dialogue on integralism symbol

7/27/2019 dialogue on Integralism Symbol

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DIALOGUEDIALOGUEDIALOGUEDIALOGUE

ON INTEGRAON INTEGRAON INTEGRAON INTEGRALISM SYMBOLLISM SYMBOLLISM SYMBOLLISM SYMBOL

BYBYBYBYARMAHEDI MAHZARARMAHEDI MAHZARARMAHEDI MAHZARARMAHEDI MAHZAR

http://integralisme.wordpress.com


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Dialogue on integralism symbolDialogue on integralism symbolDialogue on integralism symbolDialogue on integralism symbolPart OnePart OnePart OnePart One

Ni Suiti and Ki Algo is my Anima and Animus which are

the feminine and the masculine unconscious subpersonalities

within myself. They are always in continuous conversation.

even if I am in the front of one of the million eyes of the

giant Tenretni and fingering her YTREWQ fingers.

In the following, is the dialogue of them concerning

the picture that I put as myself in the my blog

integralist.multiply.com. The Q(uestioner) is Ni Suiti and

the A(nswerer) is Ki Algo. Hopefully you can all enjoy it.

Here we go!.

Q: What is the picture that Arma used as his blogidentification?

A: Thats a part of a geometric pattern in the coverof his first book : Integralism.

Q: What geometrical pattern?

A: Aperiodic tesselation.

PERIODIC TESSELATION:

CRYSTALS

Q: What is tesselation anyway?

A: Tesselation is the covering of infinite planewith a finite set of tiles. If the tesselation periodic,

from infinitely many possible regular polygons


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only three can tile a plane periodically: triangle, square and

regular hexagon. Periodic tesselation means that you can shiftthe tiling pattern translationally to get the same pattern

We have 3-fold rotationally symmetric tesselation

and the 4-fold rotationally symmetric tesselation

and the six-fold rotationally symmetric tesselation


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There are exactly 17 possible tilings of the plane

with 3, 4 and 6-fold rotation symmetry. 13 of themcan be found in Alhambra (I see it in here )

The combination of triangles, squares and hexagons

can make a periodic tesselation such as

Q: Beautiful!. All of them is periodic, meaning

you can shift the pattern and get the same pattern.

I see it in many mural decoration in islamic mosques and palaces

and it can also be found naturally in the structure ofall crystals. But your pattern is not periodic.

APERIODIC TESSELATION:

FROM 20.426 to 2A: Thats why I call it aperiodic, following the

tradition of mathematics literature.

Q: Why do you interest in such tile?

A: Well, an article in Scientific American in the 60s

was caught in Armas eyes. It was written by thelogician Hao Wang. He asked if an infinite setof finite kinds of 2-way square color domino can

fully cover all the plane periodically. It is calledtiling problem.

Q: But the tile in Armas integralist symbol are

not square, right?

A: Please do not interrupt me. The story to followis an amazing story of mathematical simplification.


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It began in 1966 when Robert Berger demonstratedthat the question Wang asked is unanswerable.

Mathematically the periodic tiling problem is in fact not

decidable. He proved that if a finite kinds of tile can be

used to cover all the plane, then it can not be filled in

periodically. Such tiling called aperiodic. To proveit, he construct very large set of prototiles consisting

20,426 prototiles. He showed that that they cantiles a plane aperiodically. Fortunately, he was able to

reduce the number of aperiodic tile

to relatively small set containing 104 tiles.

Following Berger discovery, there is a rush of simplifications

of the prototiles set. For example in 1968 Donald Knuth was

able to reduce the number to 92, then Robinson reduced it in 1971 to 35.

Roger Penrose improved it to 34. Robinson made more improvementby reducing to 24. Karel Culik II finally in 1996 gave an example of the set of 13 tiles

which tile the plane aperiodically.

By allowing rotation, Robinson had been able to reduced the number

of prototile to just 6 tiles as it is shown in the following

Amazingly, three years later in 1974, the well known

UK physicist, Roger Penrose had been able to reduce

further the total number of required prototiles to just 2.The trick is to change the shape of the tiles from

squares to rhombi. Well for me it is very impressive,

reduction from more than 20,000 to only 2 in lessthan a decade.


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The two rhombi are the thick and the thin ones.Let us call them Thicky and Thinny

By joining the edges of thickies and thinnies we can form

the following tesselation covering the infinite plane

Q: See, it is interesting but it is not the same as

your integralism symbol.

A: Well, the Penrose rhombi can be each cut in halfand rejoined edge by edge to form these Penrose

Kite and Dart tiles. Joining two halves of Thinnymakes the Dart and joining two halves of Thicky

makes the Kite:


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we can form the following aperiodic tesselation.

