Thinking of Transcendental π (pi) and Brahman on March 14.....
(Compilation for a discourse at Sri Ganesha temple, Nashville, USA, March 15, 2014)
Even with elementary knowledge of mathematics all of us who have attended school know what is π (a Greek alphabet) a constant used in the calculation of area of a circle. If you divide the circumference of a circle by its diameter (C/D) you arrive at a never ending constant 3.1415926……… This is a mystery Pi number which is transcendental and irrational number. For convenience sake this has been rounded off to 3.14. The simple beauty of Pi inspired Congress of USA to pass a resolution in 2009 to declare March 14 every year as “Pi Day”.
By a providential and spiritual coincidence this day is also the birth day the famous scientist and Nobel Laureate Albert Einstein. Famous Scientist Albert Einstein was a philosopher and spiritual thinker. He was born in the year 1879. He was fascinated by Hinduism and was fond of Mahatma Gandhi. Shocked by the sudden assassination of Mahatma Gandhi he lamented: “It is too dangerous to be too good”. One of his famous quotes is “Science without religion is blind and Religion without science is lame”.
Some of you living in Nashville might have read the following information contained in the column Teachable moments by Frank Daniels III, in The Tennessean, March 14, 2014:
“Pi is the ratio between the diameter of a circle and its circumference; C/d=3.1415926…….. (dot, dot, dot represents that pi has an unlimited succession of non-repeating decimal digits). Though irrelevant to reaching an accurate answer to a problem, pi has been calculated to more than 10 trillion places—a number that has an amazing as the one representing the US National Debt.
The pi ratio is also used in a variety of formulae to determine area and volume of circular and elliptical objects, the motions of pendulums (watch the pattern they inscribe in sand) and for electrical circuits.
Contemplating pi drove ancient mathematicians crazy. The idea that a relationship between the diameter of a circle and its circumference was not rational i.e., could not be represented as a fraction, like ½, was not, well, rational. Mathematicians gave a name to these kinds of numbers irrational. You all know there are also dimensionless numbers in mathematics.
The Babylonians first expressed the relationships in a circle about 4000 years ago as 25/8. In 1650 B.C.E. Egyptian mathematician calculated the ratio as 256/81. And then in 250 B.C.E. the Greek mathematical genius Archimedes determined that the ratio was somewhere between 223/71 and 22/7 by using polygons to ‘Square the circle’. In 250 B.C.E. Ptolemy using Archimedes’ polynomial method of squaring the circle fixed the value of Pi at 3.1416, close enough for most of us.
The idea of irrationality drew mathematicians like honey, and they continued to calculate their pi-accuracy. In the 17th century, mathematicians have advanced the calculations to 39 places, that is all we need to make accurate measurements, including the volume of our universe. They used a new technique, infinite series, to extend the accuracy. It is one of the techniques we are supposed to learn when we learn calculus.
In 1706, the Welsh mathematician, William Jones, who was a close friend of Sir Isaac Newton and Edmund HHHHhalley, proposed the Greek symbol ’pi’ pronounced ‘pie’ to represent the ratio, a good idea that was quickly adopted. Though irrational, pi represents one of the constants of nature. It is an unvarying relationship, grounded in reality which allows us to understand the world, and universe, around us”. His column ends with a humorous note; “Who can resist a transcendent irrational number that is a constant? So enjoy a bit of pie today to celebrate pi and Einstein!”
