Cantor then rigorously proved using his famous “diagonalization proof by contradiction” that whereas our numbering system on the left a_{1}, a_{2}, a_{3}, ….. belongs to the set **א _{0}**, the set of numbers on the right will

A corollary to this is also very interesting – Cantor proved that the set of fractions like ^{1}/_{2,} ^{1}/_{3},^{1}/_{4}, ^{1}/_{5 }…… ^{2}/_{3}, ^{2}/_{5}, ^{2}/_{7}, ….. ^{3}/_{4}, ^{3}/_{5}, ^{3}/_{7} ……. and so on, also belong to the “countable infinite” set **א _{0} **and even though this

No wonder on the title page of his Chapter “Who is the I?” Mishraji gives the *Shānti Pāṭḥ***[22]** :-

*“Om poornan adah poornam idam, poornāt poornam udachyate, poornasya poornamādāya, poornam ewaawshishyate.”*

**That is whole; This is whole. That is Infinite; This is infinite. When the infinite is taken out of Infinity, What remains is Infinite.**

Now, coming back to the Sibilants, the *Vedās* treat the idea of *Shakti *or energy very differently from the western scientific method. The *Shakti *unfolds as part of the individual consciousness. Its perception is always as a ‘movement’ a *kriyā*. The first Sibilant *‘sh’ is Shri Lakshmi. *It is the countable infinite and belongs to the domain of **א _{0}**. Here the energy transactions are conserved. It moves from one place to another without leaving anything behind. I give you money, it decreases with me but improves your balance. This energy is discrete.

The next letter is *‘shha’* and it signifies *Ushā* the *Shakti* that keeps getting replenished. ….the rays of the sun; the flowing rivers; the sprouting leaves are all examples of this form of *Shakti. * The reservoir of energy is so huge that we get a feeling of ‘continuity’ in using it. I go to the river and take a bucket of water, I get it but the river immediately fills up. This belongs to the domain of **א _{1}** and it is continuous.The third Sibilant

The trees are a good example of the balancing of all these three *Shaktīs* – the trunk belongs to *Shri* because they are countable. We could actually go about the task of numbering all the trees in the world. The leaves belong to the realm of *Ushā*. Their number keeps changing and replenishing, it is dynamic and continuous. But, if we were to ask how many fruits and seeds can grow on all these trees and how many more trees and seeds can subsequently grow? It is an endless task and this is *Saraswati.*

We are equipped now to truly appreciate the last passage from “Reflections” – Mishraji writes (quote)**[23]** – “I sketch consciousness as an enthralling Goddess; a finite figure on the limitless canvas of infinity. A sculptor carves her in stone. A painter draws her on the walls of a cave. These are efforts to convey the incommunicable. Ecstasy captured in a poem. Infinity secured in finiteness. The limitless sky caged within the confines of my mind. Indescribable beauty imprisoned in an image”.

- As we perceive the Universe these
*Shaktīs*seem to be enmeshed in it in an endless layer of symmetries. However, from the largest galaxies to the smallest of atoms what we ‘sense’ is only their vibrations. From light to matter to stars it is all a big cauldron or*kalash*of rhythms.

“What is there before the beginning? What is there after the end?” Mishraji asks in “Reflections”. And then he answers in the same breath (quote)**[24]** –“There is a rhythm in the Universe. The planets move regularly. The stars ride their appointed paths. Everywhere, there is the Law of Rhythm. Everything conforms to that Law.”

The rhythms of the Universe are non-linear. They merge mysteriously into each other. That which is linear lends itself to straight ‘cause & effect’. I push the pencil and it moves – this is linear. All machines are based on this linear mathematics. But in a non-linear world – the cause does not immediately come up with an immediate ‘effect’.

A push here may not result in an immediate effect there, the effects may collect over ‘space and time’ zones to precipitate *entelechies*, sudden occurrences or epiphanies which seem totally disconnected or small effects can cause huge changes.

In reality, all processes are cyclical, in that, the effects are again fed back to the original causes through various loops of energy**[25]** and this makes mathematical calculations by hand impossible. The global weather problem was the first non-linear equation to be widely studied and Edward Lorenz showed in 1963**[26]**, how very small changes in weather patterns could precipitate huge changes thousands of miles away. He coined the phrase ‘the butterfly effect’ whereby he meant that a small butterfly flapping its wings in Peking could change the weather in New York. And this was prophetic indeed because the ‘El-Nino factor’ is now legendary. A small current in the Pacific has been empirically found to effect world weather.

The advent of super-computers in the 1980s actually brought about the detailed study of these ‘Non-linear’ equations and this gave birth to the fields of ‘Chaos and Order’**[27]** and ‘Fractals’.**[28]** The western scientists and mathematicians saw that in real-world problems there was no absolute size. As you scaled the solutions, that is looked at bigger or smaller sizes the same forms and designs kept repeating themselves. There was symmetry within symmetry endlessly. Chaos Theory and Fractals are today being applied to just about every subject ranging from economics, share prices to study of heart beats. The list is endless.

This leads to the understanding of the performing methods of the yajnas and the sacrifices to agni, the sacred fire. The “Supraphysical” energies are variously enhanced and these are...

Two important distinctions emerge from Radhakrishnan’s extensive writings extracted above. Firstly māyā is not the illusionary world around us as is commonly interpreted. This world is...