Syneces
A synex is, simply put, the path drawn between any entities in the Worldtree. This seemingly trivial definition hides a wealth of interesting and illuminating structure.
Indeed, syneces are the source of all structure in the Worldtree — the reason for this is straightforward, but will require us to go back to the definitions. Since a semon is by definition undifferentiated, any two sema’s existence as separate entities hints at a disconnect between them (ie, an asymmetry). Hence, a plurality of sema requires that each be located on its own branch of the worldtree, with the respective and unambiguous signature determining its genealogy. As we already know, a synex is a pathway linking two entities (sema, systems and whatnot) together; so, given the shared origin of all sema, it’s no surprise that any such one has at least one synection to every other entity in the worldtree — that’s the reason why we shouldn’t speak of them as a primitive (there’s no such thing as “the synex”, but “a synex between A and B”). Suppose then that we have a synod with two sema and somewhere else a single semon; it is clear that each sibling from the first synod will have a different set of synections to the second semon (even if they differ by a single digit in their signature). If, ad absurdum, they were to share all the same synections, how could they possibly be distinguished from each other? Remember that sema have no intrinsic features of their own, being all essentially (but not contingentially) the same; it’s only through this particularity (their signature) that we are able to tell them apart, and it’s the arrangement of sema in their respective branches of the worldtree that determines the syneces that each will enable. Very roughly speaking then, we can say that a synex is a conversion factor between entities; it is not a thing as much as a relation between things. In mathematics, proofs, transformations (or morphisms in Category Theory), equations (or inequalities) and algorithms are all instances of syneces; and in linguistics, all translations between different languages are effected through them. This becomes even clearer once we look at their symbolic representation — they appear as simply two signatures weighed against each other, like in the following example:
10110:1101
Example of a synex (in this setting, a signature’s 1 correspond to a rightwards partition, while a 0 corresponds to a leftwards one)
One might object such simple concept hardly translates into anything of interest, but it does.
For starters, it provides us with a very concrete and natural ontology of logic: logic is defined as a semonic-preserving entailment relation. There are two types of logic, with every synection being characterized as either one of them: full logics (those of the tautological sort, ie, synections connecting equally-valued entities) and quasilogics (those between differently-valued entities). And since every entity in the Worldtree is ultimately bound together by the Semes, we can assert “logic” is what underpins the entire fabric of reality, such that if a phenomenon is found without any sufficient material cause — resulting in an apparent ‘ex nihilo’ -, it must be the case that some non-apparent factor is acting beyond our ability to apprehend it and never that it’s “just the way nature is”, for that would imply nature can behave inconsistently, which is in itself absurd.
Reality then, according to our worldview, is much like a dictionary, where everything is, in a sense, self-referential (as in sharing kinship), and every word can be defined, if only by an arrangement of other words within the same book. In this metaphor, a synection is the very definition of a word: a cobbling up of terms brought together to provide it with substance by displaying its linkage with others of the sort; none of which, alone, can account for themselves — with the notable exception of the word “dictionary”, that we might regard as the equivalent of the Semes in this setting.
Syneces also offer a more intuitive grasp on the concept of computation. The essence of computation lies in the notion of substract-independence — that any device allowed to store information in a memory and follow a set of read/write procedures over that memory (ie, a Turing Machine), coupled with a description of how the device operates, can be made to output the exact same results as any other. Turing’s universality thesis was that anything could be made to compute; from a bunch of rocks to planets or electrons, the fundamental rules of information processing don’t care for the nature of the data being juggled, only its aggregate properties. In principle, anything your smartphone does could be made to run on a Commodore 64, or inside another, virtual computer (say, Minecraft), or in a contraption made entirely of coconuts representing the binary digits; given enough of them, it would run just as smoothly as it does on the device you’re holding. That may not seem like a big deal, but it was a major realization which sparked the informational age we now live in, and it was all based on the simple notion that all computers are equivalent regardless of the materials they’re made of. The now formalized theory of computation was hence a structuralist discipline in its core, and as such defined its elements in terms of reducibility and expressivity: which computational structures (or programs) allowed for interesting behavior — and, in particular, which could be used to emulate others, or subsumed them. The ones with this furtive, yet valuable quality were precisely those which tapped the deepest into computation’s universality aspect, providing the same results with lesser demands in terms of steps (algorithms) or resources (memory). That constitutes the very essence of computation (analogy), and can be fulfilled with relative ease within a worldtree setting. Two entities are analogue, or computationally equivalent, if they are homomorphic to each other — that is: they have the same shape or setup, which, nonetheless, may vary in order, locus or size, without however varying in the output produced by their interaction with a third party. That’s what computing is all about!
