My Computing - 2

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The anteroom of my Father (HM)'s Office Room served as a minuscule science museum cum lab. There was a sensitive balance we were not allowed to touch and several beakers and bottles. My Father who taught Science and English equally well used to bring once a fortnight a couple of demo experiments to the delight of us all; microscopes we were allowed to peer through one by one, a simple pendulum where we were allowed to handle an expensive stop-watch, reagents that change color like litmus solutions and such.

On top of the science almirah was a curious harp-like object with several wires through which colored beads were strung like in a japa mala. No one ever touched it and it was gathering dust and cobwebs. I asked my Father one day what it was and he said: Abacus. And he said it is a device for adding and subtracting manually. I could feel he was not very forthcoming and comfortable about it, so I let it go at that.

I met the word thirty good years later while reading the Feynman crazy book, Surely You're Joking. and realized that what I saw was the first 'computer'. Of course, it was not as sophisticated as that of the Japanese salesman who beat Feynman in a Restaurant till he challenged: "Raios Cubicos! with a vengeance" and was beaten hollow. The encounter was very instructive. Here it is:

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A few weeks later the man came into the cocktail lounge of the hotel I was staying at. He recognized me and came over. "Tell me," he said, "how were you able to do that cube-root problem so fast?"

I started to explain that it was an approximate method, and had to do with the percentage of error. "Suppose you had given me 28. Now the cube root of 27 is 3..."

He picks up his abacus: zzzzzzzzzzzzzzzzzzzz---"Oh yes," he says.

I realized something: he doesn't know numbers. With the abacus, you don't have to memorize a lot of arithmetic combinations; all you have to do is learn how to push the little beads up and down. You don't have to memorize 9 + 7 = 16; you just know that when you add nine you push a ten's bead up and pull a one's bead down. So, we are slower at basic arithmetic, but we know numbers.

Furthermore, the whole idea of approximation method was beyond him...."

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In short Feynman was saying that the Jap abacus expert was at best a robot. I don't think the Marwari shop teenager or the students at Cincinnati I talked about yesterday are any better; instead of pushing and pulling beads they are punching keypads. And unlike me, they have been doing it from their pre-school years (like Ishani is going to do). I am no good at numbers and extracting cube roots by approximate methods; but when my son and I are together, he often asks like what is 7.5% of 2.25 lakhs and pulls out his cell phone to do it on (I too have one with a calculator, but I rarely need it). Invariably I beat him to it by, let us say, as in this example by converting the decimals into fractions, getting a rough answer good enough for estimates before taking a loan ;-)

When I entered University, we were asked to buy Clark's Mathematical and Physical Tables (and Worsnop & Flint's Practical Physics...a great book) before entering the Phy Lab. The first half of Clark's is Logarithms and Antilogarithms followed by trigonometric functions. They were four-figure tables. We used them so much that we all had the values of Logs of integers from 1 to 9 by heart (I checked that I still can recall the first five). But then this lateral entry whizkid in our fourth year (YSTR, who went to TIFR) challenged us to ask the four-figure Log of any number between 1 and 10, say, Log 6.7 (the whole lot of two pages of close print). And he was always right. We were wondering how he could do it; maybe he has a secret series formula up his sleeves, but we never asked, for fear he would refuse to divulge his trade secret...attitude problem.

But in that crazy book, Feynman says about Hans Bethe at Los Alamos who invariably beat him:

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"Oh," he says, "the log of 2 1/2 is so-and-so. Now, one-third of that log is between the logs of 1.3, which is this, and 1.4 which is that, and so I extrapolated."

So I found out something: first he knows the log tables; second, the amount of arithmetic he did to make the interpolation alone would have taken me longer to do than reach for the table and punch the buttons on the (Marchant) calculator. I was very impressed.

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This reminds me of the Big Brother Bull story I read in Reader's Digest:

http://gpsastry.blogspot.com/2010/11/big-picture.html

I learned a lot of Physics (and Math) from that Jokey book.

For instance, there was this perennial confusion in the terminology of STR and GTR in what the texts used to call the 'proper' time of a clock, which got clarified by that question Feynman put to Einstein's Assistant (and answered it himself).

In our fourth year, we learned the Bohr theory. And I got curious enough to whip out my Clark's Tables and calculate the theoretical value of the Rydberg Constant substituting the various ugly powers of e, h, m, pi, in the numerator and the denominator using the log tables. And lo, and behold, it agreed famously with the experimental value. That was the first time I put in numbers in a theoretical formula and checked, and got a thrill. The second and last time came 40 years later when I was teaching Quantum Statistics to Second Year B Techs for a couple of years before I retired. And that was to decide if MB statistics would do in a given situation or one has to necessarily go to the BE or FD statistics. That required putting the Boltzmann constant k in too.

But by then I got spoiled and was using my son's Casio scientific calculator...


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