The Quran As a Complex System

Concinnity & Modularity

A concinnity, which we defined in a previous video, describes how a thing is a synthesis of many other things. The meaning of a concinnity is distinguished by the fact that it comes from other concinnities. I.e it’s a certain configuration whose constituents are also concinnities, linked by a state called modularity. I,e I understand a sentence, a grammatical unit as a configuration of words structured in a certain way, a subject, predicate, conjunction etc.. a sentence in this case, only insofar as it comprises the above, is meaningful.

You may ask, aren't all concepts, then, concinnities?, 

Yes, but a concinnity is the meaningful position which a certain concept merits in a specific systematic whole. Thus a sentence is a concinnity insofar as we’re talking about the system of grammar in which a certain systematic relation holds between a sentence and a word, a clause, a morpheme. The concinnity of a term is invoked when the class of terms of which it is a member is also invoked. However, the full meaning of concinnity is consummated when a term, even when not the focus of the phrase, still gives meaning, albeit elliptically, in virtue of its membership and by extension ‘instrumentality to the class. in the same way that the number 3 is meaningful with respect to 6 though it’s 6 that’s being asserted.  Thus when made the focus, it’s the whole, but when something else is made the focus it becomes instrumental to it.

In this same fashion, are the chapters, or, as we call them, concinnities of the Quran are structured. The Chapter titled The Cave (18), will be found in other concinnities in which it’s not the main focus, though its core function as a concinnity, its modularity cannot be attained before we've abstracted its modulus, which of course can only be done by understanding the chapter, i.e by defining it in terms of other concinnities, the relative proximity of some and relative remoteness of others, and discerning the certain hierarchical expression that results from emphasis on this or that component-- or what’s generally known as ‘self-organizing criticality’, which defines a state whereby, given a particular system, the meaning of any component, is tantamount or coterminous with the specific way in which the rest of the components of this system are arranged. 

For example, we say that a specific circumstance conditioned such and such event, that a situation is auspicious or conducive to a certain activity, but conducive to such a degree that by its mere presence or indication the event is directly implied, and vice versa. Rain explains, the self-organizing criticality of the constituents of the phenomena whose ‘product’ is rain, i.e. the clouds, condensation of vapor, precipitation, warming and evaporation, convection, temperature, etc.. Here the phenomenon ‘rain’ is interpreted through a method analogous to that of algebraic factorization, reducing rain into its constituents, and arranging them into a logical series, likewise, we can rightfully, substitute rain with precipitation, and note how through our given familiarity with the general phenomenon summed up as ‘rain’, the rest of the components arranged themselves differently than the first time, and have done so in such a way as to specifically express precipitation; Here rain, what eventually is to happen, becomes an index through which precipitation is ‘gauged’, and precipitation, as well as all other phenomena, take a logarithmic form in relation to rain. This modularity applies to any and all components of a compact system

The interpretive methodology of the Quran does not differ from this, as in both cases, whether it's statistical analysis, physics, or applied mathematics, since in all these cases we’re dealing with compact systems. The meaning of a particular chapter is a certain sum of all the rest. 

Everywhere in the Quran, we come across the number 7, a number though it is, we find it used in an oddly conceptual or thematic sense, for example, Seven Heavens and Earths, seven ears of grain, seven seas, seven gates, seven cows, seven years etc.. this has to do with the symbolic value accorded to the concept of number in the Quran as opposed to the technical one known to conventional mathematics, we discussed this in a previous video. We find here that the use of the number, 7, as a speculative instrument in verse 22 of chapter 18’s ‘The Cave’ is quite unorthodox from the perspective of conventional math, why should the number of the cave sleeper matter to the speculators who we read built what to us is a research institute or lab dedicated to the study of this phenomenon, what does their number reveal?, as we see, to conventional math, such detail is no more than a statistic, and thereby of secondary importance to the physicist whom such a phenomenon concerns?

This use of numbers, however, is no longer unorthodox once we turn

to the Quran, as we find that everywhere in this book, propositions pertaining to numbers are used in a way that accords with how we think and experience things in general; all experience is of the same sort, in that they’re only ever measured in one way, by how complete it is, i.e logarithmically. The number of something here refers to how ‘turing complete’ it is,  

"Turing complete" refers to a system or computational model's ability to simulate a Turing machine. It’s the notion that certain foundational elements or principles are sufficient to encompass and simulate the complexity of broader systems or phenomena. It reflects the notion that simplicity at the core can give rise to intricate and comprehensive outcomes.

Or to cite an example from the very area from which this idea was abstracted. 

