Thursday, March 30, 2006

Thus Ends the Discussion

Thus ends the discussion of Raju Chidambaram's theory of a mathematical description of Advaita over on the Yahoo Advaitin List. That discussion has been blogged here for convenience and posterity. I may have missed a few posts, but I believe I got most of it. Here was my final post (a bit embellished).

Namaste,

I have blogged the final Advaita math posts at Advaita Math Blog. These include Rajuji's final post on "Will Spirituality Be Taught in Schools in Future as Part of Science?", and the posts on Kundalini and time contraction, as well as all the responses to both of these (see the comments section of the blog posts).

If I have missed anything or made some typos, please tell me.

It was a very interesting theory and discussion.

It seems that people were a bit intimidated from either agreeing or disagreeing. Fortunately, we can take comfort from the fact that Shankara wrote all that he did without a lot of math! :-)

Still, I am quite convinced that if Brahman and reality are identical, then there must be profound scientific implications. Examples, might be that the conservation of mass/energy is somehow related to the unity of Brahman, that the omnipresence of the laws of physics is related to the omnipresence of Brahman, or that the peculiarities of quantum mechanics point to the necessity for introducing consciousness as the fundamental reality.

Raju's theory revolved around the time contraction experienced by the realized soul, per the scriptures and experiences of realized souls. He developed some of the geometrical consequences, which may serve as an aid to understanding and teaching Advaita. There is an obvious relationship with relativity theory, where space and time also expand and contract, depending on the observer.

Hari Om!
Benjamin

Time Alteration Experiences (continued)

From: V Subrahmanian
Date: Mon Mar 13, 2006 2:06 am
Subject: Time alteration experiences


Dear Sri Raju ji:

Namaste.

Thank you for your response. Let me tell you how I looked at the time alteration incident quoted by me: After hearing the detailed description of Acharyal's vision-experience, the disciple, in the normal state, estimated it to have taken about one hour. But actually it had taken only 3 minutes in the vision as the 'replay' of the vision confirmed. From this I decided that relative to the estimated time of a normal person, the actual time taken in the extraordinary vision is less and therefore there has been an instance of time contraction for the one who actually had the vision.

Let me present a few more incidents, initially from the experiences of the Acharya Himself and later from the life of the revered disciple.

From the book 'Yoga, Enlightenment and Perfection': Page. 66:

(Acharyal:) The words relating to the pañcopacàra-pujà (following the dhyàna-sloka) took only some seconds for Acharyal (Sri Chandrasekhara Bharati Mahaswamigal) to utter and for Me to repeat. Yet, I experienced no shortage of time in elaborately worshipping the Lord (Narasimha) mentally in My heart with offerings of sandal paste, flowers, incense, lamp, food and so on. I can attribute only to divine grace the irresistible urge that led Me to begin the worship. During naivedya, I served the Lord a variety of dishes in a jewel-studded golden plate, put a little food into His mouth, waited for Him to masticate and swallow and only thereafter offered another morsel. It was as if the several seconds miraculously became extended to over half an hour from My perspective. Even while performing the worship with concentration and dedication, I was able to see Acharyal and repeat His words without delay.

(I think this is a case of 'Time expansion')

Page 109:

In a matter of seconds, I could feel a tingling sensation between My brows. This gradually increased in intensity. I also began to see an attractive, blue disc of light. This resembled the light from the jewel on the Mother’s face. The main difference†was that this was diffused. I then visualised a diminished version of Her idol emerging from the disc and occupying the lotus of My heart. The great clarity of the image in My heart and the readiness with which I had been able to visualise it pleasantly surprised Me. I focused on the form. My chanting of the Pranava stopped.

Moments later, I opened My eyes. Actually, about half an hour had passed. During this time, I was unaware of the surroundings and My body. I realised that while it is perfectly possible to picture a form without adopting the procedure taught by Acharyal, the latter facilitates the visualisation of, and focus on, the form. Further, I understood that the light apprehended mentally can be related to the light seen before gazing at the space between the brows.

Page 144 (Acharyal:) As I focused on the form, My awareness of the surroundings and the body vanished. Soon, My mental chanting of the Pancakshari-mantra (Om NamaH Shivaaya)came to a stop and My mind thoroughly locked on to the divine form in the heart. Suddenly, the form became extraordinarily vivid. No effort to concentrate was needed any more. I could then literally experience the immediate presence of Siva. The affection and smile that I beheld in the Lord’s†ishaana-mukha (upward face) in particular still enthral Me. I was overwhelmed with joy.

After about one and a half hours, as I discerned later but what then seemed to Me to be just a moment, I became lightly aware of the body. I opened My eyes. I could see the sun close to the horizon and feel a gentle breeze. I could, at the same time, clearly apprehend the Lord associated with Ambà in My heart-lotus. The Lord appeared to be emerging from within and expanding. A deep long sound of Om was audible. I then definitely beheld Siva in front of and facing Me. Oh, what a glorious sight that was!

Page 157: I initiated My meditation as usual by gazing at the space between the brows and chanting the prà_ava. I apprehended a blue hue, just as I often did. At this point, instead of conceiving any divine form, I mentally uttered once the words: "I am indeed the Supreme Brahman, the One free from decay and known as Vàsudeva (He who resides in and shines in all)."

Then, without repeatedly chanting the words like a mantra, I strongly held on to the idea conveyed. Immediately, I felt Myself expanding and becoming pervasive like space. A great wave of joy arose and submerged Me. After what seemed a trice, I gained mild awareness of the body; actually, about 30 to 45 minutes had passed.

Page 159: Consciousness shone clearly without any object and without limitations. I was overwhelmed by bliss, which was far greater than on the previous evening. The awareness of any distinction between the bliss and Myself was almost absent. About an hour passed thus but I was totally oblivious of the passage of time. I then emerged from savikalpa-samadhi and gradually became aware of the body.

Page 174: The notion, “I am the non-dual Brahman apart from which nothing whatsoever exists” that was prominent and naturally persistent since the previous†evening had been intensified by My savikalpa-samadhis of the morning and by My reading and reflection of the afternoon. So, I did not have to cultivate it. I had barely seen the soothing expanse of blue when it vanished. I felt Myself expanding and becoming like space. The sense of I nearly vanished and My mind entered savikalpa-samàdhi.

The bliss was very great. However, with effort, I restrained Myself from being overwhelmed by it and thought, “I am not the one experiencing bliss but am bliss itself.” In a trice, a sharp change occurred. Awareness of the distinction of the concentrator, concentration and the object of concentration completely disappeared. No more was there any sense of individuality or of space, time and objects. Only Brahman, of the nature of absolute existence, pure consciousness and ultimate bliss, shone bereft of the superimposition of even a trace of duality.

After about two hours, the mind descended to the level of savikalpa-samadhi and mild awareness of the distinction of the concentrator, concentration and the object of concentration reappeared. Though the bliss of savikalpa-samadhi was by far greater than the joy of any worldly enjoyment, it was nothing compared to the absolute, non-dual bliss of nirvikalpa-samadhi. Gradually, I became lightly aware of the body and of the build up of breathing that must have almost totally stopped earlier.

Now the experiences of Time alteration in the case of the disciple, Sri R.M.Umesh as reported in the book 'The Crest Jewel of Yogis Vol.II':

Page 148: Assuming a meditative posture I gently closed my eyelids. The Mantra rumbled on but slowly faded away. The mind became increasingly calm and in a few moments I lost all awareness of the body and surroundings. I felt as if I was expanding. I beheld a vast expanse of intensely bright illumination and had the experience of merging into it. Waves of bliss submerged me and the sense of time was lost. In what seemed a trice I regained light consciousness of the body. Actually an hour had passed.

Page 164: Acharyal asked me to accompany Him to the Kalabhairava Temple and there He sat down for meditating. He asked me sit close to Him and then remarked "We will meditate". I saw His eyes close partially. Slowly the heaving of His chest became slower and slower and soon no trace of breathing was discoverable by me though I was very close to Him. He seemed to radiate peace. Suddenly I felt a force dragging me into meditation. I too closed my eyes and my mind soared to the heights of concentration. I thought that a moment had elapsed before I was able to regain awareness of the body. I opened my eyes and observed Acharyal. Slowly His breathing commenced and in a few moments He opened His eyes. Turning to the Kalabhairava idol He shouted out the Lord's name and after prostrating, came out of the temple. Actually over half-an-hour had elapsed. On coming out of the temple He said, "Nirvikalpa Samadhi is very nice. Is it not?"

Page 166: Acharyal then said, "He is now in Nirvikalpa Samadhi". This passed on. Finally Acharyal decided to bring him out of Samadhi. He told me that He would be erasing the memory of the Samadhi state because the time was not yet ripe for this state which He had granted (to that boy) in response to my wish. He said further, "He will feel as if only a few minutes have elapsed and that he never went into any firm concentration at all, for he continuously heard other sounds".

Accordingly, as per Acharyal's instructions, I repositioned my hands and gradually observed the boy. He opened his eyes and I asked him what had happened. Exactly as predicted by Acharyal, he said that he felt that only a few minutes had elapsed. Actually a long period had passed.

Page 169: In 1982, however, He permitted me to spend long durations in meditation and I went over to Sringeri on 4th October. At that time Acharyal was on tour and had directed me to stay at Bhairava Kripa, a house built by Him on the way to Kalabhairava Temple. I was the sole occupant of the place and had all my time to myself. By Acharyal's grace, for over two months I was able to spend my time in Samadhi spending as long as 20 hours a day in that state itself. I found that the need for food became almost nil and I was taking a very meagre amount of food merely because of Acharyal's instructions. Sleep, however, could be dispensed with for days without any problem at all.

This following one is excerpted from the book 'Divine Discourses', p.55: Chapter: The Goal and the Means:

There is a disciple of mine. Owing to the special merit acquired by him in his earlier birth, on his sitting in Samadhi, the acme of Yoga, he does not get up even when three days have passed. One may ask, " Has Sandhya Vandanam not got omitted?" He is doing something that is far superior to Sandhya Vandanam. LiinaH Pare Brahmani (He is absorbed in the Supreme Brahman)

I (Acharyal): What was it like when you remained for three days in Samadhi? Were you aware of day and night?

Disciple (Sri R.M.Umesh): No, I was aware of nothing external. I just abided in that state.

I: How did you know that three days had passed?

D: I had kept a watch with me. When I got up, I learnt from it that three days had passed.

When he has attained such a high state, is it necessary for him to perform Sandhya Vandanam or to perform Abhisheka to a Shiva Lingam? No.

On the other hand, suppose there is a person who desires to eat tiffin, drink coffee and go out and wander in the streets, and also does all this but remains without performing worship of God. What can we say to him except "You are a thorough Nastika"?. On the other hand, it must be said about this disciple of Mine that he is the ultimate Astika. Why? Because, in Samadhi, he does nothing. If he were to engage in activities then it might be suggested to him to do Sandhya Vandanam too. But he does nothing whatsoever, even food is not needed by him. There do exist such persons.

What I am saying is what I have seen in My disciple. His achievement is because of the special merit acquired by him in his previous birth. He told Me, "I wish to go to a forest and sit in penance".

I: For how many days?

D: One month.

I: What will you eat?

D: I shall keep with me a little Aval (flattened rice).

I: What will you do if a tiger comes?

D: "Oh am I not there as food for that tiger? If it feels like eating, let it do so."

That is the extent of his firmness of mind. One day, when he was seated, a tiger actually came there. He saw it and felt, "God has come to me in the form of this tiger. He is revealing himself like this." He just remained seated. The tiger observed him and saw whether he was moving his hands, or legs or head. He did not move at all. What did the tiger think? Perhaps, it concluded that this person must actually be some stone. It went away. If we get that kind of capacity, need we do worship of God? No, God would be experienced by us right where we are.

End.
Om Tat Sat.
subbu

A final word from Raju Chidambaram

From: Raju Chidambaram
Date: Tue Mar 7, 2006 5:21 pm
Subject: Will Spirituality Be Taught in Schools in Future as Part of Science?


I truly appreciate the various comments and questions raised in response to my last posting.

