Jan 2, 2011

I wish my son/daughter to be born on the day of Solar Eclipse on 4th Jan 2011

I see loads of superstitions in my family and neighborhood, not that this is the only such place in the world. Most of these superstitions are harmless, meaningless, costs a little, and typically gets the tag of culture. The rationale I keep hearing is - our ancestors have started this practice, they must have done it for a good reason, it could be valid forever, and it's like insulting them if we don't continue it. Irrational orthodox people do it because of the fear of god - if we do it, god helps us, otherwise god punishes us.

Here's how a typical superstition looks like. Few centuries ago, there was an orthodox Hindu family in a village. They had a cute cat in the house. Normally, they liked the cat running around the house. In one of the festive events, they felt it was annoying to see the cat coming in the way of holy rituals. So, the father asked his son to hide the cat in a basket. He used an ingeniously made basket which was used to store grains. They started using this simple trick during all the festive events in the family. More than a couple of generations passed by, this trick was kind of inherited as a family tradition. The family expanded with marriages and as the marriages mostly happened within the caste (a particular caste of Hindu), the tradition gradually became a tradition of the caste. If they didn't have a cat in the house, they borrowed a cat from the neighbors for the tradition. By this time, it's no more just a trick, it's a superstitious tradition. Coming to the present time, one such family residing in Bengaluru city, on every festival, gets a cat from neighbors. They have bought a traditional ingeniously made basket only for the tradition. Over the time, some other processes are added to the tradition by the religious gurus of the caste. The father has to hand over the basket to the eldest son during auspicious time of the day. The basket and the cat should be decorated like holy deities. They need to put a red dot (tilak/kunkum) on the forehead of the cat and feed it with a glass of cow's milk before hiding it in the basket, which is to be kept in North-East corner of the house. This tradition brings peace and prosperity in the house and if it's broken, it'll reduce the age of the father by an year. Some descendants staying in North America, rents a cat from local pet-store on every festival. They twisted the tradition a little bit by using a plastic basket, which made their relatives in India very angry because they think that's going to cost their father's age. Because they are smart and moderate, they convinced their relatives that they haven't forgotten the tradition unlike some so-called-rational relatives in India. If this looks like I'm exaggerating it, some of our superstitious traditions are worse.

In the cat-under-the-basket tradition, it's clearly started for a reason. It's just that along with the tradition, the reason didn't pass through mostly because we don't question our elders. Questioning is not taken so well, especially youngsters questioning the rationale behind the traditions is treated like a sin. Probably this is the main reason for the existence of superstitions in India. Some traditions may still have a significance, but a lot of them are obsolete. This is one class of superstitions - they started for a reason long time back, and are continued even when the it doesn't make sense.

The reason behind most of the superstitions around pregnancy and child-birth are relatively easy to understand. Pregnancy is one of the most significant natural processes in our lives. Not much was known about how the baby was being developed and how the external factors affect the sensitive fetus and the mother. It was very sensible to play safe when things are very unsure especially when it matters so much to us. The recommendations somehow turned into must-do things either because they were told by our elders or because someone has introduced the fear of god in process. Here are the typical traditions/myths/superstitions around the eclipses that I keep hearing.

1. Do not step out during the eclipse. Otherwise, it damages your eyes badly if not other parts, and damages the fetus of pregnant women.
2. The food is poisoned during the eclipse. Hence trash all the food after the eclipse and cook fresh food.
3. Eclipse is an evil phenomenon. After the eclipse, you should take bath and also sanitize the house by sweeping the floor and/or throwing drops of holy water.

