Monday, January 3, 2011

Golden Ratio, SriYantra and Kuber's Treasure

Hello Readers,

Happy New Year 2011!

I have just revamped my Gandhi Stamps and Philatelic Materials website. Now it has an all-new design, with user friendly features that can help you navigate through the countries that have honoured Gandhiji easily. Please have a look:

Last month (December 2010), Notion Ink, a Bangalore based company formed by IITians launched Adam, a notepad that has been termed as an iPad killer. Notion Ink is an indigenous Indian company that had built up a lot of expectations from its users all over the globe due to its superior product offering and lower price.

The personal connect they had with their blog-followers did pay off, and the high-end version of Adam was sold out within a day of its release. I am sure all of us feel proud that a new, wholly India-based company could conceptualize, design, market and deliver such a world-class product. The response at the CES has been amazing. Hats off to them!

As I was going through their blog, I read references to the Golden Ratio (1.618), a figure sacred to designers. The Golden Ratio is also known by the number phi, and is otherwise called the Golden mean, Divine Proportion or the Golden section. This ratio can be described from the below figure:

As is seen, the ratio of one of the sides to the other is the same as the ratio of the sum of the sides to the former. This Golden Ratio has prime importance in architectural design, as it lends a very aesthetic appearance to the object. The Pyramids in Egypt have their dimensions in a proportion equal to it. Leonardo da Vinci, the famed inventor and artist, has used the Golden ratio is many of his creations, most famously, the Vitruvian man (brought into limelight through the book "The Da Vinci Code"). Even the ratio of Fibonacci numbers (1,1,2,3,5,8,...) is successively approximate to the Golden ratio.

I wanted to find out what relevance the Golden Ratio had to India and Hinduism, and I did find something interesting. Many of you would have come across the Sri Yantra, an object of meditation that finds place in Puja Rooms:

Now, Sri Yantras are formed by 9 interlocking isoceles triangles. 4 of them point upwards and represent the female energy Shakti, while the other 5 point downwards, representing the male energy Shiva. These triangles are not ordinarily composed, but have aspects of the Golden Ratio in them. Just as we can have rectangles drawn to the specifications of the Golden Ratio, triangles too can have their properties.

Triangles have 3 variates: The base length, the slant length and the height. The angle also plays a major role. What is amazing is that the triangle of the Yantra is a proportionate cross-section of the Giza Pyramid, incorporating both special numbers pi (3.142...) and phi (1.618...) ratio. And the base angle of the triangle in the Yantra is seen to be around 51 degrees, the same value that was attributed to the base of the Great Pyramid of Giza.

The standard form of the Sriyantra, with the 9 interwoven triangles, constitutes a total of 43 triangles. Different versions have circles and squares surrounding the triangles, and they are said to form the boundary within which Gods residing in the intersections can stay. The centre of the Yantra has a Bindu (dot), which is the focus of the way you can meditate. You can either start from the inside and move out, or do it vice versa. The former is seen to be a constructive view, while the latter a destructive one.

The Sriyantra might look a fairly simple design, but the construction is a highly complex affair. There are innumerous intersections that take place between the lines of the 9 triangles, and these cuts are supposed to be concurrent. Thus, changing the position of any one shape will require adjustments in all the corresponding figures. If the intersection of the lines does not happen at a particular point, the concurrency is lost, and so is the significance. There is a lot for research going on to find out the true meaning of the Sri Yantra. Some consider it the primordial source of life, and there was a finding about how it was a manifestation of the DNA form, etc. also

Now, there is another separate reference to the Golden Ratio in connection with Kuber, the God of Wealth. It is said that Lord Kuber's treasure, the most prized collection of wealth in the universe, is hidden inside the mystical Mt.Meru. This is guarded by Nagas, or serpents. Now, Mt.Meru is also the name given to a special triangle formed by the ancient mathematician Pingala, and is called MaatraMeru. And this triangle is today called the Pascal's triangle, which some of you might be familiar with:

What is of interest (as you will observe in the above figure) is that when you move diagonally upwards starting from the first digit on each line and sum the corresponding digits along each diagonal, you end up getting the numbers of the Fibonacci series, which in-turn are in the Golden ratio. Thus, it can be inferred that our ancient texts give special importance and reverence to this "divine ratio", forming it the basis of how one reaches the treasure of the Gods.

Till Next time, Happy and Prosperous New Year 2011! May you find health, wealth and happiness equivalent to Lord Kuber's treasure!

Nikhil Mundra


Friday, October 29, 2010

Indian Calendar - Panchang

Hello everyone,

The Diwali / Deepavali post last year:

seems to be bringing in truckloads of traffic to your blog. As I happened to glance at the calendar to count the days left for the festival of light, I got the inspiration for this post.

