eon

Posted by tpc at April 30th, 2006

I came across the “send more money” puzzle in a worksheet for 11 year olds. It took me a good 15 min to crack it but it was fun. But 11 year olds? I guess there are many very smart kids around. I’ll see when I try to teach the enrichment class next month.

The linked site is a very nice page containing many more puzzles for you to crack your head against. This reminds me of the first puzzle of the google aptitude test, I still have not managed to solve it completely by hand. (Yes, I’m aware of answers available on the web.)

Posted by tpc at April 24th, 2006

The following is a quote from Mario Livio’s The Golden Ratio, which in turn quotes Tobias Dantzig’s Number.

A squire was determined to shoot a crow which made its nest in the watch-tower of his estate. Repeatedly he had tried to surprise the bird, but in vain: at the approach of man the crow would leave its nest. From a distant tree it would watchfully wait until the man had left the tower and then return to its nest. One day the squire hit upon a ruse: two men entered the tower, one remained within, the other came out and went on. But the bird was not deceived: it kept away until the man within came out. The experiment was repeated on the succeeding days with two, three, then four men, yet without success. Finally, five men were sent: as before, all entered the tower, and one remained while the other four came out and went away. Here the crow lost count. Unable to distiguish between four and five it promptly returned to its nest.

Posted by tpc at April 20th, 2006

I’m a fan of google. I mean who would not like a story of how math geeks triumph over the world. (Although now that they are in the big leagues, it remains to be seen if they can stay rooted to their original mindsets and not end up being big bullies.)

If you are a user of gmail, you know that they are constinously increasing your storage quota. Today’s snapshot shows 2716….

I have been waiting for it to show 2718.2818 for quite sometime. Would they stop at exactly e or would they go to ?

Update: They went past e (or more precisely 1000 e ) without stopping. The best screen cap I got was at 2718.000001 megabytes.

Related post

Posted by tpc at April 9th, 2006

Another gem from The Lady Tasting Tea.

The mathematical theory of input-output analysis requires that the matrix that describes the economy have a unique inverse … Leontief’s initial set of sectors led to a 12 x 12 matrix, and Jerry Cornfield proceeded to invert that … It took him about a week, and the end result was the conclusion that the number of sectors had to be expanded. So, with trepidation, Cornfield and Leontief began subdividing the sectors until they ended with the simplest matrix they thought would be feasible, a 24 x 24 matrix … During World War II, Harvard University had developed one of the first, very primitive computers … Cornfield and Leontief decided to send their 24 x 24 matrix to Harvard … When they sought to pay for this project, the process was stopped by the accounting officer of the Bureau of Labor Statistics. The government had a policy at that time; it would pay for goods but not for services. The theory was that the government had all kinds of experts working for it. If something had to be done, there should be someone in government who could do it. They explained to the government accountant that, while this was theoretically something that a person could do, no would be able to live long enough to do it. The accountant was sympathetic, but he could not see a way around the regulation. Cornfield then made a suggestion. As a result, the bureau issued a purchase order for capital goods. What capital goods? The invoice called for the bureau to purchase from Harvard “one matrix, inverted.”

Posted by tpc at April 9th, 2006

Honestly, I know next to nothing about statistics. It’s no wonder that I have not heard of this book, and most of the actors in the stories within. This is a good book that tells the tales of the origin of statistical studies and should be a must-read for all statistics majors. One major flaw was that he was writing too much for a layman, and most of the details are hidden behind some general explanation. While this is alright for a brief history of the subject, I sincerely believe that anyone who is willing to read a 300 page book on statistics, would like to see a deeper discussion. Another gripe is that the author seem to come across as one who is very critical of those who are only interested in pure theory/mathematics. That aside, the book is filled with gems.

I particularly like this delightful quote attributed to R. A. Fisher

A scientific career is peculiar in some ways. Its raison d’etre is the increase of natural knowledge. Occasionally, therefore, an increase of natural knowledge occurs. But this is tactless, and feelings are hurt. For in some small degree it is inevitable that views previously expounded are shown to be either obsolete or false. Most people, I think, can recognize this and take it in good part if what they have been teaching for ten years or so comes to need a little revision; but some undoubtedly take it hard, as a blow to their amour propre, or even as an invasion of the territory they have come to think of as exclusively their own, and they must react with the same ferocity as we can see in the robins and chaffinches these spring days when they resent an intrusion into their little territories. I do not think anything can be done about it. It is inherent in the nature of our profession; but a young scientist may be warned and advised that when he has a jewel to offer for the enrichment of mankind some certainly will wish to turn and rend him.

Posted by tpc at April 8th, 2006

We are all familiar with the process of tallying, putting down a vertical stroke for each count and for every fifth count, crossing out the four vertical stokes with a horizontal one.

An interesting quote from The Lady Tasting Tea by David Salsburg

It is a foolish way to tally, said John Tukey. Consider how easy it is to make a mistake. You might put the cross over three instead of four lines, or you might put down five lines and then a cross. The incorrect tally is hard to spot.

Quite true. Interestingly, the old folks here use the following Chinese character: æ­£ , as a tally. Every five strokes give you a complete character, which addresses what Tukey was unhappy about. Moreover, this character “zheng” actually means upright or correct.

Somewhat related to this, for certain chinese dialect, there is actually no words for right and left. Right is also denoted by the same character æ­£, while left is denoted by a character signifying opposite. In case you are wondering, in official Chinese “Han” the character for right is 右, while left is å·¦.