A set of numbers, in general, can be classified into three types in mathematics. They are as follows :
Finite Sets : These are finite in the sense that they have a starting value and an ending value. For example, {1,2,3,4,5,6}.
Countably Infinite Sets : These are infinite but can be counted, like for instance {1,2,3,4,...,}.
Uncountably Infinite Sets : These are also infinite but they cannot be counted. For example, numbers between 1 and 2 (They include fractions and non-fractions like sqrt(2)).
A simple observation behind these numbers leads to the following philosophies.
Philosophy of Finite Sets : Finite set of numbers can never become infinite.
Philosophy of Countably Infinite Sets : Countably infinite set of numbers are infinite but each number maintains their 'individuality' in the sense that there is a clear notion of separability between two numbers (i.e, two numbers are not that close, there are a unit distance away in the above example).
Philosophy of Uncountably Infinite Sets : Uncountably infinite set of numbers are infinite but two numbers can be as close as possible. There is no clear notion of 'individuality' between two numbers (for example, sqrt(2) and 1.41421356, the difference is almost zero).
Let's now see three major philosophies of Vedanta in crude terms.
Dvaita : Jiva-atmans can never become Parama-atman.
Visishtadvaita : Jiva-atmans are also Parama-atman but they maintain their individuality.
Advaita : Jiva-atmans and Parama-atman are one and the same (there is no notion of individuality).
Assuming Parama-atman to be infinite and Jiva-atmans to be set of numbers.
Dvaita : Jiva-atmans are like finite set of numbers and they can never be infinite, which is Parama-atman - Philosphy of Finite.
Visishtadvaita : Jiva-atmans are like countable set of numbers, they are infinite (Parama-atman) but they maintain their individuality - Philosophy of Countably Infinite.
Oh, how similar !
Finite Sets : These are finite in the sense that they have a starting value and an ending value. For example, {1,2,3,4,5,6}.
Countably Infinite Sets : These are infinite but can be counted, like for instance {1,2,3,4,...,}.
Uncountably Infinite Sets : These are also infinite but they cannot be counted. For example, numbers between 1 and 2 (They include fractions and non-fractions like sqrt(2)).
A simple observation behind these numbers leads to the following philosophies.
Philosophy of Finite Sets : Finite set of numbers can never become infinite.
Philosophy of Countably Infinite Sets : Countably infinite set of numbers are infinite but each number maintains their 'individuality' in the sense that there is a clear notion of separability between two numbers (i.e, two numbers are not that close, there are a unit distance away in the above example).
Philosophy of Uncountably Infinite Sets : Uncountably infinite set of numbers are infinite but two numbers can be as close as possible. There is no clear notion of 'individuality' between two numbers (for example, sqrt(2) and 1.41421356, the difference is almost zero).
Let's now see three major philosophies of Vedanta in crude terms.
Dvaita : Jiva-atmans can never become Parama-atman.
Visishtadvaita : Jiva-atmans are also Parama-atman but they maintain their individuality.
Advaita : Jiva-atmans and Parama-atman are one and the same (there is no notion of individuality).
Assuming Parama-atman to be infinite and Jiva-atmans to be set of numbers.
Dvaita : Jiva-atmans are like finite set of numbers and they can never be infinite, which is Parama-atman - Philosphy of Finite.
Visishtadvaita : Jiva-atmans are like countable set of numbers, they are infinite (Parama-atman) but they maintain their individuality - Philosophy of Countably Infinite.
Advita : Jiva-atmans are like uncountable set of numbers, they are infinite (Parama-atman) but there is no clear notion of individuality - Philosophy of Uncountably Infinite.
Oh, how similar !
9 comments:
Nice analogy! I liked it.
When we say a number, eg. '2', it is the tag that is given for the value between 1.9999.... to 2.000...1. Thus all the numbers are in a continuum, and can be made distinct as 1 or 2 or 3, for the purpose of understanding... ;)
For understandin the Brahman, we split ourselves from Brahman, as we do for the numbers, resulting in the multiple theories.
Nice one. I learn something new from most of your posts.
Michael Crichton in SPEHRE writes about 2 kinds of child prodigies - math and musical. Then he generalizes it into MATH alone, since music is fundamentally math. After seeing your post, it looks like MATH is subsumed by Vedanta!.
Maybe you were a child-prodigy too!.
Ahaa, Kasthuri & TJ, pul arikardhu ungaloda analogy ellam :-)
Keep it up !
TJ & Kasthuri: Keep it up! :) Great analogy.
whoa..nice comparison..everything seem 2 be interlinked only 2 be discovered by people like u... :)
btw..just noticed that my blog link on ur blog roll is pointing to one of my historical posts..:)..
dear kasthuri,
lets look at your analogies
advaita is a system which refutes individual existence and resorts to ilusionism to support its orthodox monism. therefore your idea of comparing advaita to philosophy of uncountable infinite is not tenable. as the advaitin recognises only the atman which is infinite and exists as the only reality, the question of jivathma is taken up by advaita only to be refuted later.
as for Visishtaadvaita, the notion of samanadhikaranayam is used to explain passages that proclaim identity between jivathma and paramathma. again your analogy is not tenable according to visishtaadwaita as expounded in the SRIBASHYA.
however your comparison of dwaitham with philosophy of finite is beautiful.
I know my comment sounds different from those of others who have commented before me but I have written all this based on your post and hope you understand.
my post on the text AHAM BRAHMASMI is due in a couple of days. please comment on it in the same way as I have commented here, so as to enable me to assess my understanding and correct my ideas which are not logical.
SARVAM SRIKRISHNAARPANAMASTHU!
Everything connects to the other at some point. The basic tenets of inductive reasoning rests on this factor - connection and patterns.
You have made the connections with vedanta so beautifully.
beautiful post
@ tj : Cool.
@ tt_giant : Good to hear that the posts do make some sense. Yes, music is subsumed by math. As far as Vedanta goes, I am not sure it is entirely subsumed by math but I am positive that it can be given a formal modern logical framework. It would be good if more people work on these lines. Child-prodigy - good joke :-)
@ the aviator : I came to know that these tapes are false. Recorders were not there during those days-otherwise the entire proceedings of "Parliament of Religions" would have been recorded. Thanks for the info btw.
@ arvind, ranj, krishna, ganesh: thank u guys.
@ anand : What u say might be right.
These are just analogies than rigorous comparisons. As u said Advita refutes individual existence and so does the philosophy of uncountably infinite. Similarly the case of Visishtadvaita which doesn't refute induvidual existence coincides with the countably infinite. So, the point is I am not claiming the precise synchronization of theories but merely admiring the patterns shown in both the theories.
@ paavai : Thanks for visiting. Yes, that's true. Inductive reasoning lies on recogonizing the two factors. That's what we essentially do when proving something through mathematical induction.
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