The calendar that we follow today is the Gregorian calendar, which was introduced in 1582. This was after it was found that the calendar in use till then, the Julius version, accounted for 365.25 days in a year, when in effect it was 365 days, 5 hours, 48 minutes and 46 seconds, thus slightly lesser than the assumed value. As a result, the equinox was moving steadily ahead in the year, and this was considered unacceptable.

As you know, in the current system, we have a leap year once every 4 years to compensate for the extra fraction of time taken by our beloved earth to revolve around the sun. In school, the unlucky individual whose birthday fell on 29th February was always urged to change his date of birth in order that he celebrate it ! The leap year problem is also an essential part of any quantitative aptitude test to ascertain the time period elapsed, etc.

Now, as the Gregorian calendar adds 1 day at the end of 4 years, it is not moving in synchronism with the sun. Spare the electrical jargon, but this is like a fixed step size, and does not vary smoothly taking into account the sun's variation.

Comparing the Gregorian with the Hindu calendar, generally referred to as the Panchang, we see that the Hindu version has a much more scientific relationship. While the former is based on the Solar variation and accounts for the earth's revolution around the sun as 12 months each having 30 days, the latter is based on the moon's revolution around the earth, where each month takes 28 days. To compensate for the loss of days, and extra month, called the Adhik Mas (mas is the word for month), is added every 30 months.

The Hindu counting of years generally concurs with the reign of a prominent king. For instance, the current year is the Vikram Samvat 2067, signifying that King Vikramaditya's reign started as many years ago (in 57 BC). There are many such Samvats known, but the Vikram Samvat is what is the most widely accepted and in use currently. The various months in the Vikram Samvat are listed below along with their approximate Gregorian Calendar counterparts:

Each of these months in the Hindu calendar (with 28 days) is subdivided into 2 cycles of moon waxing and waning. The 1st half is called the Krishna Paksha (dark period), where the moon wanes till Amavasya (new moon), and the Shukla Paksha (bright period), where the moon waxes till Purnima (full moon). This can be understood from the below image:

You can also check out my earlier post on the relevance of Ekadasi, the 11th tithi of the calendar:

The Hindu calendar in use is a combination of both solar and lunar inferences. The months are based on the moon, while the seasons are governed by the sun. A prominent example of a solar festival is that January 13-14 is celebrated as Pongal (in Tamil Nadu), Sankranti (north India) and Lohri (Punjab). All of these herald the entry of the sun into the Makar rashi, or the northward movement of the sun. Though the date is supposed to be somewhere between December 20th and 23rd, due to earth's tilt, it has kept sliding over years. Don't be surprised if in your future births, you find that Makar Sankranti is being celebrated in May, but that will take 1000s of years to come.

In fact, in certain temples, it is seen that on Sankranti day, sunlight graces the presiding deity. One of the temples that I can remember is the Sri Gavi Gangadhareshwara Temple in Bangalore, where the sunlight falls on the Shiva Lingam through Nandi's horns. Trust the ancients to establish the exact angle to honour God on the auspicious day !

Coming back to tithis, the days are calculated based on the actual longitudinal angular difference between the respective positions of the moon and the sun. Thus, it is common to see that the tithis vary in length, some shorter than our regular 24 hours, some extending beyond, and this leads to certain auspicious days being celebrated across 2 days of our Gregorian Calendar.

The Zodiac Signs or Rashis are another integral aspect of the Calendar, with 27 Nakshatras (Constellations) forming 12 Rashis, each of the latter accounting for 2.25 of the former. This is the basis of Indian Hindu Astrology, which again is a scientific art, and is very different from the general characterizations governing the Western Zodiac Date-of-birth based astrology. But more on that later, as it would requisite a separate post altogether...

For now, advanced wishes for a very Happy and Safe Diwali / Deepavali !

Nikhil Mundra

29th October 2010

Sunday, October 10, 2010

Jantar Mantar - Temple of Instruments

Hello Readers,

Being in Delhi, anyone fascinated by India's ancient scientific brilliance cannot afford to miss the Jantar Mantar. This historic observatory is located on Sansad Marg near Connaught Place. If you are in the mood for a walk, you can do so from the Rajiv Chowk Metro Station. Otherwise, it's a 5 minute ride in an auto-rickshaw.

The "Jantar Mantar" is a common name used to denote the set of 5 astronomical observatories built by Maharaja Jai Singh II. Apart from the Delhi, these observatories are located in Jaipur, Mathura, Ujjain and Varanasi. Except the one in Ujjain, all the others have stood the test of time.

The term Jantar Mantar seems to be a corruption of the term "Yantra Mantra", where Yantra means Instrument and Mantra means Formula. It can also be a corruption of the term "Yantra Mandir", which translates into Temple of Instruments.

