The Definitive Infinity beyond All Other Infinities
My first interaction with infinity came very late in my life despite, in my chosen profession I have used the symbol, not infinite number of times, but millions of times.
I was in the tenth standard I think and my cousin who was in IIT Bombay (who was then in his second year and was a show-off, much later) then posed the question, how many particles of sand are there in the expanse of Marina Beach in Madras (now Chennai). I said a large number and he asked how large. I was in 10th standard and I knew what he was getting at, I cried instantaneously and loudly, “INFINITY!” Well, I later learned that that was not the correct answer.
Once I read how Richard Feynman sort of played with the three or four year old son of Hans Bethe at Cornell University. Feynman asked the toddler to give him the largest number the child knew. Pat came the answer, thousand! Feynman challenged this answer and gave his number 1,001, which even the child acknowledged as larger than 1,000. So, he said, 1,002. Feynman responded, 1,003. This went on for a few series of “I’ve got the highest number” before the kid caught on to the truth that infinity is merely a concept. As an aside, isn’t that a terrific way to teach?
Where does the series of bigger and bigger numbers end? At infinity? No, it appears not. What Feynman showed was only one kind of infinity. There are at least six kinds of infinity.There was a time when I bought many layman books on topics of interest in science, math included. One such book was The Infinite Book by John D. Barrow. I dug in and could understand much in it and was at sea on much other; as it was a book on infinity!
I give here the conclusion of a logical argument given as a brain-teaser: The curious feature of infinity is that it can be put in direct correspondence with a part of itself (Albert of Saxony’s Paradox). This appeared on page 53 of a total of 274 pages (with extensive notes and index) in the book, and I was hooked. I learned that there are at least six different kinds of infinities!
Here, I am going to add one more, the seventh, theological infinity. Hinduism appears not to have a unique and uniform theology; it rather abounds in philosophies, traditions and religions, each espoused through sacerdotal observations that do not accord with each other.
But when Lord Krishna (Vishnu) shows Himself as Infinite to Arjuna in the battlefield, I do not know whether Lord Vishnu was within Himself in as Lord Krishna and Lord Vishnu simultaneously (both ever smaller but equally large) in that revelation, like nested (yes, that is the right word here, the Russian nested dolls!), maybe.
I say this because, if this was really so, then Hinduism offers clear, non-contradictory explanation to the supposed paradox mentioned above, and this is important, eons before Albert of Saxony did! Each vision of the Lord “can be put in direct correspondence” with a part of itself!
This is well within, indeed endorses Hindus’ claim, “Been there; done that!” Of course it includes plastic surgery (Lord Vigneshwara), and airplane (Ravan abducts Sita Devi on Pushpak Vimana) too, as our much beloved Prime Minster of India said.
But the most revealing and engrossing thing I came across in the book is the following: one infinity can be bigger than another! In fact, “there is no end to the ascending hierarchies of infinities.” So, no infinity is the biggest infinity! We have graduated from integers stopping at an infinity to nonstop infinities themselves.
That is, if Lord Vishnu is an infinity, so are Yahweh, Allah, Shiva, Mahavir Jain, Buddha, and even every one of the 0.33 billion Devas (in the Hindu pantheon) and every other divinity conjured by any number (definitely a large number, yet not quite infinite) of civilizationsindividually an infinity! No wonder religious wars (at least wars fought in the name of religion) are infinite.
If you would like such wars to vanish, I offer you the following: abolish all the religions. This could take infinitely long. I have infinite time on my hand, just being reborn infinite times!
Raghuram Ekambaram