I hope you will see that my integralist symbol is nothing but a subconfigurationof the above tesselation.

Q: OK. I see it now.

It is wonderful. It is Mathematical.

Mathematics is beautiful.

But it is really unnatural.There is no such pattern in the crystal.


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Well, I could hardly hear what Ki Algo said in

answering Ni Suiti. I think he was mumbling,

and there was long silence after that.

I will try harder later to eavesdrop their conservation

and report it to you to be enjoyed. See you next time.


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Dialogue onDialogue onDialogue onDialogue on integralism symbolintegralism symbolintegralism symbolintegralism symbolPart TwoPart TwoPart TwoPart TwoNi Suiti is my Anima who loves visual arts, chemistry and geometryand Ki Algo is my Animus who loves music, physics and algebra.They are still discussing my integralism symbol in the cover of myfirst book which is factually a Penrose tiling. In the followingdialogue S is for Suiti and A is for Algo. Let us see, what are thefacts known by Ki Algo on the realization of Penrose tiles in nature.

PHYSICAL REALIZATION:

QUASICRYSTALS

S: Armas symbol for integralism is a Penrose tiling and it isbeautiful alright, but it is just a mathematical game. I think

it will not appear in nature such as the 17 patterns

of periodic tiles appear in crystals. It is forbidden. Am I wrong?

A: Well, you are wrong. It is true that there are only 17 patterns of crystal symmetry,

none of them have 5-fold rotational symmetry, but exactly one year afterthe publication of Armas first book Integralism, the physicist Dan Schechtman

announced the discovery of a phase of an Aluminium Manganese alloy which

produced tenfold symmetric X-ray diffraction photograph. It may be similar tothis photograph.

This symmetric pattern can only be explained if the atoms arearranged aperiodically in the form of three dimensional

generalization of Penrose tiling as it is discovered by

the amateur mathematician Robert Ammann.


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S: So, I am sure that they are not crystals. What are they?

A: Steinhardt and Levine, shortly after the announcement of Shechtmans discovery,

used the term quasicrystal By the end of the 1980s the idea of quasicrystal becameacceptable and in 1991 the International Union of Crystallography amended its

definition of crystal, reducing it to the ability to produce a clear-cut diffraction patternand acknowledging the possibility of the ordering to be either periodic or aperiodic.With the new definition, quasicrystal is just a kinds of crystal: the aperiodic crystal.

S: How many types of quasicrystal are there?

A: In the same year of Schechtman publication, Ishimasa and coauthors

published their discovery of twelvefold symmetry diffraction pattern of Ni-Cr particles.Soon another equally challenging case presented a sample which gave a sharp

eightfold diffraction picture. Lately, a team led by An Pang Tsai from Japans

National Research Institute for Metals in Tsukuba has discovered quasicrystals of

cadmium- ytterbium that are stable and exhibit three-dimensional icosahedral symmetry.So there are four types of quasicrystals:

8-fold or octagonal symmetric quasicrystals

such as

lV-Ni-Si

Cr-Ni-Si

Mn-Si

Mn-Si-Al

Mn-Fe-Si

10-fold or decagonal symmetric quasicrystals

such as


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Al-Ni-Co

Al-Cu-Mn

Al-Cu-Fe

Al-Cu-Ni

Al-Cu-Co

Al-Cu-Co-SiAl-Mn-Pd

V-Ni-Si

Cr-Ni

12-fold or dodecagonal symmetric quasicrystals

such as

Cr-Ni

V-Ni

V-Ni-Si


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Dodecahedral symmetric quasicrystals

such as

Al-Mn

Al-Mn-Si

Al-Li-CuAl-Pd-Mn

Al-Cu-Fe

Al-Mg-Zn

Zn-Mg-RE

Nb-Fe

V-Ni-Si

Pd-U-Si

S: Beautiful, but whats the use of quasicrystals technologically?

A: Until now there are several applications, for example

thin film quasicrystal coating are used as a non-stick surface for saucepans.

razor blades and surgical instruments are made from quasicrystalline material

Quasicrystals have also been associated with hydrogen storage

Metallic alloys are reinforced by deposition of icosahedral particles

to improve the materials ability to withstand strain

S: I wonder if quasicrystal patterns also occur in cultural artifacts in history?

A: I think you can asked Armas friend Tenretni immediately

I think we have to wait what Ni Suiti find as her answer.Bye, for now.


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Dialogue onDialogue onDialogue onDialogue on integralism symbolintegralism symbolintegralism symbolintegralism symbolPart ThreePart ThreePart ThreePart Three

In the previous dialogue, Ki Algo was explainingmathematical and physical aspects of my integralismsymbol. In the following dialogue, Ni Suiti reporther findings of the cultural realizations of theaperiodic tiling in history. Listen!