Michael ji’s concern appears to be the potential for scientific evidence conflicting with scriptural pronouncements. True, the potential for conflicts can get higher as and†when science gets more and more involved with spirituality. But that fear is no reason for science to stay away from an honest, unbiased enquiry into something as vital as spirituality. If conflicts arise, they have to be dealt with on the merits of each case. I feel confident that when we we apply ourselves singularly to truth without bias, there will be a resolution to conflicts.

My faith in Advaita being what it is, it appears more likely to me that the most relevant and basic of scriptural declarations will be in fact affirmed by science. The benefit from such a positive outcome outweighs the cost of potential conflicts. With the support of scientific evidence behind it, spirituality can more easily gain the much needed entrance into public education. A case in point is the research into yoga and meditation that I alluded to in my posting. There was a story in TIME that some schools in Colorado are introducing meditation even at the Primary class level. It is doubtful this would have happened without the endorsement received from the scientific community.

What is my view of evolution? My view is in fact noted in the footnote on Page 24. A subsequent question arising from this footnote might be: Why does Ishwara take this difficult road to perfection, attended with all the drama of evolution’s trial-and-error approach? Why not†“intelligently design”†the perfect creature right away? Of course†only Ishwara knows the answer to this question, but we as jeevas can at least say this: The question presumes that Ishwara’s purpose of creation is to create the perfect†creature. In fact Advaitins tend to view creation as a lila or sport of the Lord only where there is plenty of room for imperfection. Besides, from the Absolute point of view, are we not already Perfect?

The need for public education in spirituality has been very eloquently argued by Prof VK ji in his latest posting, in response to a comment by Sunder ji. I cannot agree more with VK ji’s views. Spirituality is not going to get†“hard”†and become soul-less by contact with science; on the other hand science stands to be†“softened”†by its†acceptance of the reality of spirituality.

Sada ji’s statement that Advaita Vedanta does not rest on any axioms is certainly reassuring. The difference may be in what one considers as an axiom versus a self≠evident principle. The euclidean axiom that there is one and only one straight line connecting two points appears self-evident but is still viewed as an axiom. Whatever one’s preferred choice of terms, it does not alter the main point: That science on the whole should feel more at home with Advaita’s approach to spirituality than with†those of traditional religions.

The anecdote posted by Subrahmanian ji on Sringeri Acharya is amazing in its details. I confess its significance is far more than what I can readily apprehend. But it does illustrate vividly how time experienced depends on “how much”†is experienced. Authentic anecodotes of this kind are valuable data points as we strive towards complete†understanding of the spiritual realm. Hence I for one will be happy to see more such postings. The interesting thing about this anecdote is that it is an example of “time†expansion”†and not contraction. What is only of the order of 3 to 4 minutes is experienced by the Acharya’s disciple as an hour long expedition into a spiritual wonderlandƆ†Yogis with mastery over mind can use that power to stay firmly absorbed in Self, nearly shutting out all experiences and freezing time. They can also use their siddhi for gaining themselves, or conferring on anyone they choose, extraordinary experiences leading to a significantly altered experience of time. The very rich and vivid details of the experiences undergone by the disciple can account for his subjective time expansion. This is how at least I read it.

Hari Om!

Raju Chidambaram

Time contraction phenomenon

From: V Subrahmanian
Date: Sat Mar 4, 2006 5:28 am
Subject: Time contraction phenomenon

Ref: Previous post: Will Spirituality Be Taught in Schools in Future as Part of Science?


Namaste Sri Raju ji:

At the outset let me state that I am not a scientist. For this reason, I would not say that I appreciated the earlier posts of yours in this series. However, this latest post of yours did interest me and your following observation enthuses me to share with you some details pertaining to the perception of time during meditation. What I propose to present here is the experiences of Jagadguru Sri Abhinava Vidyatirtha Mahaswamigal, who adorned the Sringeri Sri Sharada Peetham upto 1989. There are a few instances mentioned in the book 'Yoga Enlightenment and Perfection' pertaining to the Acharyal's meditative and other extraordinary experiences where the 'time contraction' phenomenon was conspicuously experienced. I recalled these when I saw your following words:

Is there any experimental validation of the time contraction result derived from the model? I recently raised this question with Prof Sara Lazar, of Harvard Medical School, where numerous studies on the effect of meditation have been carried out. According to Dr.Lazar, there have been no quantitative studies to measure the effect of meditation on time perception, but expects someone to do that sooner or later. Regarding contraction in perceived time, Dr. Lazar however noted in her e-mail that “this phenomenon is often mentioned by practitioners (along with need for less sleep)

The above book is written by Sri R.M.Umesh. The revered author has narrated in the above book what transpired during his interactions with Acharyal on various occasions. Although what I want to convey is found in the end of the following narrative, I decided to present the entire narrative, though quite lengthy, so that the 'time contraction' phenomenon could be better appreciated by the readers. The narrative is about the Kundalini yoga and many technical terms connected with this sastra. As the portion is culled out from the soft copy of the book as I have it, the portions in Sanskrit fonts and those with diacritical fonts appear in this presentation in an odd way. However, this does not hamper the main purpose that we have on hand. In case you feel I can go ahead and present the other few instances in the book depicting the time contraction phenomenon, pl. indicate.

With warm regards,

subbu



6. Exposure to Kundalini Yoga

The following conversation took place in May, 1978 at Sringeri. Acharyal sent for me in the afternoon. He was seated alone upstairs in the eastern side of Sacchidananda Vilas. He gave me two books in English in which the authors had written about experiences associated with the arousal and ascent of the ku_áalinä-ëakti. Acharyal had first enlightened me about Kundalini yoga in 1973 and had subsequently thrown further light on it on some occasions. He asked me to read the books and give Him my comments on the contents. Then He queried, “Is there anything you would like to ask?”

I: Would Acharyal please tell Me about Acharyal’s first experience of the kundalini and the chakras?

Acharyal: This took place a few months after My being initiated into Sanyasa (on May 22, 1931). I had just finished My morning ahnika and was about to get up. Without premeditation, I joined My palms and said, “Obeisance to the glorious Narada." Abruptly, I felt an upsurge of joy and stopped being aware of My surroundings. It began to seem that My body was becoming transparent and that I was seeing My backbone from some vantage point in front of My chest.

I: Did Acharyal apprehend the backbone together with the rib cage, internal organs and so on?

Acharyal: No. It was the backbone that stood out, whitish in colour, with the silhouette of the body appearing dark like a shadow. The backbone then seemed to become translucent to reveal a canal in its interior. In moments, the canal’s width became greatly magnified. I could then see a tube, red and bright like fire, traversing the length of the canal. A mellifluous female voice announced, "This is the sushuma-nada”

I: Could Acharyal perceive the speaker of the words?

Acharyal: No. I just heard the words.The width of this fiery canal then expanded and a section along the length vanished to reveal another canal within. This one was coloured like the sun half an hour after sunrise. I heard the words, “This is the vajra nada." The width of this canal too abruptly increased and a section along the length faded away. A pale tube looking like the moon seen through a thin layer of cloud became visible within the earlier tube. At this juncture, the words that I heard were, "This is the citri?a-nada. The brahma-nada is here. It is even termed sushumna” The meaning that flashed in My mind was that the pale tube was called citri?a, its hollow interior formed the brahma-nada and that the name sushumna has been employed even to denote the citri?a or brahma-nada. The fiery, sun-like and pale canals did appear to form a unit.

The scene underwent a change. I could then discern that the triad of nadas stretched from between the anus and the penis on the lower side to above the level of the eyebrows, into the head, on the upper side. Next, there appeared a moon-like tube that was distinctly coupled to the triad both at the base of the latter and between the eyebrows. On its upper side, this tube continued from the junction between the eyebrows to the left nostril. On its lower side, it ended at the right testicle. Between the two junctions, it formed arches on the triad’s left and right sides, with the crossovers occurring at the levels of the throat, chest, navel and genital. For a moment, this shape was replaced by one in which the tube formed a bow-like arch between the lower and upper junctions and towards the body’s left side. I felt that both the forms may be met with.

After the earlier shape was restored, I heard the words, “This is the ida-nada.” Something appeared to be moving through this tube in synchronism with my breathing, which, I somehow felt, was taking place through just the left nostril. Also, the flow within this tube seemed to have a cooling effect.

In moments, this tube disappeared. Instead, another tube manifested that was red and bright. This too was clearly coupled to the triad between the brows and at the lower end of the triad but, unlike the ida, continued to the right nostril and the left testicle. Between the upper and lower junctions, it formed arches on the sides of the triad, with crossovers at the levels of the throat, chest, navel and genital. However, wherever the previous tube traversed from left to right this crossed from right to left and vice versa. Then, for a moment, the shape changed and the tube resembled a bow between the upper and lower junctions, lying on the right side of the triad.

The words I then heard were, “This is the pingala-nada.” I began to feel that My breathing was taking place through just the right nostril. In synchrony with the breathing, I could apprehend something moving through this tube. The flow seemed to have a heating effect.

A few moments later, the moon-hued tube that had disappeared again came to sight. I could then see both the arching tubes simultaneously. Next, My breathing shifted from the right nostril to the left nostril and, with this, I noticed the activity in the reddish tube giving way to that in the moon-hued tube. Shortly, I felt that breathing was taking place through both the nostrils; I could then apprehend activity in both the tubes.

{Later, Acharyal said, “Three shapes of the ida and the pingala have been spoken of. The first is characterised by each of the two nadas forming arches alternately on†the left and right of the sushumna. The second form is that of a near straight line from the base of the sushumna to the middle of the brows; the ida remains on the left, while the pingala lies on the right of the sushumna. The third shape is roughly like that of a bow in the chest lying on one side of the sushumna. The first and the third shapes are the ones that are poles apart: the second can be regarded as a variant of the third in which the bow’s curve is negligible with respect to its length. Acharyal then read the following portion of Kalicara’s commentary on the first verse of the ???.

It is said in the Yamala, “The ida and pingala are on its left and right. These two either proceed straight up to the nostrils, or do so by alternating from the left to right and from the right to left and going round all the chakras.”…By this, two positions of the ida and pingala have been shown. The occurrence of a shape resembling the curvilinear part of a bow has been stated elsewhere. For instance, it is said, “Know the ida and pingala nadas to be shaped like a bow.”

Acharyal: The scene soon underwent a change and centred on the lower end of the triad of tubes. There, I could see a beautiful lotus with four petals that were deep red in colour. The voice announced, “This is the muladhara chakra." At the pericarp of the lotus, there was a sivalinga. A cobra lustrous like lightning lay with its body making about three and a half turns around the linga. The serpent’s hood rested on the upper end of the linga and its mouth effectively blocked the passage to the triad of tubes. The serpent was motionless and appeared to be fast asleep. Yet, it was somehow unmistakable that it was the embodiment of unbounded power. I was told that this was the kundalina.

Then, for a few moments, I saw on each of the four red petals, a distinct, bright golden letter; the letters were ?, ?, ? and ?. Simultaneously, I could apprehend a yellow, square region enclosing the pericarp. Inside this yellow square was an inverted red triangle; the kundalini lay in the red triangle. The letter ? appeared in the square accompanied by the smell of the earth at the start of a spell of rain.

I: Did Acharyal feel that the lotus itself smells like freshly wet earth?

Acharyal: No. From the appearance of the prithvi-baja (?) and the smell, I just understood that the muladhara chakra is associated with the element prithvi (earth), which is characterised by the quality of smell.

Then, there manifested within the yellow square a white elephant with multiple tusks. On it was seated a deva with four arms, holding a thunderbolt in one of them. I further saw a swan on which sat a deva with four heads. A red-eyed deva with four arms was also visible. From the voice, I learnt that the elephant was Airavata and the divinity on it was Indra; the other deva was Brahma, while the deva was Uakina (?). The divinities then disappeared and I could see just the lotus with the linga and kundalini.

I: What was the overall impression that formed in Acharyal’s mind?

Acharyal: I got the feeling that the kundalini was primary and that a way of contemplating on the muladhara chakra was in association with the letters and divinities as seen by Me.

Thereafter, the scene shifted up the sushumna to around the level of the root of the penis. There, I beheld a lotus with six vermilion-hued petals. The voice said, “This is the swadisthana chakra.” The central region of the lotus was white and comprised a figure resembling the crescent-moon. Then, the letter ? manifested briefly in that region and, simultaneously, I felt the taste of water. The apo-baja and the taste led Me to understand that the swadisthana chakra is associated with the element apas (water) characterised by the quality of taste.

