The Chinese Challenge :: 中国挑战

"The Chinese Challenge"-Teamblog is opening up a discussion about a possible new rationality hidden in the Chinese writing. The main question is: What can we learn from China that China is not teaching us? It is proposed that a study of polycontextural logic and morphogrammatics could be helpful to discover this new kind of rationality. Those topics of polycontexturality are presented at my website and at the complementary Blog Rudy's Diamond Strategies. Start with the "Pamphlet".

The Chinese Challenge :: 中国挑战-Video

PAMPHLET Chinese English

New Blog: Diamond Strategies

 

Tuesday, June 10, 2008

Short Studies 5. Diamond Web2.0

How social is social networking?

"
He said, 'For instance, what a student in Guangzhou prefers may be exactly opposite to that of a student in Beijing, and in CityIN we try our best to cater for different preferences'."
CityIn: A Lifestyle Social Networks
Written by Tangosaon March 5, 2008


Questions

– What does it mean for social networking to search for sameness?

– How is such sameness dealing with its opposites?

– Which kinds of opposites do we know, and know to use?

– How global is social networking if it is limited to one and only one world-model?

– What does it mean that Web2.0 is mobile if it is restricted to information exchange with all its features of text, sound, video, and more?

– Will social networking not dry out soon and becoming boring if it is not able to support inter-actional creativity?

– Is it necessary to reduce the Web2.0 possibilities to global Web Services?

The following study is risking a very first approach to such questions by applying the Diamond Strategies.

Towards a Diamond Web2.0?

The Web2.0 understanding of societal activities is based on a non-societal model of hierarchical, mono-centered and solipsistic orientation.

Sociologically, it is based on the dichotomic distinction of the singular private and the plural public. 


A first step to diamondize Web2.0 approaches has not to go into the basics of transforming Web2.0 into the dynamic semantic Web3.0, it would be a reasonable transitional step, first to diamondize the existing technologies and user interfaces of Web2.0.

This could happen along the main metaphors of the Web2.0: social, global, mobile in connection to interactional and reflectional.



The sketched ideas for a diamondization of Web2.0 technologies is taking the slightly futuristic position to propose Diamond Web2.0 from the position of the insights into the emerging Web3.0 and contrasting it from the more traditionalist concepts and technologies of the Web1.0.

In this sense, Diamond Web2.0 could be understood as a transitional concept to a social Web3.0, hence as a Web2.5.



With Chang, I try to avoid the interesting discussion about the technological legitimacy of such a thing as Web2.0. There are enough arguments pro and contra, especially from the standpoint of Web1.0, to deny the technological relevancy of the term Web2.0.

But also from the position of an emerging semantic Web, i.e. Web3.0, Web2.0 is lacking significant conceptual changes to challenge the well known concepts and technologies of Web1.0.

On the other hand, it seems, that enough new features emerged, at least in the general use of the Web, i.e. Web services, to put it together as Web2.0.




A little typology of the development of the Web is sketched. The idea behind this typology is to reflect on the degree of the involvement of the user (subject, reflexivity) into its usage.

It is also proposed that in contrast to the main stream opinion, the difference of surface- and deep-structure of the Internet and its form of usage, is of great relevancy.

Obviously, the pragmatic terminology of use, usage and user is applied, and for Web4.0, deconstructed, against its singularity.

It is obvious that this little typology is not proposing a predictional or futurological typology or design in the sense of Spivak and Kurzweil, but nothing more than a conceptual offer for possible orientations in what is and what might emerge in the future of the Web. 



It seems that such a change in optics, towards conceptual and paradigmatic analysis, is a necessary step to wake up from an enthusiastic but unrealistic dream.

Little typology

1. the information tools using user, Web1.0,
2. the media participant user, Web2.0, 

3. the knowledge producing and sharing user, Web3.0,

4. the paradigm co-creating (interacting and intervening) user, Web4.0.

Content of the Study:

1. Diamond Strategies

2. Interactional diamondization

3. Web2.0 as "social”:: Social networking

4. .................."global":: World-models

5. ..................."mobile”:: Metamorphosis

6. ...................“Interactional and reflectional"

Full Study (in progress!):

http://www.thinkartlab.com/pkl/media/Diamond_Web2.0/Diamond_Web2.0.html
http://www.thinkartlab.com/pkl/media/Diamond_Web2.0/Diamond_Web2.0.pdf

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Sunday, June 08, 2008

Short Studies 4. Which Equality?