CULTURAL REALIZATION:

ISLAMIC ARCHITECTURE

A: Hello Suiti. Do you have some answers from my giant fried Tenretni.

S: Yes, she told me that the physicist Peter Lu from Harvard University did

some field research in Iran, Turkey, Azerbaijan and India and found a surprising factthat Islamic maths was 500 years ahead. See ABC News in Science webpage

http://www.abc.net.au/science/news/stories/2007/1855313.htm?ancient .

A: Thats big news, but the data is too little to be significant.

S: There are so many discoveries To convince you I will list some of the strange

ancient artifacts chronologically ordered. The decoration of the artifact

is in the leftside and the aperiodic pattern is in the rightside.

The Gunbad-i Kabud tomb tower in Maragha, Iran (1197

CE.),


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Abbasid Al-Mustansiriyya Madrasa in Baghdad, Iraq (1227-34 AD),

The Ilkhanid Uljaytu Mausoleum in Sultaniya, Iran (1304 AD),

The Mamluk Quran of Sandal (1306-15 AD)

The Mamluk Quran of Aydughdi ibn Abdallah al-Badri (1313 AD),

The Timurid Tuman Aqa Mausoleum in the Shah-i Zinda complex in Samarkand,

Uzbekistan (1405 AD).


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the Ottoman Green Mosque in Bursa, Turkey (1424 AD),

The shrine of Khwaja Abdullah Ansari at Gazargah in Herat,

Afghanistan (1425 to 1429 C.E.) (3, 9),

The Darb-i Imam shrine in Isfahan, Iran (1453 CE)


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The Friday Mosque, Isfahan, Iran (late 15th century AD).

A: Wow! So many forms in ancient artifacts structurally similar to the postmodern

physics discoveries. Where do you find such data?

S: The above information are from supporting online material for the article inthe magazine Science 315 (2007), 1106-1110 by

Peter J. Lu and Paul J. Steinhardt,

Decagonal and quasi-crystalline tilings in medieval Islamic architecture,

The article is also available online in one of the author webpagehttp://www.physics.harvard.edu/~plu/publications/

A: I think, only scientists will read the article.

S: Oh no, the findings are so surprising, so it was reported all around the world in newspaper,magazines, radio and television broadcasting

Firstly in Lus campus

http://www.news.harvard.edu/gazette/2007/03.01/99-tiles.html

But there is also an article in New YorkTimes

http://www.nytimes.com/2007/02/27/science/27math.html?hp Another in Newsweek International

http://www.msnbc.msn.com/id/17553752/site/newsweek/

The BBC news in bahasa Indonesia is inhttp://www.bbc.co.uk/indonesian/news/story/2007/02/070223_geometricislamicart.shtml

The list for other worldwide news on the discovery can be found in Peter Lu webpagehttp://www.physics.harvard.edu/~plu/research/islamic_quasicrystal/


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A: Oh my goodness. I have never expected such explosion of news.

Its very exciting. Ive never known that art, mathematics and physicshas such a common underlying form.

I hope you enjoy my report of eavesdropping

Ki Algo and Ni Suiti dialogues.I will report more on their dialogues,if I find something interesting to be sharedin cyberspace.See you later


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Dialogue onDialogue onDialogue onDialogue on integralism symbol:integralism symbol:integralism symbol:integralism symbol:Part FDourPart FDourPart FDourPart FDour

In the last dialogue, Ni Suiti was explaining her discoveries in the answers of the she-giant Tenretni about the aperiodic pattern by the ancient muslim architects. It surprisedKi Algo. The following dialogue is their philosophical reflection ignited by such surprisingdiscovery.

A:Why did aperiodic tiling has so many realizations? The concept, as mathematical entity, isrealized in the mind of mathematicians. Afterward, it was discovered that it is realized physically

in quasicrystals.

S:

Astonishingly, it has also been realized in the mind of muslim architects for about fivecenturies. Because it is discovered in nature, then it should be there before it exists in the

mind of mathematician or even the architects. How can it be?

A:

Looking at these facts, I think the aperiodic tiling pattern is outside human mind and it is

also outside natural world. I suppose that it must be in some kind of Platos World of Ideas

of Mathematical Forms.

S:

Well, if it is really there in the outside, it seems to me that it can be intelectually seen with

our minds eyes mathematician sees them because they use their intuition. With the sameintuition, they accept undefined concepts and underived axioms of any mathematical

formal system such as geometry and arithmetics. The traditional muslim architects saw it

there first because their remembrance practice, so their intuitive eyes are clear so the

remember the form first before the mathematician. Plato called it anamnesis

A:

Well, reflecting more deeply, I see that your analogy begging a question. If our mind can


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see the form behind the thinks we see, can the mind also see the Forms behind the

forms behind the things with our innermost eye?