The Jantar Mantar in Delhi had a total of 4 major instruments, listed below:

1) Samrat Yantra
2) Ram Yantra
3) Jai Prakash Yantra
4) Mishra Yantra

The images of these instruments are shown below. It is understood that the Samrat Yantra is unparalleled in its size, and is clearly the largest sundial in the world.

Please find all scientific information about the instruments in this enlightening document:

It is wonderful to note that Indians used scientific instruments of such huge proportionality so many years back !

Till next time,

Nikhil Mundra


Friday, August 13, 2010

Square Root Computation - Aryabhatta

Hi there,

If you would ask me to vote for the most horrifying part of mathematics in school, I wouldn't bat an eyelid before screaming : Square-root ! A common Maths joke is illustrated below:

For me, and for countless other school-children, determination of Square Root of a given number (running into numerous digits) would always prove an arduous task. Thank God we are allowed to use Calculators in colleges!

The standard method taught was that of the long division, shown below:
But did you know that the method to determine a Square root was devised by Aryabhatta, as early as 475 AD? Though the knowledge of Square roots existed in India from the BC ages, proof of the method is given in Aryabhatta's celebrated work, Aryabhatiyam. The relevant Sloka is given below:

Translated into English, it says:

Divide the Non-square place by twice the Square Root of the Square place, then subtract the Square from the next Square place.

Thus, a definitive method of finding the Square root was expounded by the great Indian mathematician and astronomer, Aryabhatta.

Till next time,

Nikhil Mundra


Saturday, May 15, 2010

Chess aka Chaturanga and Vishy Anand triumphs in Sofia, Bulgaria

Hello friends,

Vishwanathan Anand is World Chess Champion again ! The way Vishy beat Veselin Topalov with Black pieces speaks volumes of his brilliance. Playing on his opponent's home ground in a seemingly hostile environment, Anand held his nerves, the mind-champion that he is.

After Vishy was acknowledged as a prodigy, the interest in Chess in India, and particularly in the south, has been growing at a tremendous rate. We now even have national tournaments for age categories as low as Under-5 !

To celebrate, I found it apt to make a post on Chess, which has it's origins in India. It is believed that the game was called Chaturanga, and was developed somewhere in the 6th to 8th century during the rein of the Gupta Dynasty.

Chaturanga also translates into a 4-limbed creature, possibly referring to an army that had 4 divisions. It is to be noted that in the Mahabharatha, it is clearly mentioned that the army was subdivided into 4 - Infantry, Cavalry, Chariots and Elephantry.

Chaturanga was played on an 8x8 board called Ashtapada (or) Astapada.

The pieces that we are now familiar had similar roles and moves, but the names were in the Indian context. Given below in the list - first the modern names and then the Ancient:

King - Raja

Queen - Senapati (Prime Minister)

Bishop - Gaja (Elephant)

Knight - Asva or Ghoda (Horse)

Rook - Ratha or Chariot

I have also heard that the Bishop was referred to as Oonth (Camel), which was used in battles earlier.

The Prime Minister's role in Battles is definitely more predominant in strategic planning and execution. This is proven by the multitude of powers vested in the particular piece's hands, and the way the Prime Minister can control the entire board by moving left,right,forward,back and diagonal. Thus, the presence of the Prime Minister in the ancient form is justified.

In ancient times, it was unconventional for the demure Queen to go all out in a War. How the Prime Minister piece came to be called Queen in modern-day chess is a mystery. I guess it must be in line with the western idea of creating a pair and a romantic setting, and that a King without a Queen would not seem fitting.

Chaturanga became to be called Shatranj in Persia, and then was adopted by the West.

I found an image of a miniature painting that shows Krishna and Radha engrossed in what seems to be a game of Chess.

I also remember reading an interesting story in Tinkle some time back. A pandit brought a board to the king and explained him the concept of his game, called Chaturanga. The king was non-plussed about it and didn't think it was worth bringing the pandit and his game into spotlight. So the pandit challenged the king that he should place 1 grain of rice on the starting square of the board, and then continue multiplying by the serial number of the next square and placing equivalent number of rice grains.

As it turned out, the last square needed 64! (64 factorial = 64x63x62x61x60x......x1) grains, while the kingdom could not even provide the number of grains needed till half the board was accounted for. The king then understood the significance and power of the game and introduced it in his kingdom.

So this is a proud moment for all Indians that our very own Vishy Anand is at the top of the world with this Championship win in Sofia, Bulgaria. He has brought laurels to the game that is a testimony to Indian intelligence ! There couldn't be a more fitting brand ambassador for Indian Chess !

Nikhil Mundra

15th May 2010


Sunday, May 9, 2010

Scientific Indian Thali

Hello everyone,

Finding an article about the Science behind the Indian Thali, I just couldn't resist combining my top 2 passions - Scientific India and Food !

