Knots in Art

Which is the use of the knot theory?
I'm very often asked the question.
(By people, who are not able to tie properly their shoelaces.
I happen to know some. They claim that finding an ideal knot is a problem of logistics.)
Gosh! Have a look at historical paintings by Grottger. There you will find the answer,
Let me explain. Polish national sport is plotting uprisings.
It is important, since it is only due to the sport that we managed to survive as a nation.
To win an uprising you need weapons.
The picture, to which I am drawing your attention, shows Polish mathematicians preparing lethal knots.
You may recognize the face of one of the fellows who hammer the knot.
Yes. It is our Canadian ally, Rob S.. the famous knot plotter.
(Thanks Rob! Great job! It's not your fault that the uprising was lost.)

Strange enough, most applications of the knot theory are connected with rather violent events.
To support my claim let me present another historical masterpiece by Matejko.
This time he reconstructed a really gloomy story.
One of our best queens, Bona, was poisoned. She had lots of enemies. It was her to introduce la verdurra into our traditional kitchen.
As the legend says, the royal knot theorist, Jon S. was trying to save her life with the extraction from an ideal knot.
(Click on the image to see it better.)
And what?...I am sorry to say - it did not work.
I think he used too simple knot. He used a trefoil. Perko claims 10.161 or 10.162 would be better.

The royal knot theorist trying to save Queen Bona
(based on Poisoning of Queen Bona by Jan Matejko)

Question "Why does the trefoil knot weaken ropes more than the figure eight knot?" bothered human race for centuries.
Some people lost their lives trying to find the cause of this crucial law of nature.
In vain. The puzzle remained unsolved.
It needed the brilliance of Giovanni D., his Italian fantasy, to arrange a proper experiment and find out the truth.
Once more let us visit the gallery of Matejko's work.
The picture below shows Giovanni D. at the moment of the discovery.
Notice the bunch of spaghetti at his feet. Crucial experiments were done before.
What you see is but the moment of illumination: CURVATURE!
Yes! CURVATURE!

Giovanni D. discovers the truth
(based on: Copernicus or the dialog with the God by Jan Matejko)

Matejko, Matejko... Not too much of the Matejko? NO!
He deserves it. It were his paintings that stimulated our imagination where we were children.
Stories told by Matejko's brush get deep into the memory of every Polish child.
For instance, the story of the alchemist Greg B. vel Sedziwoj.
He was an alchemist. But he was different from other alchemists.
They were looking for the philosophical stone. He was looking for the philosophical knot.
He succeeded. The picture shows Sedziwoj showing the philosophical knot to the King Sigmund III.
(I think, it's 4.1. Ideal conformation.)

. Sedziwoj presenting the philosophical knot to King Sigmund III
(based on Sedziwoj by Jan Matejko)

It would be an unforgivable mistake, if you were not introduced to the art of Jacek Malczewski.
His painting is highly symbolic. Things and events you see in his pictures have hidden meanings.
Looking recently at one of the pictures I realized how prophetic Malczewski was.
The mysterious Coronation of the Swiss King of Knots now reveals its sense.
I think I recognize the face of the king. Yes. No doubt. It's Andrzej S.
He accepts the crown with dignity and modesty.
One cannot oppose the will of gods.
Amen.

Coronation of the Swiss King of Knots
(based on Tobiasz i Parki by Jacek Malczewski)

As mentioned above, Malczewski's paintings are full of symbols.
Their meaning was a mystery for his friends. But today all becomes simple and clear.
Have a look at the picture below.
What, for goodness sake, are the balls released by the mysterious gentleman?!
First of all, these are not balls, but holes. Magnetic holes.
The fellow who releases them into this world is Arne S. A Norwegian.
(The Norwegians were always doing strange things!)
Which is the use of them? This you will become clear soon.

Arne S. releasing magnetic holes
(based on U studni by Jacek Malczewski)

Thus. Which is the use of Arne's holes?
This is demonstrated by his former Ph.D. student Geir H.
The holes can be used to plait wonderful braids.
And you know, how ladies are fond of braids.
Look at the girl. She really seems to be interested by what Geir is doing for her.
You may try to do the same for your girls, but mind your feet!
Looks easy. Is not.

Geir H. plaiting a braid
(based on Polonia by Jacek Malczewski)

Sorry, but I cannot help returning to Matejko.
Why? Because in Part IV I recklessly mentioned the CKS proof.
I expressed a bitter opinion that the proof lacks warmth and feeling.
One can understand why is that so.
The work on it was full of violent clashes between the three giants of the knot theory.
Presenting a proof it is not dating a girl, although results may be similar.
The sharp eye of Matejko managed to grab the very moment in which
Jason C. shows his version of the proof to Rob K. and John S.
You may ask, why he put on his armor, why pulled out the sword.
Look at the faces of the other two fellows.
What I see is sarcasm and irony.
It is not easy to be a mathematician. Maybe it is fortunate that I am only a physicist?
(By the way. Do you know who the other two fellows are?)

Jason C. presenting his proof
(based on Wladyslaw Lokietek by Jan Matejko)

A work on a proof of a non-trivial theorem is a fight, sweat (even booze).
But, when the proof is ready - GLORY! The author enters the limelight.
His fellow mathematicians are truly happy. No sign of envy. No more ironic or sarcastic remarks.
Let me present the last, (cross fingers - the last!) of the Matejko's paintings.
It shows the triumph of Jorge C.
He spent days and nights trying to prove that the knot shown in one of the flags does not exist.
Matejko portrayed him in the happy moment at which, blessed by his adviser (on the left), Jorge C. delivers his
proof to the editorial office of Journal of Knot Theory and Its Ramifications.
You may ask why Jorge C. wears this out-of-fashion, heavy duty helmet.
Well. When working with physical knots you should really take precautions.
Remember! I know something about it!

Jorge C. delivering his proof
(based on: Constitution of May 3 by Jan Matejko)