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
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
posted by Benjamin at 9:33 AM
8 Comments:
Date: Thu Nov 10, 2005 2:42 pm
Subject: Re: The Waves in the Total Mind (MTS-5)
Namaste,
I see a tremendous discussion of topics peripherally related to Raju's paper, but very little on the paper itself. I will limit myself to discussing the paper itself, and those are the messages that will be posted on the blog at http://advaitamath.blogspot.com/
Raju says that the OET is the world of the "seen", where cause and effect sweep along inexorably. This is samsara, a big river that would seem to be carrying us helplessly along, if there were not an escape promised by the scriptures.
The escape is in the "seer", the counterpart to the "seen", which is much neglected by modern science and materialistic philosophy in general, with its obsession with the seen. The seer thus merits a second vertical axis to complement the horizontal axis of the OET or seen. (Of course, the OET axis is multidimensional in its own right, with the 3 dimensions of space and one of time. I'm not so sure about the vertical axis of the Self. We'll see.)
Now one question one might ask is whether the distinct axis of the seer or Self violates the advaitic unity of Brahman. Are seer and seen not ultimately identical? Perhaps "reality" is not even an axis but a mere point. Or even less. Is Brahman not "without parts"? To a considerable extent, this depends on whether we are speaking from the phenomenal or vyavaharika level or from the higher level of paramarthika.
From a spiritual point of view, Raju surely wishes to have another axis than samsara, or there would be no moksha. But bondage only exists from the level of ignorance, which seems to confirm what I said above.
The quadrant enclosed by the two axes is called the Space of Experiences by Raju. The cause and effect chain of the horizontal axis becomes spreading waves in the quadrant. What does this mean?
For one thing, each wave marks an instant of "cosmic time". (So don't think of time as being one of the axes, as an engineer or physicist might be inclined to do!) The origin is the beginning of creation, and from there the waves radiate. Each successive wave represents all possible states that might result from the preceding wave, considered as a cause. Only one of these possibilities becomes true on the OET axis, due to the will of Ishwara.
Now one question immediately arises. Consider one such wave. It will be like a quarter-circle. The projection on the horizontal axis is well-determined by R cos(theta), where R is the radius of the wave and theta is the angle from the origin to some point on the wave. Thus each point of the wave is associated with one point on the horizontal OET axis, and it would seem that each moment of OET corresponds to one and only one possibility, assuming that each point along the circular wave represents a possible state. This would deny Ishwara's freedom, so I must be missing something.
What do you say Raju?
Hari Om!
Ben
Date: Fri Nov 11, 2005 8:40 am
Subject: Re: The Waves in the Total Mind (MTS-5)
Dear Ben-ji !
I do admire the way you initiated the discussion on MTS and assigned this topic a 'sacred' space in your Blog -
Also, it is magnanimous of Sri Raju who responded to your request to address this topic in spite of his busy schedule
Let me confess that i am not very 'mathematically' oriented. IN FACT , IN TAMIL , THE SAYING GOES " KANAKKU SUTTU POTTALAM VARATHU " ( even if someone 'burns' me with a hot iron rod , i cannot do Maths)
As Indians we should be proud of One fact - INDIA has produced two Great men both named 'Ramanujams'
Srinivasa Ramanujam (1887-1920) is , the greatest mathematician . the world has ever known!
A French writer named Nonn comments :
"Ramanujam is extraordinaire. He did mathematics all the time, even for recreation. His work is prodigious," Ramanujam, in the short span of his 32-year life, has left behind three notebooks containing as many as 4,000 formulae.
"He was ingenious and intuitive. What he worked out so many years ago is now being proven thanks to computers. When we keep pushing logic to the limit, mysteries get resolved naturally," Nonn says.
(source- The Hindu -2000)
Here is a little anecdote regarding this great Mathematician.
Ramanujan had an intimate familiarity with numbers, and excelled especially in number theory and modular function theory. His familiarity with numbers were demonstrated by the following incident. During an illness in England, Hardy (ANOTHER FFAMOUS MATHEMATICIAN) visited Ramanujan in the hospital. When Hardy remarked that he had taken taxi number 1729, a singularly unexceptional number, Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=13+123=93+103.
In Vedic times, it is believed, math formulae were often taught within the context of spiritual expression (mantra). Thus while learning spiritual lessons, one could also learn maths.
Vedic Maths is based on 16 Vedic sutras or aphorisms, which are actually word-formulae describing natural ways of solving a whole range of mathematical problems. Some examples of sutras are "By one more than the one before", "All from 9 & the last from 10", and "Vertically & Crosswise". These 16 one-line formulae originally written in Sanskrit, which can be easily memorized, enables one to solve long mathematical problems quickly.