The epitome of Indian food is the quintessential Thali. It is little wonder that any travel-documentary is incomplete unless the presenter visits a restaurant that claims to serve the "Authentic Indian Thali".

Translated from Hindi as "Plate", the Thali comprises all the essential ingredients in a menu. The Thali has various variants that depend on the region where it is being served, but all the nutrients that are part of it remain almost the same.

So here comes a short post about the "Scientific Indian Thali". Check out the below link from Deccan Chronicle, one of the leading national dailies:

As mentioned, the Thali has all nutrients required for the effective functioning of our body.

However, in today's fast-paced world, such an elaborate arrangement with A-Z dishes is quite a luxury. No wonder we prefer fast-foods, that help bring down our health at a faster pace :-)

Nikhil Mundra

9th May 2010

Sunday, February 28, 2010

Holi, Colours and Bhang

Hi there,

Wishing you, your family and your friends a very Happy and Colourful Holi !

On this Joyous occasion, let me describe the significance of the Holi Festival and it's inherent meaning.

Holi is celebrated on 2 days:

1) Day 1 - Burning of a ceremonial pyre of wood and other waste materials

2) Day 2 - Playing with colours

For the background of the Prahalada and Hiranyakashyap legend, you can refer to my earlier post about the Narsimha Avatar of Lord Vishnu:

Here, before Lord Vishnu takes the form of Narasimha to kill the evil Asura Hiranyakashyap, there is an episode about the Asura King's sister Holika. This sister was very resourceful - she had the magical ability to withstand any degree of fire-burns, which meant she was invincible when it came to fire.

In order to get rid of Prahalad, Hiranyakashyap asked Holika to sit in a burning pyre with his son on her lap. Thus, he assumed Prahalad would get burnt, while Holika would come out unscathed. But to his horror, the exact opposite happened. Prahalad kept chanting Lord Vishnu's name and came out unhurt, while Holika went up in flames.

This event is celebrated each year as the 1st day of Holi, when a huge pyre consisting of wood, hay, and other items which are not useful is set up and then burnt. This scene is visible in various community centres where people gather to build up the pyre by contributing articles from their homes and then lighting it up.

This entire ritual is a symbolic rendition on the Triumph of Good over Evil. Moreover, lighting the pyre is a way to cleanse our house of old and useless things and to start afresh. The burning is done in community centres to bring about a sense of oneness.

The next day is what Holi has become most popularly associated with - the day when you play with colours. It is a fantastic sight to see people getting rid of their inhibitions and coming out in full force to drench each other in a variety of colours. The entire atmosphere looks like a huge canvas where everyone is a painter busy applying different shades of Red, Pink, Yellow, Green and Bloue onto his work of art. Dry colours (powder), Coloured Water and Small Balloons filled with water are all part of the celebratory instruments.

The entire atmosphere is ecstatic and one in which you flow with the happenings. Even the most introvert of persons tend to forget their shyness and mingle with people starting from friends right upto those whom they have never met in their lives.

Playing Holi is most famously associated with Lord Krishna, and in Mathura and Vrindavan witness beautiful scenes where Holi is played with a fervour like nowhere else.

One of the most controversial practices of the Colours Day is the consumption of Bhang. Extracted from the Cannabis plant (Cannabis indica), Bhang is an intoxicant which is known to be a stress reliever. Bhang is often associated with Lord Shiva, and his followers, the Naga Sadhus of the Kumbha Mela, are often seen smoking Cannabis.

Keeping with the free-spirited Colours Day, Bhang is mixed in Laddoos and a drink called Thandai. There is a good section that takes it willingly, though it is also a cat-and-mouse game with people trying to get others consume these intoxicating drinks without their knowledge. The results vary with the individual, with some getting mentally knocked out while others starting to blurt out hitherto hidden facts in their frenzied state.

Though Bhang (Cannabis) is banned in certain western countries, in India it is known to be a relaxant and helps those who can handle its effects. It has been part of the Ayurvedic tradition for a long time, and it is offically sold in Government Authorized shops in certain parts of India. Bhang is a big hit during the Holi season.

This day of playing with colours is what Holi has come to be most famously associated with. Metaphorically, it is an opportunity to splash colour into your plain life. Also, it a great chance to get to know new people from diverse backgrounds, or to bond up with old pals. It is a time to forget all your qualms, live life to the fullest and celebrate the joy of bonding with your friends.

Reader Mr.Koushik Roudra added the following - Holi is celebarted at the advent of spring. Burning the Holika also has a scientific significance - by burning the waste we are also creating flames, which will drive away the mosquitos. Also authentic gulal has a medical value for the skin, as in the earlier days it was made from Turmeric, Neem and other herbs.


Nikhil Mundra


Monday, February 22, 2010

Speed of Light

Hi there,

Posting after ages about a quantity that is a source of energy to all living beings on earth : LIGHT.

