Monday, June 10, 2024

Master the 16 Sutras of Vedic Math and Solve Problems Faster Than Ever Before

Vedic Mathematics, a collection of techniques and principles derived from ancient Indian scriptures known as the Vedas, has captivated the interest of mathematicians and educators alike. This fascinating system of mathematics is renowned for its simplicity and efficiency, making complex calculations remarkably easy. As we delve into the Sutras of Vedic Mathematics, we'll explore its origins, techniques, benefits, and how one can master this ancient knowledge system.


The Origins of Vedic Mathematics

The term "Vedic Mathematics" was popularized by Swami Bharati Krishna Tirthaji Maharaj in the early 20th century. His book, "Vedic Mathematics," published in 1965, compiled various mathematical techniques that he claimed were derived from the Vedas, particularly the Atharva Veda. Though the historical accuracy of these claims is debated, the effectiveness of the techniques is undisputed.

Vedic Mathematics is built upon 16 sutras (aphorisms) and 13 sub-sutras, which are concise formulas or principles that can be applied to various mathematical problems. These sutras provide innovative methods for arithmetic, algebra, geometry, calculus, and more, promoting mental agility and speed.


Examples of Vedic Math Techniques

One of the most celebrated techniques in Vedic Mathematics is the "Vertically and Crosswise" method, which simplifies multiplication. Let's explore this with an example:

Multiplication of 32 and 43

Step 1: Write the numbers in a vertical format:

       32

    × 43


Step 2: Multiply the digits in the units place (2 and 3):

    2 × 3 = 6

    This is the units place of the answer.


Step 3: Apply the crosswise multiplication and add the results:

    (3 × 3) + (2 × 4) = 9 + 8 = 17

    Write 7 in the tens place and carry over 1.


Step 4: Multiply the digits in the tens place (3 and 4) and add the carry-over:

    3 × 4 + 1 (carry) = 12 + 1 = 13

    Write 13 in the hundreds place.


Thus, the product of 32 and 43 is 1376.


Another technique is the "All from 9 and the Last from 10" method, used for quick subtraction:

Subtraction of 1000 - 678

Step 1: Subtract each digit of the subtrahend from 9, except the last digit, which is subtracted from 10:

    9 - 6 = 3

    9 - 7 = 2

    10 - 8 = 2

Therefore, 1000 - 678 = 322.


Benefits of Learning Vedic Mathematics

1. Speed and Accuracy:

Vedic Maths significantly enhances the speed and accuracy of calculations. The techniques allow students to solve complex problems faster than traditional methods.

2. Mental Agility: 

Regular practice of Vedic Maths sharpens the mind, improving concentration and memory. It encourages mental calculations, reducing the dependence on calculators.

3. Foundation for Higher Mathematics: 

The principles of Vedic Maths provide a strong foundation for understanding higher mathematical concepts. It simplifies complex algebraic and geometric problems, making them easier to comprehend.

4. Confidence Boost: 

Mastering Vedic Maths techniques builds confidence in students. The ability to solve problems quickly and accurately instills a sense of achievement and encourages a positive attitude towards mathematics.


Mastering Vedic Mathematics

1. Start with the Basics:

Begin by familiarizing yourself with the 16 sutras and 13 sub-sutras. Understanding these foundational principles is crucial.

2. Practice Regularly:

Consistent practice is key to mastering Vedic Maths. Work on different types of problems to apply the techniques and improve your proficiency.

3. Use Resources: 

There are numerous books, online courses, and videos available that teach Vedic Mathematics. Swami Bharati Krishna Tirthaji’s book is an excellent starting point. You can get a copy of the above book from Amazon

4. Join Study Groups:

Collaborating with others who are learning Vedic Maths can be beneficial. Study groups provide support, encouragement, and opportunities to discuss and solve problems collectively.

5. Apply in Daily Life: 

Incorporate Vedic Maths techniques into your daily life. Practice mental calculations while shopping, during travel, or in any situation that involves numbers.


Conclusion

Vedic Mathematics offers a glimpse into the profound knowledge systems of ancient India. Its techniques, while simple, are powerful tools for enhancing mathematical skills. By embracing Vedic Maths, students and enthusiasts can develop a deep appreciation for this ancient wisdom, experiencing the joy and confidence that comes with mastering the art of calculation.