Why Sutras? In order to help the pupil memorize the material assimilated, they made it a general rule of practice to write even the most technical and abstruse textbooks in sutras or in verse (which is so much easier — even for the children — to memorize)... So from this standpoint, they used verse for lightening the burden and facilitating the work (by versifying scientific and even mathematical material in a readily assimilable form)!
Vedic Maths is becoming popular and is being taught in Maharishi Mahesh yogi schools world-wide .
"Vedic mathematicians strongly felt that every discipline must have a purpose, and believed that the ultimate goal of life was to achieve self-realization and love of God and thereby be released from the cycle of birth and death. Those practices which furthered this end either directly or indirectly were practiced most rigorously."
http://hinduism.about.com/library/weekly/aa062901a.htm - 31k -
And the Other Ramanujam is none other than the great sri Ramanujacharya Ramanujacharya: (1017-1137) Chief exponent of the Vishishtadwita school of Vedanta and the greatest exponent of Bhakti marga !
Having said all this , Ben - today is Auspicious Friday ! The day we honor 'sri Lalithambike'
One of the Names of Sri Lalita in ( Sri LALITA ) IS
Trikona Deepika
AND WHAT IS 'TRIKONA' - a triangle !
YES ! DEVI IS THE 'ULTIMATE' LIGHT IN THIS TRIANGLE in the Sri Chakra!
"sarva siddhi prada chakra, the bestower of all attainments. It's form is that of an inverted traingle. This is the primary traingle centrally situated. It is called kAmakalA. The deity presiding over this chakra is tripurAmbA and the aides are collectively called ati rahasya yOginI (extremely secret). The three corners of the traingle represent the three forms of power of the Goddess namely, kAmEshvarI, vajrEshvarI and bhagamAlinI who represent the unmanifest (avyakta), the great (mahat) and the ego (ahankAra) respectively. The three corners also suggest the three fundamental tendencies of human existence, namely, ichA (desire), jnAnA (knowledge) and kriyA (activity) as also the three states and the three bodies. The lalitA sahasranAmA says ichAshakti jnAnashakti kriyAshakti svarUpiNi (658th nAmA). The three lines of the triangle represent the three gunas — satva,rajas and tamas. This triangle is white in colour which signifies pure sattvA. sarva siddhi is the union of the individual soul (jIvA) and Brahman. In this chakra, the spiritual aspirant has transcended the triads of cogniser, cognised and cognition (subject, object and perception) that is the basis of ignorance and is ready to enter the bindu where is seated lalitA tripurasundarI, i.e., he is ready for the final emancipation. "
( This is based on a Kriti by sri Muthuswami dikshitir - a great Sri Vidya upasaka -the 8th kriti in Kamalamba Navavaranam)
http://www.sangeetham.com/knavavaranam8.htm - 37k
Smile! so how can we ignore 'maths' in spiritual pursuits ? Devi is everywhere - In the Triangle and outside of it !
love and regards
ps - on another note, i was remembering you when i was writing about LORD MURUGAN- remember we both met when we were witnessing a dance drama on Lord Muruga at THE LANHAM TEMPLE?
's
Date: Fri Nov 11, 2005 6:14 pm
Subject: Re: The Waves in the Total Mind (MTS-5)
> I do admire the way you initiated the
> discussion on MTS and assigned this
> topic a 'sacred' space in your Blog -
Hi Adiji,
There are several reasons for this:
(1) Raju has worked very hard at it.
(2) His theory is quite pathbreaking and daring.
(3) I've heard ad nauseum about IIT and the technical prowess of Indian students, so I expect some interest here, even if Adiji the poet recuses herself.
That being said, your post was informative and colorful, as usual. You do know how to research a topic!
As for temples, I've discovered new ones in the area, like Rajdhani and Durga. Well, now we're getting off-topic.
Back to math and spirituality. Another reason to care: the Greek philosopher Plato "worshipped" mathematics, and there are more than a few resemblances between his philosophy and vedanta, for those who cam read between the lines.
Ben
Date: Fri Nov 11, 2005 4:18 pm
Subject: Re:Waves in the Total Mind (MTS-5)
On 11/10/05 Ben writes:
“..Now one question one might ask is whether the distinct axis of the seer or Self violates the advaitic unity of Brahman”…..”
“Bondage exists only from the level of ignorance which seems to confirm what I said above.”
Also “..Thus each point of the wave is associated with one point on the horizontal OET axis...”