Simultaneously, there appeared on the six vermilion petals, one bright letter each; the letters were ?, ?, ?, ?, ? and ?. In the white zone, I could see a crocodile on which was seated a deva with a noose. Further, I beheld the figure of Vishnu seated on an eagle and bearing in His four hands, a conch, cakra, mace and lotus. A dark, three-eyed deva was also visible. The voice informed Me that the deva on the crocodile was Varuna and that the deva was Rakina.

The scene shifted farther up the sushumna. At the level of the navel, I could see a lotus with ten petals that were dark like rain-bearing clouds. In the interior region, there was an inverted red triangle. The words I heard were, “This is the manipuraka chakra." On the ten petals flashed blue letters ?, ... ?. The appearance of the agni-baja, ?, within the red triangle together with a sensation of heat led me to understand that this cakra is associated with the element fire that is characterised by heat and form. I also saw in the red region a deva with four arms seated on a ram, Rudra smeared with ashes and seated on a bull and a dark devä with three faces wearing a yellow dress. I was told that the deva on the ram was Agni (Fire) and that the deva was Lakina.

I: Was there anything explicit to convey that the kundalini can rise from the muladhara to the swadisthana and then to the manipuraka?

Acharyal: No, but there was the hint provided by the shift of focus up the sushumna from one cakra to the next. At any rate, of its own accord, a conviction arose on beholding the swadisthana that this was a centre to which the kundalini could ascend through the brahma-nada. A similar certitude arose about the manipuraka.

From the manipuraka, the scene shifted up the sushumna to the level of the chest. I could see a lotus with twelve red petals. The voice informed Me, “This is the anahata chakra.” In the interior, there was a smoke-coloured, hexagonal region formed by an upright and an inverted triangle. An inverted triangle lay within this and contained a lustrous linga. This chakra with a linga seemed to be a pure and sacred place. A non-vocal, internal sound became audible. I spontaneously felt that sound that was in an undifferentiated form in the muladhara passed on to a slightly less subtle state in the manipuraka and then reached the stage prior to spoken and heard speech here.

After this, the letters ?, ?, ... ? manifested for a few moments on the petals. In the hexagonal region, I saw the vayu-baja, ?, and simultaneously felt a slight breeze. This led me to understand that the anahata chakra is associated with vayu (air) characterised by the quality of touch. I further saw in the hexagonal region, a four-armed deva of a smoky hue seated on an antelope, a very attractive three-eyed deva displaying the abhaya and varada mudras (symbols of granting fearlessness and boons) and a deva. The voice announced that the deva on the antelope was Vayu, the other deva was Iva and that the deva was Kakina.

The focus shifted farther up the sushumna to the level of the throat. There, I beheld a lotus with sixteen petals that were smoky in hue. The voice stated, “This is the visudda chakra.” In the interior, there was a white circular region. For a few moments, the vowels manifested in red on the petals. The appearance of ?, the baja of akasha, in the circular region accompanied by the feeling of My being in vast expanse led Me to comprehend that this cakra is associated with akasha (space).

In the interior region, I also beheld a deva seated on a white elephant, Siva with five faces and ten arms together with Parvati, and a deva clad in a yellow dress. The voice announced that the deva was Ambara, that the Lord was here as Sadàëiva and that the deva was ?akina. This chakra gave the impression of being an exalted centre.

The scene moved even farther up the sushumna to the level of the eyebrows. I could see a glorious lotus with two white petals. The voice informed Me, “This is the ajana chakra.” In the central region, there was an inverted triangle wherein there was a linga. Above the triangle was a crescent. Then, the letters ? and ? manifested in the two petals and the Pra_ava in the interior region. The ? of the Pra_ava was above the crescent, in bindu form. I could also see a deva with six faces. I was told that she was Hakina. Beholding this cakra itself gave great joy.

Then, above the end of the sushumna and within the head, I saw a lotus with very many white petals hanging downward and arranged in multiple layers. All the fifty letters of the Sanskrit alphabet could be seen here. The voice told Me that this was the thousand-petalled sahashrara. At the pericarp of the lotus was a region that resembled the full moon and shed nectarine rays. Inside this was a bright triangle. I heard the words, “Herein abides Paramasiva” While I could somehow sense the presence of a few zones between the ajana and the sahasrara, I did not directly apprehend them. Even without hearing any words to that effect, I felt certain that the ascent of the awakened kundalini shakti ended at the sahasrara, wherein shakti united with Paramasiva.

At this point, My experience ended. As I opened My eyes, I was a bit bewildered whether I had been dreaming or vividly hallucinating or had had a divine experience. Without giving the matter any further thought, I got up and left for Acharyal’s presence as it was time for Me to offer My obeisance to Him

I: How long did the experience last?

Acharyal: What do you think would have been the duration?

I: Between half and one hour.

Acharyal (laughing): It lasted less than five minutes.

Clearly amused at my surprise on hearing this, Acharyal asked, “What is the time now?” Looking at my wrist watch, I said, “4:43". I was seated cross-legged in front of Acharyal with my arms resting on my legs and with my palms joined. Acharyal leaned forward and grasped my joined palms in His right hand. Closing His eyes, He said, “Amba". Suddenly, all that Acharyal had described began to unfold before me with great clarity. I even heard the voice that Acharyal had spoken of. My experience ended where Acharyal’s had.

I regained awareness of My body and surroundings and saw Acharyal withdrawing His hand from mine. “What is the time now?” He asked. After checking, I reported that it was 4:46. As you can see, less than five minutes has passed,” remarked Acharyal, with a smile. He then instructed me, “Describe what you saw in the hands of Hakina in the ajana chakra." As the vision had been very clear and the memory fresh, I promptly said, “The abhaya-mudrà, the varada-mudrà, a book, a skull, a áamaru (small drum) and rudràkóa rosary.”

With a nod, Acharyal said, “Yes, that is just what I saw then. I asked you about what I had not described earlier to confirm the similarity of our visions. They being similar, it would be reasonable to take it that both lasted for the same time rather than that your vision lasted for three minutes and Mine for half to one hour.”˝

End of the portion of the narrative.

Will Spirituality Be Taught in Schools in Future as Part of Science? (MTS-Final)

From: Raju Chidambaram
Date: Thu Mar 2, 2006 3:22 pm
Subject: Will Spirituality Be Taught in Schools in Future as Part of Science? (MTS-FINAL: Towards A Mathematical Theory of Spirituality Based on Advaita)


Ref Pages 29-30 of Advaita Math Paper

Spirituality has been more or less the exclusive province of religion since civilization began. Religions- especially those founded on the worship of a personality rather than on universal truths- are not overly comfortable with the idea of scientific enquiry in the spiritual field. For its part, Science as developed in the West has also generally behaved as though spirituality does not even exist. That is, Science has tried its best to subsume the vertical axis of our mathematical model under the horizontal axis, but without any success. The present relationship between science and religion is one of wary tolerance for each other, somewhat like the relation between the East and West during the heydays of the Cold War. An uneasy truce between the two has been accomplished by erecting an arbitrary “BerlinWall” separating the spiritual from the material and the “religious” from the “secular”.

Advaita is a science that views the spiritual and material realms as one unbroken continuum. It admits no division between the spiritual (aadhyaatmika) and the material (aadhibhautika); its sweeping vision of the cosmos folds everything into one reality. Tattwabodh and similar texts describe the orderly process by which the gross, subtle, and causal project out of Brahman. Our experience also confirms this holistic view. As embodied beings, we are endowed with both spiritual faculties and material bodies. Yet we are not two separate entities, but one integral whole.

If science is uncomfortable with traditional religions, it is far less so with Advaita. There are a number of reasons for this. One is Advaita’s approach which is close to that of science itself. Some of the basic tenets of Advaita are no doubt axiomatic since they must be taken on faith and cannot be absolutely proved. These axioms however do appeal to our intuitive sense of what Truth ultimately must be: a) “satyam”- must “ring true” so that the mind naturally accepts it without need for external proof; b) “shivam”- capable of bestowing peace on the knower of the Truth; and c) “sundaram”- beautiful in its simplicity. Using logic, Advaita then develops these axioms into a theory that covers the full gamut of experience, spiritual and material. In this Advaita is very much like any other branch of science that starts out with axioms. The proof of a science lies in how well the statements it makes accord with verifiable experience. Some of the assertions made by Advaita are verifiable in our day-to-day lives, while those dealing with the realized state appear reasonable and also stand attested by the reported experience of Yogis.

A second reason for science’s affinity with Advaita has to do with the discoveries made in relativity theory and quantum mechanics in the last century. These discoveries have thrust suddenly and irrevocably into fundamental science what many think is a decidedly spiritual element. The world-view of the new physics, it has been often noted, shares much in common with Advaitic and Buddhist teachings.

Yet another window to spirituality has been opened with advances in neurophysiology, concurrent with an increased acceptance by the public of yoga and meditation. Study after study by researchers equipped with latest neuro-iamging techniques is bearing out the views long held by Yogis. There is growing consensus affirming the real benefits that meditation and yoga confer on the mental and physical health of the practitioners, irrespective of their age, religion or other background. These studies also provide evidence that the benefits are not limited to the duration of the meditation, but carry over to the rest of the daily activities- in other words, they transform life. This probably marks the first time anything approaching a universal spiritual law has been scientifically tested and validated.

Taken together, these theoretical and experimental developments augur well for the greater involvement of science in spirituality in the future. It is just possible that out of this work will grow a new discipline of science of spirituality bearing, for aforementioned reasons, similarity to Advaita.

What role will Mathematics play in this future scenario? The work reported in the last twelve postings has hopefully demonstrated that some of the concepts of Advaita can be captured through mathematical models. Admittedly, what is presented is only a first baby step, a sort of “proof-of-concept”. Yet, it shows how the entire continuum “from the Knower of the Field to the Field” (i.e. everything save the Brahman Itself) can be represented by a two dimensional geometry and the state of spiritual evolution of a jeeva by a single variable. It also yielded results in the spiritual realm with unexpected similarity to results from the material world.

Is there any experimental validation of the time contraction result derived from the model? I recently raised this question with Prof Sara Lazar, of Harvard Medical School, where numerous studies on the effect of meditation have been carried out. According to Dr.Lazar, there have been no quantitative studies to measure the effect of meditation on time perception, but expects someone to do that sooner or later. Regarding contraction in perceived time, Dr. Lazar however noted in her e-mail that “this phenomenon is often mentioned by practitioners (along with need for less sleep)”.

In pages 29-30, I have mentioned some of the ways that the model could be developed further with future work. There is of course no guarantee if any of this work will be fruitful, but we should leave that to the Lord.

Time was not too long ago when mystery and secrecy surrounded the practice of medicine by the village “magic healers”. All that changed with the impressive progress in life sciences over the last three centuries. Today there is a uniform standard for the medical profession around the world, a standard built on “evidence-based” medicine. Very few will deny that the changes to medicine brought forth by science have been on the whole only beneficial to mankind. Now, physical and mental health is important to a human being, but spiritual health is even more so. Could, or should, there be a similar revolution using evidence-based spirituality?

When science and mathematics do succeed in understanding and affirming spirituality in their own terms, the wall separating science and religion would have to come down, inaugurating a new era in human history. Spirituality would become part of the science curriculum in schools. Religion as it is practiced today would be changed for the better, stressing more on their underlying universal spiritual laws and de-emphasizing their mere exterior ornamentations. The effect would be to liberate spirituality from the superstitions surrounding religions.

I end this series with these optimistic thoughts. I thank Ramachandran ji for inviting me to present my ideas and sincerely appreciate the comments from readers. Presenting my ideas in this forum has been tremendously useful to me and I hope some of you also saw some value in reading it.