The most well-known source of light is the Sun, or Surya Dev in Hinduism. Suryadev has been worshiped in India since time immemorial following the traditional way of respecting and worshipping important forms of nature. Suryadev is a part of many festivals, including Pongal or Makar Sankranti, Chattha Puja, etc. The Surya Namaskara is a complete exercise procedure that is part of the daily-morning routine of many Indian homes. Will surely put up a post on this beautiful Yogic exercise soon...

It is a well-known fact that light travels at a phenomenal speed of 3 x 10^8 metres/sec. This value is etched into the memory of students in their early years in school, and is useful is solving umpteen number of problems where the constant 'c' is used to denote the Speed of light.

This value of the Speed of Light was established by the experiment conducted by Michelson and Morley, celebrated American Physicists in the 19th Century.

But did you know that a very close value to the calculated one was determined in the 14th Century AD in India? The below sloka is part of the Rig Veda:

Saint Sayanacharya (c.1300's), after reading the Rig Veda, gave the following comment:

The above translates into:

"It is to be noted that the Light due to the Sun travels 2202 Yojanas in half a Nimesha"

Now for the calculation. Converting the units used in ancient India to those used presently :

1 Yojana = 9 miles

2202 Yojanas = 19818 miles

1 nimesha = 0.21333 seconds

1/2 nimesha = 0.10665 seconds

Speed = distance / time = 19818 / 0.10665 = 185822 miles per second = 299044 kms per second.

The value calculated by Michelson and Morley was approximated to 186000 miles per second, which is used these days along with the more common 3 x 10^8 metres per second.

It must also be noted that Sayanacharya was only commenting on the Rig Vedic text. It is possible that even earlier interpretations and findings existed, but have not stood the tests of time.

Thus, our Ancient Vedic Indians had established the Speed of Light much before scientists in other parts of the world ! This again proves the Scientific knowledge of Ancient India. Very Enlightening, isn't it?

Till next time,

Nikhil Mundra


Thursday, October 15, 2009

Diwali / Deepavali - Festival of Lights

Hello everyone,

Coming back after a month long hiatus with a post on probably the most celebrated festival in Hinduism, Diwali.

As you know, people from all parts of the country celebrate Diwali with the same gusto and splendour. It is a time to visit friends and family, exchange wishes, interact and bond. It is also a time of great rejoicement and festivities. Diwali is a more general form of pronouncing Deepavali, which means an array of Deeps (lamps).

When I was young, Diwali for me was a day when I had a holiday from school (very important!), could wear new clothes and burst sparkling fire-crackers. Slowly, the concept has changed. Now Diwali has a deeper and more profound impact on me, and that is exactly what I would like to share. So let us look at the legends behind Diwali:

The first one is from Ramayan, which describes Diwali as the day when Lord Ram returned victoriously to his kingdom of Ayodhya after defeating the demon king Ravan of Lanka. Lord Ram was given an arousing welcome, and the entire city dazzled with Diyas. This was later celebrated as an annual festival called Deepavali or Diwali.

The second reference is related to Lord Krishna. Once there was an evil demon called Narakasura, who was a tyrant and was forever oppressing the common people. All of them prayed to Lord Krishna to relieve them from his clutches. Thus, Lord Krishna came and after an intense battle, he killed Narakasura using his Sudarshan Chakra. The people rejoinced, lit the city with lamps, and this incident came to be annually celebrated as Diwali.

If you look at the common thread between these 2 legends, it portrays the victory of good over evil, of light eclipsing the darkness, and of righteousness holding forth against all odds. Thus, the Diwali festival is a very symbolic one that extols us to kill our inner demons (negativities) and purify our soul by lighting it up with goodness.

Now let me give a brief description of the festival. Diwali is celebrated across 4 days, starting from the 13th day of the month of Ashwin. This day is called Dhanteras, literally translated into wealth-thirteenth. Interestingly, though the number 13 has negative connotations in some other religions, this day is considered a very auspicious one. It is an age-old tradition to buy gold and other ornaments on Dhanteras. Also, if one sees a house-lizard on that day, he/she is considered to be lucky. So do look out for those slippery creatures tomorrow!

Why is it good to buy jewelery on Dhanteras? I don't think there is any specific reason, apart from instilling a sense of savings in the family. If you consider the price of Gold, it is forever on the rise. If one has cash, there will be a tendency to spend it even for wasteful/useless purposes. But on the other hands, a solid ornament of gold can be a form of a saving, and a good investment too. This might also be the reason why purchase of gold on Akshaya Tritiya is suggested to be very auspicious.

The next day is the Choti (Small) Diwali, while Diwali and Badi (Big) Diwali follow the smaller one. For us Marwadis, Diwali is of special significance because of the Lakshmi Puja conducted on the main Diwali day. Lakshmi, being the goddess of wealth, is requested to forever remain in our home and not desert us. Diwali is considered the beginning of the new financial year, and new account books are opened on Diwali. The books, pen and the ink-pot is also venerated.

