i, The Maya Operator and a Big Thanks to Profvk ji

[Guest guest]

Profvk ji’s observation that use of mathematical models is similar to the use of

analogies in Advaita is quite helpful and I thank him for bringing that out.

Mathematical models have the same purpose and limitations as other analogies do.

 

May be it was only a fortuitous coincidence that Profvk ji chose to illustrate

his observation with the example of complex numbers, or may be it was more than

that. Ever since I was introduced to Advaita, I have been tempted to call the

unit imaginary number, i, as the Maya Operator of Mathematics. Like Maya, the

“number” i is illusory, hard even to imagine and altogether quite mysterious.

Illusory Maya cannot be seen, but its product, namely this world, is all too

real to our senses. Similarly, even though i is called imaginary, it plays such

a vital role in science and engineering that some of today’s technological

advancements would be nearly impossible without it. Schrodinger’s wave equation,

which is fundamental to the understanding of the behavior of matter, contains

this mysterious i as though to proclaim that the seen world owes its existence

to it!

 

Maya, by its aavarana sakthi covers the Real to make it apparently unreal. At

the same time, by its vikshepa sakthi Maya makes the unreal world appear real.

Compare this with a property of i: a real number when multiplied by i becomes

imaginary while an imaginary number multiplied by the same i becomes real! Thus,

to my mind, i deserves the name “Maya Operator”.

 

I also realized after reading Prof ji’s posting that the complex number

t.exp(i.theta) (where exp is read as “e to the power of”, e being the Euler

number 2.718..) can be used to denote jeeva’s “coordinates” as (t.cos(theta),

t.sin(theta)). The “path” of the jeeva in the Cartesian coordinate system in Fig

10 can be written as the integral, with respect to t, of the complex function

exp(i.theta(t)), theta(t) being a function with value between 0 and pi/2 radians

for all t. When theta(t)= pi/2 (i.e. at the time of Realization), the integrand

becomes exp(i.pi/2). Interestingly enough, the value of this expression is

derived from what has been called the most beautiful of all identities in

mathematics:

 

exp(i.pi) = -1.

 

This identity is remarkable in that it ties together very elegantly the two most

important transcendental numbers in mathematics, namely e, and pi, with the

imaginary number i. e and pi are numbers which rather mysteriously surface in

many scientific investigations. Mathematicians tend to be mystics and many

eminent mathematicians, I understand, have tried over the past few centuries to

fathom the mystic significance of this supernatural looking identity.

 

That such an expression should show up in a mathematical model based on Advaita

(and that too in reference to the point of Realization in a jeeva’s path) is

quite satisfying! It does not however solve the mystery behind the identity,

rather adds to it.

 

Thank you, Profvk ji for the lead!

 

Hari Om!

 

- Raju Chidambaram

[Guest guest]

advaitin, aiyers@c... wrote:

>

>

>

> I also realized after reading Prof ji's posting that the complex

number t.exp(i.theta) (where exp is read as "e to the power of", e

being the Euler number 2.718..) can be used to denote

jeeva's "coordinates" as (t.cos(theta), t.sin(theta)). The "path" of

the jeeva in the Cartesian coordinate system in Fig 10 can be

written as the integral, with respect to t, of the complex function

exp(i.theta(t)), theta(t) being a function with value between 0 and

pi/2 radians for all t. When theta(t)= pi/2 (i.e. at the time of

Realization), the integrand becomes exp(i.pi/2). Interestingly

enough, the value of this expression is derived from what has been

called the most beautiful of all identities in mathematics:

>

> exp(i.pi) = -1.

> That such an expression should show up in a mathematical model

based on Advaita (and that too in reference to the point of

Realization in a jeeva's path) is quite satisfying! It does not

however solve the mystery behind the identity, rather adds to it.

>

> Thank you, Profvk ji for the lead!

>

> Hari Om!

>

> - Raju Chidambaram

 

Namaste, Raju-ji. Thanks for the kind words. I have followed your

above observations with interest. 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' !!!

 

PraNAms to the Mathematics of Advaita!

profvk

[Guest guest]

Namaste Prof-Ji:

 

IMHO -

 

If we say that reorganization that "i", (the individual jIva) is not

different from the "I" is advaita. This will then satisfy the

fundamental "aham brhmamaasmi" statement.

 

I think the dot on the top of little "i" is the ah.nkaara, and the

removal of that individualistic "dot" is the key in the

reorganization process.

 

Please correct me if I am missing something.

 

Warm Regards.

 

Dr. Yadu

 

 

 

advaitin, "V. Krishnamurthy" <profvk>

wrote:

>

> advaitin, aiyers@c... wrote:

> >

> >

> > > - Raju Chidambaram

>

> Namaste, Raju-ji. Thanks for the kind words. I have followed

your

> above observations with interest. 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' !!!

>

> PraNAms to the Mathematics of Advaita!

> profvk

>