Ben:
The seer and seen are but One, as you correctly surmise, at the paramaarthika level. The model, however, is at the vyavahaarika level only, as mentioned in the first or second posting. At the highest level, there is Brahman only and there is nothing that can be shown on a piece of paper to indicate That. However, at the lower level where the seen – seer duality (apparently) exists, we show these two in orthogonal axes. We show them in orthogonal axes following the mathematical convention to reflect their (apparent) mutual independence. Where is Brahman in this representation in Fig 3? Answer of course is that It is everywhere, as Ishwara, Hiranyagarbha and Virat in the first quadrant and as Itself in the other three quadrants. The origin “A” in Fig 3 represents the beginning of creation. At that instant, the manifest and unmanifest are all together as just one point. Before that (i.e. before creation starts) It is not even a point perhaps, as you have pointed out.
The O-E-T, by the way, is not just a 4 dimensional space, since each point in that continuum must represent the physical-emotional-intellectual status of all things and beings at a given time. It is a multi dimensional space of very large number of dimensions.
“Bondage exists only from the level of ignorance”- that is true. A key result of the model is in fact the demonstration of a jeeva’s decreasing bondage to samsar as its Self-Knowledge increases. I hasten to add that the model has not discovered here anything previously unknown to Vedantins. It is nevertheless gratifying that the model is consistent with this fundamental assertion of Advaita and indeed of all spiritual traditions.
Your other question regarding projection of each wave on the horizontal axis may be the result of misunderstanding some details of the model, which are yet to be discussed in these postings. Each wave in the Total Mind represents the various possible states the cosmos can be at that time. This is not unlike the thoughts of various options existing in our mind when we have to make a decision. Only one of these possibilities will be realized and that is what shows up in the O-E-T and that is what the jeevas in samsar will get to experience. To be more specific, in Fig 3, at time=1, DH is the wave representing all possible states and the point D, at the “foot” of that wave in the horizontal axis, is the state actually realized. Whereas before actualization the whole wave DH exists, after actualization the wave collapses into a single point D. Thus, there is only one point in O-E-T corresponding to each wave. I hope this helps.
Hari Om!
- Raju Chidambaram
Date: Fri Nov 11, 2005 6:56 pm
Subject: Re:Waves in the Total Mind (MTS-5)
Hi Raju,
I agree with you on the paramarthika/vyavaharika distinction, as well as on the >4 dimensional nature of OET. I forgot that it includes the psychological realm of thoughts and emotions.
As for the projection question, it would seem that your axes are not quite the same as standard cartesian axes. Any point on the quadrant will have coordinates corresponding to the horizontal and vertical projections, as you know. Hence, my impression of what a point represents will be the one most people assume. An avant-garde usage of axes is fine, as long as carefully defined. Modern math is full of innovative formal structures, but their careful definition and consistency is crucial.
Also, I would like to know, does one continuously traverse all possible states as one traverses the quarter-circle from D to H? This looks like a 1-dimensional path, but the space of possibilities surely has a high dimension too.
Hari Om!
Ben
Date: Fri Nov 11, 2005 10:22 pm
Subject: Re: Waves in the Total Mind (MTS-5
Jai Sadguru
The appropriate model is something like this.
The Origin is O. The X axes , are I am this in the positive and I am not this in the negative. The Y axes are "this belongs to me or I own this" in the positive and "this does not belong to me or I am not the owner of this". The Z axes are in the positive, I want this-desire, and in the negative, Imust get rid of this or that-fear:
So the model is complete . Any movement from "I" the origin, creates the world of BMI, OET and PFT, which is Swami Chinmaya's model. Stay put at the origin, is staying in the profound peace and deep silence of the Atman. As ben has rightly put, in this multidimensional model, this pseudo-entity, the presumed "I" swings from one axis to other and from one dimension to the other at such speeds, it is hardly noticed. Meditation is unburdeneing of these notions and presumptions, and an attempt to stay put at the Origin. To what extent one can be succesful is one's own destiny.
Being aware of three axes butremaining in the Origin is Savikalpa samadhi.Not being aware of these three axes but being aware of presence in Origin is Nirvikalapa Samadhi. Not being aware of the axes or the origin is Deep Sleep.
Namasthe
JS
Date: Mon Nov 14, 2005 4:31 am
Subject: Re:Waves in the Total Mind (MTS-5)
Respected Dr. Raju Chidambaram-ji.
Sir, I went through your paper "Geometric Representation Of Advaitic Principles And Its Relevance To Modern Physics". As I was off the List for some time, I hadn't had the opportunity to go through your first few posts and the responses thereto. As such, I didn't know that you have initiated this thread on the request of our respected Ramji. Well, I was baffled with a mathematical model coming up for Advaita and my bafflement resulted in certain tangential remarks in the List questioning the validity of such an attempt.