S:

The eyes that is behind the mind eyes behind the physical eyes arethe spiritual eyes. But

what is the FORM behind the Mathematical Forms behind the physical forms?

A:

Let me guess. All geometric forms are generated by using simple rules. I think there is the

Forms behind the forms. I can discover it with logic. You can say that I see it with my

minds eyes. But I can see it deeper. I see a FORM exists behind all the logical generating

rules namely all your Forms. It is structured set of relations between all the rules. It is the

principle behind the rules. For such formal rules, the principle is symmetry. Periodicity is

just one kind of symmetry. In fact, the aperiodicty of quasicrystals can be described as the

projection of periodicity in higher dimensional space.

S:Periodicity in space is like musical rythm in time. In music, the rythm is the framework for

the melody. The counterpart of melody in space is the mutual transformations of material

forms. Thats it the mathematical forms is forming a the great symphony within what the

ancient muslim philosopger called the knowledge of God.

A:

Thats a good metaphor. But what is the real reality?

S:

The symmetry is the mathematical version of Beauty. The Beauty is the ultimate value

beyond our world but penetrates to our world. Philosophers like to call such beyondness as

transcendence and such penetrateness as immanence. Religious person call the Ultimate

Transcendence as God. Beauty is just one of the characteristic of the Ultimate

Transcendence.

A:

What are the other ones?

S:

The other characteristics of the ultimate transcendence is Truth and Goodness. Without

Truth we can not get science. Without Goodness we can not have dynamically ordered

society. The Goodness in society is Justice. If the Beauty manifest in the symmetry, The

Truth manifests in the consistency and the Good manifests itself in the optimality.

A:

What an enlightening vision!

S:

Beauty, Truth and Goodness as the Atributes of the Ultimate Being are universal entities


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which are realized differently in different cultures. But they are also realized universally

and naturally in different forms of matter as natural Symmetry, Consistency and

Optimality.

A:

How can we see such Universal Trio?

S:

The important thing is to know how do we see Beauty, Truth and Goodness. Symmetric

Beauty can be realized by emotion or feeling, Consistent Truth by reason or Logic and

Optimal Goodness by intuition.

A:

Yes, I think we see such immaterial things through feeling, reason and intuition. But all

those immaterial things is revealed in material things which we can see with sensation.

S:The late psychologist Carl Gustaf Jung said that those are the fundamental psychological

function: (1) sensation, (2) feeling, (3) thinking and (4) intuition. Arma think that they are

correlated to (1) matter, (2) energy, (3) information and (4) values respectively. We sense

matter, feel energy, think information and intuit values. So, the fundamental psychological

functions are correlated to the four categories of relative substances in integralism.

A:

What Arma did not k

now is that you are the archetype of Intuition and I am the archetype of Logic. He also did

not know that your grand-daughter Si Nessa and my grand-son Si Emo is the archetypesthe archetype of Sensation and Feeling respectively.

It is surprising to me that beside the two eldery archetypes, Ni Suiti and Ki Algo, thereare two child archetypes, Si Nessa and Si Emo, who are accompanying them.Pondering on the names of those archetypes, I finally found out that their names are theanagrams of indonesian terms related to the four psychological function that was listedby Carl Gustaf Jung. Wow! Can you find it? See you later.


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AfternoteAfternoteAfternoteAfternote onononon integralism symbol:integralism symbol:integralism symbol:integralism symbol:

Dan Shechtman had obtained his Ph.D. from Technion Israel

Institute of Technology, and in 1983, he managed to get Ilan Blech, a colleague at his alma mater,

interested in his findings of the "forbidden" 10-fold symmetric diffraction pattern.


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Together they attempted to interpret the diffraction pattern and translate it to the atomic patternof a crystal. They submitted an article to the Journal of Applied Physics in the summer of 1984.But the article came back seemingly by return of post the editor had refused it immediately.

Shechtman then asked John Cahn, a renowned physicist who had lured him over to NIST in the

first place, to take a look at his data. The otherwise busy researcher eventually did, and in turn,Cahn consulted with a French crystallographer, Denis Gratias.

In November 1984, together with Cahn, Blech and Gratias, Shechtman finally got to publish his

data in Physical Review Letters. The article went off like a bomb among crystallographers. Itquestioned the most

fundamental truth of their science: that all crystals consist of repeating, periodic patterns.

After a long waiting time, the Nobel Prize in Chemistry 2011 was finally awarded to Dan

Shechtman "for the discovery of quasicrystals".

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