Some days back, I had written rave reviews about Godel, Escher, Bach: The Eternal Golden Braid. The author of this book Hofstatder claims that even though the book explicitly deals with meta-mathematics, art and music, the major theme is about discovering the self, or the soul. I agree with the author that the book is about soul searching. It is my feeling that the book would have been more complete with the philosophy of Vedanta incorporated. But that would have made it even more specialized and highly technical. It may also be that, the author is not aware of this profound philosophy. Anyway, what I am about to write is the result of some of the things that I was able to appreciate in GEB along the lines of Vedanta.
Let's first consider the following M.C.Escher's painting.
It should be no doubt that the painting is beautiful although it is highly illogical (water defying gravity ?!). There is a clear sense of ambiguity in the painting. A cyclic waterfall is absurd without external energy. The presence of water cycle without external energy is the cause of ambiguity here. Let's see how does this relate to the last post.
I hope some of you might have given a thought about it. (If not, I would strongly encourage you to give it a shot before proceeding). The last post asks "Is the set of all sets, a set ?". At first, it would seem like "it is a set" since it is the "set of all sets", but on the other hand we'll see that "it is not a set" because "a set of things is not that particular thing any more" as shown in some examples in the post and "thing" can be replaced by a set. This ambiguity is due to the cyclic nature of our logic that we many times think, if something is true then the negation of that is also true. If 'A' exists then 'Not A' also exists. I'll call this as duality in logic. Thus, the presence of duality in logic without any singularity is the cause of ambiguity. Again, how does this relate to the painting ? Notice that the duality is a cycle, we think something as true and after some time as non-true, again after some time as true,...so it is a cycle of assigning truth which causes ambiguity. Okay let's see what Sri Krishna says.
Everyone in this world does something or the other at any given point of time. It can be classified into two things : thinking and acting. Here I am considering sleeping as an activity too. Thus, we are constantly engaged in the cycle of thoughts and actions. In the Escher's painting the presence of water cycle can be attributed to our vision, in logic the presence of duality can be assigned to the existence of our intellect. Similarly, the presence of the cycle of thoughts-actions can be attributed to the existence of our Ego (remember, even in deep sleep, our Ego is constantly working whereas the intellectual faculty remains dormant, and that's why we say we had a good sleep). Thus, the cycle of thought and actions (caused by Ego) without realizing the Self is the cause of ambiguity in life.
So, what is the point ?
Realize the beauty in the painting by raising above the ambiguity (attributed to vision) caused by the water cycle.
Realize the beauty in the logic by raising above the ambiguity (attributed to Intellect) caused by the duality in logic.
Realize the beauty in the life by raising above the ambiguity (attributed to Ego) caused by the cycle of thoughts-actions.
11 comments:
kasthuri,
kandippa indha post ai print out eduthu.. innorukka padikanum.
onnume puriyala...
way over my head.
give me some time. let me read and get back to u.
kasthuri
you hit the nail right on the end, even though our debates are phenomenally interesting, realisation comes with the cessation of fragmentation, cool post
dualism is sewn into the very fabric of the phenomenal universe
for example
time- we experience partite time
whereas rela time is declared to be impartite according to Ramanuja, also review the concept of imaginary time in cosmology.
wave-particle duality,
pair production, presence of matter and anti-matter
I believe that this duality is the result of Maya and can be transcended only if we relate to the paramatman SriKrishna. for people like us living in a world which has multiplied sensory inputs and created more reasons and means for enjoying life, a true contemplation of the impersonal absolute may be next to impossible , besides Maya will not let you continue such attempts consistently. by subordinating ourselves to Narayana who wields control over Maya we can gain the understanding we require to transcend this duality.
this is my humble opinion.
Raise above the duality, and Realize the beauty of logic!! I liked it.
Adishankara says, when we talk abt logic, we talk abt relating two things [like, if X is this, then Y is that..]. For this, we assume X and Y are seperate entities, which by itself is fundamentally not true according to advaita. :)
Kasthuri,
Pheewww!!! Went way over my head. Like prabu says, I am going to print it out and read it again :)
kasthuri
I have taken your email id will mail today. I think much can be done in this area of research (if you want to call it that). yes we'll correspond at length , the blog is too limited a medium for the kind of serious discussions you have in mind. thanks for being a regular visitor to my blog.
good one.
too much for me...
will re-read it..
@ Prabhu : Don't worry...my latest post gives another example of duality in logic.
@ anand : Thanks...yes Maya may be beyond comprehension in this plane.
@ tj : Yes..Advita is amazing. Thanks.
@ ranj : Hope my latest post makes more sense.
@ anand : I've emailed you.
@ lavan : thanks.
@ tt_giant : probably the post demands more description. I have a latest post with a similar paradox in logic.
Kasthuri,
we have to 'raise above the ambiguity' - interesting.
IMHO, i'd rather say that, it is not possible for us to raise above the ambiguity, but just submit to the fact that, we 'are' ambiguity 'itself' :-)
May be, that realization is 'raising above the ambiguity' ;)
@ arvind : Cool...I belive realization is raising above the ambiguity as u pointed out.
Namaste Sri Srinivasan,
It's kind of surprising that my first thoughts while studying the advaita philosophy were about sets and supersets. And co-incidentally I found your blog while searching for Advaita, and Godel.
However, I failed to understand one thing. You say, "If A exists then the negation of A also exists". But this won't hold good if I assign "A = existence"! Again, one could argue that the "If" in the proposition would be redundant when we assign A as existence. So, I consider that the nature of the variable in the above proposition is not absolute but is relative.
One other thing. While studying the upanishad from my shakha, the Aitareya upanishad, I could not but help thinking of power sets.
Consider the following:
"In the beginning, the Power-Set function alone was. It acted on a set representing itself. And so the universe was born"!
It's like as if the Power-set function thought:
Only I am there. Nothing else is there.
{Only I} am there. {Nothing else} is there.
Thus the power-set of the set representing power-set function has two elements. The set representing power-set function itself and the null set. But isn't the null set just a "representation" of "nothing else"? Thus in terms of representations there are two sets but in terms of what they represent, there is only one!
My apologies for this long comment. I couldn't find any other place on the web where I could share these thoughts!
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