Questions from Profvk ji and Ben ji (MTS: Towards A Mathematical Theory of Spirituality Based On Advaita)

[Guest guest]

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

[Guest guest]

advaitin, aiyers@c... wrote:

> 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.

>

>

> - Raju Chidambaram

 

Namaste Raju-ji

 

It is going to take some time for me to digest your answers to what

I thought was an innocuous question of mine. The mathematics that is

imbedded in your thesis is deeper than what I thought it was on a

first impression. I have begun to love it as mine own!

 

In the meantime I want to approve your observation about the

distinction between Vasanas and Karmas. Vasanas determine the

tendencies of thinking and acting, but the karma (action) itself

determines the prArabdha and samchita which are the ones that

contribute to the unseen 'forces' that weave the future

circumstances that confront a person. Vasanas only influence the way

one reacts to that circumstance or happening, but the happening

itself has origins for which the Vasanas may or may not have

contributed! A pictorial representation of these facts can be seen

in

http://www.geocities.com/profvk/LHGWchart3.html

 

PraNAms to the Mathematics of Spirituality!

profvk

[Guest guest]

Raju,

 

I just noticed this post and Prof VK's response. I have copied them over to the

blog. I

didn't find any other responses, but if there is one please let me know.

 

As you know, I have been preparing for my trip to India, which includes

finishing a report

for my boss, so I haven't had time to comment on this. I'll do it when I get

back, though

the discussion may have moved on quite a bit by then...

 

Ben

 

 

 

advaitin, aiyers@c... wrote:

> 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.

 

[continued]