Unusual Mathematical Ability:

Okay, so here is my completely random post of the week. I have a friend, now around 40, who has a rather astonishing ability to calculate numbers in his head. He can multiply three digit numbers by three digit numbers, divide three digit numbers by other numbers, and even do square roots, all in his head, in real time. I wouldn't believe it if he didn't prove it to me over the course of an evening: you can call out all sorts of calculations that most of us would take a minute to do on paper and he can answer back without even pausing to appear to think of the answer. As he tells it, he has had this ability ever since he was a little kid, and he can just "see" the numbers and how they multiply or divide.

Obviously being a human calculator isn't as cool as it was before, well, before the invention of the modern calculator. But I was wondering, has anyone ever heard of anything like this before? I know a lot of people who are extremely good at math, but I have never seen anything quite like this. I wondered if anyone else has.

And so endeth the completely random post of the week.

UPDATE: In response to the comment thread, my friend wrote in with a response:

Obviously being a human calculator isn't as cool as it was before, well, before the invention of the modern calculator. But I was wondering, has anyone ever heard of anything like this before? I know a lot of people who are extremely good at math, but I have never seen anything quite like this. I wondered if anyone else has.

And so endeth the completely random post of the week.

UPDATE: In response to the comment thread, my friend wrote in with a response:

When Orin sent me the link and I saw some of the posts, I wanted to respond both to try to eliminate some misperceptions but also because I thought people would find some of what I am saying interesting.

1) While it is true that computational abilities are not the same as mathematical abilities/logic/abstract reasoning, I am quite strong at all of these. Orin knows this, so when someone went after him saying that he does not know the difference, that was wrong.

2) I only estimate square roots, and I can usually go out to at least 4 or 5 decimal places, but I don't need to use tricks. In some cases, I can use some tricks I've developed to facilitate my computations, but they are tangential to the process and I can do any of the calculations without these, and for the most part, do.

3) While at least short-term memory is critical to the process of this ability, I do not memorize the answers. It would be impossible given the number of possible mathematical computations that can be asked/done. There are certain "sub"-calculations I sort of just "know" immediately, but that is just sort of a combination of being innate and from doing lots of math/computations over the years.

4) I find the division to be the most unusual part as I can go to as many decimal places as one wants as quickly as I can talk.

5) The limitation I have with the calculations is primarily with multiplication. I can at times do up to 4X4 digits (or 5 or 6 by 3 sometimes), but it depends on my focus/concentration. I am sure if I work on my memory, I can do more than that, not that that is so easy. With division, it is really just the 2 numbers I need to remember and as I say the string of decimal places, I don't need to recall everything I've said to that point. With addition/subtraction, it is essentially a "running tab," so again I don't need to remember a lot of numbers at any one time, unless I happen to fall behind. I can add 1, 2 or 3 digit numbers, sometimes more -- this is with saying them as quickly as you can put them in the calculator or computer and it can be many, many numbers.

The limitation with multiplication is the need to multiply the different pieces of the numbers (as one of the postings referred to) and remember those answers while also multiplying the other pieces that it needs to be added to.

6) While some of this can be taught in terms of the process, and while practice and improving one's memory helps, for the most part this is an innate skill. I have had this as long as I can remember. In fact, I was quicker with this when I was much younger and had fewer other things to think about and more time and interest in utilizing these skills.

7) Anyway, it's strange, but I've rarely talked about this (and certainly never written about it) before, certainly never close to in this level of detail or at this length. It is interesting to see what people think.