Tuesday, November 30, 2021

Mind your language!

There were a language family of ancient India; usually this family is called Indic by modern linguists. There were a number of dialects. This language was preserved in epics and ritual incantations that were carefully memorized and passed down through the generations. Because of the religious nature of these pieces there was a religious devotion to preserving them exactly.

About the fifth or sixth century BCE a grammarian named Panini carried out a program of regularizing Indic. In effect, he created a dialect of Indic in which the irregularities were eliminated. He formulated nearly four thousand rules concerning grammar and morphology (the formation of words) for this dialect. Thus this dialect of Indic was called the perfected or refined language. That is the meaning of Sanskrit, the perfect language. 

The period of Classical Sanskrit is designated as c. 500 BCE to 1000 CE.
Observing some of the quotes, one can infer that the western society had high regard to Sanskrit
"Sanskrit is the original source of all the European languages of the present day." (By Mons. Dubois)
"Sanskrit is the mother of all languages" (By Francois Gautier)
In 1980 NASA declared it to be "The most unambiguous of all human speech and best suited for Computer processing and artificial intelligence".

There are 51 letters in the Sanskrit alphabet. These are properly arranged and alphabets are spoken from particular part of mouth or throat or nose. Due to this scientific nature of the method of pronunciation of the vowels and consonants in the Sanskrit, every part of the mouth is exercised during speaking. This results into speakers of Sanskrit being able to pronounce words from any language.

“Every one of its vowels and consonants has a particular and inalienable force which exists by the nature of things and not by development or human choice… its (Sanskrit’s) basis is universal and eternal.” ~ Sri Aurobindo

It is said that the language of Sanskrit itself arises from these very root sounds or vibrations of the Universe. The various vowels and consonants that make up Sanskrit words represent these core sounds, known as beejah. Whilst in states of deep resonance with the cosmos (in other words, while in meditation), the Rishi could perceive these beejah sounds; and from this profound sense of perception, they recognized the inherent sounds of each and every thing. A Sanskrit word is not randomly chosen to name something, in fact, proper, or rather, perfect, pronunciation of Sanskrit words, it is told, can replicate the exact nature, or essence, of that which it is referring too. 

In July 1987, Forbes magazine published news that, "Sanskrit is the most convenient language for computer software programming".

Well-known linguists and computer-scientists have expressed the opinion that Sanskrit is the best language for use with computers. Based on the paper by Rick Briggs, published in AI Magazine that talks about using Sanskrit in natural language processing (NLP). The idea of using natural language for computer programming is to make it easier for people to talk to computers in their native tongue and spare them the pain of learning a computer friendly language like assembly/C/Java! So in that way Sanskrit speakers would be almost ready made computer programmers!

What you write is what you speak.
Sanskrit is phonetic language so unlike other crude languages where every word has different spelling and pronunciation, here in Sanskrit you speak what you write!

And the whole aim of developing a language is wasted if we need to remember two versions, one for writing and one for speaking!

Also every word can be broken into sub parts by using rules of Viched (separation). If you use rules of Sandhi-Viched (combination-separation) then even if you know only thousand words, you will develop your vocabulary of several thousands of words!


Grammatically Perfect & Rock Solid!!
Sanskrit grammar (Panini) is perfect without exceptions so you would not have sentences with ambiguous meanings. 

Pāṇini's grammar is the world's first formal system, developed well before the 19th century innovations of Gottlob Frege and the subsequent development of mathematical logic. In designing his grammar, Pāṇini used the method of "auxiliary symbols", in which new affixes are designated to mark syntactic categories and the control of grammatical derivations. This technique, rediscovered by the logician Emil Post, became a standard method in the design of computer programming languages.

In Optimality Theory, the hypothesis about the relation between specific and general constraints is known as "Panini's Theorem on Constraint Ranking”

Pāṇini, and the later Indian linguist Bhartrihari, had a significant influence on many of the foundational ideas proposed by Ferdinand de Saussure, who is widely considered the father of modern structural linguistics.