All these are myths! Solar Eclipse is a spectacular natural phenomenon. When the Moon comes in between the Sun and the Earth, the shadow of the Moon falls on the Earth blocking the view of the Sun. In olden days, when they didn't know it, were naturally frightened by the look of it because it looks like the so powerful Sun is being eaten by some dark force. That must have given the sense of evil act. Sun light is not just the bright visible light, it has ultraviolet rays which are harmful to some extent. Even on non-eclipse days, we are exposed to this light and we don't stare at the Sun in bright light. During eclipse, mostly because of blocking the brightness and the spectacular-ness of the event , people are tempted to stare at it. This may harm your eyes if you don't use UV protection glasses. So, use UV protection glasses and enjoy the spectacular event. During the eclipse, a part of the light is blocked by an obstacle (the Moon), which is not synthesizing any new radiation. It doesn't poisons the food. If this poisons the food, we would have to throw all the green leaves and vegetable grown/growing in the fields. Or we must stop eating green leaves and vegetables for few more months because they might have poisoned by the eclipse few days back when it was in the field/storage. Don't waste food for this fear. If you are taking bath immediately after the eclipse and cleaning your house for the fear, good for you, thanks to the eclipse. I pity you for needing a false reason to do a good job.



The image you see here is from a traditional calendar in Kannada. It essentially says - Solar eclipse is from 12:10PM to 4:30PM peaking at 2:20PM. It asks senior citizens, kids, ill people and pregnant women to have food before 7:30 AM on Tuesday. It indicates that all these people shouldn't eat from 7:30AM till the eclipse ends in the evening. It also mentions that the eclipse brings bad luck to all the regions on which it appears.

As solar eclipse is treated as an evil phenomenon and also it's a new moon day, obviously a child born on that day is considered very unlucky. If my son/daughter is born on such a day, it gives me a chance to make a point that it really doesn't matter. There is a risk of my relatives pointing to it whenever a little something happens to my child. I don't think the day the child comes out of its mother's womb matters so much on its behavior and the luck. Genetic behaviors are mostly decided much before the delivery day, mostly at the time of inception. As far as luck is concerned, no one knows because of the complexity of the world we live in, or at least not based on the day/time the child comes out of its mother's womb.

If you agree with me about the above mentioned practices as myths, you can try to convince your relatives/friends by demonstrating the following act. Solar eclipse on Jan 4th is a partial one and it's not going to be seen in India, at least not in South India. But our traditional calendar says the whole duration is from 12:10PM to 4:30PM with peak time as 2:20PM. At around 2:20PM, go out in the Sun for couple of minutes. There's no point in staring at the Sun because the Moon's shadow is not falling in our region. Also, during the eclipse time, make sure to grab something to eat. These are simple acts to demonstrate that we now know that these are myths.

The reasons behind superstitions could be a simple trick like the one in cat-under-the-basket tradition or lack of knowledge at that time. It's the responsibility of younger generations to reason it out and stop the traditions which doesn't make sense now.

Regards,
Channa Bankapur

Nov 3, 2010

These Religions are obsolete

Religion is not something you believe or not. It's a set of rules to follow for a better living. Unfortunately, most of the known religions are based on the concept of God just to implement the rules effectively. Over the time, people glorified the concept of God with superficial rituals burying the core rules for a better living. Typical core rules of most of the religions are:
1. There is a creator of the universe called God.
2. Don’t kill or hurt anyone.
3. Marriage is a holy bonding and don’t commit adultery.
4. Don’t lie.
5. Help the needy people.

All these core rules makes proper sense for us to have a civilized society (except for the first one). The people who were instrumental in forming these religions were intellectuals with probably good intentions of building a better society. They knew the truth that they needed an imaginary superpower concept called God to make the people follow the rules. Otherwise, people don’t have any incentives to follow these founder’s advice. So, the good intellectuals used the concept of God which was elegant to build a better society in which people doesn’t kill each other for personal benefits.

In comparison, the Constitution of India can be treated as a book of religion for the citizens of India. It's not whether you believe or not in the Constitution of India, you got to follow it if you want to be in India. The Government including Judiciary is the care-taker of the Constitution to preach and enforce it. Similarly, the religions also nominated some people to preach and spread the religion. The Constitution of India which was written 60 years back was a great effort to put the rules together. Nevertheless, it's good to amend (modify) it time to time to tune the rules and make it better. Similarly, religions like Hinduism and Christianity were formed many centuries ago and the intellectuals who are instrumental in forming these set of rules have done a great job. Christianity was formed out of an amendment to the old testament, which is still followed by Jews. Hinduism might have amended a few times in its early times. Later, the people stopped amending them because they lost the clue of how and why they were actually made and strongly believed that they were made by the God and hence should not be amended by people. Somehow, the God which was used as an instrument to implement the religions has become the obstacle of its evolution.

