11 - Is Knowledge essentially Simple ?


ISSUE No. 11

Vedic Mathematics is becoming increasingly popular as more and more people are introduced to the beautifully unified and easy Vedic methods.
The purpose of this Newsletter is to provide information about developments in education and research and books, articles, courses, talks etc., and also to bring together those working with Vedic Mathematics.
If you are working with Vedic Mathematics- teaching it or doing research- please contact us and let us include you and some description of your work in the Newsletter. Perhaps you would like to submit an article for inclusion in a later issue.
If you are learning Vedic Maths, let us know how you are getting on and what you think of this system.
This issue's article:

The article below was written by Andrew Nicholas at the request of the Chairman of SEAL (The Society for Effective Affective Learning) and was published in the July issue of their journal. This directly relates to Vedic Mathematics in that Vedic Mathematics presents mathematics in its simplest form.


Whenever I have understood something I have always found it to be simple. Others tell me that is what they have found, too. This leads me to think that perhaps knowledge IS simple, essentially. I'm talking about knowledge as the understanding of something, not just the gathering of facts.

There's another consideration which supports this idea. Major advances in science simplify things, and make them more readily comprehensible. Copernicus gave us a much simpler cosmological system than Ptolemy. He did so by putting the Sun at the centre of the universe, with the Earth and planets going round it in circles. This replaced Ptolemy's more complicated description of the motions of the heavenly bodies, placing the Earth at the centre of everything.

So if the most important advances in science are simplifications, what are the ultimate consequences of simplification following on simplification? Do you think it might be something fairly simple? That is what I am inclined to think. So here's a further reason for supposing that knowledge is essentially simple.

But what about these contexts one finds difficult, as I've been finding, recently, trying to set up a palm-top computer to send e-mail? However, as I've gone on it's become easier. Past experience has shown me that when I don't really understand something I can find it difficult, and then it gets easier as the understanding grows. Eventually I may even find it quite easy. At this point it seems I have connected with the underlying simplicity.

Is it possible that those subjects which are generally found to be difficult are awaiting THEIR 'Copernican revolutions' - to be followed, perhaps, by further simplifications? [I am assuming that the problem is not just the unnecessary use of jargon.]

So there you have it. I am suggesting that perhaps, when we really know something, it is found to be simple. Otherwise put, to know something is to connect with its essential simplicity, and to see its pattern as a whole.

But what is simplicity? I once heard Professor Karl Popper remark that simplicity is not itself a simple concept. That is not a view I take myself. However there's no doubt that there's a lot to simplicity.

Back to the suggestion that knowledge is essentially simple. There's a well-known phrase: it's easy when you know how. In many contexts this can be expressed as: it's simple once you understand it. Time and again people have told me that that is what they have found, but they have had to struggle and do a lot of work to get there.

We would be greatly helped if ways could be found of taking us quickly and easily to that understanding without having to go through the intervening struggle. THE IDEAL FORM OF STUDY WOULD BE ONE WHICH TAKES US DIRECTLY TO THE UNDERLYING SIMPLICITY.

Here is an example of what I have in mind. It's taken from my recent book on geometry, 'The Circle Revelation', which is written for the non-mathematician. It uses the basic principle, or fundamental theorem, that figures which are constructed in the same way are identical. This applies also to parts of figures. One consequence is that, if two sides of a triangle are equal, the angles facing them will be equal also, being constructed in the same way.

The aim underlying this book was to produce a system of geometry in which the methods are simple enough to be used in the context of an oral tradition, with no writing, just drawing figures and speaking. In consequence, the bulk of its contents can b presented to non-mathematicians as a short course, lasting little more than an our and a half, going from first principles to elementary properties of circles. This was not previously possible - at least, not in recorded history.

Geometry is built up step-by-step, revealing a steadily enlarging 'picture', into which the parts fit like pieces in a jigsaw puzzle. This system uses simple steps to enable the 'student' to appreciate larger and larger wholes - all connected by the golden thread of reason.