The Puja is conducted in the evening, after which, it is time to burst crackers. This is probably the most exciting part of Diwali. Crackers of all shapes, sizes and varieties light up the sky, and provide a visual treat to all the spectators. Though earlier the crackers were just a symbolic representation of light illuminating our lives, these days it has become a contest among people to show off their wealth by spending a lot of money on crackers.

Not only does this one-upmanship contribute result in literal "burning" away of money, it also contributes a lot towards environmental pollution. Crackers that illuminate are understandable to be synonymous with Diwali, but why do we need ear-deafening bombs and Ladis? It is beyond my comprehension. Also, let us look back at what goes into making these crackers. Helpless child-laborours working in inhuman conditions by foregoing their education produce the fire-crackers. Do we really need to burst crackers to enjoy a few moments while our brethren suffer for years?

So this Diwali, I hope we can go for a pure Diya day or just a minimal amount of cracker-bursting. Let us focus instead on lighting up our lives by killing our inner defects and illuminate the lives of others with our goodness.

Happy Diwali !

- Nikhil Mundra
15th October 2009


Friday, September 4, 2009

Vedic Maths

Good Afternoon,

Another appaling newspaper headline - A person in the USA applies for patenting the Vedic Maths method! Similar to patenting the physical practices like Yoga and Thoppukaram (alias Super Brain Yoga), people in the USA have now begun to patent our intellectual concepts like Vedic Maths as well...

So what is Vedic Maths? It is a way of computing Mathematical quantities at an extremely fast rate and is based on 16 basic Vedic Slokas/Sutras. The list of Sutras as mentioned in the Vedic Maths Foundation are given below:

The method, found in the Vedas, was lost for centuries, but was brought to light by Sri Bharti Krsna (Krishna) Tirthaji Maharaj, Jagadguru of the Puri Mutt from 1925-1960. After painstakingly researching the Atharvana Veda to make a compendium of all the shortcuts involved to make maths simpler, the Jagadguru was shocked when his entire manuscript was found burnt in a house fire. But he didn't lose heart, and before breathing his last, he rewrote parts of the huge-resource, even though we will never get to know the entire list of formulas.

The most simplest and commonly used method of Vedic Maths is the multiplication of large numbers in a fast way. Consider you are multiplying 123 and 456. You can either go for the long multiplication method, or use the one I have stated below, which can be done mentally (The lines between numbers denote multiplication) :

Finally, the result is 56088, which is the actual answer. The beauty of this technique is that it can be extended upto n digits in both multiplicants, and we could still use a one-line or mental calculation method. Do try it out for other numbers as well as larger ones...

For those of you who are interested, you can check out the book "Vedic Mathematics", authored by Tirthaji Maharaj himself:

Apart from this multiplication technique, it contains several other techniques that can be used to simplify topics such as Quadratic and Cubic equations, fractional coefficients, geometric applications of equations, Hyperbolas, Asymptotes, etc. Unfortunately, there is only a small intro to Integral and Differential Calculus. If only these topics would have been dealt in detail, it would make the life of so many school-children and would-be engineers. It certainly would have made mine a lot better :-)

- Nikhil Mundra


Saturday, August 22, 2009

Ganesh / Vinayaka Chaturthi - Surgery/Transplant & Moon-Waxing,Waning


I am a big fan of our Hindu traditions and our calender, simply because there is no month devoid of festivities! The basic background of celebrating so many times a year is that these festivals give us reasons to meet our relatives, interact with

them and share our joys and sorrows. Thus, we are forever in touch with our friends and family, and thus these festivals create a sense of bonding that unites us.

Why I particularly like them so much is that I get an excuse to gorge on the umpteen amounts of sweets that are prepared for each of these events :-)

This month (August) witnesses 2 biggies - The Krishna Janmashtami (celebrated earlier on the 14th of August), and the Ganesh or Vinayak Chaturthi, which falls tomorrow.

Lord Ganesha, also known as Ekdanta (one with a single tooth), Vinayaka, Vignaharta (remover of obstacles), etc., is the only mainstream God to have a non-human face. Legend has it that Goddess Parvati, wife of Lord Shiva, created a boy out of the cosmetic paste applied before her bath. The boy was beautiful and strong, and she instructed him to guard her home while she was bathing. Presently, Lord Shiva came and wanted to talk to his wife. The boy, unaware of who Lord Shiva was, refused to allow him inside. Even though Lord Shiva explained his relation, the young boy stood his ground, unwilling to waver from his mother's orders. Agitated, Lord Shiva ordered his army to attack him, but so brave was he that each of his Ganas bit the dust.