The perfect interdependency of computer hardware components is crucial for the seamless functioning of a computer system. A central processing unit interprets and executes instructions, to do so it requires a memory unit in order to store and retrieve data, this function is fulfilled by the RAM, which stores data and instructions, for quick access by the processor, and together they read, write and encode data. But the reading, writing, and encoding of data requires a medium that can host those operations, this is handled by the storage. Now the three processes, in order to work together, require a physical medium, a hub or circuitry by which to coordinate the ceaseless traffic of information, the motherboard. The instructions generated by the processor require input systems, the keyboard and the mouse, and an output source, the monitor, and another output to represent digitally all our inputs, this is carried out by the graphical processing unit. All these complex operations are meaningless without a power supply and a cooling system that regulates the temperature produced by the system. 

It’s in this sense that anything can be called complete, and number, in this case, is a measure of the function of the system at any given point of its operation. We notice here that all the components are united in their objective, embodied in the central processing unit, to represent an algorithm, but at the same time, we see that in this objective is contained the notion, of a medium or mediums specializing in tasks which the processor does not cover, we ask logistical questions, namely, ‘‘how are we going to represent an algorithm’. To represent an algorithm is too general that its actualization requires the deployment of other specialized components. It’s this distance phenomenon which gives the idea of completeness its significance. On the other hand, we face the same predicament, the same proviso, whatever the medium of choice happens to be, i.e a keyboard which primary task is to key in language units, requires all these other mediums in order to function. We also see that all mediums, however parochial or general their functions happen to be relative to each other, are all united in their objective to ‘represent an algorithm’.  The fact that the processor is the component in which this simple objective is embodied, we can say that, because certain components of the system assume a more general role compared to others, and other more specific or parochial roles, that this is how we can represent them numerically. 

Given that all the components share a single objective, which on assessment, we find to be the spectrum on which the rest of the functions are arranged, and that the relation between the objective and each of the components is symmetrical, i.e  goes only one way, for instance, we can say that a keyboard, which has its own objective, to key in language units, that the overall objective ‘represent an algorithm’ can also be said to be its objective. However, the opposite, namely, ‘keying in language units’ could not be asserted with respect to the system as it’s not inclusive enough as to be true of each and every one of its components, unless we generalize that function, i.e, to speak of the keyboard as a system in itself, in which case we are to think of the keyboard exclusively in terms of its own constituents, i.e the keys, the key switches, keycaps, circuitry, etc.., only by objectifying the keyboard in such a way can we hold it to be ‘The system’, however, once we take a more general standpoint, and consider the system in which the keyboard is a mere component, we defer that superordinate position formerly given to the keyboard, over to whatever the keyboard is instrumental to. This position is what’s symbolized by the number one. What remains true at the highest level, and consistently as the system grows more complex and diverse. 

Thus only what’s true of all the system at large can be called one. 

The fascinating part is that this system need not be a computer system, but anything that can be called a system, anything that can be called ‘turing complete’ or judged by the criterion of completeness, which is everything, an atom in this sense is every bit as ‘turing complete’ as a computer system, as a water droplet, a snowflake, a human society, the wing of a fly. It’s this universal standard that allows us, as Husserl says, to equate, compare or count things of radically different kinds, 

For the formation of concrete totalities, there actually are no restrictions at all with respect to the particular contents to be embraced. Any imaginable object, whether psychical, abstract, or concrete, whether given through sensation or phantasy, can be united with any and arbitrarily many others to form a totality, and accordingly can also be counted. For example, certain trees, the Sun, the Moon, Earth, and Mars; or a feeling, an angel, the Moon, and Italy, etc. In these examples, we can always speak of a totality, a multiplicity, and of a determinate number. The nature of the particular contents therefore makes no difference at all. — ‘Philosophy Of Arithmetic’, Chapter 1, section 10–20.

The reason we’re able to perform this is because this faculty of enumeration which we said is different from normal counting, is rooted in the thinking subject themselves. It’s also what enables things to interact with one another, , it’s because an interaction between two radically different things is possible only in the presence of a third which superordinates them, we find this idea in Hegel’s system. This notion of completeness allows us to speak of the number of individual objects, for instance, the number of A laptop, like the one that i’m writing this on, which may seem contradictory, but makes total sense if we reflect that number here is an index that represents how ‘complete’ an object is. If i ask the number of a computer system, I’m in essence breaking it down into its parts, assessing the exact state in which the system happens to be at that moment in relation to what I presuppose to be its overall objective, thus, if I say 7, I’m not proposing seven different computer systems, but one of the above-described levels at which a computer system is said to operate. 

The numbers are here differentiated by determining what relations are more inclusive and general, and we, in turn, ascertain that by identifying the different modes of dependency and shaping them into a hierarchy, a pyramid seems appropriate, at the bottom most of which would set the most general and universal process, the processor, and at the very top, the least general, i.e the most specialized or intricate, which tends to be the least general.