Kurt Gödel warned us, there would be questions we could not answer without appealing to a larger system in a universe with one puzzle nested inside another.

 

The Golden Road to Samarkand

“Kurt Gödel warned us, there would be questions we could not answer without appealing to a larger system in a universe with one puzzle nested inside another.  There is nothing for it but to see where it goes; to see if the program halts. To do this we will have to believe in partial answers and the promise of more to come.  Call it faith, call it a wager, or call it the poet James Elroy Flecker’s description of travelers at Baghdad’s Gate of the Moon.” (Richard Fernandez)

The Way is a river  

flowing and overflowing everywhere.  

Completely reliable, it receives every thing.  

Whatever it does, it does without effort,  

and when the job is finished it lets go.  

It touches everything and controls nothing.  

That is why whatever it touches is eternal.

Lao Tzu, (#34)

!

A voice cries: ‘In the wilderness prepare the way of the LORD;    

make straight in the desert a highway for our God. 

Every valley shall be lifted up,    

and every mountain and hill be made low; 

the uneven ground shall become level,    

and the rough places a plain. 

And the glory of the LORD shall be revealed

Isaiah 40:3-5

 Remember not the former things,    

nor consider the things of old. 

 Behold, I am doing a new thing;    

now it springs forth, do you not perceive it?

 I will make a way in the wilderness    

and rivers in the desert.

Isaiah 43:18-19

James Elroy Flecker

SCENE II

At the Gate of the Moon, Bagdad. Blazing moonlight. 

MERCHANTS, CAMEL-DRIVERS and their beasts, PILGRIMS, JEWS, WOMEN, all manner of people. By the barred gate stands the WATCHMAN with a great key. Among the pilgrims, HASSAN and ISHAK in the robes of pilgrims.

THE MERCHANTS

(Together)

Away, for we are ready to a man!

Our camels sniff the evening and are glad.

Lead on, O Master of the Caravan,

Lead on the Merchant-Princes of Bagdad.

THE CHIEF DRAPER

Have me not Indian carpets dark as wine,

Turbans and sashes, gowns and bows and veils,

And broideries of intricate design,

And printed hangings in enormous bales?

THE CHIEF GROCER

We have rose-candy, we have spikenard,

Mastic and terebinth and oil and spice,

And such sweet jams meticulously jarred

As God's Own Prophet eats in Paradise.

THE PRINCIPAL JEWS:

And we have manuscripts in peacock styles

By Ali of Damascus: we have swords

Engraved with storks and apes and crocodiles,

And heavy beaten necklaces for lords.

THE MASTER OF THE CARAVAN

But you are nothing but a lot of Jews

PRINCIPAL JEW

Sir, even dogs have daylight, and we pay.

MASTER OF THE CARAVAN

But who are ye in rags and rotten shoes,

You dirty-bearded, blocking up the way?

ISHAK

We are the Pilgrims, master; we shall go

Always a little further; it may be

Beyond that last blue mountain barred with snow

Across that angry or that glimmering sea,

White on a throne or guarded in a cave

There lies a prophet who can understand

Why men were born: but surely we are brave,

Who take the Golden Road to Samarkand.

THE CHIEF MERCHANTS

We gnaw the nail of hurry. Master, away!

ONE OF THE WOMEN

O turn your eyes to where your children stand.

Is not Bagdad the beautiful? O, stay!

MERCHANTS

(In chorus)

We take the Golden Road to Samarkand.

AN OLD MAN

Have you not girls and garlands in your homes?

Eunuchs and Syrian boys at your command?

Seek not excess: God hateth him who roams!

MERCHANTS

(In chorus)

We take the Golden Road to Samarkand.

HASSAN

Sweet to ride forth at evening from the wells

When shadows pass gigantic on the sand,

And softly through the silence beat the bells

Along the Golden Road to Samarkand.

ISHAK

We travel not for trafficking alone;

By hotter winds our fiery hearts are fanned:

For lust of knowing what should not be known,

We take the Golden Road to Samarkand.

MASTER OF THE CARAVAN

Open the gate, O watchman of the night!

THE WATCHMAN

Ho, travellers, I open. For what land

Leave you the dim-moon city of delight?

MERCHANTS

(With a shout)

We take the Golden Road to Samarkand!

(The CARAVAN passes through the gate.)

WATCHMAN

(Consoling the women)

What would ye, ladies? It was ever thus.

Men are unwise and curiously planned.

A WOMAN

They have their dreams, and do not think of us.

(The WATCHMAN closes the gate.)

VOICES OF THE CARAVAN

(In the distance singing)

We take the Golden Road to Samarkand.

CURTAIN

PSALM 146 

Praise the LORD, O my soul! 

    I will praise the LORD as long as I live;    

  I will sing praises to my God while I have my being. 

