Penrose and Gödel: What does it mean to “understand” and “see”?

“Consciousness is the phenomenon whereby the universe’s very existence is known”

Roger Penrose

“Either mathematics is too big for human mind or the human mind is more than a machine.”

Kurt Gödel

Roger Penrose has a theory about human consciousness,  which is claimed by him to be strictly larger than Artificial Intelligence, where he makes use of Kurt Gödel’s incompleteness theorem along with certain theorized extensions of Quantum Mechanics. The incompleteness theorem, which is related to Alan Turing’s undecidability results in theory of computation, asserts that if a mathematical system with its axioms and rules of inference has to be consistent then it has to be also incomplete. There will be mathematical statements which can not be proven or disproven. Gödel meticulously constructed the following self-referential statement in such a formal system:

“This statement is not provable”

The statement is not provable or disprovable, because if it were, then we have contradiction. Is it true? Yes, it is obvious to us, but an AI system can’t infer it based on an algorithm which works with axioms and computation steps. One has to step out of the proof machinery to see its truth, which we can do.

Penrose also speculates that Quantum Mechanics, which is currently incomplete (not in Gödel’s sense, but in the sense that it doesn’t unify with gravity and it has inexplicable measurement problem), can be extended in which some non-computational aspects will appear, at the very microscopic fabric of universe, where consciousness resides. There we “see” the truths, which AI will never be able to.

When you are reading something or working out math, what does it mean to understand? Many mathematicians state that lot of their thinking is visual. What is vision? What exactly does it mean to see?

One can refer to literature and mythology for some pointers, as this is a fundamental question, which all of us are interested in.

I was reading a book Unseeing Idol of Light  written by K. R. Meera.

It is a novel in which there is love and and there is loss. There are themes of light and darkness, of vision and blindness, in a metaphorical sense, and which really relate to the same topic which Penrose is interested in. What does it mean to feel, to know, and to see? The story moves you. Literature tells us that we “see” somewhere deep inside us, but we can also lose the capacity to do so. To see is to feel.

Kabir on Transience

Had-had tape so auliya

Behad tape so peer

Had-anhad dono tape

Wako naam Fakir.

-Kabir

One who transcends limits is protector

One who transcends limitless is spiritual guide

One who transcends both limits and limitless

Is called Fakir.

-Kabir

Kabir, the ultimate Fakir and a renowned mystic poet from 15th century India, saw clearly how temporary everything is.  As children growing up in India, we had Kabir’s Dohe (couplets) in our textbooks. Here is translation of one of his poems Mat Kar Maya ko Ahankaar, Mat kar Kaya ko Abhimaan. Liberty is taken not to translate verbatim but to capture the meaning. It was fascinating to read 500 year old Hindi.

Kabir first tells about a powerful king in past and how small is human life span in backdrop of flow of time.

There was a strong emperor

All powerful and ruler of lands

Elephants in his majestic court

All in the end

As ephemeral as dew drops

Then Kabir reminds us that we all face grief over losses due to impermanence of things.

Parents and family

And all attachments

Why feel grief over loss?

Everyone eventually passes away

As ephemeral as dew drops

Finally, Kabir tells us that message of humility is what one should learn.

Don’t be so arrogant of wealth

Don’t be so proud of looks

This body is more frail than clay

Just a gust of wind, even a small one,

Can turn you into dust

Sahir Ludhianvi and Mystery of Time

 

When I was growing up in India, like everyone around me, I was fortunate to experience some great music from Bollywood. Wonderful voices of Rafi Sahib, Asha Ji, Kishore Da, Lata Ji, and many other great singers, combined with poetry of many talented writers, provided a deep aesthetic experience for our growing minds. Radio used to be always on in my childhood home.

In particular, Sahir Ludhianvi’s poetry stood out. I remember two songs “sansaar ki har shay ka” and “aage bhi jaane na tu” which made me wonder as there seemed to be a jewel hidden in the songs.

Later I learned how physicists are grappling with the nature of time. Whether it is Arthur Eddington’s Arrow of Time, or The Wheeler-DeWitt equation of a timeless universe, or emergent space-time in quantum theory, time remains a fundamental mystery. Even the notion of the present moment and how we perceive it, is amazing as shown by Einstein in relativity of time and in relativity of simultaneity. Thanks to my daughter who keeps me updated with all this wonderful science. 🙂

In “sansaar ki har shay ka”, here is the translation of one of the stanzas:

where is this path from, where is it leading to,

nobody knows the secret of this mystery.

on the Eyelid of this moment, rests the cosmos,

till the closing of the Eye, all this is a beautiful game

and, here is from “aage bhi jaane na tu”:

you don’t know what is ahead, you don’t know what is behind you,

whatever is, is this moment alone

Sahir is expressing his awe and sense of mystery, and how our subjective experience of the present moment creates the magic of universe and brings it to life to us.

A poet’s expression and a theoretical physicist’s equation. Two sides of a great effort to understand.

I wish all the bright minds, and students in sciences, and new generations, very best to unravel this deep mystery.

Amazing Train: A Poem for Children

Children, let us go on a wonderful train.

We will board it at Big Bang.
In a dazzling explosion of light
Our train will begin journey!

Galaxies will spin
Like fireworks around us.Through the window
We will witness
Greatest wonder

As life in its humblest origin

Of floating specks full of potentialities,

Transforms into men and women and their cities
And their short lived dreams

And their final anguish,
When we will see the Sun finally die
And we will cry for our dearest beautiful Earth.

Train will keep on speeding
Through the strangest vistas

Inside Black Holes
And even beyond.

Trillions of trillions years will pass,
We will be just as amazed
By what we will see and hear and know.

Will we ever get answers to your questions:
What is all this? Who are we?

In a dream-like landscape,
Our train will just keep on going
Towards Eternity

You and I listening to the most melodious

Vibrations of Space-Time

As finally we become one with the Music.

(May 1, 2012; Written for all science loving children and my kids.)