Adi Shankara and His Incomprehensibility Thesis
Shankara (788-820) was born in a small village called Kaladi in Kerala (God's Own Country, a "must see" place of National Geographic), India, and died at the young age of 32. In this short span of life he traveled the four corners of the Indian subcontinent and established the four most revered places of worship which are thriving even today. He wrote Atma Bodha, and commentaries on Brahma Sutra, Bhagvad Gita, and the most important Upanishads. Atma Bodha is about the awakening of the mind and Brahma Sutra is about the structure of Reality. When Ervin Schrodinger says that Atman and Brahman are the same, we can see from where the idea originates. The celestial song of India, Bhagvad Gita, has dictated the sense of ethics for India for the last two millennia and also it seems to have given consolation to many who had to face the harsh realities of life. Shah Jahan, the Mughal emperor of Taj Mahal fame, who had to suffer the atrocities of his son Aurangazeb, was the one who got it translated into Persian. Warren Hastings, the first Viceroy of India, who had to face the impeachment of his Parliament, ordered it to be translated into English, saying that it is a document that will survive in civilization long after the British Empire is gone from India. Mahatma Gandhi has said that he had turned to Gita whenever he had not even a ray of hope in his predicament with the British. Suffice it to say that Shankara did not leave any of the important literature of the time uncommented.
Real Estate and Intellectual Properties. Unlike these days, in olden days it was unnecessary to say "don't be evil" or "don't kill unborn babies", people were born pious and mostly remained pious. Totally egoless, Shankara never wrote his name in any of his voluminous writings. In his time, owning real estate property was frowned upon and intellectual property right was considered disgraceful. He wrote many hymns which are popular even today. He is the originator of Advaita Philosophy, a sophisticated form of Vedanta.
Shankara's Incomprehensibility Thesis. Stated simply, Shankara's contention is that even metamathematics (or any other form of rational thinking) is not enough for a complete understanding of Reality. An important concept initiated by Shankara is called "Maya", loosely and perhaps wrongly, translated in English as "illusion". I look at it differently and call it Shankara's Incomprehensibility Thesis (SIT): a kind of extension of Goedel's Incompleteness Theorem (GIT). My view is that every formula in any axiomatic theory can be put in one of four categories: theorem, falsehood, introversion, profundity. Introversions arise when we attempt to use the theory to investigate itself, and profundities are the profound concepts which we are not sure to choose or not to choose as axioms. While GIT says that there are introversions in any significant theory, SIT says that there will always be profundities in any branch of knowledge, no matter how much we advance in our understanding. Of course, Shankara did not say this in bland logic, but with religious fervor in the form of hymns.
The following quote from Will Durant gives a rough idea of the line of thinking adopted by Shankara to reach his conclusion:
Sankara establishes the source of his philosophy at a remote and subtle point never quite clearly visioned again until a thousand years later. Immaunel Kant wrote his Critique of Pure Reason. How, he asks, is knowledge possible? Apparently, all our knowledge comes from the senses, and reveals not the external itself, but our sensory adaptation-perhaps transformation of that reality. By sense, then, we can never quite know the "real"; we can know it only in the garb of space, time and cause which may be a web created by our organs of sense and understanding, designed or evolved to catch and hold that fluent and elusive reality whose existence we can surmise, but whose character we never objectively describe; our way of perceiving will forever be inextricable mingled with the thing perceived.
Note that it is only in the twentieth century that quantum physicists grappled with the idea that the observer and the observed cannot be seperated from an observation.
Further reading. To get a gist of Shankara's philosophy, see Will Durant. To know more about Adi Shankara, type "shankara" without quotes