Hari Om! With Pranams to Gurudev Swami Chinmayananda ji,

Raju Chidambaram

Wednesday, February 15, 2006

The Spiritual Evolution of Jeevas (MTS-12)

From: Raju Chidambaram
Date: Mon Feb 13, 2006 10:51 am
Subject: The Spiritual Evolution of Jeevas (MTS-12: Towards A Mathematical Theory of Spirituality Based on Advaita)


Ref Pages 24-29 of Advaita Math paper

Jeevas evolve constantly barring only periods, such as deep sleep, when they have no interaction with the O-E-T. Every transaction with the O-E-T entails a change of some magnitude in the jeeva, either adding to, or detracting from, its spiritual detachment depending on the manner in which the transaction is conducted. This evolution continues, with its ups and downs, until the jeeva attains perfection in some particular life time.

The spiritual detachment, theta, of a jeeva therefore varies with time. There can be even short term variations over hours and days or long term variations over years as well as over lifetimes. When the polar coordinate pair (t,theta) is plotted for such a jeeva what we get is a curve reflecting the ups and down in its spiritual progress. We may call this graph of (t,theta) as the spiritual progress chart of the jeeva. We can also define a function theta(t) which gives the spiritual detachment as a function of t, with theta being always in the range (0, pi/2).

Fig 9 on page 25 illustrates the above idea with the progress chart of a jeeva J3 from the beginning of time until the jeeva’s realization after several lifetimes. During the period A to E, theta is nearly 0 indicating that this is a jeeva very much bound to O-E-T in its early lives. In the period E to C, possibly representing several life times, the jeeva begins to develop spiritually. From C to B, the jeeva’s spiritual development increases dramatically, such as is the case when, under the guidance of a Guru, it enters serious saadhanaas. At point B, theta=pi/2 indicating the attainment of Realization. The jeeva’s journey has ended at this point, though it may continue its bodily existence as a jeevan muktha to complete that lifetime.

In an earlier posting in response to a question from Prof VK ji, we have seen how the mathematics for this general case can be presented using complex variables. We will not go over that again now, but will make the following observations to clarify the spiritual significance of the various mathematical expressions and also to distinguish the general case from the special case of uniform detachment that we dealt with before.

1) In the general case, there are two distinct representations: one is the progress chart such as in Fig 9, showing the values of theta over time in polar coordinates. Here the two axes simply represent the two end point values for theta, namely zero and pi/2. Progression of (cosmic) time is represented by the circular waves. The jeeva’s experienced time cannot be read off the horizontal axis in the general case.

2) Fig 10, page 27, shows a different representation of the jeeva’s evolution. This graph, in cartesian coordinates, gives the jeeva’s “path” with tau(t) and G(t) defined in page 26, as the horizontal and vertical axes respectively.

3) The coordinate pair (tau(t), G(t)) is a summary of the jeeva’s spiritual history from the beginning of time to the present time, t. Tau(t), the experienced time, shows how well the jeeva has performed spiritually so far- the more evolved a jeeva, the lower the experienced time. G(t), on the other hand, is best interpreted as the “accumulated merit” of the jeeva due to all the good karmas in its many lives. Hence it as an indicator of how well the jeeva is expected to perform in the future. We may compare this pair of statistics to the way a tennis professional’s history can be quantified. We may indicate how many tournaments the pro has won so far in his career and separately also show how he is presently “ranked”. The former is a measure of past performance while the latter indicates how well he is expected to do in the coming tournament.

4) Jeevas with uniform, non-varying, spiritual detachment is not realistic, especially over long periods of time, but was included in the discussion as a special case to reveal some basic relationships. For this special case, the “progress chart” of Fig 9 and the “spiritual path” of Fig 10 are identical and it was possible to show both on the same axes system.

How does a jeeva progress spiritually? This of course is a core question and one which is not addressed by the model at this time. The different yogas and saadhanaas an aspirant should undertake in order to make spiritual progress are exhaustively dealt with in our scriptures. The model only attempts to capture the effect of a jeeva’s spiritual detachment profile on its worldly experience; it does not incorporate the forces that affect the spiritual progress over time.

In the next, and last, posting of this series, I will conclude with some observations on the model, its utility, and possible ways for its further development.

Hari Om!

- Raju Chidambaram

Tuesday, January 31, 2006

Ishwara – the All Powerful, the All-Pervasive (MTS-11)

From: Raju chidambaram
Date: Fri Jan 27, 2006 4:03 pm
Subject: Ishwara - the All Powerful, the All-Pervasive (MTS-11: Towards A Mathematical Theory of Spirituality Based on Advaita)


Ref Pages 43-45 of Advaita Math Paper

In our conceptual model, Ishwara is seen as exercising control over all things and beings at all times using His Free Will, while still staying within the bounds of the laws of Prakriti. This is possible since the laws of Parkriti are not totally deterministic, but probabilistic.

Three questions arise at this time: a) Do not the probabilistic laws also constrain Ishwara’s Free Will in some manner? b) Does not randomness contradict the purposefulness of Ishwara’s Will? c) Where is Ishwara so that He can control all things and beings at all times?

The first two questions were touched upon previously in observations posted by Benjamin ji and deserve some detailed answers regarding the nature of randomness and probabilistic laws.

Randomness and probabilities are concepts extensively applied today to solve practical problems, yet they remain rather vague. It was Bertrand Russell I think who quipped “Everybody talks about probability, but no body understands it”.

“Observations that are random….. cannot be explained by a theory” says Dr. Gregory Chaitin in an interesting paper on Randomness and Mathematical Proof. Any attempt to explain, or attempt to postulate a causative mechanism with some predictive value, must fail when confronted with a truly random phenomenon and therefore such phenomena are “beyond cause.” Randomness can be also associated with freedom since there is no underlying deterministic law to constrain it. Interestingly, Ishwara, is also described in similar terms in many religious traditions. He is the “Original Cause” or the “Causeless Cause” meaning He is “beyond cause”. He is also viewed as endowed with full freedom of Will.

This similarity is only to be expected when we admit that it is Ishwara’s Will which is behind events that appear as random (i.e. unexplainable) to jeevas. God alone knows the why and wherefore of His actions, not the jeevas. There is no reason however to conclude that Ishwara’s actions are wanton. On the contrary, Ishwara exercises His Will while fully respecting Prakriti’s laws. These are probabilistic laws which afford considerable freedom of choice in the short term. Therefore there is room for Ishwara to display His universal compassion and justice in individual instances, if He so wills. In the longer term, a greater degree of compliance with the law is to be expected, as known from Laws of Probability. But we note that even this is an expectation only, the extent to which the expectation is fulfilled still depending on His Will.

Thus we have here a very satisfactory, workable relation between Ishwara and His freedom of Will on the one hand, and Prakriti and Her laws on the other. For jeevas the result is a world that is an admirable mixture of order and uncertainty- a combination that makes for an exciting, yet manageable, life. Without the order engendered by Her laws, life would be nightmarish, and without the freedom of possibilities inherent in His Will, life would be dreadful with no room for hopes and dreams. But with Ishwara and Prakriti working together, life is beautiful, notwithstanding an occasional heartbreak.

Ishwara must be all pervasive and all powerful in order to control the evolution of everything in the cosmos every single moment. Where exactly is He in order to accomplish this enormous task? Appearing as Lord Krishna, Ishwara himself answers this question in the Bhagavad Gita:

isvarah sarva-bhutaanaam hrd-dese 'rjuna tisthati bhraamayan sarva-bhutaani yantraarudhaani maayaya

Seated in the heart-space of all things and beings, He, the Omniscient and Omnipotent, controls them. The heart-space is also identified in Mandukya Upanishad and Karika as the seat of the Prajna, the microcosmic counterpart of Ishwara. What is even more revealing is how the Upanishad extols Prajna, the individual in the causal state, using terms one normally reserves for Ishwara, such as “sarveshwara and sarvajna”! The significance of this, as I see it, is that at the causal level there is really no individuality, but only the Totality. Stated another way, at the causal level all things and beings are merged into one whole, with Ishwara presiding over it. Commenting on this part of the Upanishad, Swami Krishnanandaji of The Divine Life Society observes: “The Mandukya Upanishad seems to make no palpable distinction between the individual and the cosmic, and it harmonises the relation between Jiva and Isvara.”

It is as though the space that separates individual things and beings at the B-M-I level (i.e. the vaiswanara and taijasa level) is not there at the causal (prajna) level. The individual entities in the cosmos appear to be far flung at the sensory B-M-I levels, but Ishwara controls them all at the causal level as one single entity. This should be welcome news to Quantum physicists spooked by the specter of “entangled particles”. In the article “Entanglement: The Weirdest Link” (http://www.biophysica.com/quantum.htm) Michael Brooks writes: “This (entanglement) is no longer just a curiosity of the quantum world, visible only in excruciatingly delicate experiments. Physicists now believe that entanglement between particles exists everywhere, all the time, and have recently found shocking evidence that it affects the wider, "macroscopic" world that we inhabit.” In other words, entangled at the causal level, this cosmos could as well be a single entity. Modern science appears to be approaching a view that the seer of Mandukya Upanishad envisioned long ago.

To sum up, the cosmos is seen as one single pulsating entity, where events, controlled by a compassionate and just Ishwara, unfold in unpredictable ways, yet remaining within Prakriti’s laws that give a reassuring measure of orderliness to the proceedings.

Hari Om! - Raju Chidambaram

Thursday, January 19, 2006

The Cosmic Dance of Ishwara and Prakriti (MTS-10)

From: Raju Chidambaram
Date: Wed Jan 18, 2006 12:27 pm
Subject: The Cosmic Dance of Ishwara and Prakriti (MTS-10: Towards A Mathematical Theory of Spirituality Based on Advaita)


Ref Pages 6, 24, 35-36 of Advaita Math Paper

We return now to a theme first sounded in the third and fourth postings of this series, namely the divine dance of Ishwara and Prakriti that underlies the moment-to-moment evolution of the cosmos. Mystics who have seen with their spiritual vision the “ananda thandava” of the Lord of Dances tend to break into ecstatic poetry. I am not in this league of exalted beings, but nevertheless did attempt to “poeticize” the mathematical model. The result is the rather amateurish poem you see on page 2. I call it as Uma-Maheshwara’s dance, but one could as well visualize Lakshmi-Narayana or Raadha-Krishna etc in that dance, whichever way the predilection of the bhakta lies.

In this dance, Prakriti, as the beautiful mother, leads her endlessly enchanting child, the cosmos, in a dance around the father, the majestic Ishwara. The child takes each step guided by his mother, to the beat of the father’s damaru (cosmic drum). The vast dance hall is filled with golden cloud so thick no one can ordinarily see the Prakriti or the child as they shuffle silently between steps. But accompanying each beat, there issues forth a brilliant flash, briefly parting the clouds and illuminating the child in a different dance posture. A jeeva which takes itself to be just part of the cosmos participates in the dance without witnessing or understanding it; as a result it is often confused and agitated. The jnaani, on the other hand, rejoices in the dance, feeling secure in the loving presence of the Mother and Father. The jnaani’s participation in the dance is with the knowledge that he/she is not in fact dancing, but it is mother Prakriti in the presence of Ishwara executing the steps.

This is the romantic vision, the more mundane mathematical version is provided in Page 6 (Fig. 2), Page 20, and Pages 35-36 (Note 6) of the paper.



As illustrated by Fig. 2, each moment, marked by the beat of the damaru, sees the world in a different state. The interval between the rhythmic beats measures out the Cosmic Time. The Lord does not sound the drum to the beat of anything other than His Will; therefore time is under the control of the Lord and not the other way around. Now, after each beat, there is an interval of silence followed by the next beat. Two events occur during these two distinct phases: 1) During the silent period following a beat, Prakriti transforms the present state of the world into a “superposition” of the several states possible in the next moment. No one can ordinarily see the world in its superposed state; it exists in the Total Mind as possibilities; 2) The silent period ends when Ishwara sounds the drum and “collapses” the unobservable, superposed world into one observable state. The chosen state becomes observable to jeevas only in the illuminating light accompanying the sound; this is the light of Pure Consciousness, which Ishwara in reality is. The world thus changes constantly to the sound (naada) and light (bindu) of the Divine: a cosmic “son-et-lumiere” show!