What the columnist here missed or kept silent knowingly or unknowingly is the fact mentioned about Aryabhatta (499 A.D.), in my discourse on "Early and Medieval Hindus Contribution to Science and Technology". Relevant portion from my discourse is reproduced below: "Aryabhatta, probably influenced by Greeks, found the area of a triangle, a trapezium and a circle and calculated the value of pi at 3.1416—a figure not equaled in accuracy until the days of Purbach (1423 A.D.) in Europe. Trigonometry evolved as an integral part of astronomy. Bhaskara crudely anticipated the differential calculus; Aryabhatta drew up a table of sine and the Suryasiddhanta provided a system of trigonometry more advanced than anything known to Greeks. The method of extracting the square and the cube roots of integral numbers can be traced to Aryabhatta” We have also the following information from Encyclopedia Brittanica "Ganita Aryabhata names the first 10 decimal places and gives algorithms for obtaining square and cubic roots, utilizing the decimal number system. Then he treats geometric measurements—employing 62,832/20,000 (= 3.1416) for π—and develops properties of similar right-angled triangles and of two intersecting circles.
The concept of zero and infinity, the decimal and duo decimal systems were all familiar subjects to our ancient sages. The use of word numerals such as Kha, Aakaasa or Sunya to represent zero, Kshiti, Dharaa and Prithvee to represent the figure 1 and so on in our scriptures enabled authors of mathematical treatise to verify their ideas and express them concisely. But for the concept of Zero, Infinity and counting up to very huge quantities like Paraardha (10 raised to the power of 14 mentioned in our religious sankalpas), the decimal and duodecimal systems known to our ancient sages the calculation of the value of π to 10 trillion places by Western scientists would not have been possible without the knowledge coming from our Spiritual Sages.
The above information carried my thoughts to spiritual heights, (unlike that of Frank Daniels who ended up with a sweet pie focusing on food for the stomach than thought) having focused my thoughts on odd even numbers in Chamakam and on Divinity of Numbers in Hinduism in the past. Concept of decimal system based on zero makes pi transcendental. Hindus gave the concept of Zero to the world. The concept of mathematical mystery number zero is evident even in the Veda Mantra “Poornamadah”, which reads:
Poornamadhah poornmidam porrnaat poornamadychyate |
Poornasya Poornamaadaaya poornameva avasishyate ||
[That which lies beyond is Plenum (full and undiminished). That which appears as this here (i.e., universal) is also Plenum equally full and undiminished. Out from Plenum, Plenum arises. Plenum having been taken away out of Plenum, what remains is still the same (undiminished) Plenum]. This means Purusha (Saguna Brahman), the timeless, Space-less Being cannot be divided.
The number zero (0) could mean Poornam. Zero when divided or multiplied by another zero or added to another zero remains zero. Therefore 0 symbolizes Nirguna Brahman as stated in my previous discourses. Also beyond decimal point any amount of numbers of zero added has the same value. This very much reflects the contention of the above mantra.
Also 3.14 the value of pi now limited to two decimal places offers infinite possibilities. In this three could mean Trinity Saguna Brahman in its three aspects of Srishthi (creation), Sthiti (maintenance) and Laya (dissolution). This is again a circle being cyclic in nature. Pi cannot be dissociated from circle or ellipsoid. Even though in sectarian view Linga is worshiped as Siva, Linga is symbolic of Trinity as already explained in my previous discourses--top part Siva, middle part Vishnu and base part Brahmaa in their aspect of dissolution, sustenance and creation. The base is often shown as square, the middle portion octagon and the visible part representing universe is circular. This could again be interpreted as a point (Bindi or dot in Srichakra) assuming square form or four directions (Brahma) which in turn becomes octagon or eight directional (where all Vishnu spreads) that end up as circular or visible universe. Thus it is a continuous manifestation and dissolution.
The beautiful marble like Linga stones shaped in the form of an ellipsoid found naturally in the Narmada river are considered most sacred. This Linga ellipsoid is fixed in such a way that one half of it lies embedded on the earth e while the other half remains outside the surface. The upper half that appears above the surface is visible manifest while the other half submerged in the earth is the un-manifest. Thus the ellipsoid represents the Reality –the un-manifest and manifest that is Brahman. When a cross section of the ellipsoid is cut along the axis it is ellipse; when cut at right angles to its axis it is a circle. An ellipsoid is thus a combination of ellipses and circles. The circle represents Supreme Reality. A circle has no beginning or end. Reality has also no beginning or end. The entire universe consists of an atom right up to the solar system (circular or elliptical) of the sun with planets revolving round it. Circle or ellipse or ellipsoid cannot be dissociated from the thought of transcendental Pi.