  Put not your trust in princes, in a son of man, 

  in whom there is no salvation. 

  When his breath departs, he returns to the earth;    

  on that very day his plans perish. 

  Blessed is he whose help is the God of Jacob,    

   whose hope is in the LORD his God, 

  who made heaven and earth,    

   the sea, and all that is in them, 

   who keeps faith forever;   

  who executes justice for the oppressed,    

  who gives food to the hungry. 

The LORD sets the prisoners free;    

     the LORD opens the eyes of the blind. 

The LORD lifts up those who are bowed down;    

     the LORD loves the righteous. 

The LORD watches over the sojourners;    

     he upholds the widow and the fatherless,    

     but the way of the wicked he brings to ruin. 

The LORD will reign forever,    

    your God, O Zion, to all generations. 

Praise the LORD!

https://youtu.be/bT7Hj-ea0VE

All Along The Watchtower, Bob Dylan

“There must be some kind of way out of here,”

Said the joker to the thief

"There's too much confusion

I can't get no relief.

Businessmen, they drink my wine

Plowmen dig my earth

None of them along the line

Know what any of it is worth."

“No reason to get excited,"

The thief, he kindly spoke.

"There are many here among us

Who feel that life is but a joke.

But you and I, we've been through that

And this is not our fate

So let us not talk falsely now

The hour's getting late."

                     All along the watchtower

                     Princes kept the view

                     While all the women came and went

                     Barefoot servants too

                    Outside in the cold distance

                    A wild cat did growl

                    Two riders were approaching

                     And the wind began to howl

Kurt Gödel and Albert Einstein

https://voegelinview.com/godels-theorem/

Kurt Gödel[1] was a Platonist,[2] logician and mathematician who developed the intention of making a profound and lasting impact on philosophical mathematics. His next task was to think of something! Amazingly, at the age of twenty five, he achieved his goal, publishing his incompleteness theorem.

A good friend of Albert Einstein’s, Einstein once said that late in life when his own work was not amounting to much, the only reason he bothered going to his office at the Institute for Advanced Study at Princeton was for the pleasure of walking home with Gödel.

John von Neumann wrote: “Kurt Gödel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel’s achievement.”[3]

While at university, Gödel attended a seminar run by David Hilbert who posed the problem of completeness: Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?

Gödel’s incompleteness theorem published in 1931 proved that this was not possible.

The point of Gödel’s Incompleteness Theorem is that not everything that is true can be proven to be true by showing that statements are logically derived from axioms. In a “complete” system, every statement that falls within the purview of the system is “decidable;” it can be shown to be either true or false. Only inconsistent axiomatic systems have this ability, at least beyond a certain low level of complexity – but this means permitting contradictions and since there are no true contradictions, a complete system will end up apparently proving that false things are true. Better to opt for an incomplete system where not everything is proved. Settle for proving too little rather than too much!  As Verena Huber-Dyson wrote: “There is more to truth than can be caught by proof.”[4]...

We can intuitively perceive the truth of the Gödelian proposition “This statement is not provable within this axiomatic system,” though the perception of this truth is not derived from an axiomatic, rule-driven system. The human mind can do something that a rule-driven device like a computer cannot do...

The validity and truth of an algorithm cannot be algorithmically determined. Alan Turing’s halting problem proved that there is no general algorithm for finding and proving all other algorithms. It is necessary to step outside the narrowly rule-driven confines of a mechanical decision procedure to assess the truth and validity of mechanical decision procedures...

Stanley Jaki writes: “The fact that the mind cannot derive a formal proof of the consistency of a formal system from the system itself is actually the very proof that human reasoning, if it is to exist at all, must resort in the last analysis to informal, self-reflecting, intuitive steps as well. This is precisely what a machine, being necessarily a purely formal system, cannot do, and this is why Gödel’s Theorem distinguishes in effect between self-conscious beings and inanimate objects.”[19]...

Scientists have to retain a similar openness to truth not derivable from axioms. They must just hope that reality has some knowable structure. At this point in time, quantum physics which applies to the subatomic scale is inconsistent with the theory of relativity that applies to the very big and the very fast, approaching the speed of light. Since quantum physics and relativity are complex formal systems they will generate Gödelian propositions and this seems to mean that there can be no “Theory of Everything.” The very name is suggestive of an obnoxious hubris and Gödel seems to show that it is in fact an illusion...

C. S. Lewis writes in The Abolition of Man, that if some truths are not treated as self-evident, no truths can be known. Gödel’s Theorem takes this even further and shows that in complex axiomatic systems there will appear true propositions not provable even on the basis of any consistent set of axioms...

Aristotle recognized the provisional nature of axioms when he wrote that first principles are not provable. Now it turns out that no set of axioms are sufficient to capture all true statements no matter how the axioms are modified – at least when it comes to first-order logic.