воскресенье, 15 мая 2016 г.

Mnemotechnics

Soon the examinations time will come. It is a good occasion to talk about mnemotechnics. I often take an advantage of using them when I'm trying to memorize a number of things logical connection between which I fail to grasp. Instead, I create my own links and my own logic. That's effective, that's not time-consuming (at least, after some practice), and, finally, that transforms boring things into funny ones. I'd like to show you a couple of examples. I hope they're not too mathy.

Last summer I took an exam in mathematical logic. One of the last questions became a sticking point for many of my coursemates. The goal was to enumerate nine axioms of Zermelo-Fraenkel set theory. Yup, just to reproduce nine obvious statements. However, that turned out to be a challenging task. Even though wiki states that "there are many equivalent formulations of the ZFC [Zermelo–Fraenkel choice] axioms", we had to remember the formulations which our lecturer presented to us. Otherwise, it'd be too easy to make a mistake by providing a redundant axiom or by missing out one. On the other hand, the lecturer didn't explain us why those nine statements consitute the full set of axioms, or how do they relate to each other (I'm even not sure that a good explanation exists). Thus, we had no logical links and no alternative but to cram the statements. But how? They don't even rhyme! Luckily, a few days before, I attended a meeting at Psychological volunteer club "Insight" where my friend was teaching us how to embed various technics in the exam preparation process. Although I had already been familiar with most of the technics, just theory is never enough. Thanks to the exercises we made together in a friendly atmosphere, I gained an insight into how mnemotechnics can help me. By the time of the exam, the exercises hadn't yet slipped my mind. On the last evening, I "built" a memory palace based on my room and managed to memorize ZFC axioms immediately after the first perusal. Moreover, I remembered them even several weeks after the exam without rehearsal. Here is how my links looked:

  • On the shelf on the western wall of my room I have two identical books received on some programming competitions. To make sure that they are the same, I leaf through them and see that the corresponding pages look similar. Axiom of extensionality. Two sets are equal (are the same set) if they have the same elements.
  • I turn to my escritoire. Pens and pencils are in the same box. Axiom of pairing. If x and y are sets, then there exists a set which contains x and y as elements. Here x stands for pens, y substitutes pencils, and the box is the enclosing set.
  • Now I'm near the eastern wall looking at the other shelf. For every set of books (in particular, for the set formed by the third volume of Knuth's monograph and by Tanenbaum's "Modern Operating Systems" standing on the right), imagine that you tear them all into pages (please, don't repeat that anywhere but in your mind). Axiom of union states that "For any set F there is a set A containing every element that is a member of some member of F". F is the set of books, thus a member of some member of F is a page, and A is exactly all those pages torn out and put together.  
  • ... and so on.

My second example relates to December 2015. One definition from computational methods course contained the formula presented below:

In other words, I had to keep in mind the following sequence of numbers: 1, 1/2, 5/12, 3/8, 251/720. This time a rational explanation existed but I started my preparations too late to dig into every detail like that. Hence I had to memorize a sequence of random numbers. First four of them look easy to keep in mind. As for the fifth one...


To recall what the fifth number is, I looked at the third fraction. I formed the numerator of the fifth fraction from the digits of the third one in the order shown by the arrows on the picture above, and then divided it by the factorial of 6. Weird? Sure. Easier to remember and to keep in mind for long? Absolutely!

Honestly, neither of these methods actually helped me during the exams because I got other questions. However, thanks to mnemotechnics I was more confident than usual. At least, there were some questions I couldn't forget answers to.

I wish you to come up with right associations at the proper moments. Exams are coming!

1 комментарий:

  1. Very interesting! We also have a blog about Mnemotechnics @ http://www.thememorycityblog.com/

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