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mental exercises

Mental Exercises: Working with Number Sequences

While thinking about material for this site, I recalled a system of mental training from Pumping Ions by Tom Wujec that seemed worth digging up. I’ve been accumulating books on mind and intelligence for quite a few years now, and many of them simply rehash the same patterns. Pumping Ions suffers a bit from a slightly precious “mental gymnasium” metaphor, but there’s a lot of good material. I hadn’t looked at the book for a number of years, but I did finally manage to dredge it out of my library.

Most unusual are a set of exercises that mix visualization, multitasking, and mental endurance. Wujec attributes them to A. R. Orage’s Mental Exercises and Essays. (Some research reveals that this is probably the wrong title; then again, it appears that the book was published under at least four separate titles: The Active Mind: Adventures in Awareness; Psychological Exercises; Psychological Exercises and Essays; and The Active Mind: Psychological Exercises and Essays. Perhaps there are more editions.)

Orage became a disciple of G. I. Gurdjieff in the 1920s, and by 1930 (when Exercises was published), was well within his ambit. I’ve not read the original book, but I’ll be ordering a copy soon, and will certainly relate my impressions in this forum.

The first set of exercises, which will be presented today, deals with sequences of numbers. The individual manipulations are quite simple, but by layering several operations together you can build your powers of mental concentration. Start with the simple exercises, and over time, build to the more complex patterns.

The Exercises

  • Either out loud or silently, count by 1’s:
    • From 0 up to 100
    • From 100 down to 0
  • Count by intervals:
    • From 0 up to 100 by 2’s, by 3’s, by 4’s,…, by 9’s
    • From 100 down to 0 by 2’s, by 3’s, by 4’s,…, by 9’s
  • Count up or down by two sequences simultaneously, for example:
    • Up by 2’s and 3’s: 2, 3; 4, 6; 6, 9; … ; 66, 99
    • Down by 3’s and 2’s: 99, 66; 96, 63; … ; 3, 2
    • Up by 7’s and 4’s: 7,4; 14, 8; … ; 98, 56
  • Count two sequences, one up and one down, for example:
    • Up by 3, down by 4: 3, 100; 6, 96; … ; 75, 4
    • Up by 9, down by 3: 9, 99; 18, 96; … ; 99, 66
  • Name all numbers from 1 to 100 with a particular property:
    • All numbers containing a particular digit; e.g., 2: 2, 12, 20, 22, 23, … ,92
    • All numbers containing either of two digits
    • All numbers the sum of whose digits total a particular number
    • All numbers whose digits are divisible by a particular number
  • Count three sequences together, either all up, all down, or a mix, for example:
    • Up by 2’s, 3’s, and 4’s: 2, 3, 4; 4, 6, 8; … ; 48, 72, 96
    • Down by 8’s, 7’s and 3’s: 96, 84, 36; 88, 77, 33; … ; 8, 7, 3
    • Up by 2’s, down by 2’s, and up by 3’s: 2, 66, 3; 4, 64, 6; … ; 66, 2, 99
  • Count four sequences together, either all up, all down, or mix, for example:
    • Down by 7’s, down by 9’s, up by 2’s, up by 5’s: 77, 99, 2, 5; 70, 90, 4, 10; … ; 7, 9, 44, 55

The above constitute a basic set of exercises. While straightforward, they require careful attention to avoid losing one’s place. There are obvious ways to keep changing things around: for example, don’t always start from 0, or don’t limit the count to 100. In future posts, we will look at elaborations beyond simple counting.

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