How equal are equal human beings?

Abstract

"All human beings are equal”. What does “equal” mean? What are the many definitions of “equal” and “equality"? From a Diamond perspective, concepts of sameness, from equality, similarity, bisimilarity to hetero-morphism and more are sketched in respect to their usage in ethical discourses, e.g Human Rights, of mono-, multi- and trans-cultural formations. What happens in such scenarios to the Golden Rule of ethics? The family of mankind? The brotherhood?

The following Short Study "Which Equality?", might be wrong in time. Things are still sub-human. The human rights not realized at all. On the other hand, what do we understand by equality if this term is defined only in a negative way, i.e. by exclusion of non-equality?

Despite the wrong timing, a conceptual effort to achieve a positive and constructive understanding of equality, anticipating futures to come, appears to be a reasonable entertainment.


Content

1. Interdependency of context and composition

Life under the regulation of equality has stopped to be funny. To do the same, which can have strictly different meanings and significance, can end up in prison, deportation or execution if judged by identity-trained forces and institutions of our free society.


2. Laws in mono-, poly- and transcultural formations

2.1 Mono-cultural formation
2.2 Poly-cultural formation
2.3 Trans-cultural formation

3. Facets of togetherness

3.1 Modi of togetherness
3.2 Equality
3.3 Similarity
3.4 Bisimilarity
3.5 Dissimilarity
3.6 Groups of Diamonds
3.7 The paradox of simplicity

4. The Queer World of the Golden Rule

4.1
Dissemination of GR
4.2
Paradoxes of an Ethics for Others


Full Study:
http://www.thinkartlab.com/pkl/media/Equality/Equality.html
http://www.thinkartlab.com/pkl/media/Equality/Equality.pdf

Wednesday, May 07, 2008

Rudolf Kaehr über Künstliche Intelligenz

You might enjoy to watch some videos about Artifical Intelligence

produced in the early 90s by the filmmaker Thomas Schmitt and myself.

FREISTIL, oder die Seinsmaschine
Mitteilungen aus der Wirklichkeit

http://www.tagtraum.de


Regie Thomas Schmitt, Text Rudolf Kaehr

parts are re-published at:

http://www.vordenker.de/ggphilosophy/freistil.htm

The main thesis is focusing on the necessity of Artificial Living systems for the development of Artificial Intelligence.

Artificial Living systems are conceived as well separated from classical, symbol-based
artificial intelligence research and from neural network developments, which had
been in fashion in the 80s/90s.

In contrast to what we can learn today from experts, the message of these videos is
strictly conceptual and based on the insights of polycontextural logics and kenogrammatics.

Hence, what is still of interest is the idea of a new kind of machines beyond Turing-Machines.

Without doubt, the esthetics is still quite impressive.

Part 1 to 6:
http://tw.youtube.com/profile_videos?user=ggjpspecial

These videos, in German language, are parts from the whole TV-Film "Die Seinsmaschine" broadcasted by the German Westdeutscher Rundfunk (WDR).

Part 1 of the video

Wednesday, April 30, 2008

Short Studies 3. Chez Maxime's

Human rights in a polycontextural world

Excerpts

From another story we might have experienced a first conflict involving ethics. 

"Without doubt, our fish had a knowledge that he was living in water and not a perception; there was nothing to see at all. What he could perceive was his complex world full of strange stuff, and this funny fish girl. But not the water. What the fish girl didn’t know, neither Heinz, was that he properly acted according to Heinz’ CybernEthical Imperative:

"Always act to augment the amount of possibilities of the others!"

But he, our fish, not Heinz, didn’t accept the fish girl’s ignorance to try to reduce the necessities of his insights. Therefore, intuitively, his dual imperative of Heinz’s altruistic maxim came into force.


"Never contemplate to reduce the amount of necessities of yours!"


This dual maxim has to be set into a complementary maxim to conflict the Golden Rule of ethics. This is not simply involving a negation of selfless altruism, hence selfishness, but a first step into a liberation of ethics from ontology. 



Only if we accept the slavery of classical logics, which is declared as universal, natural and ultimate, again and again, we would have to believe that a rejection of altruism must necessarily be an affirmation of selfish egoism. 

The fish was not selfish but true to the alter-ego of his fish girl.



