Thursday, January 20, 2011

More on mental calculations

Just a quick post today. I found this article in Nature Neuroscience from Wikipedia's page on mental calculation.  The abstract follows:
Calculating prodigies are individuals who are exceptional at quickly and accurately solving complex mental calculations. With positron emission tomography (PET), we investigated the neural bases of the cognitive abilities of an expert calculator and a group of non-experts, contrasting complex mental calculation to memory retrieval of arithmetic facts. We demonstrated that calculation expertise was not due to increased activity of processes that exist in non-experts; rather, the expert and the non-experts used different brain areas for calculation. We found that the expert could switch between short-term effort-requiring storage strategies and highly efficient episodic memory encoding and retrieval, a process that was sustained by right prefrontal and medial temporal areas.
It seems that individuals who are naturally gifted at mental calculation possess a sort of encoding mechanism for rapid recall of previously acquired mental facts.

Fortunately, I believe our brains are not hard-wired but able to adapt to imposed stresses and routines so that even non-prodigies can become proficient at performing tasks such as these.

Thursday, January 13, 2011

Science and cooking online

Those who know me are aware that I am a big science buff. Those who know me even better know that I also am an avid cook and baker.

Harvard gave a lecture series this past fall on science and cooking and have graciously posted the lectures online. I recommend taking a look here.

Topics include thermodynamics, colloids, and sous vide cooking.

Tuesday, January 11, 2011

Mentat training

For Christmas I received a "Lightning Calculation" calendar. It's a wall calendar that explains techniques for performing mental calculations, such as finding what day of the week a date fell on and performing fast multiplications. In addition, there are historical bits on famous individuals who have been able to perform incredibly complicated mental calculations. I've spent at least half an hour in my office every morning reading through it and trying the practice problems (of which there are hundreds, if not over a thousand).

Something I've learned is the anchor method for multiplication of two, two-digit numbers. It may seem complicated at first, but it's actually incredibly powerful. First consider the product to be found as a product of two sums, each one "anchored" to a nearby round number. This product can be written as

(a + c)(a + d) = a^2 + ac + ad + cd
(a + c)(a + d) = a(a + c + d) + cd

where a is the anchor. From the right-hand-side of the last line above, the anchor is multiplied by itself with the sum or difference terms c and d. Then the correction term cd is added or subtracted, depending on whether the signs of c and d were the same or not, respectively.

For example, consider the product 17 * 18. This can be written as (20 - 3) * (20 - 2) = 20(20 - 3 - 2) + (2 * 3) = 306. The algorithm is easy to carry out because the first product is 20 * 15 = 300. Cool stuff.

The information for the calendar can be found here: It's very nicely done and I highly recommend it for all those mentats in training =)