Unable to bear further humiliation, Lord Shiva resorted to a trick, where he confronted the boy from the front, while Lord Vishnu sliced off his head from behind with his Sudarshan Chakra. When Goddess Parvati came out, she was enraged to find her son dead. And when the mother Goddess, the source of all energy itself is angry, the world falls in a pall of gloom. The Devas realised that they had committed a huge crime, and tried to pacify her. But she would just not listen to them.

Finally, the Devas decided that the only way to create harmony was to bring back the child to life. But as the head had been mutilated, they could not use the same one. Thus, they went east, brought the head of the first baby elephant they encountered, affixed it on the boy's body, and brought him back to life. As an icing on the cake, the Devas agreed that from that day onwards, Lord Ganesha would always be the first God to be worshipped, and all Pujas would begin with him being venerated first.

Coming to the scienctific part, this legend indicates the first ever surgery/transplant taking place in history, with the head of the elephant being made a substitute for the slain boy's head. This would have involved a unique surgery, and we already know that our ancient Indians had a great knowledge of surgery from the books of Sushruta (More about his surgical brilliance in the future).

Another scientific connection related to Lord Ganesha is a legend associated with one of his early birth anniversaries and the waxing/waning of the moon. Baby Vinayaka, dressed up in all his finery was welcoming the various Devas for a grand celebration on his birthday. But he had not even touched a morsel of food since morning, and was feeling extremely hungry. On getting the first opportunity, he started eating all the dishes excitedly. This amused Chandradev (Moon), who openly ridiculed Lord Ganesha by laughing, thus making fun of his way of eating and his pot belly. All the Devas were shocked, as they knew that however childish Ganesha was, he was extremely knowledgeable, powerful and brilliant. Thus, the moon had incurred Ganesha’s wrath by insulting him like this.

Lord Vinayaka grew angry, and wanted to punish the moon for being proud and vain of his handsomeness. But Lord Shiva intervened and requested his son to be mild in his judgement. Ganesha then decreed that the moon would be confined to the night only, and would also lose some of its beauty. He added that the moon would not be visible in its full glory all the time, and would be waxing and waning in cycles. The moon, humbled by his offence, agreed to abide by these conditions. And Lord Ganesha went back to his merry eating.

Thus, we notice that the concept of the moon’s blemished surface (as seen from earth due to craters) have been mentioned in the texts of yore through this legend. Moreover, the phenomenon of the waxing and waning cycle of the moon has also been mentioned using this legend relating Lord Ganesha and the Moon.

Ganapati Bappa Moriya! Wishing all of you a Happy and Prosperous Vinayak Chathurthi.

-Nikhil Mundra


Friday, August 14, 2009

Jayadeva & Geeta Govinda - Stamps on Lord Vishnu's Dasavathars

Good Morning,

Though this post is slightly off-topic, it is related to the Dasavathars.

One of the things I am quite passionate about is Philately. I focus on all philatelic material (stamps,covers,etc.) related to Mahatma Gandhi. You would be surprised to learn that more than 90 countries have issued stamps on Mahatma Gandhi. The detailed scans are available on my website:

India recently issued a set of 11 stamps (yes, 11!) on the 12th century epic "Gita Govinda" by Jayadeva. This is perhaps the largest single set of stamps issued on a single topic together. The scan is shown below:

The stamp on the top is that of the author Jayadeva, while the other 10 stamps depict the Dasavathars.

The Gita Govinda is written with the view of Lord Krishna as the supreme being, and the Dasavathars being incarnations of Lord Krishna. What is interesting is that all the Avathars (Mathsya, Kurma, Varaaha, Narasimha, Vamana, Parasuram, Ram, Balaram, Buddha, Kalki) are the same as those described to be Lord Vishnu's Dasavathars.

Thus, it can be termed as just a different view-point, with the Dasavthars being a common link for the different chapters of Hindu worship.

- Nikhil Mundra
14th August 2009

Saturday, August 1, 2009

Dhwaj (or) Dhvaja Stambha - Flag mast - Lightning Arrestor

Hello everyone,

Stambhas (pillars) play an important role in both Hinduism and our ancient history. Kirti Stambhas were erected by Kings to commemorate their famous victories. The most famous one among them is the Vijay Stambha in Chittor, Rajasthan (shown below).

Literally translated into "Tower of Victory", it was made by Rana Kumbha to celebrate his victory over the combined forces of Malwa and Gujarat led by Mahmud Khilji in 1442.

The other variety of Stambha is the Dhwaja Stambha, which is a very common feature in most of the Indian temples. It is a tall post-like structure, which is referred to as the flag-mast of the deity of the temple. The Dhwaja Stambha is different from the Kirti Stambha, as it is characteristically thinner. Also, it is made of metal or has a metal covering rather than the former, which is made predominantly of stone.

