I am back after a long absence _____other activities pull one away. About this bit : ” The study of lightning calculators of the past is a fascinating one for me from a mathematical aspect more than a psychological one. We’ve seen years of articles by educators bemoaning the dependence of students on calculators, but I see little in school textbooks on mental math other than simple estimation. And yet when I have presented basic methods of mental calculation to classes (elementary and college), I’ve met with incredible interest. Certainly the BrainMan documentary is a very popular one. But these types of presentation generally ascribe abilities in these areas to mysterious machinations in the minds of remote geniuses, which makes for a good story but can be discouraging. In fact, these individuals through talent and training acquired a knack for racing headlong through calculations that are not mysterious at all once the methods are taught.

And they are not being taught. Mental calculation can be a highly creative and satisfying endeavor offering a variety of interesting strategies, more than I have presented here and many more than most people realize. It is a skill that engages both children and adults, and one that naturally leads to a real familiarity with the properties and relationships of numbers. It provides a useful and fun approach for developing a number sense and generating a true appreciation for the elegance of elementary mathematics. It should not be a neglected art. ”

There are 2 points worth informing you about. ONE : When you describe the fantastic abilities of the brilliant mental calculators , it over-awes the common plodders , like me.

TWO : i have been chasing this * mental maths* for donkey’s years. The major problem is ** HOW TO HOLD the INTERMEDIATE NUMBERS IN ONES HEAD , while doing, for instance , the squares of 3 and 4 or 5 figure numbers. !!
Further, i have taught mental maths by going to a local school. Yes, the kids are very eager to learn. They do pick up our mental ,quick calculation methods. HOWEVER, the maths TEACHERS are too OLD ( mentally) to learn our methods. ERGO, no follow up work is done in the regular mathematics classes in the use of the mental ,quick methods. Alas , it , thus remains just a curiosity.

Not the kids, but their teachers need to be taught these methods.

I do teach maths ( Calculus etc) at home to students every evening, 3 pm to 7 pm_____but that’s my hobby not my profession.

I once read that Thomas Edison could recite the contents of a page from the Webster’s unabridged dictionary after a brief perusal. I also read that an example of photo-memory was someone being able to count the bricks in a wall after a quick look.

My own experience is the occasional after-image experienced on photos of aircraft projected onto a screen at shutter speeds in the hundredth of a second (aircraft recognition training). The lingering impression would remain for a second or two and I think they were in negative image.

Yours truly,
Jay Sicard

Hi, Jay. From everything I’ve read on the subject, memory, and especially photographic memory, is a huge benefit in mental calculation, pretty much a prerequisite for real achievement. This was particularly true back when lightning calculators were asked conversion questions (for example, the number of seconds in 250 years) where the calculator knew all the conversion factors and therefore most of the work was already done. But this is true generally in all kinds of calculating tasks: knowing powers and primes, knowing logarithms for non-integer roots, knowing all 2×2 digit products, knowing factors and reciprocals of a variety of numbers, knowing a lot of reference dates for calendar calculations, and so forth. Smith’s book “The Great Mental Calculators” (which I absolutely recommend) describes the ubiquitous role of memory among lightning calculators. I think, too, that this kind of knowledge is naturally attained anyway by someone enamored with numbers. I certainly don’t have a photographic memory, but I think I once had some ability of this kind. I remember in 5th grade when a teacher questioned something I said in Geography class, and I told her the sentence, page and location on that page where I had read it in our thick textbook. That created a bit of a stir in the class and with her when she looked it up. I recall that I had an exact mental image of the page. I couldn’t do that today, I don’t think. It would be interesting to hear if your “flash” training gives you the same ability with the page of a book or a table of numbers. Maybe you can try it and let me know if it works. As far as counting things instantly, the physicist Richard Feynman recounted (in his book “Surely You’re Joking, Mr. Feynman”, I believe) how with some practice he learned to instantly count the number of toothpicks dropped on a table based on patterns or such. — Ron

He holds/held the European/British record. The World record is current 67,890 digits, cf. http://pi-world-ranking-list.com/lists/memo/.

Ah, right you are–my mistake. I’ve updated the online essay and I’ll do so for the PDF file as well. Thank you very much for taking the time to correct this! — Ron