Passing away of Paul Cohen leads me on to thoughts on the 'anirvachaniya' of mAyA

[Guest guest]

advaitin , " V. Krishnamurthy " <profvk wrote:

>

> Meaning, By raising objections to the wonderfulness of mAyA we do not

solve

> the mystery. Besides, we also can raise serious counter-objections.

What is

> essential is that we should eradicate mAyA by systematic enquiry.

Further

> arguments are useless. So do not indulge in them.

 

 

Namaste,

 

Another mathematician-philosopher, A.N.Whitehead (co-author

with Bertrand Russell, of Principia Mathematica), said:

 

Philosophy begins in wonder. And, at the end, when philosophic thought

has done its best, the wonder remains.

 

Alfred North Whitehead

 

 

 

Regards,

 

Sunder

[Guest guest]

advaitin , " V. Krishnamurthy " <profvk

wrote:

>

> of almost a hundred-year old search for the truth of the Continuum

> Hypothesis. Don't ask me what the CH is. I will have to give you

a whole

> lecture on Foundations of Mathematics!

>

> This 'undecidability' of the truth of CH and AC leads me on, in

this

> advaita forum, to talk about the 'anirvachaniya' status of mAyA.

 

 

Pranams ProfVK,

 

I am sure you will enjoy this quote:

 

http://pascal.iseg.utl.pt/~ncrato/Math/Einstein.htm

 

Geometry and Experience

Albert Einstein

Lecture before the Prussian Academy of Sciences, January 27, 1921.

The last part appeared first in a reprint by Springer, Berlin, 1921

 

" ...... How can it be that mathematics, being after all a product of

human thought which is independent of experience, is so admirably

appropriate to the objects of reality? Is human reason, then, without

experience, merely by taking thought, able to fathom the properties

of real things?

 

In my opinion the answer to this question is, briefly, this: as far

as the propositions of mathematics refer to reality, they are not

certain; and as far as they are certain, they do not refer to

reality........... "

 

 

Regards,

 

Sunder

[Guest guest]

advaitin , " Sunder Hattangadi " <sunderh

wrote:

 

Pranam!

 

> Geometry and Experience

> Albert Einstein

> Lecture before the Prussian Academy of Sciences, January 27, 1921.

> The last part appeared first in a reprint by Springer, Berlin, 1921

>

> " ...... How can it be that mathematics, being after all a product

> of human thought which is independent of experience, is so

> admirably appropriate to the objects of reality? Is human reason,

> then, without experience, merely by taking thought, able to fathom

> the properties of real things?

 

This seems to pre-suppose what " real things " are and then goes about

questioning if human reason is able to fathom them!

 

What *is* a " real thing " * needs to be addressed prior to determining

if human thought is a sufficient or necessary condition to fathom

it. What is real may not be a " thing " after all.

 

> In my opinion the answer to this question is, briefly, this: as

> far as the propositions of mathematics refer to reality, they are

> not certain; and as far as they are certain, they do not refer to

> reality........... "

 

Likewise for that opinion too! As far that opinion refers to

reality it is not certain; and as far it is certain, it does not

refer to reality!

 

I recall a profound and insightful remark of distinguished

astrophysicist and Nobel laureate Subramanyan Chandrasekhar that

made a good deal of impression on me. When asked about Einstein's

famous observation that is quoted often- " God does not play dice " ,

Chandra responded with a question " How does he know? " I guess only

Chandra had the stature to question thus Einstein.

 

Regards

-Srinivas

[Guest guest]

advaitin , " V. Krishnamurthy " <profvk

wrote:

>

> Namaste all.

>

> A few days ago Prof. Paul Cohen, Fields Medalist in Mathematics in

1966,

> passed away at the age of 74. He was the one who finally proved the

> undecidability of the Continuum Hypothesis (CH) and the Axiom of

Choice (AC)

> in the context of accepted norms of Mathematical Logic. Earlier in

the

> thirties, Godel proved that by accepting the CH or the AC no

inconsistency

> would arise which is not already in the system of Logic without

them. In

> other words, AC or CH cannot be disproved. It was Cohen who proved,

in 1962,

> that by denying the AC or CH, also, no inconsistency would arise.

This

> means AC or CH cannot also be proved. His method by which he

created a

> model with the negation of these axioms was technically

called 'Forcing'.

> It was for this discovery he was awarded the Fields Medal. Because

of this

> method of creating non-standard models of Mathematics, the whole

field of

> non-standard Mathematical Analysis arose thereafter. It was a

culmination

> of almost a hundred-year old search for the truth of the Continuum

> Hypothesis. Don't ask me what the CH is. I will have to give you

a whole

> lecture on Foundations of Mathematics!

>

> This 'undecidability' of the truth of CH and AC leads me on, in

this

 

 

Namaskaram Sri ProfVkji,

 

I believe the mathematician's or logician's formal position is as you

have stated " accept: then this follows; don't accept: then this

follows " . The truth is undecidable; so don't approach with an

intuitive favouritism.

 

But the question arises: does truth exist, though beyond our capacity

to understand? That AC's truth or falsehood would not lead to

contradictions in other axioms of mathematics does not mean it is

true and false, or neither. It just means that within our accepted

framework of assessing Reality (in the mathematics kingdom), either

position is safe. Perhaps this fact merely shows the limitations of

our kingdom, that it cannot cover all grounds. (How can there be a

Vyavahaarika picture that captures it all? Does AC think there can

be?)

 

Einstein and de Broglie wanted Truth to be open question regarding

QM, whereas Bohr, Heisenberg, etc. were content with the axiomatic

approach. Physics is not universally agreed on this issue; in

particular, whether it is appropriate to shut out the questions that

appear or are beyond our reach.

 

In our religious perspective, the primary axiom is the Reality of

Brahman. This axiom, the fundamental one, is not undecidable. In

fact, the Vedas hold it as truth, and our sages proclaim the same.

Thus the apparent axiom which cannot be verified through ordinary

logic (within " maya " ) can be " realized " as Truth (by " transcending

maya " ).

 

So the position of religion regarding its " axiom " is different from

that of science. Standard logic and science fall within the realm of

duality; this framework is said to be maya for the " person " accepting

it as real at its level and not seeing beyond. This Maya is

undecidable for such a person, for the attempt to decide is also

within its kingdom. But the methods proposed by religion are meant to

get out of the " person " and into the Reality of Self. The subsidiary

axiom and framework of maya is eliminated in the Truth of Brahman.

 

thollemelukaalkizhu

 

(I may not stay in conversation now but will return in May. Please

let me know your thoughts now or then. Thank you.)