This intricate togetherness of a dual imperative for actions, which always are a composition of actions and never occur in the majesty of a singularity, is highly intriguing and needs, thus, a formalization in an appropriate formalism, like the diamond category theory, which is offering additional space for the togetherness of complementary and antidromic statements.

Therefore, the two imperatives have to be embedded into a complementary and reflectional interplay:


Co-CybernEthics
"Always act to augment the amount of possibilities of the others!"
"Never contemplate to reduce the amount of necessities of yours!"


Universal, fundamental, natural, global

Universal human rights are declared as universally valid and fundamental; as holding universally. What to do, if we don’t belief in a universe in which human rights could hold. What if we belief, instead, not in a uni-verse but in a pluri-verse or a multi-verse or even neither in a uni-/pluri- nor in any -verse at all? Are we then still entitled to be respected by the intentions of the Human Rights?

And if we still are entitled to be respected by the human rights, do we really want to be honored by an idea of humanity, which is stupidifying its members in such a radical way?
Wouldn’t it be a better choice to search for chances of post-technological trans-humanism? 




Co-Article-0:
Everybody has the right to be a human being.
No human being has the obligation to remain as a human being.
Diamondization of the declarations

Article 1

"All human beings are born free and equal in dignity and rights.[...]"



No human beings are born non-free. No free born being is human. No born being is human. All human beings are different in dignity and rights. All dignities and rights are equal to different human beings. All dignities and rights are different to equal human beings. No dignities and rights are equal to different human beings.


Co-Article-1:
All human beings are equal.
No equal is a human being.
Article 2

"Everyone is entitled to all the rights and freedoms set forth in this Declaration [...]."



Nobody is entitled to all rights and freedoms in this Declaration. There is no Declaration for everyone to be entitled to all rights and freedoms set forth in this Declaration. There is nothing set forth for the rights and freedoms of everyone.
Everyone is free. Nobody is free. Nobody is unfree. No free one is everybody. 

Co-Articel-2:
Every one is free.
No free one is everybody.
This game of deconstruction has to be played situatively, every time, until an agreement is reached in the actual group as a result of contextural, i.e., interactional, reflectional and interventional, negotiations.


FULL TEXT: http://www.thinkartlab.com/pkl/media/Chez_Maxime/Chez_Maxime.html

Short Studies: 2. Fishes and Birds

A Tale of Fishes, Birds and Diamonds in Second-Order Epistemology


Why it is useless to speak about the mono-contexturality of alphabetism and digitalism


The Endness of Events

The endness of events in a open/closed world are not simply ending in an unqualified way. Endness has to be connected with rhythms instead of linear or non-linear progressions.

The endness of events in a open/closed world are not simply ending in an unqualified way. Endness has to be connected with rhythms instead of linear or non-linear progressions. 

A rhythm has a beginning and an end; endlessly. An open/closed world is poly-rhythmic. Scientific linear time structures of whatever complexity are without rhythms. Western science beliefs in a 1-rhythm world: from the big bang to the wee crash.


In many papers I emphasized the importance of linearity for the Western way of thinking and its mathematically based technology.

In-between I have the feeling that I always experienced a strange lack of response to my argumentations. In a metaphor, I feel like a fish telling his female fish friend: "Honey, do you know, we are living in water?" And getting the harsh response: "Shut up you wancker, I don’t fancy you!".


OK, not everybody can be mesmerized like Monsieur Jourdain after he learned that he is speaking all his life prose. And not everybody thinks that this is trivial anyway.


For good reasons we can belief that there is no reason to think that the fish girl was stubbern or even stupid. She easily could have pointed to the un-denial fact that there is no such thing like water in the water to perceive.

What is in the water are all these different plants, stones, animals, and surely, other fishes. But no water at all. This is more than clear. There might be some areas where it is harder to swim or where other stuff is moving very fast or areas where nothing is moving at all. The stuff might also move in all direction, at once. And as far as she can swim there is no limit and no reason to stop her swimming. What can be perceived and sensed in her world as a fish are objects of all sorts but not water.

Another approach, which has not to struggle with the problems of the abstractness of the arguments for linearity of alphabetism with its atomicity, abstractness and ideality of signs, could be the more generally acknowledged fact of the endless repeatability of (sign) events.

This concept is independent of dimensionality, parallelisms, circularities, interactions and other seemingly non-linear complex and pictorial or sonic processes and structures.