I apologize sincerely for my hasty remarks. Having read your paper and the circumstances of your presenting it on the List, I now feel that I should better have controlled my eagerness to express.
I am no mathematician. I was rather very poor in maths in my school days. It was only in later years that I developed some fascination for the subject. That can be called a flirtation without a solid basic foundation. Yet, I should perceive that my later liking for the subject has helped understand various scientific principles to at least a healthy lay level.
It is with this meager resource that I am going to present my observations on the geometric model. If I am wrong, please bear with this layman's apparently impertinent foray into the lofty citadel of mathematics.
Besides, our Benji has stated that the discussions so far have been only peripheral. I notice from your acknowledgements that he was associated with the project. He is a professional too. He is therefore in a position of advantage to be really incisively insightful about the mathematical nuances of the model. Being a layman, I would restrict myself to the basics – the very foundations of the model - and avoid the mathematical equations, which I can safely assume are strongly well-built on your mathematical prowess and accomplishments.
Many doubts cropped up in my mind as I progressed through your paper until I reached the derivation of the mathematical equations and your brilliant conclusion "Self = Space, Maximum Knowledge of Self = Maximum Speed in Space, Knowledge of Self = Speed in Space". I had your paper printed out in hard copy and, as I progressed through the pages, I jotted down my doubts. Fortunately most of them cleared as I reached the equations leaving only one behind unresolved and that is the main theme of this post.
To illustrate this lingering doubt, let us take an ordinary graph where time (t) is plotted on one axis (vertical) against the movement of an object (displacement) (d)on the other (horizontal). It is a very simple graphical representation and each plotting on the graph represents the position of the object at a given time. This means that there are always two coordinates for the position of the object – t and d. The two axes on your graph represent change on the horizontal and "Experiencer/Awareness" on the vertical. The state of a jIva in the field of all potential experiences should, therefore, have two coordinates. This is fine till the jIva reaches the vertical axis. When it reaches the vertical axis, the value on the horizontal will be 0, whereas the value on the vertical can be an immeasurable anything. On the simple graph of time against displacement, this can never happen because when the object reaches (returns to) 0 on the horizontal, it would logically mean that it has reached the point from where it started. The time in which the object reached its original position can be read from the vertical.
On the simple graph, time is progressive. That is why we are able to assign values to it and plot it on a graph, whereas, in your model, Awareness takes the place of time. In order to interpret your model logically, we will have to consider Awareness as progressive. Advaita will not accept such a proposition of a progressive Awareness with definite values on the vertical.
I am sure you are aware of this drawback because you have explained on page 15 that "It (the erstwhile jIvA who is now enlightened) is everywhere along the vertical axis at the same time. It witnesses all cause-effect waves from beginning to end of creation at the same experienced time".
Well, the explanation is quite advaitic and acceptable on its own merit. But, it looks like having been imposed on the geometric model by assigning an axis (vertical) to Awareness, which is neither progressive nor can be empirically measured. If the model is really geometric, both the axes should be measurable or at least conceivable.
On the time/displacement graph, when the object returns to its original position, it is back at zero after a lapse of measured time on the vertical. In the geometric model, therefore, we have to assume that when the jIvA's path touches the vertical, creation (horizontal) is folded up (0) after "a lapse of measured Awareness". Isn't 'measured Awareness' a very outlandish thought? Moreover, it would also mean that the kalpa has ended as far as that jIvA is concerned whereas it continues for others. Is the ending of the kalpa, self-realization?
The number of years in a kalpa is quoted in the paper. So, that is a very mathematically conceivable (if not measurable) entity, which finds support in BG 8-17. I notice that Sankara has not interpreted this verse or the one following it elaborately. The horizontal in the geometric model represents this kalpa, which means you have a very conceivable horizontal by virtue of BG 8-17. However, the vertical remains inconceivable. Can any geometric model have a conceivable axis against an inconceivable?
There is another major problem. Creation is conceived to begin at 0 on the horizontal. Geometrically, it is 0 on both the vertical and horizontal. What is 0 meant to represent in maths? To my lay mind, it is nothing. Nothing is not really nothing epistemologically. It is the absence of something. Something therefore gives sustenance to nothing or something and nothing are mutually indispensable. Mathematically, 1 has its validity because it is flanked by 0 and 2. 0 should therefore derive its validity from -1 and + 1. That points at the possibility of a universe in the opposite direction. We can call it anti-universe or (-) creation, which is another dimension to the so-called reality we perceive. We need not restrict ourselves to just a second dimension only. There could be an infinite number of dimensions sprouting from 0.
