infinity, brahman, pUrnamadaH pUrNamidaM

[Guest guest]

namaste.

 

A very useful thing that evolved out of our previous

discussion on *definition* of brahman recently is the

analogy between infinity of mathematics and brahman of

advaita.

 

I am grateful to shri sunder hattangadi for suggesting

the reference to Rudy Rucker's book "Infinity and the mind".

This is an excellent book which should certainly be studied

and contemplated on. Two other books I found very useful

are (i) George Gamow "One, two, three ... infinity" and

(ii) N. Ya. Vilenkin "In search of infinity". All the three

books deal with the abstract infinity and there are glimpses

of what we understand as brahman in these writings. There

are some aspects where infinity does not meet our understanding

of brahman and I will try to bring it up at the end.

 

I am not a mathematician and hence my understanding may not

be right; with that limitation, I would like to attempt at

a search for similarity between the various levels of infinity

and the famous shAnthipAThaH of Isha upanishad 'pUrnamadaH

pUrNamidaM ...'.

 

It was shown by Georg Cantor that there are various

levels of infinity. The simplest level of infinity

is the number of counting numbers of all integers and

fractions. We can show that there is a one-to-one

correspondence between a set of all natural numbers,

set of all odd numbers, set of all even numbers, set

of all perfect squares, set of all cubes and so on.

That is the infinity of even numbers (or odd numbers

or all squares or cubes) is exactly as large as the

infinity of all numbers. This is paradoxical since even

numbers (or odd numbers or squares or cubes and so on)

is only a part of all natural numbers. One lakshaNam of

infinity is that the whole should equal the part or part

should equal the whole (Bertrand Russell)(similarity to

advaita is very direct here). Some nice examples of this

paradox are given in the references that I gave above

(the example by Hilbert of a hotel of infinite rooms

which is fully occupied being able to accommodate infinite

number of new guests arriving without reservation, is a very

nice one). What this means then is (we are still looking only

at one level of infinity)

 

set of numbers: 1, 2, 3, 4, 5, 6, 7, 8, ...

set of even numbers: 2, 4, 6, 8, 10, 12, 14, 16 ...

set of odd numbers: 1, 3, 5, 7, 9, 11, 13, 15 ...

set of squares: 1, 4, 9, 16, 25, 36, 49, 64, ...

 

all have one-to-one correspondence and are exactly as large

as the other one. All the latter sets are part of the original

set of numbers. We can also show that the infinity of integers

has a one-to-one correspondence with the number of all ordinary

arithmetic fractions as well.

 

The next question that need to be asked is: are all infinities

equal to one another?

 

We can find an infinity that is larger than the infinity of all

integers or all arithmetic fractions; for example, the number

of points on a line. We can show there are more points on a

line than there are integers or fractional numbers. This belongs

to a different class of infinity. Belonging to this class of

infinity (or having the same number of elements as on a line)

are the number of points on a plane, or in a cube.

 

The next higher level of infinity is the number of elements

on a variety of all possible curves, including those of most

unusual shapes.

 

Georg Cantor, the creator of the infinite set theory, denoted

the infinite numbers by the letter aleph with a subscript to

indiate the order of infinity. Aleph(0) is the number of all

integers and fractional numbers. Aleph(1) is the number of

all geometrical points on a line, on a plane, or in a cube.

Aleph(2) is the number of points on all geometrical curves.

According to mathematicians, nobody yet is able to conceive

any definite infinite collection of objects that should be

described by aleph(3). So, the numbers now run as shown

below in what I call line 1.

 

1, 2, 3, 4, 5, .. aleph(0) ... aleph(1)... aleph(2)... aleph(3)....

 

Now, the shAntipAThaH of Isha upanishad says

 

pUrNamadaH pUrNamidaM pUrNAt pUrNamudacyate

pUrNasya pUrNamAdAya pUrNamevAvashiShyate

 

This verse has profound advaitic meaning and we have

discussed this many times. I will simply give the meaning

here and try to explore the similarity with the infinity

of mathematics.

 

The meaning of the verse is: the invisible brahman is Full;

the visible universe is Full. From the Full (brahman), the

Full (the visible universe) has come. Even after the Full

(the visible universe) is taken out of the Full (brahman),

the Full (brahman) remains the same Full.