Referring to Fig 8, in page 24, the cause-effect waves shown there represent the superposed states of the world in successive moments. AC is Brahmaji’s path cutting through these waves. The waves collapse into a definite state of O-E-T as Brahmaji’s path intersects them. For example, the wave GG’ collapses into the definite state G, as Brahmaji’s path intersects it at the point G(sub1). The state G into which the wave collapses is chosen at the Will of Ishwara and executed through Brahmaji. Jeevas see (i.e.experience) the state chosen for O-E-T at Ishawara’s Will, only with the illumination provided by the Pure Consciousness reflecting on their individual M-I.

Now, all jeevas (with the exception of jeevan mukthas) are at all times either on, or to the right of, AC, Brahmaji’s path. Therefore, the experienced time that elapses before a jeeva perceives the chosen state of the O-E-T is greater than the experienced time that elapses before Brahmaji creates it. This assures that jeevas at any time do not get to experience the world before Brahmaji has the experience of creating it. Our model suggests that jeevan mukthas however can see (that is, foresee) what is to come in future. There are anecdotes in our mythology to support this.

What is the significance of Brahmaji’s trace of imperfection in the two-step process? The quantity 0.5x10(exp-25) by which Brahmaji’s state falls below the perfect 1, can be related to the time it takes for each wave to collapse as Brahmaji’s path crosses it; i.e as the fraction of time occupied in each cause-effect cycle by the “collapse” phase. Brahmaji’s attention on creation, rather than on the Self, is only during the second phase.

Page 36 illustrates the cause-effect chain as a series of equally spaced “pulses” along the time line. Each pulse represents a “beat of the drum”, or the “collapse phase” of a cycle. The interval between two consecutive pulses is one cosmic unit of time. How long is one cosmic unit of time? In answer we could ask: how frequently does the state of the cosmos change? We do not know the exact frequency of change, but it should be an enormously high rate. If the cosmic unit time is “lambda” seconds as shown in page 36, the duration of each pulse (or the “pulse width”) is lambda x 0.5 x 10(exp-25) secs.

Quantum physics says that the smallest measurable unit of time, called Planck’s Time, is of the order of 10(exp-44) seconds. Is Planck’s Time related in any way to the pulse width computed above? In our model, the pulse width is the time taken for each wave to collapse and hence it can be argued that it should not exceed the Planck’s Time. Now, (1/lambda), signifying the frequency of change in cosmos, has to be at least as high as the highest frequency known in the universe. Gamma Rays, one of the highest energy radiations known, has a frequency of 3x10(exp+20) per second. If we assume a value for lambda based on this Gamma Ray frequency, the duration of the pulse is 1.5 x 10(exp-45) seconds. This is less than, and very close to, 10(exp-44) secs, the Planck’s Time. This analysis is no doubt conjectural to a degree and not very rigorous, but it does suggest interesting possibilities by which to relate concepts in quantum physics with those of Advaita.

Hari Om!

- Raju Chidambaram

Thursday, January 12, 2006

The Brahmalok (MTS-9)

From: Raju Chidambaram
Date: Thu Jan 12, 2006 12:39 pm
Subject: The Brahmalok (MTS-9: Towards A Mathematical Theory of Spirituality Based on Advaita)

Ref Pages 20-24 of Advaita Math Paper

In the last posting, the relation between contraction in experienced time and degree of Self-Knowledge was derived for jeevas of uniform spiritual detachment. In the present posting, the time contraction result is applied to a very special being with a known time contraction rate, namely Brahmaji.

The ancient Hindu scale of time is truly a wonder ranging as it does from milliseconds to trillions of years. The fact that it comes remarkably close to modern concepts of time has not been lost on scientists such as Carl Sagan. (By the way, Prof VK ji’s web site has a very good summary of the Hindu time concept.) What is interesting to note from our point of view is that one Brahma-day is said to equal 4.32 billion human-years or, equivalently, one Brahma-second equals 100,000 human-years. One way to interpret this is to say that what passes as 100,000 years to a jeeva bound to creation appears as a mere second to the Creator. A little calculation shows, as in page 21, that the time compression ratio applicable to Brahma-ji relative to that of a jeeva bound to O-E-T is approximately one-trillionth of 0.317.

A high rate of compression in experienced time, we saw, is associated with high degree of Self Awareness. With experienced time less than trillionth of that of ordinary jeevas, Brahma-ji is nearly completely established in Self. Quantitatively speaking, Brahma-ji’s Relative Awareness differs from 1 (i.e. Perfection) by a very very small number (calculated in the paper as 0.00000000000000000000000005, written also as 0.5 x 10 exp(-25).) The spiritual detachment of Brahmaji is nearly complete; in Fig 6, Brahmaji’s “path” AC practically overlies the vertical axis AF, the angle CAE being nearly 90 degrees.



A natural question to ask at this juncture is why there should be even this tiniest degree of imperfection in Brahma-ji’s state and whether there is any support for it in our scriptures. If I am not mistaken, Brahma-ji comes across in our mythology as somewhat less perfect than, say, Vishnu or Shiva. I have also heard that formal worship of Brahma-ji is seldom practiced anywhere in India, but the reasons behind this injunction are not clear to me.

Here is something else I found today in the wide world of wisdom known by the initials www: “Being instructed by Lord Vishnu he oversees the creation and all diversity throughout the universe. In our universe he has four heads, one in each direction. Brahma has heads in proportion to the size of the universe he occupies. Because there are unlimited universes throughout the creation that means there are unlimited Brahmas as well. In most cases he is a Jeeva soul. The scripture's say: when there are no qualified Jeevas to do the job, Lord Vishnu will do it. By dint of Brahma's self searching consciousness he realized the Supreme Being, his eternal abode and his eternal service. He then recited what was witnessed for all souls to hear. Brahma Samhita”

As a more direct answer to the question, I have also quoted in page 23 of the paper a picturesque analogy given by Swami Chinmayanandaji to illustrate the tiny fraction of distraction caused in the Creator by the affairs of creation. Immeasurably large and unimaginably complex is this cosmos; yet it is taken care of by the Creator using only an infinitesimally small fraction of His attention. This is the insight provided by Gurudev Swami Chinmayanandaji and the result we have from the model only quantifies it.

Our scriptures speak of the Brahmalok, the abode of Brahma, as the penultimate state of perfection. In the “krama-mukthi” scheme of evolution, a jeeva advances by stages spiritually until it attains to the highest of the seven worlds, namely the Brahmalok. The jeeva spends a length of time in this world before attaining full liberation from the samsar. The passage from the Brahmalok to ultimate Realization is instantaneous and occurs by the grace of Ishwara alone.

In Fig 6, the path AC is viewed as the Brahmalok. Having reached it, the next stop for a jeeva is final liberation, namely the vertical axis AF. Therefore, no jeeva, we may assume, is strictly within the very thin wedge between AC and AF. This implies that no jeeva in this creation (with the exception of fully liberated jeevan mukthas) is more spiritually advanced than the Brahma-ji Himself. As mentioned in the paper, this also ensures that no jeeva is ahead of the Creator in terms of experienced time; that is, no jeeva gets to experience an event in creation before Brahma-ji has created it.

There appear to be two different scriptural views regarding Brahma-ji’s role in creation. One view holds that there is a Brahma associated with each of the infinite number of universes, the beginning and end of a universe coinciding with the finite life span of its Brahma, namely 100 Brahma-years. It is as though a special, very highly evolved jeeva is appointed by Ishwara as the Brahma-ji “in charge” of each universe; in this view Ishwara is eternal, but Brahma-ji is not. A second, and more common, view is that Brahma-ji is part of the Brahma-Vishnu-Shiva trinity representing Ishwara and as such eternal. Perhaps someone in the Advaitin list can clarify this aspect of our scriptures and possibly even reconcile the two points of view. I have followed the former view, noting that Brahma-ji administers the universe as per Ishwara’s Will alone.

In the next posting, we discuss the role of Ishwara’s Will in creation, controlling everything from the proverbial “Brahma-ji to a blade of grass”.

Hari Om!

- Raju Chidambaram

Blog Suspended from Dec 7 through Jan 6

From 7 December 2005 through 6 January 2006, I was traveling in India, where I was unable to update the discussion on the Yahoo Advaitin List. This blog tries to capture the important points of that discussion regarding Dr. Raju Chidambaram's theory of Advaita Math. Unfortunately, a month of discussion has been lost. I will now resume with his posting today on the Advaitin List. If time permits, I will add portions of what I missed before, which will be back-dated thanks to a special feature that Blogger provides.

Monday, December 05, 2005

Raju Answers Questions from Profvk and Ben

Date: Thu Dec 1, 2005 4:07 pm
Subject: Questions from Profvk ji and Ben ji


Profvk ji asks:

"At the point of realization, the integrand, which gives the Jeeva's path, becomes exp(i.pi/2) which is nothing but "i". Two observations on this; 1. What does this mean mathematically? I am not able to see this. 2. It is the point of time, according to advaita, when the small "i" (the individual Jeeva) becomes the large "I" , the Universal 'I' !!!


Namasthe.

In order to fully answer the questions raised, it may be useful to jump ahead to a discussion which I had planned to undertake in a later posting. This has to do with the meaning of the coordinate axes, a question that Ben ji also had raised. The need for the simultaneous use of polar coordinates (t,theta), cartesian coordinates (cos(theta(t)), sin(theta(t))), and now additionally the complex variable exp(i.theta(t)) may also require some explanation.

The complex variable representation is simply a handy alternate representation of the Cartesian coordinates and, if so desired, can be avoided altogether as done in the paper itself. But it is useful for simplifying the presentation, so I will follow it here. Part of this posting is necessarily mathematical, but the discussion about the meaning of the axes is rooted in Advaita. In particular, there is a reference relating to the concept of “accumulated merit” on which Advaitins in this list will hopefully contribute.



Figures 9 and 10 should be useful regarding the dual use of polar and Cartesian coordinates that Ben ji wants to see elaborated. Fig 9, which is simply a plot of the function theta(t), is in polar coordinates. The curve A-E-C-D-B is the function theta(t) for J3. The axes corresponding to theta=0 and theta=pi/2 in this chart are the two extremes of spiritual orientation; namely total identification with the Seen/Experienced in the first case and with the Experiencer/Seer in the second case.



Fig 10, on the other hand, is a plot of the jeevas path in terms of two Cartesian coordinates (Tau(t) and G(t)), which are defined by the integrals in page 26. We represent the jeeva’s path graphically by plotting the coordinates (Tau(t), G(t)) for various values of t. (Fig 11 is a numerical example done on Excel spreadsheet for a case where the integrals can be easily evaluated. This example was done only to confirm that the free hand drawing in Fig 10 is representative of an actual computed case.)



In general, the polar coordinate plot of Fig 9 and the cartesian coordinate path of Fig 10 are different representations of a jeevas spiritual history and cannot be plotted on a graph under a single coordinate system. However in the special case discussed in pages 11-18 of jeevas with uniform spiritual detachment, it so happens that plot of theta(t) in polar coordinates and the path (Tau(t), G(t)) in Cartesian coordinates are identical, making it possible to present both in the same chart with dual meaning for the axes. Now, what is the meaning of the axes in cartesian coordinates?

The integral of the exp(i.theta(t)) over (0,t), which gives the value of these coordinates at time=t, is a complex number, the real part being Tau(t) and imaginary part being G(t). Tau(t) is the total time experienced by the jeeva over the cosmic time interval (0,t). The concept of Experienced Time was introduced in the last posting. We saw how experienced time depends on the jeeva’s attachment to its lower self: that is how frequently it is “eating” rather than merely witnessing.

The coordinate G(t) is less straight forward to explain. The best way to interpret G(t) is to first ask what this function looks like for the ever Perfect Being, i.e. a Being with theta(t)=pi/2 for all t. For this Being G(t)=t and hence G(t)/t=1 for all t. (As an aside, this implies that G(t) changes at the rate of one unit per unit cosmic time for the ever Perfect Being, a fact which we will put to use shortly.) For other jeevas, G(t)/t will be less than 1 depending on how less perfect the jeeva was over the time interval (0,t). G(t)/t therefore is a measure of perfection of the jeeva averaged over (0,t). In the paper we call it the "average relative awareness" of the jeeva. It depends not only on the jeeva’s level of perfection at time t, but also on its entire past spiritual history through time=t.

