2014 February 13

Mathematics made difficult: A handbook for the perplexed

http://i7-dungeon.sourceforge.net/math_hard.pdf

“Are any two numbers comparable? Objection. The kinds of comparison - the absolute, comparative, and superlative - are called degrees. Hence the question refers to the numbers of degrees used in recording temperatures. But if the temperature exceeds a certain level, mathematics is impossible, since mathematicians require pencils and paper and these would ignite. Hence only small numbers are comparable to other numbers. Reply. A mathematician can deal with arbitrarily large temperatures under the most comfortable working conditions, simply by inventing new scales for a measurement of temperature. This is done by means of a ‘scaling factor’ which converts one degree into as many degrees as one likes in the new scale.”

This is also the only math textbook I’ve seen that references Borges. And that teaches how to count and add having presumed proficiency in category theory.

“Simplicity is relative. To the great majority of mankind it is a simple fact that, for instance, 17 x 17 = 289, and a complicated one that in a principal ideal ring a finite subset of a set E suffices to generate the ideal generated by E. For the reader and a select few, the reverse is the case. One needs to be reminded of this fact especially as it applies to mathematics. Thus, the title of this book might equally well have been Mathematics Made Simple; whereas most books with that title might equally well have been called Mathematics Made Complicated.”

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