The agreeable eye

an eudæmonistarchives

all gibberish

I felt a downright fear of mathematics class. The teacher pretended that algebra was a perfectly natural affair, to be taken for granted, whereas I didn’t know what numbers really were. They were not flowers, not animals, not fossils; they were nothing that could be imagined, mere quantities that resulted from counting. To my confusion these quantities were now represented by letters, which signified sounds, so that it became possible to hear them, so to speak. Oddly enough, my classmates could handle these things and found them self-evident. No one could tell me what numbers were, and I was unable even to formulate the question. To my horror I found that no one understood my difficulty. The teacher, I must admit, went to great lengths to explain to me the purpose of this curious operation of translating understandable quantities into sounds. I finally grasped that what was aimed at was a kind of system of abbreviation, with the help of which many quantities could be put in a short formula. But this did not interest me in the least. I thought the whole business was entirely arbitrary. Why should numbers be expressed by sounds? One might just as well express a by apple tree, b by box, and x by a question mark. a, b, c, x, y, z were not concrete and did not explain to me anything about the essence of numbers, any more than an apple tree did. But the thing that exasperated me most of all was the proposition: If a = b and b = c, then a = c, even though by definition a means something other than b, and being different, could therefore not be equated with b, let alone with c. Whenever it was a question of an equivalence, then it was said that a = a, b = b, and so on. This I could accept, whereas a = b seemed to me a downright lie or fraud. I was equally outraged when the teacher stated in the teeth of his own definition of parallel lines that they met at infinity. This seemed to me no better than a stupid trick to catch peasants with, and I could not and would not have anything to do with it. My intellectual morality fought against these whimsical inconsistencies, which have forever debarred me from understanding mathematics.

—Carl Jung (Memories, Dreams, Reflections, trans. Richard and Clara Winston, p. 28)

* * *

Why do we call something a “number”? Well, perhaps because it has a – direct – relationship with several things that have hitherto been called “number”; and this can be said to give it an indirect affinity with other things that we also call “numbers”. And we extend our concept of number as in spinning a thread we twist fibre on fibre. And the strength of the thread resides not in the fact that some one fibre runs through its whole length, but in the overlapping of many fibres.

—Ludwig Wittgenstein (Philosophical Investigations, trans. G.E.M. Anscombe et al., §67)


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