G(t)/t is the average, and hence G(t) itself is a summation of the jeeva’s level of perfection during (0,t). I believe this sum is best interpreted as what is frequently called the “accumulated merit” of a jeeva, a concept probably unique to Hinduism. As I understand it, accumulated merit depends on the karmas of the jeeva in its present and past reincarnations and denotes a jeeva’s “spiritual wealth”. (I do not think accumulated merit is quite the same as accumulated vasanas of a jeeva, though both depend on past karmas. Accumulated vasanas determine what life experiences may be in store for a jeeva in the future; the accumulated merit determines how well, spiritually speaking, the jeeva may confront those experiences. G(t) is related to accumulated merits in the latter sense only. Others in the Advaitin list may be able to throw more light on these concepts, for which I would be grateful.)

The two coordinates, Tau(t) and G(t), are thus a summary of the jeeva’s spiritual life history upto time=t, Tau(t) being a measure of how well the jeeva has spiritually weathered the samsar until that time and G(t) signifying how well it is equipped to meet future challenges and even climb out of samsar totally. But past performance is no guarantee of future results, as they say in the Wall Street! A jeeva’s spiritual prognosis is not totally determined by its past history, but depends on its present status and its future saadhanaas. It is the optimistic premise of Advaita that all jeevas can progress towards salvation, no matter how long and how sinful the past. There is no concept in Advaita of a specific “day of reckoning” failing which it is eternal hell for a jeeva.

Mathematically rephrasing, future depends on how theta changes from time t onwards in response to the jeeva’s spiritual efforts. In our model, the real and imaginary parts of the integrand exp(i.theta(t)) show the rate at which Tau(t) and G(t) are changing with t. If the saadhanaas are intense leading to high spiritual detachment, Tau(t) will change very slowly, while G(t) will climb rapidly. This is the twin effects of having a high value for theta. At the time of realization, theta reaches the maximum = pi/2 and the integrand becomes the complex number (0,1) (i.e. 0+i.1) showing Tau is stationary while G(t) increases “one unit” per unit cosmic time. Stationary Tau implies that experienced time comes to a stop. Unit increase in G(t) per unit time indicates that the jeeva, from then on, has the same characteristics as the Perfect Being.

I hope this answers the first of the two questions raised in Profvk ji’s posting.

Regarding the second point, it is certainly interesting that the letter “i” should be used to symbolize the unit imaginary number, with its obvious relation to I, the first person singular in English. But we should not read too much meaning into it since the choice of this symbol is arbitrary and its relationship to “I” is meaningful only in the English language. Electrical and communications engineers, for example, seem to prefer the letter “j” to denote the square root of (-1).

The imaginary axis is commonly associated with the vertical axis, which in our case is the Experiencer. One may wish to see the Maya operator label “i” associated instead with the O-E-T in the horizontal axis. This can be done by recasting the model (for example by considering theta as the angle with respect to the vertical axis in which case it represents the degree of attachment to O-E-T, rather than detachment from O-E-T) but this does not add any real value to the model.

I apologize for the lengthy posting, but hope it has been helpful. It has been quite valuable for myself.

Hari Om!

- Raju Chidambaram

Friday, November 25, 2005

Spiritual Detachment of Jeevas (MTS-6)

Dr. Chidambaram's Post #6

Date: Wed Nov 23, 2005 11:42 am
Subject: Spiritual Detachment of Jeevas (MTS-6: Towards a Mathematical Theory of Spirituality Based on Advaita)


Ref: (Pages 11-15 with frequent reference to Fig 3 on page 8)
Advaita and Mathematics Paper



In the last posting, creation was modeled as waves in the Total Mind, the latter being the quadrant space enclosed by the two axes of Experiencer and Experienced. Everything of the phenomenal world, i.e. all non-Self, from the grossest Experienced O-E-T to the subtlest (namely, Experiencer) is represented within the quadrant. O-E-T itself is the “material world” whereas the rest of the quadrant space may be viewed as the “spiritual realm”. As spiritual entities, jeevas, and their creator Brahmaji, have their being in this spiritual realm. While jeevas differ among themselves in countless ways materially (i.e. B-M-I wise), the spiritual distinction among jeevas is captured in our model by a single parameter, a parameter denoted by the greek letter theta. This parameter represents the “spiritual detachment”, or spiritual orientation of the jeeva. It is a variable determined by the degree of purity of the jeeva’s mind-intellect, the cumulative result of its sadhanas over many a lifetime.

Jeevas vary in their degree of spiritual detachment all the way from total attachment to the O-E-T (represented by the horizontal axis corresponding to a theta value of zero) to total detachment from samsar (represented by the vertical axis corresponding to a theta value of 90 degrees, or pi/2 radians). Most jeevas that have attained a human form possess some viveka and usually fall somewhere in between, with a theta value between zero and pi/2. We must note too that theta due to presence of spiritual forces (such as sadhanas, grace of Guru etc), the spiritual detachment of a jeeva, can and does vary over time. A jeeva’s spiritual state may be represented in terms of two coordinates (t, theta) as shown in Fig 3 indicating its spiritual detachment theta at time=t. To start with, we will assume jeevas with same theta over all time, which is to say jeevas in a “spiritually inertial” field. The “path” of a jeeva in this inertial field (i.e. a plot of its positions over time) is a straight line going through origin A.

“Time and tide wait for none”, goes the old adage. In Fig 3, time indeed shows up as tides. No jeeva can escape moving with time; however, the direction in which a jeeva moves in the spiritual field depends on its spiritual orientation. A jeeva fully attached to O-E-T (e.g. J1 in Fig 3, with theta=0) is pushed from change to change along the horizontal axis by this tide of time. This is the pitiable case of a jeeva drowning in samsar “now sinking, now coming up for a gasp of air”. At the other extreme, a totally detached jeeva (J3 in Fig 4 with theta= pi/2) moves with cosmic time along the vertical axis without being affected by any changes in the O-E-T.



How about jeevas in the middle (e.g. J2 in Figs 3 and 4)? We can hazard the guess that their condition will be better than that of J1 but not nearly as perfect as that of J3. The model indeed confirms this guess. In doing so, the model uses the picturesque analogy of “twin-birds” from Mundaka Upanishad. According to this analogy, every jeeva has a “lower-self” attached to O-E-T that eats the fruits of samsar; it also has a “higher-self” that merely is a witness to the samsar. The higher self sees the samsar without eating its bitter sweet fruits.

Spiritual detachment does not imply or require physical or mental separation from the material world. The lower-self of the jeeva (i.e. its Body and also its extroverted M-I) is necessarily in the O-E-T. But the jeeva, at any and all times, has the freedom to identify wholly, partially, or not at all with its lower self, identifying instead with its higher-self. Theta, spiritual detachment, denotes the degree of identification with the lower-self. In Fig 4, J2 is a jeeva with theta=60 degrees and its path, the line AC, is at an angle of 60 degrees to the horizontal axis. How much does this jeeva identify itself with its lower self? The reasoning given in pages 12-14 is to show that the answer may be given in geometrical terms as the “projection of the line AC on the horizontal axis”. The jeeva J2 projects itself on the O-E-T half as much as a jeeva (such as J1) bound totally to O-E-T. Following the Mundakopanishad analogy, we may say that J2 eats only half many fruits as it would have eaten had it been, like J1, fully bound to O-E-T. In the true spirit of the Upanishadic analogy, we do not say that J2 “sees” only half of the fruits. It sees them all, but eats only half.

What does “eating” versus “seeing” mean? All Advaitic masters have held that life and life’s activities are not bad by themselves and are indeed unavoidable due to praarabdha. But being involved in life with the self-centric notions such as “I want”, “I do” and “I enjoy” determine whether or not we are merely “seeing” and not also “eating”. In a jeeva where these self-centric notions are constant, its identification with lower self is complete and spiritual detachment is zero.

We previously defined a unit of experienced time as the interval between two consecutive experiences of a jeeva, experience being “eating”. J2, in Fig 4, experiences, over a given interval of cosmic time, only half as many changes as it would have, had it been bound to O-E-T. In this sense we may say that experienced time contracts by 50% due to J2’s spiritual detachment and its suffering in O-E-T also diminishes to the same extent. Generalizing, we conclude that as spiritual detachment increases, the jeeva’s suffering in O-E-T decreases. This, we note, is consistent with a basic promise offered in all our Upanishads, Gita (e.g. “..kauntheya prathijanaahi…” in Ch IX) and other scriptures. This result is so fundamental to what spirituality has to offer to a suffering humanity that one may well call it as a fundamental theorem of spirituality.

All religions of the world make similar promises to their faithful practitioners, but may use different terms of expression. The saadhanaas emphasized can be different and the benefits of the saadhanaas may be described in such terms as paradise and eternal life. Sometimes even benefits in the material world are held as a reward for the saadhanaas. In Advaitic teaching, however, all valid saadhanaas have the singular goal of purification of mind leading to spiritual detachment from O-E-T. Advaitins also hold that spiritual practices should have no negative impact on either the physical and mental health of the practitioner or on the world around them. Whether or not this is true of all religious practices of all world religions is debatable.

In our next posting, we formalize the fundamental result relating experienced time to spiritual detachment.

Hari Om!

- Raju Chidambaram

Monday, November 07, 2005

The Waves in the Total Mind (MTS-5)

Dr. Chidambaram's Post #5

From: aiyers@...
Date: Sat Nov 5, 2005 12:37 pm
Subject: The Waves in the Total Mind (MTS-5: Towards a Mathematical Theory of Spirituality Based on Advaita)


Ref: (Pages 7-10) http://sunyaprajna.com/Advaita/Advaita_Math.pdf



Fig 1 (in page 4) portrays the world as moving inexorably from one state to another, sweeping away all things and beings in its current of unstoppable time. This model is true, but luckily not the whole truth. It adequately represents the purely materialistic view of the scientist, but is incomplete from a spiritual stand point. Incomplete because it ignores the repeated assurance given to jeevas in scriptures that there is a way to cross this current of constant birth and death, called samsar.

The O-E-T of Fig 1 is the realm of the “seen” or experienced. A basic tenet of Advaita is that there can be no seen without a seer and that the seer and seen together define the experience of seeing. What is missing in Fig 1 is this seer and seeing aspects of reality. To rectify this shortcoming, Fig 3 (in page 8) expands the one dimensional geometry of Fig 1 into a two-dimensional one, incorporating the “Experiencer” as an axis vertical to the Experienced O-E-T in the horizontal axis.



The quadrant enclosed by the two axes called Experienced and Experiencer defines the space of Experiences, which includes, as we will see, all actual and potential experiences. In this expanded geometry of Fig 3, the cause-effect chain of Fig 1 is replaced by cause-effect waves spreading through this space, the distance between successive waves being one cosmic unit of time as before. Each wave is the effect of its preceding causal wave.

What are these waves and what is the space they travel in? Advaita often refers to creation as “Waves in the Total Mind”. Fig 3 gives a literal shape to this allegory. In our model, the waves have a two-fold significance. Firstly, they mark the cosmic time. The origin A where the two axes intersect is the beginning of creation; i.e time=0; the first wave DH is the first time line (also called first “now-line”) when one cosmic unit of time has elapsed; the wave EF is the second time line at time=2 etc.

The wave representation also captures nicely the uncertainty in cause-effect transitions. Thus, the wave DH, which is the uncertain effect of original cause A at t=0, represents all possible states the world can be at time=1. Since there is a probability associated with each possible state, it is appropriate to call the waves as “probability waves”. Indeed what we are showing in Fig 3 is what a quantum physicist might call as the probability wave of the total cosmos from the beginning of creation. The waves collectively portray all possible ways the universe can evolve over time under Prakriti’s laws and hence contain all actual and potential experiences the jeevas can have in this universe. Therefore we are justified in referring to this space as the “field of all potential experiences”. The actual experiences jeevas do encounter are represented by the horizontal line O-E-T which is now just a small part of the total possibilities.

What is the space in which the probability waves exist? In answer, let us ask: where do possibilities and probabilities exist? Possibilities eimagined by a jeeva, as we know from our individual experience, exist in the jeeva’s mind. Similarly, the possibilities for the total cosmos exist in the Total Mind. Total Mind is often taken to be the Hiranyagarbha aspect of Totality. Fig 3 shows the material space of O-E-T as contained in this larger space of Total Mind. Sri Ramana used to say that the mana-akaasa contains the bhuta akaasa, whereas both are contained in the supreme akaasa of Pure Consciousness. The measure of distance in this Total Mind, as shown in Fig 3, is cosmic time.