We can also use syneces to explain homology, or the fact that some structures, despite sharing a single origin, behave differently on the offset. This is, of course, due to their different signatures. Homology is the antithetical property of analogy, and operates exactly how one would expect: if a semon splits into two, the offspring will be diametrically opposed in relation to each other, such that if they are in possession of a feature — such as direction, for instance -, one will point left while the other points right, or one will be up while the other’s down, or one will be matter and the other antimatter, and so on. The partition-recombination process is an essentially dialectical one, and we must always remember that it’s only the extrinsic properties of a semon that allow it to differentiate itself from equivalently-ordered sema, resting in its locus (as expressed in the signature) the determinant factor in their individuality. Think of homology as the driving force of the world’s dynamics, as it takes two homologues to effectively constitute a semon, hence being the conducive force behind all movement.
Entities with the same shape, size, degree and order, but situated on different loci, (that’s the plural of locus, BTW) form an altogether different equivalence class, one even more powerful than the formers: they are said to be symmetrical. Symmetry means that you could literally exchange any of them with any other and a very special thing would happen: nothing! Since their loci is the only aspect in which they differ, swapping them around wouldn’t alter the state of things in the slightest. Of course, the most obvious practical example of that is the symmetry-invariance duality in theoretical physics, but instances of it can also be found in more mundane settings — like, for instance, the DNA replication process, which ideally should produce a plethora of identical genotypes, but of course occasionally stumbles due to unfit environmental circumstances, producing mutations in the code and the ensuing offspring variability (the mutations are a nice example of symmetry-breaking process).
And, finally, syneces allow us to ground the notion of what a number is — and, as a result, arithmetic and the entire edifice of mathematics. Its dual facet can actually be mapped to two of the most fundamental notions in Synesism: the concept of a system’s size gives us the cardinal numbers, for it represents ultimate fungibility (since they’re all alike and only their count is able to differ an ensemble from another); on the other hand, the concept of order lets us fit these entities into neatly arranged hierarchies, which provide a sound foundation for — you guessed it! — the ordinal numbers and their many stacks. Below is an example of how both can be fulfilled using a particular construction called the ‘Surreal Number System’, which encompasses the entirety of the transfinite numerical hierarchy in the form of a simple, infinite binary tree:
So, in retrospect, here’s a nice diagram summarizing the most relevant structural components one can derive from syneces and their arrangements:
Together, these five fundamental equivalence relations constitute the basis of all qualitative properties that arise in the Worldtree. They form the acronym HASTE, which we’ll use as a mnemonic device and stands for Homology, Analogy, Symmetry, Tautology and Equality.
Now, remember back in our discussion of sema how we distinguished between basal sema (actual, ontological objects of reality) and generalized sema? As we said on that occasion, the notion that unified those two, very different sorts of entities is the one by the name of invariance, the cornerstone of this entire framework. It may have remained a mystery to some, though, exactly what form these other kinds of sema (other than basal ones, that is) might actually take. Would they possess any sort of materiality to them? Or perhaps they’d just represent mental constructs of objects’ ensembles? We can finally give an answer: non-basal sema are merely the manifestation of the structurally-invariant properties of the worldtree, as enabled by syneces!
What this means is that, given a general property of an ensemble (say: the fact that all electrons have a negative charge), this is a direct result of the fact that every electron has a corresponding mapping in the worldtree that is isomorphic to every other. In other words, if we could ‘crop’ the section that identifies an electron off its locus, and somehow exchange it for a cropped electron from some other location, nothing would happen. That’s because our entire operation was invariant with respect to the “electron semon” (specifically, invariant under the symmetric property of syneces). That’s how sema work on levels beyond that of basal entities: they no longer need to reflect the behavior of individual objects, but allow for collections of them to preserve the same kind of properties, if only under specific circumstances — and this distinction is important; syneces can emulate specific attributes from a semon, but not all of them at once, and vice-versa. Failure to distinguish between what a semon and a synex — or a quasisemon, we might say at this point — are can steer us into the wrong direction in our analyses of worldly phenomena.
Consider for instance all the hardships faced by scientists and physicians, who’ve been trying to develop a safe and reasonably effective cure for cancer with no success for decades. The main reason is that when we talk about “cancer” we’re actually talking about a host of very different ailments, each with its own unique makeup and physiological pathways within the organism. We kid ourselves to think of cancer as semon, or a single condition, because there’s greater variability amongst its many types than there is between other illnesses that afflict man (it’d be more accurate to say that there are many synections between different breeds of cancer, for the reasons already exposed); something that might work for the treatment of one kind of cancer could perform horribly on another, and so on. And though there may come a time when we’ll finally be able to cure people of all different strains of cancer, it will hardly be achieved through one swift blow or through a single technique developed.
