Archive for April, 2010

From: The Main Stream of Mathematics

April 19, 2010

When as a boy Bhaskara was not absorbed in the study of mathematics, he would brood on the nature of society about him.  The adamant wall of custom had always been a source of pain to him.  He chafed under the system that forbade him to share his scientific knowledge with youths of lower caste, or seek companionship outside of Brahmin ranks.  Bhaskara had feared to confide his unorthodox views to others, lest he be outlawed.  But it had comforted him to learn from the writings of an earlier day that men had once lived a freer life and a happier one.

Often in his later years his nervously active mind would turn suddenly, by some train of association, from serious scientific considerations to sentimental memories.  Now this old pattern of thought recurred with good reason, for today his only daughter was to be married.  He thought for a moment of the two ancient astrologers who, when Lilavati was born, had been paid to cast her horoscope; bent with age, and shorn of their dignity in his presence-Bhaskara even then had been renowned for his wisdom-they had seemed uneasy and timid, and had spoken of many things other than their business.  Finally they had predicted that Lilavati was to be his only daughter, and that she would never marry; and when they had delivered this prediction, they left hurriedly, fearful of the rage which they expected their prophecy would call forth.  But Bhaskara had sent gifts after them and a message of blessing.

Today Bhaskara recalled how Lilavati, even at the age of eleven, had preferred to remain at home and read to him her childish compositions or listen to his recitals of myths and puzzles, while her playmates celebrated as they had every year since the age of seven, the festival of Molakata, in order to ensure the speedy winning of a husband.  Bhaskara had been pleased.  More and more she had become the comfort and delight of those leisure moments which he stole from his endless work on mathematics.

But suddenly she changed.  The books, the puzzles, the lessons, all seemed to bore her.  Now she played all day with her friends at games that she had always scorned as childish.    And when in her twelfth year the festival days of Molakata came, she celebrated with the other girls of her age.  Soon Bhaskara perceived that he could not change the course of nature.

Lilavati did not then know that the astrologers had been unable to discover any time when the gods would permit a marriage for her; and when Bhaskara saw that her heart was set upon marriage and that to be denied this would cause her great misery, he laid aside his books, and for one whole day and night studied the child’s horoscope and the heavens.

At last he found an hour on a certain day when the gods would receive the marriage favourably.  He called Lilavati to his side, and telling her first that he had found a propitious date, related the findings of the old astrologers so many years before.  Then he went to a friend in a near-by village and arranged a match with the delighted friend’s son.  All this had happened three months ago.  And today Bhaskara realized with a start that within a few hours the ceremony must begin.

Soon the noisy wedding procession arrived and the great rooms were filled with chatter and laughter.  Lilavati was seated in the embrace of her uncle, as was the custom, with a screen still barring her first glimpse of her husband to be.  Then the astrologers set up the hour glass beside her, to determine the exact moment that the heavens had decreed for the performance of the ceremony.  From time to time Lilavati leaned over and gazed at the floating cup, to see how near the hour was.

To  Bhaskara the preliminaries seemed endless.  Several times he approached the priest to ask whether the propitious moment had not already come.  Then suddenly Vatsaraja, the old astrologer, bent over the hour-cup and cried out!  A silence fell on the group as he lifted the vessel from the water.  No liquid flowed through the cavity.  Just as no liquid had entered it.  As Lilavati in her anxiety had bent over the cup, a pearl had dropped from her costume and stopped the opening through which the fluid should have passed.  And so, unnoticed, the hour had gone, and now that the accident was discovered, it was forever too late.

It was the will of heaven, Bhaskara said.  And he took into his arms the child who could not restrain her weeping, and caressed her; he mustered all the words of comfort he could find; among other things, he whispered to Lilavati that the great book upon which he had been laboring for years would bear her name through the centuries.  Thus, by the promise of immortal fame did he hope to console her for the accident that had prevented her marriage.

By Edna E. Kramer, Ph.D

From The Main Stream of Mathematics, 1951



April 19, 2010

As we all know, schadenfreude means ones happiness at the unhappiness or suffering of others.  I don’t know of a word which means ones sadness at the happiness or success of others.

Where is the money sitting?

April 8, 2010

Where is the money sitting?  Do we have any statistics for this?  Do I even know what I want to know?  Keynes wrote of a speculative motive.  My question is: which are the funds that are held under the rubric of the speculative motive?  I for one have very little investible surplus.  Where are these major pools of speculative capital that issue forth in the purchase of bonds?  (Where bonds are a proxy for any business venture.)  Do I have facts and figures?  Add Calpers to PIMCO to a hedge fund?  But that might lead one into double counting.  After all, Calpers could have placed funds with PIMCO.  So: question for research-quantify the funds available at a point in time which satisfy the criterion of being funds held for the speculative motive.

Short selling

April 8, 2010

The very essesnce of business, of production, is the spirit of an advance.  When a bank grants a loan to an entrepreneur, what he is essentially doing is transferring a bundle of material goods and services to the service of the entrepreneur.  The bank is advancing to the entrepreneur command over economic resources now in the hope of an enhanced flow of goods and services in the future.

But in a short sale there is no advance.  As it happens on an exchange such as the NYSE with a broker like Lehman, when you sell stock short you get the money equal to the value of the sale.  We are told we are borrowing the stock from the brokerage, and selling it in the present, anticipating a fall in its price.  When and if the price indeed falls, we buy back the stock from the market, and return it to the brokerage.  We sell high, and buy back low.  The difference between what you got for selling the stock and what you paid for buying it back is your “return”.  I put the word advisedly in quotes, because a return as such cannot be defined for a short sale.  There is no advance of money, which when invested wisely, yields a physical or value surplus. 

To take the matter a step further, imagine that the money you got when shorting the stock was invested in buying or going long another stock.  And that long stock went up and up.  Can you calculate a return for the above transaction?

To try and clarify matters, we propose to consider the case of a short sale not of stock, but of a house.  What happens in such a case?  Must find out.

Freedom and necessity

April 7, 2010

Food for the body is like oil or fuel for the machine.  As is clothing and shelter.  The entire accounting for production, consumption, accumulation can be done in energetic or calorific  terms, and it will come out right.  The purpose of doing the accounting in terms of economic value added, however, to the exclusion of other schemes, is because it is only in the value calculus that the political struggle of individual against individual is reflected.  The valuation of one persons contribution to the social and material product in terms of the valuation of everyone else’s social labour.  But this is not the only factor in the valuation.  Because there is the simultaneous valuation of property rights.  This is a complicating, obtruding, assymetrical, and ugly situation.  Labour’s contribution I can understand.  But property?