Vasanas are not explicitly represented in Fig 3, nevertheless they are the driving force launching the cause-effect waves in the Total Mind. The Advaitic analogy of a steady breeze (vasanas) spreading waves (time and possible states of the cosmos over time) over an otherwise calm lake (Total Mind) is perfectly captured in Fig 3. Since Vasanas are thus also part of the model, we must understand that the Ishwara aspect is also included in Fig 3. In other words, Fig 3 includes all three aspects (Virat, Hiranyagarbha and Ishwara) of Totality within one qudarant. We do not show That which is beyond these three, but may view That as the other three quadrants necessarily left blank in Fig 3. This is in accordance with the concept (“tripaadasya amrtam divi”) found in Purusha Sooktham.

But how does Fig 3 help us understand the means of liberation for a jeeva from O-E-T? This we will discuss in the next posting where we introduce the parameter representing spiritual detachment of jeevas.

Hari Om!

- Raju Chidambaram

Friday, November 04, 2005

Modeling Time (MTS-4) [continued]

A further comment by Raju Chidambaram, based on the many comments to the previous post

From: aiyers@...
Date: Thu Nov 3, 2005 3:28 pm
Subject: Modeling Time (MTS-4)


There have been several interesting postings recently on this topic. At issue is the question whether there is a concept of time for the jeeva that is distinct from the “cosmic time” of Ishwara. Br.Vinyaka ji asks how there could be such a distinction when the jeevas are a part of the Total. In the same vein, Chittaranjan ji questions if the jeeva can violate the cosmic time of Ishwara.

While there is only one cosmic time for the totality and all jeevas in it, the experience of that time by jeevas can differ depending on the circumstances. This does not contradict the fact that jeevas are part of the Totality or in any sense violate the sanctity of cosmic time of Ishwara. After all, in general, a jeeva’s experience of this creation is very different from that of the Creator, and time is but one aspect of that experience.

In a previous posting I quoted a remark by Bhagavan Ramana to the effect that the experience of time is dependent on a jeeva’s upadhis. The experience for one awakening from a coma or anesthesia is that no time has elapsed. It is my understanding that the same is true during the typically short periods of dreamless sleep we have. Einstein’s theory shows how the experienced time can change markedly with motion in space.

In a future posting we will see how a jeeva’s experienced time changes with its spiritual detachment following a relation that is remarkably like the one in Einstein’s theory relating time dilation to speed in space. We will also have an opportunity to discuss at that time what other interpretations we can give to the notion of “experienced time”.

Hari Om!

- Raju Chidambaram

Monday, October 31, 2005

Modeling Time (MTS-4)

Dr. Chidambaram's Post #4

From: aiyers@...
Date: Sat Oct 29, 2005 10:37 am
Subject: Modeling Time (MTS-4)

Ref: Advaita and Mathematics Paper (also in sidebar)

Time is a very elusive concept indeed. Modern Science uses the concept routinely, but readily admits it has no idea what Time really is. Fortunately, this is not the case for an Advaitic Master like Sri Ramana Maharshi.

“What is time?” asks the Sage of Arunachala (Ramana Maharshi) echoing a devotee’s question. “It posits a state, one’s recognition of it, and also the changes that affect it. The interval between two states is called time.”

States – Recognition – Changes – Interval between states! I was very delighted when I recently came across this pithy, precise definition provided by Bhagawan nearly seventy years ago. For, it neatly summarizes the approach used in the paper for modeling time. A basic premise of the paper is that time is not an independent variable, but rather it is the changes to the state of the world that give rise to the notion of time. Where there are no changes, Time is not.



In Fig 2 (page 6) we illustrated how the state of the world changes under pressure of vasanas. We can say that state of the world at time t, including the vasanas at that time, is the cause and the state of the world at the next moment, t+, is its immediate effect. (It is implicitly understood that Ishwara’s guiding hand is also necessary in this cause-effect transition, since the cause here does not totally determine the effect.) Cause and effect are not perceived to coexist; rather effect is always seen to follow cause. It is this constant perceived flow from cause to effect that gives rise to time.



Fig 1 (page 4) presents graphically the resulting dynamics of the O-E-T beginning with the “first” moment of creation. Each moment is the cause for the immediately succeeding moment. The interval between each cause and its immediate effect is assumed to be a constant and is defined as one unit cosmic time. Cosmic time, or time, is denoted by the symbol t.

Creation, sustenance, and dissolution are in constant evidence in our universe. Indeed, as Swami Chinmayanandaji often pointed out, every change in the universe involves destruction of a previous state of order followed by the creation of a new one. The divine damaru (cosmic drum) of Lord Shiva is often associated with this Creation. It is as if the state of the world changes to each beat of the Lord’s damaru. The interval between the rhythmic beats thus measures out the Cosmic Time. During this interval two events occur as illustrated by Fig. 2: a) Prakriti transforms the present state of the world into a “superposition” of the several states possible for the next moment, and b) Ishwara chooses one of these possibilities as the state of the world. Page 36 carries an illustration of this two step process which will be subsequently discussed in detail.

Jeevas experience the changes happening in the world, but they do not by any means experience all the changes. The time experienced by a jeeva during a given interval of (cosmic) time, we postulate, is proportional to the number of changes it experiences during that interval. This postulate is again based on the principle that without change there is no time. In deep sleep, for example, no changes are experienced by a jeeva and there is no perception of elapsed time either.

Every thought modification is a change for the jeeva (and hence also for the world of which it is a part). Conversely, with every experienced change there is thought modification. With this as the perspective, Advaitins often consider (experienced) time as the interval between two thoughts. To go beyond time, one must be thought-free or hold on to one thought: “ekachintanaat naasamethyatha”, says Sri Ramana.

We have reviewed in these two postings Figs 1 and 2 representing the paradigm used in the paper for the world of O-E-T. The model, it is to be noted, does not concern itself with a study of various causes and their effects. That is strictly the domain of sciences which try to predict the course of the world as well as they can. The overarching effort in our model must be to capture the spiritual essence of experiencing changes, whatever those changes are and whatever their causes might be. Spirituality is not concerned so much with describing the material world, as it is with prescribing means by which the world may be experienced joyously.

Figs 1 and 2 are adequate representations of reality from a scientist’s materialistic point of view, but, as we will discuss in our next posting, fall short of our needs. In other words, the model needs to be expanded to include the spiritual dimension.

Hari Om!

- Raju Chidambaram

Sunday, October 23, 2005

A Paradigm for O-E-T, the World of Matter and Mind (MTS-3)

Dr. Chidambaram's Post #3

From: aiyers@...
Date: Sun Oct 23, 2005 12:32 pm
Subject: Towards A Mathematical Theory of Spirituality Based on Advaitic Principles: A Paradigm for O-E-T, the World of Matter and Mind (MTS-3)

Ref: Advaita and Mathematics Paper (also in sidebar)



Figures 1 and 2 (in pages 3 and 6, respectively of the paper) are graphical representations of the paradigm of O-E-T (the perceived or experienced world of matter and mind) used in the paper. The concepts behind these representations are discussed in greater detail in the pages 39-46 and reviewed below. For members of the Advatin List, these concepts should be, by and large, very familiar.



“Sarvam Brahmamayam” was a favorite bhajan of Swamini Saradapriyanandaji – everything there is, is Brahman alone. This fundamental notion has been repeated countless times in many different words in the scriptures. The unmanifest Brahman, by power of Maya projects itself as Prakriti (the world of things, beings and vasanas) and, as Ishwara or the mayaadhipati, exercises control over Prakriti. The same Brahman “enters” the beings in Prakriti to experience the world. Therefore this world is seen as made of God (namely Prakriti), controlled by God (as Ishwara) and for the enjoyment or experience of God (as Brahman identified with beings of Prakriti). In short “this world is of God, by God and for God”.

This world of Prakriti is in constant motion. The forces or agents of change are the vasanas. Vasanas include the natural forces affecting gross things as well as the subtle forces affecting the mind-intellect of beings. At any given time “t”, there is conceptually a “state of the world” which in essence describes the physical, emotional, and intellectual state of all things and beings of the cosmos. As shown in Fig 2, this state is momentary and will change to some other state at time “t+” (i.e the “next” moment) under the pressures of vasanas.

A key point to note is that vasanas do not totally determine the change. Even if know the state of the world completely at time t, and know all the vasanas affecting the cosmos at that time, we cannot tell for sure where the world will be at time t+. There is an element of uncertainty. We can only state the possibilities and the probability associated with each possibility. In Fig 2 this is illustrated by showing 4 different possible “states of the world” at time t+. In reality, the number of possibilities is innumerably infinite. This uncertainty is theoretically well known to modern day scientists and experientially well known to all the jeevas.

But the world is not left hanging in a “cloud of probabilities” at any time – it does end up in one definite state at time t+. This is our experience. Who or what makes this choice of one out of the infinite many? Scientists may not concede, but as Advaitins, we can safely assume that it is Ishwara who makes this choice, using His Free Will. This is consistent with the notion of Ishwara as the controlling entity of the cosmos. Ishwara decides the path of evolution from moment to moment. And He does this while still working within the limits set by Prakriti and Her natural laws.

Fig 2 is to me thus a very pleasing paradigm of how Ishwara and Prakriti – the Father and Mother of our jagat – work together in harmony and with complete respect for each other. We tend to use the masculine gender for Ishwara and feminine gender for Prakriti only to be consistent with tradition. If only we realize how interdependent these two aspects of Brahman are, and how vital both are for the evolution of the jagat, there can be no room for useless disputations claiming superiority for one or the other. Our Father and Mother are One in the Brahman. May we bow down before Them. May They Bless Us All.

Hari Om!

- Raju Chidambaram

PS: Fig 2 will be revised soon, following a suggestion by our friend Greg. In the mean time, hope the shadowed letters and figures are not too difficult to read.

Friday, October 21, 2005

The Goddess of Time

From: "Chittaranjan Naik"
Date: Thu Oct 20, 2005 5:54 am
Subject: The Goddess of Time


Namaste to all Advaitins,

> His basic idea is quite fascinating. It is based on
> the idea that 'perceived time' seems to slow down
> for the realized person.

Yes, there is no change for a realized person.

But time does not slow down. Change is a manifest feature of time, but it is not time itself.


If time is perceived to slow down, then what is the reference against which it is said to have slowed down? The phrases 'perceived time' or 'slowing down of time' are merely metaphorical ways of saying that change seems to drift by slowly – like a movie played in slow motion – rather than that time itself has slowed down. For what is it that is the reference against which the changes of phenomena are said to have slowed down if it not be something within us that forms the canvas against which change may be said to be slow of fast? What is this unchanging canvas that forms the reference for us to say that 'perceived time' is slow or fast? Is it not the unchanging reference of Time itself? Time is not temporal!

Time is Eternal. Eternal Time is Mahakali, the great Goddess than whom higher there is none. She is the Mother even of Brahma, Vishnu and Shiva: Brahman comes to be the Trimurti through Her Womb. In Creation, She appears as the consort of Shiva and the sister of Vishnu. She is the Great Womb of Time that brings forth ephemerality from Eternity – so that we may see it, experience it, and return back from it to Eternity. She is the great cycle of creation and destruction. She gives birth to Her children with great love and then devours them mercilessly through Her own mouth. She is the Great Paradox of Reality.

Kali is Dark in complexion. Shiva lies hidden and prostate behind Her Darkness while She dances Her Wild Dance of Creation. She hides the Eternal with Her Darkness, and the Eternal becomes all-devouring Death. She hangs the marks of Death – human skulls and bones – around Her neck as ornament.

Mahakali is the Dazzling Darkness of Creation. The world shines in Her Light and hides in Her Darkness. She is the Great Eclipse. She is the darkness of the eclipse in the light of the soul. She is the Fire of Ma Kundalini that rises from the chakra where darkness lies along side light like a coiled serpent.

Ma Kali is dark and She is naked. Hers is the darkness of the Great Night. Her nakedness is the nakedness of Truth!

