Monday, September 12, 2005

The Meta-Complex Brahman

A tribute to Sri Adi Sankara

Man discovered counting. As a crude mortal he was naturally satisfied with the elementary counting 1,2,3,...etc. He was living with just food and water, the gross annamaya kosha (anna means food so layer (made) of food) till one day he felt the intense need for energy (prana) to hunt and solve equations like x+2 = 0. These equations were not solvable in the domain of natural numbers (this needs x = -2). Thus, pranamaya kosha (layer of energy) gave raise to negative numbers. Did he feel happy ? No. His wandering higher mind (manas) wanted to solve larger system of equations like 2*x = 3. The integers were insufficient for this cause (this requires x = 3/2). Hence, manonmaya kosha (layer of mind) gave raise to fractions. Okay, is that all what he wanted ? How can he ever be satisfied with fractions which doesn't solve the equation x*x = 2 ? His intelligence (vignanam) urged even more. The vignanamaya kosha (layer of intellect) found the real numbers like sqrt(2) satisfied his cause. How can a man ever be happy ? Isn't this a basic contradiction in life ?There are still some complex equations like x*x = -1, which has no solution in the domain of real numbers. He confuses ananda for happiness while it denotes bliss. He wants happiness at any cost and invents complex numbers. The anandamaya kosha (layer of bliss) drives him to complex numbers. He is now not in the plane of ordinary mortals. He is full of bliss and boldly proclaims this is the largest system of numbers possible. He stops there saying there is no higher system than complex numbers**, no higher state than ananda, no higher being than Brahman. He proclaims Brahman is complex or Brahman is ananda, beyond the state of intellect, beyond the system of real numbers. But, he is not able to conceive the idea put forth by a genius of the highest state, a genius of a much higher evolution, a genius who can put all mathematicians to shame and a genius who can claim Brahman is more than complex, Brahman is more than ananda*^ and Brahman is beyond the highest being. That is Sri Adi Sankara.

** There is a proof for the algebraic closure of complex numbers which is essentially saying there is no system higher than complex numbers (in terms of solving polynomial equations) similar to saying Brahman is ananda.
*^ Sri Adi Sankara says anandamaya kosha is also a kind of maya and hence not really real - courtesy: Radhakrishnan Sarvepalli, Indian Philosophy, Pg 167-168 .

18 comments:

Anonymous said...

Dear Kasthuri,

Sri Sankara is right in saying that Brahman is not mere Ananda but the Mayavada is inherently nihilistic and seems to be the offspring of the Madhyamika Buddhist's notion of the void. the idea of denying things may seem intellectually superior at a glance but it can be shot down with a few simple arguments .
my respect for Dr.RadhaKrishnan is great but I feel in his books he has underestimated Ramanuja ( something done by Vivekananda as well).
Besides the notion that Brahman is beyond the supreme being is intimately connected to the idea that the Brahman is an attributeless thing which can never be qualified....soon after my post I checked futher arguments and as far as acceptable reasoning goes the construct is flawed and untenable.
yet the analogy with complex numbers is very nice. can you give the proof as well?
that would open up the debate on whether the advaitic conception is to be accepted evn in theory or not!
SARVAM SRIKRISHNAARPANAMASTHU!

Ranj said...

kasthuri: Very interesting analogy! I need to study Sri Adi Sankara's texts as well as Ramanuja's to learn more ... to be able to comment on your post and anand's comments. Any references for dummies?? :-)

Kasthuri said...

@ Anand : You are right. The Advitic Mayavada seems to be a revised version of Madhyamika metaphysics in Vedic terminology. Acording to Dr.Radhakrishnan the influence of Budhhism and its schools, the non-dual nature of reality and the phenomenal nature of the world came to be emphasised in the systems of Gaudapada and Sri Adi Sankara. However, I would like to let you know that the sole purpose of the post is to emphasize the genius of Sri Adi Sankara and not air views on Mayavada.
Also, regarding the closure of complex number system, it needs some sophisticated theories of Galois Field Extensisons, which may not interest people. Its most likely that only you and me will be following if I do that :-), although the Galois Theory is a beauty by itself. Also, its very true that Vivekananda does not give that much credit to Sri Ramanuja. I am not sure about Dr.Radhakrishnan though, need to complete reading his book.


@ ranj : Thanks. I am not the right person to suggest any books, for I myself is a novice (and a dummy) in these areas. Anand might be able to suggest some. Any good references Anand ?

Mysorean said...

Kasthuri,

Great post!

Am quite new to this "Kosha" funda. But could relate to your post.

There are seven stages that the human being needs to travel through his mind to attain realisation. The "Purusha" is the final state. Till then, our mind thinks that every state it has attained is the ultimate. A "Guru" is who always tells you that it can go higher. Still higher.

And who better a Guru than Sri Adi Sankara! :)

Loved reading your post!

Have blogrolled you! :)

We are co-bloggers now! [via cosmic consciousness]

Regards,
Adi.

Anonymous said...

dear Kasthuri,


no probs !
I think you can still try to explain the notion of Galois theory and all...you are good at conveying things in small packages.

what about your posts ... also I saw that you have been tageed..would love to see your responses!

SARVAM SRIKRISHNAARPANAMASTHU!