Saussure himself cited Indian grammar as an influence on some of his ideas. In his Mémoire sur le système primitif des voyelles dans les langues indo-européennes (Memoir on the Original System of Vowels in the Indo-European Languages) published in 1879, he mentions Indian grammar as an influence on his idea that "reduplicated aorists represent imperfects of a verbal class." In his De l'emploi du génitif absolu en sanscrit (On the Use of theGenitive Absolute in Sanskrit) published in 1881, he specifically mentions Pāṇini as an influence on the work.

Noam Chomsky has always acknowledged his debt to Panini for his modern notion of an explicit generative grammar. In Chomsky and Morris Halle's 1968 text The Sound Pattern of English, the authors give an implicit nod to the Ashtadhyayi by formulating their final rule "ā →   ā", which echoes the  final Pāṇini's final rule, "a a iti".

“Panini's work was the forerunner to modern formal language theory (mathematical linguistics) and formal grammar, and a precursor to computing.” Ref: O'Connor, John J.; Robertson, Edmund F., "Panini", MacTutor History of Mathematics archive, University of St Andrews

“Panini used the method of "auxiliary symbols", in which new affixes are designated to mark syntactic categories and the control of grammatical derivations. This technique, rediscovered by the logician Emil Post, became a standard method in the design of computer programming languages.”Ref: Kadvany, John (2007), "Positional Value and Linguistic Recursion", Journal of Indian Philosophy 35: 587–520.

"The Panini grammar reflects the wondrous capacity of the human brain, which till today no other country has been able to produce except India" (By Sir Monier Williams).

"The grammar of Panini is one of the most remarkable literary works that the world has ever seen, and no other country can produce any grammatical system at all comparable to it, either for originality of plan or analytical subtlety” (By Bilas Sarda)


The most Structured Language in the world  (even today)
Sanskrit is such intelligently structured that there are special six branches called Vedanga to learn various aspects of language namely Vyakaran, Nirukti, Kalpa, Chandas etc. In these you learn various aspects of language like pronunciation, grammar, etymology, sentence structuring etc. Only after studying these subjects can a person actually able to understand various works of Sanskrit, which are otherwise not understandable. Such an engineering of a language is unseen in any ancient or contemporary language of the world.

It’s all revealed through Sanskrit through Sanskrit alone
 The whole new world of Vedic Mathematics hidden in Vedas
 The highest philosophy of Darshanas and Upanishds.
 The supernatural powers of Yoga
The complex mathematical formulas from Jyotish (Vedic astronomy) and Sulba Sutra which contains differentiation and integration methods along with lot of infinite series,

The complex computational mathematics in Vastu Shastra with the help of which the great          buildings like Taj Mahal (Tejo mahalaya) were built.

The immutable science of Ayurveda, the superior science of Music (Gandhrv Veda), the science of Politics (Artha-Shastra), the science of Metallurgy (Iron pillar of India) and innumerable others, the very common works just like grammar proves the unparalleled superiority of Sanskrit amongst other languages around the world.

A comparative study:
Words represent objects/entities.
Words represent properties of objects/entities and not objects/entities themselves. For eg: Tree

A Sanskrit dictionary is really redundant (in most of the cases), if one is well-versed in Sanskrit grammar!

At any given time, there will always be a finite/fixed number of words in English. Currently, it is 5 lakh words. But, in Sanskrit, there are as many words as properties in the universe.

Whenever you think of an object, you actually think of the properties of that object, since it is the properties that distinguish that object from rest of the universe. 

The Sanskrit grammarians realized that grammar and semantics are not separate water-tight entities, but rather, are one coherent unit. In probably all the other languages, Grammar and Semantics are independent entities, but not so in Sanskrit.