O sublime Kali you dance in solitude as naked truth. Your black hair streams wildly as pure freedom. You alone can fulfil with your very being my soul's most secret yearning. No one else can offer any real response to this transcendental desire for union burning constantly in my heart.

What wild customs you follow, Ma Kali, Trampling on the naked chest of your husband. You are the naked intensity of Divine Creativity, Your consort naked Transcendence. Together you roam cremation grounds As Mystic Union of Space and Energy, Liberating the soul from its self-imposed destiny.

........ (Translations from Ramprasad)

Warm regards, Chittaranjan

Thursday, October 20, 2005

Benjamin Orion comments

From: "Benjamin Orion"
Date: Wed Oct 19, 2005 7:06 pm
Subject: Re: Towards a Mathematical Theory of Spirituality Based on Advaita (MTS-2)


His basic idea is quite fascinating. It is based on the idea that 'perceived time' seems to slow down for the realized person. This leads to a time distortion not unlike Einstein's theory. I hasten to add that the math is very simple, so nobody needs to get scared.

I hope Raju dwells on *why* time seems to slow down, or at least provides references to the scriptures. We have to start on a solid foundation. This isn't meant as a criticism. It is quite plausible. Is not Brahman without parts, including temporal parts?

Ben

Dr. Chidambaram's Post #2

From: aiyers@...
Date: Mon Oct 17, 2005 1:09 pm
Subject: Towards a Mathematical Theory of Spirituality Based on Advaita (MTS-2)


An Overview of the Paper

Brahman cannot be explained. Nor does Brahman, the Self-Effulgent, need explanation. Everything else that (apparently) exists begs explanation. “Everything else” includes the world of matter and mind experienced by jeevas. Additionally, it also includes the jeevas themselves. Bestowed with Consciousness, jeevas, we may say straddle the realm between the Brahman and the world experienced.

Science is more or less comfortable dealing with matter and mind, but it is in self-denial about the spiritual dimension of jeevas; that is, Science has chosen to ignore spirituality. Advaita Vedanta, on the other hand, has the depth of vision to see both the spiritual and material realms. The paper is basically a geometric representation and analysis of this Advaitic vision. An outline of the paper available at the following link.

is given in this posting. I expect to cover the various sections of the paper in about a dozen postings as indicated below.


An Outline of the Paper and the future Postings:

1: Postings 1&2 (Pages 4-6 of the paper): In the first two postings, we will present the concepts behind Fig 2 (on page 6) which is the paradigm used in the paper for the world of matter and mind (called the O-E-T). Basic to this model are cause-effect relationships and their relation to time. Please note that this model draws upon the concepts developed in an earlier paper on Uncertainty. This earlier work has been appended to the paper in the above web link.



2. Posting 3 (pages 7-10): We expand the model in Fig 2 as shown in Fig 3 (page 8) to include the spiritual domain of jeevas. The domain is represented as a two-dimensional space defined by two parameters (t, theta) where t is time and theta is the spiritual detachment of jeevas. The concepts behind this model use the advaitic view of creation as waves in the Total Mind. We discuss the nature of these waves and nature of the Total Mind in which these waves arise.



3. Posting 4 (pages 11-15): The significance of the parameter theta is further explored invoking the concept of “twin-birds” of Mundaka Upanishad. A qualitative analysis showing how jeevas with higher spiritual detachment suffer less in an ever-changing O-E-T is presented. Perceived time is proportional to number of changes experienced, and we thus recognize a relationship between higher spiritual detachment and contraction in experienced time. The above relationship is analyzed for a particular case of the theta= 60 degrees to lay the foundation for the more general result.

Posting 5 (pages 15-18); Definition of “Relative Awareness” as a measure of a jeeva’s spiritual perfection compared to that of the Perfect Being; this measure depends on the jeeva’s purity of mind-intellect. A quantitative result between relative awareness and contraction of experienced time is now derived for jeevas with uniform (non-varying) theta. This relationship is identical in form and content to the relation in Special Relativity Theory between the speed in space of an observer and time dilation compared to a stationary observer. It is shown how by a simple and justifiable translation of Advaitic terms into language of Physics (Self or Consciousness=Space and Knowledge=Light) the result in the spiritual dimension transforms readily into Einstein’s result.

Posting 6 (Pages 18-19): A Plausible Interpretation of the Time Contraction result- Identification with all beings is the hallmark of a Perfect Being. Ordinary jeevas are less than perfect- they have Temporal and Spatial imperfection. Interpretation of the Time Contraction result as showing how with increasing spiritual evolution, the jeeva becomes more perfect, at least in the temporal sense.

Posting 7 (Pages 20-24): Ishwara’s role in resolving Uncertainty- collapse of the waves in Total Mind to definite states of the O-E-T- The Hindu concept of Brahma days- application of the Time Contraction relationship to Brahmaji and quantification of the very very minute extent by which Brahmaji has to deviate from the State of Perfection in order to carry on the business of creation- Swami Chinmayanandaji’s analogy- Brahmaji’s path in the spiritual domain- The maximum spiritual evolution a jeeva can attain by own effort and Ishwara’s grace in gaining the final liberation.

Posting 8 (Note 6 in Page 35-36): The waves and their collapse seen in the context of the symbolism of Lord Shiva’s dance of creation and the beat of the damaru, the cosmic drum- a tentative analysis showing how Planck’s Time may relate to the duration of this beat.

Posting 9 (Pages 24-28): Generalization of the results to jeevas subject to forces accelerating or decelerating their spiritual progress- theta(t) as a function showing the spiritual evolution from time of creation to its Realization- forces acting to accelerate or decelerate spiritual progress- expression for experienced time as a function of time, in terms of theta(t)- Definition of the spiritual path of a jeeva- The path of jeeva is curved when accelerating forces are present- The expression for the spiritual path and its consistency with the concept of Realization in Vedanta-

Posting 10 (Pages 29-30 ): further possible ways to develop the theory- modeling changes in spiritual detachment- role of ego and will power in spiritual evolution- Sadhanas accelerate spiritual progress by reducing ego and increasing will power- does the will power needed to progress become greater as the jeeva gets closer to realization?

Posting 11: Concluding remarks

Hari Om!

- Raju Chidambaram

Ram Chandran replies

From: "Ram Chandran"
Date: Tue Oct 11, 2005 6:56 pm
Subject: Re: Towards A Mathematical Theory of Spirituality Based on Advaita (MTS-1)


Namaste Satsanghis:

First, I want to congratulate Sri Raju Chidambaram for taking his time developing this logically well structured paper on Advaita Philosophy. Since many of you may not know Rajuji, it is my pleasure to say a few words about him. I know him for more than 15 years and I found him a trust worthy friend and quite serious in the pursuit of Vedanta. Rajuji and his wife Srimathi Shoba are both serious Truth seekers and devotees of Gurudev Swami Chinmayanandaji. They are both doctors, Rajuji is Ph.D. in Statistics and Shobaji is a medical doctor. I always used to wonder how these two doctors find time to attend all available Vedanta and Gita classes in Washington area.

As a matter of fact, they both are instrumental in the establishment of the Chinmaya Mission Washington Regional Center (CMWRC) during early 80s. Rajuji and Shoba have been active in the Chinmaya Mission activities and they have been supporting the spread of Vedanta and Bhagavad Gita in the Washington area. They have provided their residence as a meeting place for the weekly Viveka Choodamani discourses in Northern Virginia. Rajuji is also the editor for the CMWRC magazine 'Smriti'. Rajuji has strong background in Vedantic philosophy and Bhagavad Gita and he has never missed Swami Chinmayananda's discourses or camps that were held in Washington and surrounding (up to 200 miles radius) areas. Rajuji's background in Statistics may explain why he wanted to present advaita using analytical geometry and other graphical means.

In conclusion, I request you the Satsanghis to provide feedbacks to Rajuji's postings on this important subject thread.

Harih Om!

Ram Chandran

Dr. Chidambaram's Post #1

From: aiyers@...
Date: Tue Oct 11, 2005 5:11 pm
Subject: Towards A Mathematical Theory of Spirituality Based on Advaita (MTS-1)

Today is the Saraswathi Puja day. As a student, I seek Devi Saraswathi's grace and blessings.

Following a suggestion by Ram Chandran-ji, I propose to review the contents of a paper available to you at the following link.

As an introduction, I should say a few words on what this paper is about and what it is not and what I hope to accomplish by presenting it to this elite forum of Advaitins. Talk of a mathematical theory of spirituality might sound outlandish and in fact that is how I also would have felt a year ago. But with the work done in the last few months, such a theory does appear both possible and useful. The paper presents the first elements of a possible theory based on Advaitic principles, noting that it is not 'the' theory but only 'a' theory. As it stands at this time, it is not a complete theory of everything spiritual, but hopefully it is a modest beginning towards one. Whether it does get developed further towards a more complete, full blown theory would depend much on the future contributions others may care to make. That in fact is the reason why I am presenting it to you in this and the following several postings. After reading the paper, it is my hope that many of you in this group, who undoubtedly possess the necessary skill to pursue work in similar lines, will in fact do so.

I expect a very valid question at this juncture. Why bring mathematics now into a field which is millennia old? What useful purpose does it serve? Each of us must answer these questions independently, but let me state my present views. First of all, I do not think a mathematical theory should be expected to reveal any new spiritual truth that has not been intuited already by the Masters. But it may help visualize these truths in a different manner. Secondly, while insights gained through mathematics are helpful intellectually, they are no substitute for the rigorous sadhanas which alone can guarantee spiritual progress. Personally speaking, my faith in Vedanta, as I have understood it from Gurudev Swami Chinmayanandaji’s teachings, is important to me as a guide to truth. Therefore it is a matter of great satisfaction that the results derived so far from the mathematical model are consistent with Vedanta and this I take as a validation of the model.

Mathematics has been enormously successful in transforming everything it touched, be it physical sciences, engineering, or economics. The strength and appeal of mathematics is primarily due to the twin disciplines it enforces: precision of reasoning and economy of concepts. In building a mathematical model, one consciously tries to use the minimum number of concepts and assumptions necessary to make the model work. Each concept is to be defined as precisely as possible and every assumption explicitly stated. Building the model is often the most challenging and satisfying part of the exercise.

Once the model is set up, there should be little need for depending on verbal arguments in order to reach conclusions; instead results are derived by analyzing the model using true and tried methods of mathematical reasoning, be it geometry, calculus or whatever else that is appropriate. The pay off is in being able to understand the complex relationships that exist among the concepts in a precise and even quantitative way. Relationships not suspected before also do surface from time to time. A notable feature of the model used in the paper is that the material and spiritual realms appear to be seamlessly integrated in the model, making it possible to move from one to the other rather with ease. A picture is worth a thousand words: the geometrical visualization used throughout the paper should prove useful in communicating Advaitic concepts, especially to young scientific minds.

It will be necessary to refer to the paper frequently while reading the postings, but with its availability just one mouse click away, that should pose no logistical problem to the reader. In the next posting, I will start with an overview of the paper itself.

Finally, a request. Please consider the paper as work in progress. Your helpful comments will be valued. If you intend to quote or use results from the paper in any of your own work, I would appreciate if I can be informed in advance.

Hari Om!

- Raju Chidambaram

Introduction

This blog was created to collect the messages related to the discussion on the Advaitins Yahoo! Group of a paper on Advaita and Math by Dr. Raju Chidambaram. Only those messages which contribute substantially to the discussion will be posted here. Of course, you must be a member of the Advaitins Yahoo! Group to participate in that discussion. Anyone can access Dr. Chidambaram's paper from the sidebar.

The discussion is proceeding on the Advaitins Group, since this is a large group and hopefully there will be many interested participants. However, since there are also many other threads on the Advaitins Group, the present discussion has been collected here for convenience. Note that one can comment on postings here, which will enhance the discussion. Posting privileges may be extended to certain people as well.

Dr. Chidambaram is a mathematician with a Ph.D. and a dedicated advaitin. He and his wife (a physician) have been instrumental in bringing the Chinmaya Mission to the Washington, D.C. area. The basic idea behind the paper should become clear upon reading the first few posts. Basically, he wishes to illuminate the key ideas of Advaita within a mathematical framework.

Ram Chandran is a moderator of the Advaitins Group.