I have been asked what led me to formulate this system. I did so because I believed it to be possible and worth doing. The idea of finding such a system intrigued me. It was clearly not trivial.

What resulted was simple, but that was what I was working towards. In retrospect, I was convinced that there was an underlying simplicity, waiting to be found. It was like a guiding principle, drawing me on. Without that belief I would not have been able to formulate this system.

There are plenty of examples around of the consequences of following the belief that knowledge is complex. Had that been my belief I think I would have come to the same conclusion as Professor Popper, about simplicity not being simple itself.

However, there are also plenty of examples around illustrating connections with underlying simplicity, such as the wheel. If we valued brevity and directness and simplicity more there would be a lot more of them - and not just more wheels!

Dream awhile. Suppose it to be true that knowledge is essentially simple. Then the ideal follows, surely, of having studies formulated in this way - taking us swiftly and easily to the underlying simplicity at the heart of the whole subject. That would make life a lot easier and richer for us all.





An introductory 12 week course on Vedic Mathematics starts on 16th September in Manchester, England. More details on the Calendar on the website.


The following five Workshops in Mumbai, India, are open to everyone and are virtually free of cost.

On Sept 17th
1. From around 11a.m for about 2 hours at S. P. Jain Institute of Management & Research, BVB Campus -Andheri
Contact Persons: Dr A K Sengupta; # 623-0396/623-2401/623-7454

On Sept 18th & 19th
2. From 1 p.m to 3 p.m at G.D.Somani School, Cuffe Parade;
Contact person : Mrs. Aradhana Somani ; # 2184753/2187102

On Sept 20th
3.From 10 a.m to 11.30 a.m at Bhavan's Hazarimal Somani College, Chowpatty;
Contact person : Dr. S.G.Chitale; # 3691136/3691508 Mobile : 9820191120

4. From 2.30 p.m to 4.30 p.m at Jain Academy/Philosophy Dept., Mumbai University ;
Contact person : Dr. S.S.Antarkar # 652-6091, Ext # 367,428,451 or 652-7337; Mr Doshi # 801-0058

Various other Workshops etc. are being organised by Motilal Banarsidass in Nagpur (beginning Sept 23rd), Pune, Gwalior, Jaipur, Calcutta and Delhi. We will keep you informed.


The courses/seminars at Skovde University, Sweden, have been rescheduled to take place from 24th to 26th October. There are courses for teachers at all school levels, teacher trainees and one for upper school students. More details on the website under 'Calendar'.


The previous Newsletter is now available on the website and also Dr S K Kapoor's proof of the Conjecture which accompanied the Newsletter. Discussions are still taking place on this and we will keep you informed.


If anyone can give the location of a list of current unsolved mathematical problems (or a list itself) please can you contact us on . Apparently there is a site at http://www.ams.org/claymath/prize_problems/press.htm but it appears to be down at the moment.


The Vedic Maths web site at http://www.vedicmaths.org now has seven Tutorials all of which are interactive: you put in your answer and it tells you if you are right or wrong and also your score on each exercise. Comments/suggestions are welcome:


Your comments about this Newsletter are invited.
If you would like to send us details about your work or submit an article for inclusion please let us know on

Articles in previous issues of this Newsletter can be copied from the web
site - www.vedicmaths.org:
Issue 1: An Introduction
Issue 2: "So What's so Special about Vedic Mathematics?"
Issue 3: Sri Bharati Krsna Tirthaji: More than a Mathematical Genius
Issue 4: The Vedic Numerical Code
Issue 5: "Mathematics of the Millennium"- Seminar in Singapore
Issue 6: The Sutras of Vedic Mathematics
Issue 7: The Vedic Square
Issue 8: The Nine Point Circle
Issue 9: The Vedic Triangle
Issue 10: Proof of Goldbach's Conjecture

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14th September 2000


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