Anonymous said...

Kasthuri,

your modesty is cool but as far as I am concerned you are no beginner.

as for Ranj:

you can order texts in english from the WWW.ramakrishnamutt.org
they have all kinds of things and you can buy whatever you want (please get translations of classics in vedanta and not modern books written for a western\youth audience)

SARVAM SRIKRISHNAARPANAMASTHU!

Ganesh said...

as usual great post.

tt_giant said...

counting la ivalo vishayama!. idhai enni enni paarkum bodhu aacharyamaa irukku!.

Agnibarathi said...

*Sigh* uruppadiyA mUNAng classlayE maths padichurunthA ithellAm puriyum...appO vittuttu ippO kashta padarEn!! ;) But beautiful analogy between dfifferent number systems and the kOshAs!!

Maayaa said...

first time here,
different level of thinking!! took me a while to grasp..though not completely

TJ said...

As usual a nice post Kasthuri,
Yes, Taking the analogy of the need pyramid, the Anandamaya kosha is Self-Realization. That is where the pyramid also ends.
The Brahaman is when the 'Self' has blown itself out[using Stereographic projection(!), according to ur earlier post :)] which cannot be described by the need pyramid.

Paavai said...

Trying to understand, what is a kosha?

krishna said...

genius praising genius personified..

Can it get any better?:)

Gnana Kirukan said...

Infact Kasthuri - I read u post almost 3 times from the day u posted to write the comment :)..Amazing - and surprisingly I was planning to post about the different koshas in our new blog and was withhelding it till we finalize what needs to be done. But now I have put that in our blog. I guess that was written by Swami Sivananda.

Agnibarathi said...

A vague thought...pardon me if I'm unclear, I don't understand what I'm coming up with exactly myself. Looking at the idea of kOshAs and number systems, I believe the kOshAs progress in a continuous manner (i.e.,) there is not an abrupt change from annamaya kOshA to prAnamaya kOshA but the change is gradual and smooth like in infinitesimal steps. Similarly, can we show transition between number systems themselves in small infinitesimal steps...

Kasthuri said...

@ Adi : Thank you so much. By seven states, I think you mean the seven chakras through which kundalini raises and when it reaches the seventh chakra (the sahasra chakra) we have Self-realization. Nice info. I'll also blog roll you. Yes, we are co-bloggers now.

@ Anand: I think I should untag myself. Hope I get to do that soon.

@ Ganesh : Thanks.

@ tt : Yes, its almost eons after man invented counting and it hasn't been exhausted completely.

@ agnibarathi : Thank you so much for stopping by and passing your valuable comments. Its indeed a great question. While the koshas are gradual, number systems doesn't look like that on the surface. But, if we look deeper, there is a nice way in which we can go from one number system to another in a gradual way. For example, the rational numbers can be obtained from integers by taking quotients, the real numbers can be obtained from rational numbers by what are known as 'Dedekind cuts' and complex numbers can be constructed from real numbers by taking ordered pairs. I don't think there is any uniform procedure which takes infinitesimal steps in going from one system to another. Also, please don't feel humble to ask such wonderful questions. I just put forth some things that I appreciate and it may not make any sense for knowledgeable people like u.

@ priya : Thanks. Feel free to comment without hesitation. There will always be somethings to learn.

@ tj : Nice analogy to pyramid. Yeh there is a space to reach out Brahman according to Sri Sankara.

@ paavai : Kosha means layer or sheath. So Annamaya kosha is a layer formed out of food. We can think of it as the gross body. Pranamaya kosha is layer of energy. We all function with energy. The whole idea is to see a human as not just a body but a combination of the five things which are built layer by layer. As we transcend each layer we have a different type of spiritual experience.

@ krishna : Please don't use such words which are reserved for certain people. I am just an admirer of anologies and nothing more.

@ satya : :-)

@ arjuna : Will comment on it soon. Any ideas for the issue I raised ?

Agnibarathi said...

@Kasthuri - It is a kind of dualism isn't it? The continuous and the abrupt, the analogous and the digital...certain phenomena that appear discrete in one view seem continuous in another view. Or perhaps, the discrete Sivam is held together by the continuous flowing Sakthi and what we perceive is Sivam at times and Sakthi at times. And the elusive Brahmam that we seek might as well be that in which the discrete and the continuous unite... now my idea is getting clearer!! :) P.S. I was not being humble when I commented last time, quite honestly the idea was vague in my in then!!

Kasthuri said...

@ agni : I have thought about dualism of discrete and continuous things several times. That too in the context of mathematics this becomes very important. Algebra is the study of discrete objects where as Analysis is the study of continuous things. Continuity is an abstaction of a discrete system. But more often continuous things are approximated by discrete things and so in my opinion continuity can refer to Sivam and discrete to Sakthi so one often tries to approximate Sivam through Sakthi. But yeh, the analogies can vary.

@ whoami : I could only thank you for the nice link you have sent. Thanks for visiting and leaving informative comments. Yes, I also kind of this kundalini is the byproduct of awareness. My statements could be misleading. I would be eager to discuss with you about the manuscript, but I need to go through it - which I'll do it asap. Do send me your e-mail and we can correspond off blog. Once again, please do often leave such valuable comments to get this novice learning.