blog@Yantrajaal

Better standards of living, that many parts of the world enjoy, are often traced back to the renaissance in Europe that freed man from blind bondage to belief and allowed him to fly free on the wings of rational inquiry. These standards of course are defined in terms of material comfort -- food, clothing, shelter, safety and finally the leisure to explore the arts and the sciences. This leads to technical and administrative competence and the emergence of good governance that in turn, loops back to create even higher standards of living. While every society desires this virtuous cycle, those that have aggressively adopted a scientific approach were the ones that have been successful in overcoming or converting others to their point of view. Spiralling out of Europe and reaching out into the depths of America, Africa, Asia and Australia, it has been the triumph of the rational way -- based on facts, axioms, logic and reason -- that delivers material comfort to the population. bo...

Traffic jams are an integral part of roads in India -- it does not matter if you are at Dalhousie Square in the heart of Calcutta or you are at Panagarh on the Grand Trunk Road -- and when you are stuck you have a lot of time to think on your hands. You begin with cursing people around about their lack of civic sense and road etiquette but eventually you resign yourself to the situation and start thinking about the problem analytically. Could there be a game theoretic approach to the problem ? To begin with let us define a general traffic jam a little more precisely so that the problem is more tractable and amenable to a mathematical analysis. Anybody who has lived in IIT Kharagpur for any length of time knows that just outside the campus there is a railway level crossing (actually two) which are a reliable source of traffic jams on a regular and repeatable basis. Every day, 365 days a year, the gates close two or three times every hour and each time when they reopen there is a a...

I have been teaching Quantitative Techniques [ or more simply Statistics and Probability, for those who have given a miss to B-schools ! ] and as a part of my course I have taken the liberty to "borrow" heavily from the work of other teachers and professors who teach similar things in other parts of the globe. With all the talk of digital rights management and ownership of IP I feel rather guilty for having done so ... I could have of course acknowledged the origin of the information but since I have accumulated all this for a number of years, I really have lost track of what I got from where ! So I thought of doing something else -- and have decided to publish my entire set of slides under the creative commons license. Anybody who wants to teach Quantitative Techniques [ at least the first, introductory part ] is welcome to use my slides. This covers a little less than 30 hours of class room contact, with the rest being used to solve problems from the text book by Levin ...

In an earlier post on I had tried to explain why in the study of astrology it makes more sense to observe, track and validate correlations between events in the celestial sphere and that in personal life. An analysis of correlations is a standard tool or technique in statistics and so it makes sense to apply this technique in astrology as well. However, there are certain challenges in this approach because the format in which astrological charts are created or stored is not amenable to the kind of statistical analyses that we are familar with. To overcome this limitation and I have come out with a new way to store and retrieve horoscope charts using sparse matrices and relational database management systems. You can read about this mathematical technique in my paper Statistical Testing of Hypotheses in Astrology . An unexpected byproduct of this effort was my introduction to the Scribd service that allows you to convert any form of document OpenOffice, MS-Office, PDF and what not int...

A widely held perception about astrology states that astronomical bodies influence events in human life and this influence can be benefic or malefic. This CAUSALITY is extremely difficult to justify in scientific or rational terms and has led to vague and vacuous explanations in terms of mysterious "rays" that emanate from planets -- and can be focused by gems and jewels -- or in terms of as yet unexplained gravitational and electromagnetic "action-at-a-distance" mechanisms. But strangely enough, even though astrology does not lend itself to a rational explanation we find that some of the most rational and scientific people on the planet, many of them renowned mathematicians, have a strong belief in this phenomenon. How is it that very rational people subscribe to this apparently irrational body of knowledge ? The answer is very simple if we replace CAUSALITY, as the operating principle of astrology, with the concept of CORRELATION . What does this mean ? Su...