I guess, this dead-end to the evolution of the religions has led to the formation of Constitutions/Governments like Democracy, Socialism and Communism. My comparison of the democratic Constitution of India as a religion is not incidental, that’s how a religion looks like if it’s designed today. The rules of a modern religions say, if you kill people around you, it’s not God but we’ve system in place to punish you. These are evolving unlike the religions. These forms of Constitutions are new age religions and the old age religions are still carried on as a legacy. I think these old age religions are obsolete and hence we should all stop following them.

Why do I say the older religions are obsolete? Don’t you see they are no more a reason for a better living and are often the reason for violence. Also, false concept of God has suppressed the values which were originally intended for. Just because we don’t know how exactly our universe is made and the phenomenal size of it, don’t make false assumptions of superpower called God. And, these religions are not improved/amended for tens of centuries.

People are generally excited about miracles. That's human psychology. The concept of God is an easy way to fulfill those imaginations. It’s easy to tell a kid that there is someone up there watching everything you do, so don’t do anything wrong. It reminds me of a short story. A kid who goes to a school in a neighboring village comes home after evening when it’s pitch dark on his way. He’s naturally is very scared. So, his mom tells him that ask for help of the God to look after you in such situations. Next time around, the kid starts chanting his favorite God’s name asking the God to come with him. Because the kid has diverted his attention to something else and also he’s imagining the God is with him, he’s psychologically secure and walks without fear. This ends the moral story. Here, all that’s God is imaginary, but it works for him. The imagination has helped the kid to come out of fear. But in reality, the things haven’t changed, the kid is still walking alone. The original fear of the kid is, if some thief catches him in the lonely place, he’ll be robbed. The situation hasn’t changed. If a thief finds the kid, he’ll still be robbed. The concept of God helps kids to stop unnecessary fear and also from doing bad things when no else is watching. Ignorance of the kid helps to solve the problem. Ignorance is bliss!

The points I want to stress are
1. The concept of God is imaginary and is entirely in your mind.
2. The religions are rules for a better living, but are not updated with time and hence they are all obsolete. So, stop following the obsolete rules.
3. Use your mind and take the good rules from the Religion and add them to the Constitution of your country so that you are doing your bit to make a better society around you.

Think about it!

Regards,
Channa Bankapur

Oct 4, 2009

Can't We Get Rid of Recurring Fractions ?

When I was writing about Dozenal Number System (or Duodecimal Number System), this thought struck me.

In Decimal Number System, just looking at the last digit (least significant digit or unit’s digit) we can say whether the whole number is divisible by 2, 5 and 10. Looking at the last two digits we can say its divisibility by 2, 4, 5, 10, 20, 25, 50 and 100. Looking at the last three digits the divisibility list grows little more and so on. It also means that if there is a fraction of the form k/2, k/5 or k/10 (where ‘k’ is an integer and the fractions are in their minimal form), in real number format, there will be one digit after the fractional point. Similarly, fractions of the form k/4, k/20, k/25, k/50 and k/100 will have two fractional digits. We know that some fractions like 1/3 and 1/7 will never end becoming recurring fractions. It means, to know whether the divisibility by 3 or 7, we need to see the whole number, not just a constant number of digits. What makes some denominators to end after constant number of digits (after the fractional point) and some repeat forever?