As for the swimming moves of our fish girl, which are not restricted by any obstacle, to each move there is a next move, and so on. Swimming is producing swimming; only a swimmer is swimming, and no swimming is leaving the category of swimming. Outside of swimming there is no swimming. Swimming adds to swimming, and remains swimming; endlessly. No swimming transforms into flying; no swimming permutes into walking. And so on.



OK, in real-world conditions, the fish girl will stop to swim because of physical limitations of her life-span. The same happens, evidently, to the chalk and blackboards of the high priests of formal systems. The endless iterativity of their sign systems will have, in real-world conditions, unavoidably, some natural ends.

This is in sharp contradiction to the abstractness of the definition of signs and Obs in formal systems.


Nevertheless, repeatability is open and endless. The iterability of repeatibility is stable.

The other fact, we could agree to some degree, is given by the identity of the repeated objects. It may not be a too big challenge to see and perceive, clara et distincta, that this concept of identity is best realized, as Hegel pointed out, by the Western alpha-numeric sign systems.

A number or a letter is as a number or as a letter strictly identical with itself. Take the inscription on your bank note: 5 USDollar. There is nothing to interpret, 5 is 5 and USDollar is USDollar. And nothing else. 




Hence, endless repeatability is realized within the realm of identical entities. Or: identities are realized in the realm of iterability.

There is no identity without iterability and no iterability without identity.

This, again, happens in the ideal world of sign systems, i.e., in the mind of semioticians and mathematicians; and not at the blackboard, nor in citations or plagiarism.



Therefore, if we accept iterability, we have not to struggle with the strangeness of the challenge to be aware of swimming in strange waters. Identity, at least to some degree of fuzziness, and the endlessness of repeatability in all its mathematical forms, seems to be accessible to everyone and understood universally without getting involved with the paradox of the medium we are living in.

Things are getting less natural and universal if we stipulate a pluri-verse instead of a classic universe. But this is a story to come!



It seems that nobody wants to share my linearity thesis. It is said, all over again: The world is hyper-complex, fractal, undecidable and the World Wide Web decentralized and chaotic. Old alphabetism is loosing its dominance to images, pictures, pictograms, videos and sound.

More theoretical motivated guys are talking about cellular automata, parallelism, actor communities, grid computing, etc.
Therefore, there is no such thing as a dominance of linearity and identity in a post-modern world full of paradoxes, parallaxes, ruptures and abysses.



A.A. Markov’s linearity thesis is not only unknown by media scientists but put under the carpet by computer scientists as old foundational fundamentalism (FOL) and bad reductionism.

What to do against such a poverty of thinking?



Simply, change topic!

Give it up! Ask our fish!



Hence, forget linearity! 



Enjoy endless repeatability! The world is rich and complex, and you too. 



And there is also space enough to defend this situation of repeatability before we end up in the paradoxes of self-defence.

[...]


The consequences for the entire paradigm of composability, based, as we learned, again and again, on iterability, are enormous. Not only an absolute new kind of double-compositionability appears on stage, even more.

Primary to all composition, there is the difference between superpositional and antidromic combination. Instead of dealing with superpositionality, interactionality and reflectionality between superpositional and antidromical movements, iter-/alterabilities, are taking place, well positioned in the kenomic grid of Diamond Strategies.


This is really a great relief! 



Forget debates about the monocontexturality of combinatorial logics, their fixation on alphabetism and its linearity and atomicity, as sine qua non of all composability.

Forget the postmodern theater of disseminating colored contextures of repeatability.


Forget the phantasm of our hidden universal mockingbirds in whatever fibered forests.


Listen to the songs of free mating birds! Enjoy your Diamonds!


FULL TEXT: http://www.thinkartlab.com/pkl/media/Fishes+Birds/Fishes+Birds.html

Wednesday, April 16, 2008

Short Studies: 1. Modular Bolognese

Paradoxes of postmodern education.

In a series of small texts, which I'm on the way to publish, I will develop some easy accessible thoughts concerning Diamond Strategies and Diamond Category Theory. I will collect those studies under the umbrella of Short Studies.

With all those studies I will develop some application of the Diamond Strategies to well known topics, like modular education, transdisciplinarity, human rights, Kantian Maxim, plagiarism, fashion and social networking.

