Pascal's wager and Descartes's doubt: The heart has its reasons which reason knows nothing of!

Le cœur a ses raisons, que la raison ne connaît point. On le sent en mille choses. C'est le cœur qui sent Dieu, et non la raison. Voilà ce que c'est que la foi parfaite, Dieu sensible au cœur.

The heart has its reasons, which Reason does not know. We feel it in a thousand things. It is the heart which feels God, and not Reason. This, then, is perfect faith: God felt in the heart.
~Blaise Pascal

As exemplified in the argument above, Pascal firmly believed that to understand God, we need belief, which cannot be understood with reason. 

On the other hand, Descartes gave the argument:

"God has placed within us the idea of himself as a craftsman’s stamp on his work."

 Further, he had a penchant for doubt, and therefore wouldn't take belief in God as simply a wager:

Of course, on another note:

But whatever  be their difference of opinion, they were brilliant mathematicians!

The Law and the Gatekeeper - a recursive infinite loop?

I read it first as a prologue in Chaitin's book (Meta-Math: The Quest for Omega), but Kafka's short parable had me hooked!

YouTube has enabled me to watch Orson Welles's narration of the story which Chaitin recommended as well. So here it is for sheer pleasure, shock, nightmare, soul-searching...

Although, in the literary context, people have tried to locate the parable in the novel "The Trial" in which it appears, I find it to be the crux of Kafka's personal belief system. Chaitin gives a note saying that in Hebrew, "Law" means "Torah", which also means "Truth". And I believe that is the key to understanding and applying this beautiful parable to our lives. We want the truth at all costs, but we are unable to realize that the gatekeepers are embedded in our psyche. The man spends all his time learning about the gatekeeper, never realizing that the correct question was something else. Effort has to be on realizing the law, and not being content with how to get past the gatekeeper.

Of course, on a more existential note, this is also sombre reminder of Kafka's Existential lineage. Every person's existence is unique and has a separate gate to the truth, but then all of them have the common perception of truth - uncertainty. Derrida describes the self-contradictory dynamic of the law thus:

The law is prohibited. But this contradictory self-prohibition allows man the freedom of self-determination, even though this freedom cancels itself through the self-prohibition of entering the law. Before the law, the man is a subject of the law in appearing before it. This is obvious, but since he is before it because he cannot enter it, he is also outside the law (an outlaw). He is neither under the law nor in the law. He is both a subject of the law and an outlaw. 

I am also intrigued by a recursive infinite loop in terms of the logic behind the gates of law. On the outset, Kafka tells the story of a man who believes that 'the law must be accessible to all'. But when the gate closes, the reader asks the question what is behind the gate, which is actually something for the reader to claim for himself, as 'the law must be accessible to all'!

Phi Q -- Alpha, another beginning...

The intent of Phi Q is an attempt to channelize my wanderlust for mathematics, philosophy and everything in between. My life's path has been one of many contradictions, owing to the fact that my mind doesn't seem to stay on anything for too long, and of course the general vagaries of the outer world which never lets us put our finger on the dream until it's gone and the child is grown.

Sans les mathématiques on ne pénètre point au fond de la philosophie.
Sans la philosophie on ne pénètre point au fond des mathématiques.
Sans les deux on ne pénètre au fond de rien. — Leibniz
[Without mathematics we cannot penetrate deeply into philosophy.
Without philosophy we cannot penetrate deeply into mathematics.
Without both we cannot penetrate deeply into anything.]
Source: http://www.cs.auckland.ac.nz/~chaitin/ufrj.html
http://www.umcs.maine.edu/~chaitin/midas.html

(Both are excellent sources of Chaitin's lectures and thoughts on mathematics and philosophy.)

I'll reproduce some words from the preface of Chaitin's book (Meta-Math: The Quest for Omega) here which pretty much sums up how I wish my pursuits in these fields to take shape:
"To survive, mathematical ideas must be beautiful, they must be seductive, and they must be illuminating, they must help us to understand, they must inspire us.
...mathematics as a way of celebrating the universe, as a kind of love-making! I want you to fall in love with mathematical ideas, to begin to feel seduced by them, to see how easy it is to be entranced and to want to spend years in their company, years working on mathematical projects.
And it is a mistake to think that a mathematical idea can survive merely because it is useful, because it has practical applications. On the contrary, what is useful varies as a function of time, while 'a thing of beauty is a joy forever' (Keats). Deep theory is what is really useful, not the ephemeral usefulness of practical applications." -- Gregory Chaitin

Here are some more words of mathematical madness:


Every good mathematician is at least half a philosopher, and every good philosopher is at least half a mathematician.
-- Friedrich Ludwig Gottlob Frege (1848-1925)


"Pure mathematics is, in its way, the poetry of logical ideas."
-- Albert Einstein



A scientist worthy of his name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.
-- Poincaré, Jules Henri (1854-1912).
(In N. Rose Mathematical Maxims and Minims, Raleigh, North Carolina: Rome Press Inc., 1988.)


Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.
-- Hardy, Godfrey H. (1877-1947).
(A Mathematician's Apology, London, Cambridge University Press, 1941.)


Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere—Archimedes did it in a bathtub. It is dramatic, challenging, endless, and full of surprises.
-- Richard J. Trudeau.