Tuesday, January 9, 2018

Proud Indian
Dr. Har Gobind Khorana
Won the Nobel Prize in Physiology or Medicine in 1968
Today is the 96th birth anniversary of Indian-American Nobel Prize-winning biochemist Har Gobind Khorana. Dr. Khorana was known for his extensive research on DNA and also for constructing the first synthetic gene.
Dr. Khorana and two other scientists - Robert W. Holley and Marshall W. Nirenberg – were awarded The Nobel Prize in Physiology or Medicine in 1968 for “their interpretation of the genetic code and its function in protein synthesis".
Born in 1922 in the village of Raipur, Punjab, in what is now in Pakistan, Dr. Khorana’s love for science began at an early age and that was thanks to his father who believed in the value of education. Dr. Khorana obtained a degree in Punjab University in Lahore and lived in British India till 1945. He then moved to England for his Ph.D programme at the University of Liverpool.
In 1952, he moved to Vancouver in Canada where he began his research on DNA, at the University of British Columbia. In 1960, Dr. Khorana shifted to the Institute for Enzyme Research at the University of Wisconsin.
In the early 1970s, Dr. Khorana constructed the world’s first artificial gene. Dr. Khorana was elected as Foreign Member of the Royal Society in 1978. He was also awarded the Padma Vibhushan. He died in 2011 aged 89 in Concord, Massachusetts.

More: https://en.wikipedia.org/wiki/Har_Gobind_Khorana

Thursday, June 19, 2014

Tools & Libraries for Modern Webapp development.

Most of the time i have seen people discussing about technologies and tools that can be used to enhance quality of their software development. Since i was doing the same for finding out latest web application development trends to pick a best suitable tech stack for one of my project, i had got chance to visit and try many of the tools & library offerings in web arena. Thought, sharing the same here will be helpful for successors and so listing out the much discussed HTML5, CSS3 & Javascript tools & libraries here categorically.


Sunday, February 9, 2014

GIDS 2014 Is here

The annual summit of software developers known as the Great Indian Developer Summit (GIDS) will start this year on April 22-25 at Indian Institute of Science (IISc), Bangalore. There are going to be 4 different tracks on .NET, Java, Web, Mobile & Data apart from the hands on workshop on some of these areas. To know more about the sessions and schedule check out here.


Saturday, February 8, 2014

The Vert.x platform

A couple of months back while i was exploring the options for a modern web application platform supporting server side javascript (SSJS), i was almost sure that node.js would be my final choice. But to my surprise there exists a relatively new platform which is at-par or even better compared to node.js. Yes, i am talking about the vert.x platform which is the new game changer.

Undoubtedly Vert.x is inspired by node.js, thus inherits many traits from node.js platform (deliberately avoiding the term 'framework'). But still it's a completely new platform with much more capability and flexibility. Here are some points as to why i am fascinated with it.
  • Polygot in nature:  Supports many languages out of the box. While i am writing this, the vert.x  2.1M5 is out and is has support for  Java, Javascript, Cofeescript, Groovy, Ruby & Python languages.
  • Non-Blocking & Asynchronous: The platform is based on event loop mechanism eliminating the traditional threading model. Gives a strong case for high scalability.
  • Distributed Event Bus:  The vertx.io page describes this as the central nervous systems of vert.x platform. This connects your polygot modules together. Put your modules in any where in the network, this guy will connect them all. Not over, its even capable of connecting your client side via client side javascript code running on your browser. Simply amazing. Makes the life of developer much easy and worry free.       Having said this i am not negating the fact that a poor app design can bring disaster as well.               
  • Concurrency Model: This is awesome. You write your application following single threaded model. The vert.x platform is capable of bringing the multi-threaded programming effect on it without the hassle of volatility, synchronization or lock. Also vert.x is able to create multiple threads based on the number of CPU cores in your server leveraging the full strength of multi-core programming. Clustering support is also provided out of the box. Its all automatically taken so that you can focus on your business logic.
  • Module Repository: This is something similar to NPM(node package manager) where you will find lots of prebuilt modules available for you to implement certain functionalities. Remember the DRY principle and its exactly offering the same reusability principle to you. This one is growing as more and more people are developing and contributing different modules into the ecosystem.

Vert.x is an open source independent project run by the vert.x community. Having said that the core vert.x modules are under the Eclipse foundation project. 

Looks interesting ? then move on and check out the official vert.x page here. There are some other interesting reads which i am sharing here where you can find code bytes., architecture details and comparisons on the vert.x platform.





Wednesday, July 18, 2012

Security of Internet of Things

@ Amrita Vishwa Vidyapeetham University, Amritapuri Campus. Participate in an unique conference. The very few of its kind in India.
Visit: Official Page