 

Even if we take for our consideration the infinity at one

level (say the aleph(0) and the sequence of integers);

That is Full (pUrNamadaH). Take the sequence of say the

even numbers. This is Full (pUrNamidam). Out of this

infinity of integers has evolved the infinite subset of

the even numbers (pUrNAt pUrNamudacyate). If we take out

the infinite subset of even numbers out of the infinite

set of integers (pUrNasya pUrNamAdAya), what is remaining

is still Full (pUrNamevAvashiShyate).

 

Alternately, we can look at the brahman as a different level

of infinity as stated in line 1 above. The various lower

alephs represent the universe and so on and again the meaning

of pUrnamadaH pUrNamidaM is clear.

 

In conclusion, the essence of infinity of mathematics is the

same as the essence of brahman of advaita. However, infinity

has some limitations as compared to brahman. Infinity is

anantam as brahman. Infinity is satyam as brahman. But it

seems to me there are two lakshaNams of brahman missing in

infinity. They are jnAnam (caitanya, Consciousness) and

sarvavyAptam (the pervading of everything). But this may

be my limitation in the understanding of infinity rather

than the limitation of infinity in contrast to brahman.

 

These are only not-fully-thought-out thoughts and attempts

to see the unity in two that continue to fascinate me since

a long time. I would hope the List members would correct

any mistakes in this presentation.

 

 

Regards

Gummuluru Murthy

---

[Guest guest]

Gummuluru Murthy wrote:

> namaste.

>

> A very useful thing that evolved out of our previous

> discussion on *definition* of brahman recently is the

> analogy between infinity of mathematics and brahman of

> advaita.

 

Here are a few points that need to be considered :

1. If we think of a number of infinities or levels of infinity,

how can the concept be analagous to brahman which is one without a second ?

2. If there are a number of infinities , can there be an infinite number of

infinities ?

3. If some infinities are larger than others, would it not mean that only the

largest of them

 

will be infinity by definition ?

4. Can infinity really be called a satyam (absolute reality)? Or is it a

mithyaa

(a dependent reality) as all jagat is, including mathematics ?

5. Brahman transcends Space and Time - that is the meaning of anantam. Is

infinity

bound by Space and Time or not ?

6. Infinity exists in Consciousness. But is it Consciousness, or even just

conscious?

7. Does Iishaavaasya Up. talk of two different puurNam-s, or one puurNam

viewed

from two angles ?

 

Pardon me if you think I am raising irrelevant questions. I have also not

thought

them through. I look forward to clarifications. I have raised them in the hope

that these would enable bring some sharper focus to Murtygaru's analysis.

 

Regards.

V.M.Sundaram.

[Guest guest]

>"V.M.Sundaram" <venkataraman

> Here are a few points that need to be considered :

>1. If we think of a number of infinities or levels of infinity,

> how can the concept be analagous to brahman which is one without a

>second ?

 

The word should be infiniteness - the very word meaning of Brahman - bR^ihad

dhaatu - VR^iddhi - it is a noun made out of an adjuective. I think I

discussed this in one of my notes (do not remember exacty where.) As I had

mentioned the noun qualifies or conditions the adjuctive too - like big

mosquito versus big mountain. Here when made noun out of adjective, big, it

is to indicate that it is unconditionally big, or limitless. When we say

there are number of infinities, automatically they all get qualified already

since one infinity limits the other as they refer to objects but when we are

referring to Brahman all qualifications drop out. Even in vishishhTadvaita,

Bhagavaan Ramanuja is careful to refer to the Lord as ananta kalyaaNa guNa

ashraya, here the ananta referes to each of the kalyaaNa guNa and also

infinite kalyaaNa GuNa-s. Both of them are beyond human perception. This

infiniteness cannot be within the consciouness then it gets by definition

limited. Howeer it cannot be separate from consciousness, since if they are

in the process both get limited. Infiniteness is ananda (anantameva ananda)

and that is the same as consciouness which is the same as existance. All

are the pointers to the same which is adreshyam... etc that Sunder provided

the ref from MunDaka. The Ch. U. statements - sadeva soumya idam agra asiit

.... tad aikshata etc points to this.

>2. If there are a number of infinities , can there be an infinite number

>of infinities ?

>3. If some infinities are larger than others, would it not mean that only

>the largest of them

>

>will be infinity by definition ?

>4. Can infinity really be called a satyam (absolute reality)? Or is it a

>mithyaa

>(a dependent reality) as all jagat is, including mathematics ?