What I am driving at is that our mathematical 0 is a 'something' in the `field of all potential experiences' irrespective whether the field is positive or negative or any of the infinite number of dimensions. Advaita concerns Consciousness which lends sustenance to this `0'. 0 can at best represent a body at rest in any of the dimensions and about to be displaced but not creation conceived as progressive against the backdrop of inconceivable Awareness. I have laboured with these thoughts on this List in my post # 15052 in October 2002. I would request you to kindly take a look at it, Sir, if you have time for this layman's curiosity. Incidentally, the tool I used in that post is a hypothetical graph with conceivable axes.
This is the major problem I perceive with the geometric model. I, therefore, have reason to believe that the spectacular conclusions you have reached about the coming together of science and spirituality are not based on a solid foundation. The twain shall never meet although they `seem' to do so in the glittering light of recent advances in scientific research.
Another interesting point is your conclusions about language of advaita and language of physics (page 18). In one of my earlier vagrant posts in September 2003 in our discussion on `Light in Enlightenment' (Post # 19067), I had raised the questions: "In Enlightenment known as Self-Realization, where duality is effectively undone, are we virtually *becoming* prakAsha whereby there is cessation of apparent duality?" and "Isn't *being* prakAshA the same as the hypothetical travel at the velocity of light?". These questions have striking resemblance to the conclusions you reach through your equations although I did not ask them with any mathematical support.
Our Shri Ananda Wood-ji, a physicist with whom this List is very fortunate to associate with, had then provided a brilliant reply (Post # 19111) in which he had cautioned us as follows:
"Advaita belongs to a completely different level of consideration, where knowledge is no instrumental action, but only light in which all instruments and actions are dissolved. Of that light, Einstein's own description shows its relation to instrumental sciences. As he says, it is `of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection'.
I am yet to see any comments from Shri Ananda-ji on the geometric model. It would be very interesting and enlightening if he joins in.
There is yet another problem. It is said in vedanta and affirmed by sages like Sankara that the ignorance that results in the projection of an objectified world has no beginning. How can a geometric horizontal axis, which has a definite beginning mathematically, explain this statement?
Further, the jIvA is a fallen being and has to virtually struggle back through the `field' is just one school of interpretation. This geometric model thrives on such a scenario. Personally, I do not know whether to accept this view or not. However, may I request you, Sir, to read Sw. Dayanandaji's exposition of Panchadasi 7-51 in post # 27817 where he has effectively refuted this contention. The right understanding of what he says, I am afraid, invalidates the need for a geometric model where the jIvAs, starting from the horizontal, sail on the crests of different waves of projection to reach the vertical.
When the jIvAs reach the vertical, they are assumed to be Self- Realized. Well, Advaita says a knower of Brahman becomes verily Brahman. So, the vertical cannot be considered as falling in the vyAvahArika level as you have clarified, Sir, in your reply # 28672 to Benji. The vertical is Brahman and, in that case, how is it possible to conceive the self-Realized jIvA (J3 – a fully Self-Aware Being) as `advancing' on the vertical from one point to another (page 15, under the section "Degree of Establishment In The Self Or Relative Awareness). There is no coming and going in or for Brahman (IsAvAsyopanishad). I am afraid, the Relative Awareness equation therefore has no mathematical validity.
There are a few more minor doubts. I would not like to dwell on them as this post is already very lengthy. Let me, therefore, conclude requesting your kind forbearance. Thank you, Sir.
Om Anekakoti BrahmAndajananye Namah.
PraNAms.
Madathil Nair
Date: Mon Nov 14, 2005 3:53 pm
Subject: Re: On A Mathematical Theory of Spirituality Based on Advaita
There have been postings by several advaitins in response to the MTS series and I thank each one for taking the time to do so.
Nair ji: It is going to take me sometime to read and correctly understand all the points raised. Some of the questions are best answered when I present the appropriate section of the paper in future postings of this series. The questions you raise are important and I hope to answer them with the care they deserve before concluding the series.
Hersh ji: Thanks for the links to Swami Vivekananda’s efforts to bring science and Advaita closer. I have printed out these interesting papers and am reading them as time permits.
“Adi Shakti’s” posting about the “Ramanujams” was not in response to anything specifically in the paper, but it is interesting that he brought up the name Srinivasa Ramanujam. In the biographical work on Ramanujam’s life entitled “The Man Who Knew Infinity” I found something very stirring: How Ramanujam sincerely believed that all theorems that he discovered came to him as revelations from the reigning Goddess of his village temple. He had no other explanation for his own genius.
Ben: I have your recent question regarding the meaning of the cartesian axes. I will respond to it either as part of the next posting that I am working on or separately.
Hari Om!
- Raju
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