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Saturday, October 29, 2016

Root of the mystery



In one of the well known Upanishads, namely the Chändogya Upanishad, there is a description of how this world came into existence. Let me summarize the relevant verses as follows.
 
“In the beginning, there was nothing but ‘That’ alone that existed. And ‘That’ wished to be many. It took the form of ‘Tejas’ (bright light). This ‘Tejas’ too wished to be many and it took the form of ‘Äp’ (water). This ‘Äp’ in turn took the form of ‘Anna’ (nutriment)”

What is interesting is even after taking these various forms the original ‘That’ remained as it was. Explaining the ‘creation process’ further, the Upanishad explains how each of these three forms – bright light, water and nutriment – combined among themselves and resulted in the formation of several entities each distinct in its own way. Then the Upanishad says

“Having taken so many forms, ‘That’ entered each of them in the form of ‘Jiva’ (soul) and separated ‘name’ and ‘form’”

So, in this way, the single entity that alone existed in the beginning ‘became’ many things/beings that we see around us as ‘world’.

But how is that possible? How can one entity become many and still remain as it was! We will see this in the next post.

Saturday, October 22, 2016

Strange Philosophies

Two of the highly intriguing Indian Philosophies in recent times (I am talking in a wide time frame) is the Advaita philosophy propagated by Šankara and the Dvaita philosophy of Madhva - both from Southern India, both being staunch supporters of ancient Vedic ideologies.
 
Strangely, the philosophies advocated by these two great masters were diametrically opposite! – Or at least they appeared to be so, on the face of it.

Very briefly, Šankara’s view was that the multiplicity seen in the world is just an illusion. There are not infinitely many things in this world! In ‘reality’ there is only a single entity in the world namely, the indefinable Brahma or Ätma.

While his counterpart, namely Madhva, held the view that multiplicity is the reality and there is not one, but three categories of things in this world, and each of them is real. None of these is identical, nor are they even comparable.

The interesting point to note is that both these scholars claim the Upanishads to be the basis of their assertions. Each has his own reasoning and logic to prove his point. Each has written volumes of commentaries to support his views and each has wide following.

How can the same source (Upanishads) give out such seemingly contradictory views? Strange isn’t it?

To sort out this seeming contradiction, probably we need to look at the source i.e. the Upanishads themselves. That is what I am going to do next.

Saturday, October 15, 2016

Strange Mathematics


Normally, when we remove ‘something’ from something else, the original ‘something’ will become smaller. That is elementary mathematics.

But mathematicians have a concept called ‘infinity’ – something that has no limit, something that is not finite. Take for example, the total number of whole numbers. There are infinitely many of them – you name any number, there is another number which is larger than it.

What happens when you remove something from infinity? Will it become smaller? No, not always. It depends. Consider for example, the total number of numbers. As we saw earlier, there are infinitely many of them. What happens if we remove all even numbers from this set of numbers? You are left with infinitely many odd numbers. 

You started with something that was infinite. Removed something which was also infinite (there are infinitely many even numbers!) and what you are left with was also infinite – infinitely many odd numbers.

That means, infinity minus infinity need not be zero! It can even be infinity. Or if you ponder a bit, it can be zero or finite even!

That is strange mathematics. Isn’t it?

Even in the area of philosophy there are such strange apparent paradoxes. Let us see that next.

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Saturday, October 8, 2016

My recent carvings page

I just added a "My recent carvings" page on the right column of my blog.

You can see some of my recent carvings listed on that page. I will also be showing 'ongoing carving' in a step by step manner. Keep watching this page for updates.

Strange Mantra



There is a strange mantra that is normally recited in the beginning of many Upanishads (philosophic parts of ancient Indian scriptures, namely Veda). 
 
Literally translated, the mantra says

“That is complete. This (too) is complete. (This) complete has come from (that) complete. When complete is removed from complete, what remains is also complete”

On the face of it, it sounds absurd. If something is complete, how can it remain complete when something is removed from it! 

Scholars have given varieties of interpretations to this apparently absurd mantra. Many chant it with religious fervor without bothering much about its meaning and implication. But it does have very profound meaning.

In the subsequent posts, I am going to use this mantra to explain several such seeming absurdities, be it in mathematics or philosophy.

Let me start next with a case in mathematics.