The first 4 studies in progress are listed below:
  1. Modular Bolognese. Paradoxes of postmodern education.
  2. Birds and Diamonds in Second-Order Epistemology
  3. Primary thoughts to a Manifesto for Awareness Fashion Marketing
  4. Diamond Web2.0. How social is social networking?
Let's start with the beginning of the first Short Study!
  1. Modular Bolognese –
Paradoxes of postmodern education.

Modules in Metaphors

Without doubt, I like Spaghetti Bolognese. Especially, the Bolognese between the spaghetti. Even more, I like the Bologna Reform, which is unifying European education. As we had to learn, spaghetti in their chaotic wildness are not supporting the desires of clean decomposability and reusability, needed for real-time control and surveillance. Like it happened with ravioli, the Bologna Reform invented the modularity of knowledge for university education. Each topic has to be framed by its module. Each module is cleanly separated from the other modules. Like ravioli, which are coupled only loosely and are building, ideally, a cluster, each module has its own content, structured hierarchically into topics, sections and paragraphs, enabling its specific taste and evaluation. 


[A full-fledged theory of the Pasta Strategies is available at the complete Pasta Theory of Software Development. The present text about Noodles will be published at Moodle.]



But ravioli are nothing without their sauce! That’s obvious and natural for the people of Bologna. But hard to understand north of the Alps.


What are we doing with the sauce? Is it simply another module? But how can the in-betweeness of modules in a modular system be itself a module? This contradicts academic logic; it maneuvers you immediately into headaches of logical paradoxes.

If the module between the modules is itself a module, what is the in-betweenness between this conglomerate of modules, such a meta-module, and the original modules themselves? A meta-meta-module or simply nothing? Or is it the para-module of fluidness and fuzziness, defined by Water Logic? Do we need a proto-module to manage this new inter- and trans-modular wilderness?

What happens if the sauce between the ravioli becomes a sausage?Is the sausage an ultra-module? It belongs to the modular system exactly if it doesn't belong to the modular system. The sausage is a module exactly if it is a ravioli and at the same time it is a ravioli if it is a sausage.

And by the way: Is the logic of this argumentation itself a module or is it superior or prior to all modules? Is it a a module with its own subversive logic or simply a pseudo-module? 
There are not many chances left to solve this paradoxical problem. One radical strategy tells you: Eat the sausage and forget the problem!

Yes, but what are we doing with a ravioli Bolognese without sauce? We simply could smash the dry ravioli into the bin. All problems solved!


But there is another solution too: Mediate the ravioli and the sausage with a brand new sauce, well mixed, half ravioli and half sausage. This strategy has a safe legitimation and is best evaluated by the tools of Fuzzy Logic. 



Unfortunately, the Fuzzy Strategy is of short reliance as it is demonstrated in my Warentest paper, which is probably the very first evaluation of the reliance of logical systems for interactive devices in commercial telecommunication.

Ok, the game has to go on. Why not introduce, just for academic reasons, a new mega-sausage between the ravioli and the first sausage and the ravioli and the mixed – fuzzy based – sauce consisting of ravioli and sausages between the real ravioli and the real sauce Bolognese? But what’s real in such an administrational intervention? The sauce, the ravioli, the sausage or the content in the ravioli or the European administrators of the ravioli complot?

Even worse, a good Bolognese is not a homogenous module, it is in itself full of well-balanced differences of overlapping interactions of different strength. 

Hence, the interplay between ravioli is not modular but sub-modular. Ravioli are building 3-dimensional clusters, and only a few of them are showing a flat hierarchical order of composition. It is more than clear, that the content of a single ravioli Bolognese is of no interest at all. What is of interest is the clear cut distinction between the shape and content of each ravioli and the disjunctive separation from other ravioli.


Nevertheless, each single ravioli has to pass a general test of quality: measure, weight, taste, design, originality. The evaluation is general or even universal because each ravioli is tested by strict scientific and objective quantificational methods.

There are surely differences in the general cluster, there are ravioli for the beginner, ravioli for the advanced and ravioli for the post-docs and ravioli for the tester and ravioli for the administration, etc. And all are fitting well into the European ontology of modularized knowledge taxonomies and ontologies and the qualifications of the generalized European user of the Semantic Web.

FULL TEXT here.

http://www.thinkartlab.com/pkl/media/transMODULE/transMODULE.html

Saturday, July 14, 2007

Chinese Ontology


An Aperçu


Chinese ontology (cosmology) can be put into two main statements:

A. Everything in the world is changing.

B. The world, in which everything is changing, doesn't change.

This two main statements are designing a paradoxical constellation.