What makes Pi=1415926… mystic is its decimal part which runs to infinity after the decimal point. This reminds me of the Vedic description of Transcendental Brahaman, “anoeraneeyaan mahatoe maheeyaan”—Smaller than the smallest and larger than the largest. To the left side of the number 1 to start with the decimal portion converges to a point as the smallest. To the right side it goes to infinity. The decimal part imparts to it transcendental stature while the numerical part whole rational number reminds of saguna Brahman in his three aspects of Creation (Srishthi), Sustenance (Sthiti) and dissolution (Laya).
Let us again look at pi with its decimal part leading to trillions (3.1415926…..) Here number 3 represents Saguna Brahman called Narayana resting on his Sesha (remnant) which is represented by the decimal part. Before creation Narayana rests on Sesha on the endless water. Creation cannot start out of nothing. So creation takes place from the Sesha to bring back life as before. Vedas say yathaapoorvam akalpayat –the world was created again as before. Looking at the transcendental nature of Pi these are the spiritual thoughts that come before our mind. Today that mysterious zero has created the internet world which brings in so much information that was hidden from us all along. This process is continuing, who knows where it will stop till the next Pralaya (cataclysm) comes?
Many modern religiously devoted mathematicians have tried to make perfect Srichkra of Sri Lalita by following Chakra Nirmana Krama given in Gandharva Tantra and their own and to reach the sacred center. Details are also available in the publication by Ramakrishna Math. However it is a thrilling experience to any mathematician to contemplate on the role of Pi in the construction of the Pyramid and also the construction of Srichakra. Both are believed to be efficient generators of Cosmic Power, the Entity transcending the domain of the physical Universe beyond which our mental or other faculties cannot extend. This role acquires enormous significance and profound meaning when one recalls its obvious connection with modern concept of limited but unbound Space-Time-Spherical Universe. The ancient thinkers regarded Pi of unending decimals a number not represented by conventional means in a straight line, as a mystical number.
This explains why a satisfactory diagram cannot be produced using line measures alone. The involvement of Pi, really defies all attempts to produce a perfect diagram of Srichakra. A near perfect diagram takes us very close to, though not exactly to the point where the Transcendental Energy manifests itself thereby showing how difficult is to reach Him unless He wants to. Revelation of Brahman is within the sphere of will (saameepya or nearness) of the Spirit but not the end-result of personal efforts to reach Sauujya (complete merger). In this endeavor even computers are believed to have failed to produce a satisfactory figure.
[Spiritually inclined mathematicians should refer to the work of Pandit Subrahmanya Sastri and T. R. Srinivasa Ayyangar on Soundarya Lahari, published by the Theosophical Publishing House, Chennai 1977.]
1) Frank Daniel III, 3.14 is a Day of Infinite Possibilities, The Tennessean, March14, 2014
2) Swami Nityanand, Symbolism in Hinduism, Central Chinmaya Mission Trust, Mumbai, India
3) Chatterji J.C., The Wisdom of Vedas, Master Mind books, India
2) Parthasarathy A., The Symbolism of Hindu Gods and Rituals, Vedanta Life Institute
5) Srinivasan N.R., Early and Medieval Hindus Contributions to Science and Technology, Hindu
6) Ramachandra Rao, S.K., Srividya Kosa, Sri Sadguru Publications Delhi, India.
6) Ramachandra Rao, S.K., Srividya Kosa, Sri Sadguru Publications Delhi, India.
[This is a prepared lecture compiled from above references and others for a discourse at Sri Ganesha Temple, Nashville and to benefit those who are not able to attend the same in person. You are free to download and use it for your reading and reference as well as circulate to others to spread the wisdom of Vedas and Hindu values which good act will be appreciated.]