As another example, imagine we have a classroom with around twenty students. We could choose to represent the classroom and each subgroup composed by at least some of its students as sema. Mind you though: as these are non-basal sema, they won’t necessarily be as clear-cut as we’ve grown accustomed to; matter of fact, whatever may be the ones we choose to study, they’ll probably have much fuzzier borders and even overlap with each other — things that wouldn’t be allowed if we were dealing with the ontological kind.
So, continuing with the example, suppose you’ve conducted a study on the classroom to draw a profile of its students, and this study used some criteria as guidance: gender, age, income bracket, GPA, ethnic group, interests academic or otherwise, etc. Naturally, being diverse in their constitutions, backgrounds and upbringings, the students will variedly score in each of the criteria, and if the analysis is sufficiently thorough, you should arrive at an overall picture of the group as being of average marks, while individual profiles would be all over the place (“random”) in terms of variance. Of course, this being the real world, you’d observe however that individuals seem to clump together into relatively homogeneous groups of shared attributes, and you’d decide to call these clusters. For statistical purposes, they’d do just fine in terms of managing diverse populations and trying to infer objective data from them; but though you might feel tempted to call them sema, they’d most certainly not be.
And it’s not only because they’d be synthetic constructs whereas all (basal) sema are analytic ones, but because they’d be a posteriori. A semon, be it basal or not, is the representation of an aprioristic and hence anterior — not in a necessarily temporal sense, but ontologically speaking — aspect within an ensemble of objects, that both underlies their being and joins them together in that particular respect. That is equally true for ‘partial sema’ or syneces, so even if we’re only referring to a relative trait of an object, it must be kept in mind that it’s always been there, lurking somewhere in the genealogical background, though it only found an expression once the conditions were appropriate (in fact, think of the genotype-epigenetics model as a fitting metaphor).
Going back to our example, of course we would be hard-pressed into rushing to the conclusion that the qualitative ‘clusters’ we drew the students into would themselves be valid instances of sema, even if not of the basal kind. However, at a closer inspection we’d soon realize that ALL of those we listed were actually completely circumstantial and, hence, not really reflective of deeper, more substantial phenomena at play but, more accurately, of the environmental landscape presented — there’s nothing that prohibits you, the person reading these words, of upping your GPA, moving along the income ladder, reassigning your phenotype to match your gender identity or even rewrite your own genetic code and do away with your entire hereditary marks (it may not be practical, but it’s certainly not impossible in principle); does any of that means that you’ll cease to be “you” at some point along the path? Absolutely not! As we’ve already stated, naive notions of identity fixed on physical constituents rather than actual structural invariants cloud us from seeing the agents in the world around us as they really are: processes rather than things, dynamic and fluid instead of monolithic. And if you think this contradicts Synesism’s of sema as fixed, think of a harmonic oscillator (like violin’s strings) as a suitable analogy -though the strands vibrate and resonate to the sounds, they always remain attached to the fiddle. Such is the way with sema, that though may take endless forms and guises always stay the same on the inside.
It just comes to show us that, just as misleading as is failing to recognize how different entities are merely instances of a single one, regarding as equally-footed things which do not share a close common denominator might lead us to erroneous conclusions (of course, Synesism asserts that all entities share a kinship in reality, but at which level their branches actually meet is no trivial matter, as we can ascertain from the example above, for it has direct consequences on the measures needed to address both simultaneously).
If we wish to cut across the merely armchair, philosophical digressions and delve into the messy, nonlinear world of our everyday experience — and beyond! -, syneces are the tools for us. They’re the one that allow us to organize and make sense of the world, by explicitly relating how everything interfaces with everything else, what are the most and less general principles governing beings, which sorts of deviations allow for something to arise instead other, and what courses to follow if we wish to transform the reality we’re given. Syneces are essential to the arts, as well as the sciences and mathematics, and every other instance of generality we have contact with. They are what breathes the universe with dynamism and life, and what allows us to participate in the great cosmic symphony of stars, planets and the void; the alchemist’s stone and the bedrock for all things dialectic. They represent the ultimate possibility: that everything can be changed and nothing’s set in stone, destined to stillness for all eternity. All it takes is upsetting just the right hinges, which brings us to the next topic.