 

In the ch. U. it refers to sad eva idam agram asiit - idam stands for the

universe that includes all the mathematics and concepts. Hence concept of

infinity is within the realm of vyavahaara. Here it is like indicators.

absoluteness is free from indicators - eka meva advitiiyam. Hence one

should separate the concepts pointing to the infinity versus the absolute

nature of that infiniteness - which is sat, chit and ananda.

 

>5. Brahman transcends Space and Time - that is the meaning of anantam. Is

>infinity

>bound by Space and Time or not ?

>6. Infinity exists in Consciousness. But is it Consciousness, or even

>just conscious?

>7. Does Iishaavaasya Up. talk of two different puurNam-s, or one puurNam

>viewed

>from two angles ?

 

I think I had an article related to this puurNamadaH slokam. I gave a talk

on Logic of Sprirituality in Madras organized by Prof. V.K last year and he

typed up the summary of the talk and presented to adviatin. I have to find

it.

 

That remainds me for some reason Prof. Vk has been silent for some time. we

are missing his scholarly articles.

 

 

Hari Om!

Sadananda

>

>Pardon me if you think I am raising irrelevant questions. I have also not

>thought

>them through. I look forward to clarifications. I have raised them in the

>hope

>that these would enable bring some sharper focus to Murtygaru's analysis.

>

>Regards.

>V.M.Sundaram.

>

>

 

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[Guest guest]

Namste!

 

Lord Sri Krishna describes Brahman (HImself) very precisely and concisely in the

following sloka:

 

Esha swayamjyoti aja aprameyo,

 

Mahaanubhuti Sakalaanubhuti

 

Ekoadwitiyo vachasaam virame

 

Enesshwitha Vaak savacharanti

 

He is Self -Luminous.He is Unborn.He is beyond all comparisons and all

imagination.He is the One without a second.Words fail to describe

Him,(because).He alone is making the mouths speak.(All Indriyaas function

because of Him).

 

Ananda Sagar

 

 

 

 

Kuntimaddi Sadananda <k_sadananda wrote:

 

 

>"V.M.Sundaram" <venkataraman

 

 

 

 

 

 

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[Guest guest]

Resubmitted with additions<BR>

<P>  <BR>

<P>  <B><I>BTA SAGAR

<btasagar></I></B> wrote: <BR>

<BLOCKQUOTE style="BORDER-LEFT: #1010ff solid 2px;

MARGIN-LEFT: 5px; PADDING-LEFT:

5px"><HTML><BODY><TT><BR>Namste!<BR><BR>Lord Sri

Krishna describes Brahman (HImself) very precisely and

concisely in the following sloka:<BR><BR>Esha

swayamjyoti aja aprameyo,<BR><BR>Mahaanubhuti

Sakalaanubhuti<BR><BR>Ekoadwitiyo vachasaam

virame<BR><BR>Enesshwitha Vaak savacharanti<BR><BR>He

is Self -Luminous.He is Unborn. He is the Infinite

(immeasurable )Enjoyer.He Experiences all(He knows and

experiences all that is happening through all beings).

He is beyond all comparisons and all imagination.He is

the One without a second.Words fail to describe

Him,(because)He alone is making the mouths speak.(All

Indriyaas function because of Him).<BR><BR>Ananda

Sagar<BR><BR><BR>  <BR><BR>  Kuntimaddi

Sadananda <k_sadananda> wrote:

<BR><BR><BR><BR>>"V.M.Sundaram"

<venkataraman><BR><BR><BR><BR><BR>-------------------------\

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[Guest guest]

Dear Sri Sagar,

 

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Your contributions to the list are quite inspiring. Thank you for that.

 

I remain yours,

Madhava

 

 

>

> BTA SAGAR [btasagar]

> Sunday, February 11, 2001 2:57 PM

> advaitin

> Re: infinity, brahman, pUrnamadaH pUrNamidaM

>

>

> Resubmitted with additions<BR>

> <P>  <BR>

> <P>  <B><I>BTA SAGAR

> <btasagar></I></B> wrote: <BR>

> <BLOCKQUOTE style="BORDER-LEFT: #1010ff solid 2px;

> MARGIN-LEFT: 5px; PADDING-LEFT:

> 5px"><HTML><BODY><TT><BR>Namste!<BR><BR>Lord Sri