During festivities, the Dhwaja Stambha is decorated with different types of flags to commemorate and celebrate that particular event. The Dhvaja Stambha is present in a straight line from the deity, just before the Vahana of the deity, which is also in the same axial line.

It is referred to as being a medium for the Heavens to be connected to the earth, which would refer to it being a spiritual connector between us earthlings and the supreme being, God, above.

But can this explanation have a deeper significance? Now what could be the reason behind constructing a metal pillar in the precincts of the temple? I believe that the Dhavaja Stambha is basically an ancient lightning arrestor. The principle of the arrestor is pretty simple, which can be understood from the below figure:

Whenever lightning strikes, the metal arrestor, placed such that it is the highest point of the region, induces the charge to conduct through it. The Arrestor then conducts the heavy electrical impulse directly to ground, thus preventing the building from getting damaged.

It can be noticed that the top of the Dhwaja Stambha is the highest point of the temple, and thus, whenever lightning would strike, the temple would be saved from the devastating damage that could have been caused. This is what could be meant from the explanation that it connects "Heaven to earth" (i.e.) it conducts the charges from the clouds above during lightning to earth or ground, which is the electrical term for a no-potential area.

It's really wonderful how our ancient Indian Hindus have incorporated this principle in order to safeguard the most important place of their social setting, the temples.

Till next time,

- Nikhil Mundra
1st August 2009


Saturday, July 25, 2009

Turmeric (Haldi, Curcumin) - The Magical Spice/Herb of India

Good Evening,

There are a lot of other discoveries and findings made by Aryabhatta, but I am taking a break for now. Will come back to Aryabhatta's scientific discoveries sometime later. This post deals with the various beneficial properties of Turmeric, one of the most important herbs of our tradition that has been used in India since time immemorial.

I am sure you would agree that there is no home in India which does not use Turmeric. Called Haldi in India, it is utilised for a variety of purposes in our daily lives.

Turmeric has been part of our cooking since aeons, and is used both as a spice as well as for natural colouring. Ayurveda cuisine refers to the use of turmeric in it's dishes, and that practice has been passed down the generations.

Get ready for a long post loaded with links, because Turmeric (Haldi) has a plethora of medicinalproperties due to the presence of the chemical Curcumin. Some of these are:

1) Prevention or Slowing down Alzheimer's disease. Please refer links below to understand the medical background:

One important point being mentioned is that because we have turmeric as a staple inclusion in our diet, Indians are found to be less vulnerable to Alzheimer's disease.

2) Turmeric (Curcumin) blocks Brain tumour activity:

3) Curcumin is helpful against pancreatic ailments:

4) Curcumin is anti-inflammatory, and thus is helpful in diseases like rheumatoid arthiritis and other autoimmuno diseases:

5) Turmeric helps in digestion by inducing bile juice, and is thus good for the liver too. That's why it's subscribed whenever someone in India has jaundice:

6) A summary of the anti cancer properties of Curcumin, the chemical in Turmeric (Haldi) is given below. It is observed that Curcumin aids the cell-cycle arrest, which, if allowed to continue, would help in the mutation of cells and development of cancer:

Detailed medical analysis of Curcumin is provided in the below link:

Apart from this, Turmeric (Haldi) has been used since time immemorial in India as a Grandma's cure for skin infections, cuts, wounds and lesions. Recent studies prove that Curcumin inserts itself into cell membranes, making them more stable and thus healing them. Refer the below link:

Turmeric (Haldi) has also been used in India as a cosmetic. People, especially the women-folk are advised to use it to get a glowing and radiant skin.

It is also a common ritual to apply turmeric paste on the to-be bride and groom before marriage in the traditional Hindu ceremony. Studies show that Turmeric helps fight Melanoma, a deadly form of skin-cancer. Refer below link:

I remeber my mother giving me a glass full of "Haldi ka doodh", or Turmeric dissolved in milk, whenever I had a cold/cough/fever, was feeling weak or was having body-pain. Turmeric seems to be a natural pain-killer and is seen to be helpful against all these symptoms. Please refer below links:

Another nice article summarizing Turmeric's benefits:

Phew! When I started this post, I frankly knew only about Turmeric's beneficial properties for Alzheimer's and Body pain. But even after so much of research and new benefits that I have learnt, I am sure there are still many things which have been left out. I think Turmeric (Haldi) does deserve another post in the near future.

So, the bottom-line is that Turmeric (Haldi), an inseparable part of Indian cuisine and Indian tradition, has been proclaimed and accepted as a wonder-herb for it's array of Medicinal properties. No wonder that it has been used in India for ages. Our ancestors had identified it's beneficial properties and made sure that it is both consumed on a daily basis and used for the specific ailment when required...

Till next time,

- Nikhil Mundra
25th July 2009