Hence,

1. The finiteness of the world is not closed but open.
Because of the changing statement (A) the finiteness (B) is not static.
"In a closed world, which consists of many worlds, there is no narrowness. In such a world, which is open and closed at once, there is profoundness of reflection and broadness of interaction." (The Book of Diamonds, Intro)

2. Everything in the world is connectable.
Because of the finite structure of the world, entities are accessible in many ways.

3. Connections are bi-directional.
Because of the finiteness there is no uni-directionality in linear time.

4. Bi-directionality is chiastic.
Because the world is changing, the way back is not exactly the same as the way forwards. This is defining the heterarchic grid structure of the world.

5. The modeling process of Chinese ontology is not phono-logocentric.
Because of the paradoxical character of the "ontology" it can not be represented by phono-logical statements of identity-based mathematics and logic.

Therefore,

6. Because it is written in logical sentences, this aperçu of a definition of Chinese ontology is a paradox metaphor.

7. A first operative description and formalization of Chinese ontology is proposed by the Diamond Theory, which is in a trans-phonological sense a paradox.

8. Diamond theoretic paradoxy is positively inscribed in Diamond Theory as the interplay, i.e., chiasm, between categories and saltatories. Saltatories are complementary to categories. Complementarity is not duality.

9. The structure of the interplay (chiasm) of categories and saltatories in Diamond Theory is defined by the proemial relationship.

10. The proemiality of the proemial relationship is inscribed as an interplay between order-, exchange- and coincidence relations, distributed over different loci.

11. Because of the finiteness of the world Diamonds have a location in it. The location (position) of Diamonds is inscribed by their place-designators.

Thus
,


12. The self-referential paradoxy/parallaxy of the metaphor of Chinese ontology is realized by the operative calculus of Diamonds as an interplay between categories and saltatories of Diamond Theory.


Thursday, July 12, 2007

The Complementary Blog: Diamond Strategies

Have a look at the complementary Blog to the Chinese Challenge Blog:

Rudy's Diamond Strategies.

The new Blog is presenting, step by step, new insights into the mathematical theory of Diamonds.


Chiasm (Categorification, Diamondization)

Diamond: 2-graphs with 2-structures
i) Data: 2-diagram C1–s,t––>Co/Co<–diff–C1 in 2-Set Objects in diamonds are involved into 2 operations: coincidence and difference. Coincidence is producing composition and therefore commutativity.
Differences are producing hetero-morphisms and therefore jumpoids.

ii) Structure: composition, identities + complement, differences

iii) Properties: unit, associativity + diversity, jump law

iv) Interaction: Chiasm between category and saltatory.

"In ordinary category theory we have 1-dimensional arrows ––>; in higher-dimension category theory we have higher-dimension arrows."
"...n-categories are studying morphisms between morphisms." Tom Leinster
Hence, Diamond theory is neither studying linear ordered arrows nor morphisms between linear ordered arrows but the complementarity of morphisms and hetero-morphisms, acceptional and rejectional morphisms, i.e., the relations between the operation of composition and its complementary morphisms.

In this sense, diamond theory is studying 2-dimensional, i.e., tabular categories, independent from the questions of n-categories or others.

Thus, diamond theory is the study of tabular categories as an interaction of categories and saltatories. Saltatories are the complementary diamond structures of categories.

The term interaction is correct because the interplay between categories and saltatories happens inside the diamond definition and is not only a meta-theoretical fact like the duality of categories in category theory.

Compositions as operations are not thematized in Category theory but only their result, which are new morphisms.

Diamond theory is thematizing the activity of the composition operator not as a morphogram but as a complementarity to the operator, implemented as a hetero-morphism.

Diamonds are thematizing the basic operation of category theory as such: the operation of composition. The thematization is modeled into the hetero-morphisms.

In a general setting of graphematic analysis of composition the morphogrammatics of the operator "composition" has to be taken into account, too. That is, the neither-nor gesture of categorical object and morphism has a double face: hetero-morphism and morphogram of composition.

As Categories can be generalized to n-Categories, Diamonds can be generalized to n-Diamonds.

Topics
Category Theory:
object/morphism
n-Category:
morphism/morphism
Diamond Theory: categories/saltatories.