To understand the behavior of recurring fractions, let’s dissect the base number. Prime factorization of the base number 10 is 10=2*5. This should explain the divisibility list for the last digit {2, 5, 2*5}. When two digits are considered, the prime factorization comes down to 10*10=2*2*5*5, which gives us the divisibility list for the last two digits {2, 2*2, 5, 2*5, 2*2*5, 5*5, 2*5*5, 2*2*5*5}. Consider any number of digits; they are made up of only 2s and 5s. That’s why if the denominator of a fraction (in minimal form) is made up of only 2s and 5s (and no other prime numbers), only then it ends in constant number of fractional digits. For example, 1/2000 where 2000=2^4 * 5^3 (four 2s and three 5s) would surely end with four fractional digits. And, for example, 1/6 where 6 has a 2 and a 3 will end up as recurring fraction because it has a prime factor other than 2s and 5s.

Recurring fractions are not just limited to Decimal NS, they occur in any n-base Number System (where ‘n’ is any finite integer >= 2). If the denominator of a fraction (in minimal form) has a prime number which is not in the base number, then the fraction ends up as a recurring fraction. For example, in Dozenal NS, the base 12 is made up of 12=2*2*3. A fraction in Dozenal NS, 1/5 for example, would be a recurring fraction. We can see that in any n-base NS, reciprocal of a prime number which is not in the base number, would be a recurring fraction. So, isn’t there any way of having a number system without the fuss of recurring fractions?

I think there is a way!

Regards,
Channa Bankapur

Aug 1, 2009

Dozenal Number System


During my IISc days (2003-05), I had this raw thought. I began to think that Dozenal (base twelve or duodecimal) number system should have been the de facto number system in the world instead of decimal (base 10). Couple of days back, when I set out to pen down my thoughts, I got this page on Wikipedia - Dozenal/Duodecimal Number System http://en.wikipedia.org/wiki/Duodecimal. Déjà Vu! My raw thoughts explained! Not just that, there is a whole bunch of people who feel the same. To my surprise, a book has been written on this topic long back in 1935 by Emerson Andrews; New Numbers: How Acceptance of a Duodecimal Base Would Simplify Mathematics. And, there are groups formed in the interest of Dozenal system; Dozenal Society of America (DSA) and Dozenal Society of Great Britain (DSGB).

The wiki page I mentioned above describes what I wanted to describe. However, I will write whatever I had set out to, in as far as layman’s words. I have picked majority of the terminology from the wiki page including the word Dozenal in place of Duodecimal.

What would be one reason which made humans to think of using Decimal number system? Even Roman number system basically follows Base Ten. The main reason being, people could count using fingers of both hands up to ten. That made them to invent ten symbols to start with, and then for multiples of ten and powers of ten. For all of us, Decimal system is deeply rooted in our mind. So, any new system won’t look better than that. If you are being introduced to a number system for the first time and the whole world follows the same, then which one would be great.

First, let’s see what’s wrong with Decimal system. Of the five most elementary fractions (1/2, 1/3, 2/3, 1/4, 3/4), two of them end with recurring decimals, the other two end at second decimal point, and only 1/2 ends at first decimal point. When you had to divide something for three people, haven’t you felt weird to say each one gets 33.33 percent? And, adding up 33.33 of three people will get 99.99 instead of 100. When you are given a large number, to find whether it can be divisible by small numbers, it is easy to see whether it’s divisible by 2, 5 and 10 just by looking at the last digit. But, finding divisibility by as small number as 3 needs more effort. This matters in known situations like finding modulus. Modulus is simply the reminder function. For example, if I am asked to share 127 bucks among 5 people, I immediately yell out – how do I share the last 2 bucks. Because just by looking at the last digit, we can say modulus 5 of 127 is 2. If I am asked to share among 3 people, I had to put more effort to see whether it can evenly divide for 3. We see that knowing a number whether it’s even or odd almost instantly comes very handy. In a similar way, if we could find whether dividing the number by 3 yields a reminder 0, 1 or 2, it would have been widely used by common people.

