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Continuity and Differentiability

By Kshitij Sharma, January 17, 2010

High school mathematics introduces the concept of continuous and differentiable functions as the first steps of calculus.

For a continuous function, if someone were to compute the value of a function at a point and at another point just besides it, then there would not be a lot of change in the value. In the language of mathematics, consider a function f(x), then f(x+d)-f(x) –> 0 as d –> 0. In common speech, a continuous function is one that does not change values abruptly. Differentiation (or derivative) as a mathematical concept is the rate at which a function changes value at a given point. In the language of mathematics, it is the slope of the tangent at a given point. A differentiable function is one for which a tangent exists at a point. In common speech, a derivative is the direction the function takes at a given point. Differentiability of a function determines if the function changes direction abruptly at a given point.

Life is a smooth function of time – continuous and differentiable. Taking time as the input, it does not change values abruptly, nor does it change directions abruptly. A function like life means that there are very few kinks.

Astrology that is based on movements of planets also follows this pattern. The planets move around the Sun and although we distinguish between houses and/or signs at 30 degree interval, the boundaries are blurred. Effect of one rashi can start before other ends. At rashi/bhava sandhi, a planet’s power to affect the house is almost nil, which means that it does not really matter at when it crosses from one rashi to another. It will do good or evil only when is has “fully” entered the house.

Eclipses are celestial events that affect this natural flow of life. Their occurrence helps the direction change by a small amount, but they do not at all deserve the vile reputation they continue to have. For that matter, a conjunction of Rahu/Ketu with Sun and Moon, even independently, can have a similar effect. Moon is said to be mortified of Rahu and a conjunction is said to cloud the mind and good judgment. This need not happen only during eclipses.

Astrologically, eclipses do make a difference, but people tend to make an unnecessarily big deal out of it. An astrologer cannot claim that someone became bankrupt due to an eclipse. The actual process would have started long back and a conjunction of Rahu/Ketu with Sun/Moon would be just the last straw to break the camel’s back. Still, it takes all the blame. The same event not have an equally devastating effect on a person with a strong ascendant.

From time to time, the kind of treatment Solar and Lunar eclipses gets from media and common folks is at best laughable. On the day of eclipse, almost all TV channels organize a debate between the astrologers and so called rationalists. Anchors, in a desperate effort to appear intelligent, always side with the rationalists. Sabse tez channels talk about vague combinations – “This happened 1000 years back”. They seriously need to rethink these headlines that attach unnecessary significance to such combinations. Does anyone even know if there was an event worth remembering or mentioning a 1000 years back? People use this opportunity to blame eclipses to blame everything from food poisoning to irritation in eyes, when in reality a person would have ventured outside and made the mistake of looking at the eclipse directly, against all advice.

I cannot explain natural calamities and misfortunes due to accidents where someone else’s mistake cuts short the life of many people at the same time. There is some research done in this area within astrology. However, my limited knowledge does not give me enough tools to understand and critique the theories put forward. Still, for astrology for “normal” people like me, we can live with the theory of continuity and differentiability.

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