in other words, a constant awareness of your own ignorance. ”
Isn’t she fabulous? This book (which I originally listened to on Librivox and then downloaded from Project Gutenberg) was published in 1909, and yet I find that her approach to algebra is not at all obfuscated, but rather helps me to look at it in a whole new way. I’ve been reinvestigating the subject myself, having picked up a copy of Intermediate Algebra from the library and pushing myself through the exercises at the end of each chapter. They aren’t hard, not yet; I remember enough so far. However, I’m making myself learn things like commutative law and distributive law and, like in geometry, write them down when doing the exercises. I think perhaps my problems later came from not studying enough earlier. Perhaps, also, I did not pay enough attention to my diet. Perhaps strange exercises crept into my daily habit. Being 17 has been clouded by the onward march of time.
So back I go, with Mrs. Boole as my guide and mentor. Moses and Isaiah and small winged gnats may play a part, but when I am 89 and sharp as a tack, with 17 and all its attendant cloudiness a mere speck of roadkill in my dust, just you remember how one day I picked up my algebra book, and wrote down on a piece of lined recycled paper,
x = everything I don’t know yet
Whew. That’s a long equation.