So, there are benefits of having more divisors for a base number. Ten has only 4 divisors; 1, 2, 5 and 10. We can find bigger numbers, which has lot more divisors, say 60 which has 12 divisors. But choosing bigger base number means more symbols. Using 60 symbols for a digit is not a great idea. On the other hand using very small base like 2 or 4 would mean the whole numbers will have lot more digits even for not so big numbers. For example, a three digit number in base 10 such as 800 or 900 would require 9 digits in base 2. So, we need to find a base number around 10 and has good number of divisors. I keep calling this property of having number of divisors as Composite Potency. The higher the potency, the better it is! There is a known property by the name Highly Composite Number (HCN). A positive integer is an HCN if it has more divisors than any smaller positive integers. So, HCNs are good candidates for choosing a good base number. Here are first few HCNs (in parenthesis, number of divisors).
1 (1), 2 (2), 4 (3), 6 (4), 12 (6), 24 (8), 36 (9), 48 (10), 60 (12), 120 (16), 180 (18), 240 (20), 360 (24).
Ten is not an HCN! Ten has just 4 divisors, but a smaller number six has the same potency. Why is number 10 left behind? Look at the divisors of an HCN. They get good number of lower prime numbers. 10 has got 2 and 5. 6 has got 2 and 3. Both of these get two prime numbers, but number 6 has grabbed the lower one (number 3) and hence emerges as a winner. That’s why 6 is better than 10.

Highly Composite Number (HCN) concept was presented by Srinivasa Ramanujan in 1915. He also mentioned of Superior Highly Composite Numbers, which is a subset of HCN. First few Superior HCNs are 2, 6, 12, 60, 120, 360, and 2520. Now, these are superior candidates for a great base number! Because 2 and 6 are too small and 60 (and above) are too big for a base, it boils down to 12.

We see many of these numbers (HCNs) are used in non-metric measurement systems mostly due to their ease of use in calculations. For example, there are 12 inches in a foot, 36 (=12*3) inches in a yard, 12 ounces in a pound, 24 (=12*2) hours in a day, 60 minutes in an hour, 60 seconds in a minute, 12 months in a year, 12 old British pence in a shilling, 12 items in a dozen, 360 degrees in a cycle, etc. Metric system has been introduced to align these measurements with Decimal number system.

With Dozenal number system, the all five most elementary fractions (1/2, 1/3, 2/3 , 1/4 , 3/4) ends at first decimal point, which simplifies a great deal of calculations. Look at the factors of 12; 1, 2, 3, 4, 6, 12. It covers five of first six natural numbers. However, handling with number 5 becomes tougher when compared base 10. If we try to include 5 also in the base, the base number would jump to 60 (=12*5), which is too big a base number. It’s interesting to note that base 60 (Sexagesimal) number system has been used in some ancient cultures like Babylonian.

To adopt Dozenal number syste, we need twelve symbols to represent a digit. We could use 0 to 9 similar to decimal and two different for decimal equivalents of ten and eleven. 10 of Dozenal would be 12 of Decimal. We could simply use A and B for decimal ten and eleven for now. However, there have been varied suggestions for the two new symbols. Emerson Andrews suggested symbols which mostly looked like “x” and “e”, which were inspired by “X” of Roman 10 and “E” of word “Eleven”. Dozenal Society of America and Dozenal Society of Great Britain promote the widespread use of Dozenal number system. In Dozenal system, “Dozen” is the word for 10 of Dozenal (12 in Decimal), “Gross” for 100 (144=12*12 in Decimal), and “Great Gross” for 1000 (1728=12*12*12 in Decimal).

I personally feel that if we could replace Decimal by Dozenal Number System, the coming generations would grasp Number System fast and will hate Mathematics little less. And, even for higher end Mathematics, things would become easier and faster. Obviously, overnight replacement is impossible and doing it in couple of years is also foolishness. It should be over generations and phase out Decimal system gracefully. Next generation should be introduced to both systems and they will treat them as two languages of Mathematics in which Dozenal is for the newer world and Decimal is legacy. Wherever needed, conversions across systems should be simple. Does it makes sense to spawn “Dozenal Society of India”? What do you say?

Regards,
Channa Bankapur