Systems

When a semon partitions, it does more than just bringing upon new entities into the world; it creates a tangled web of relations between its elements that ultimately hinges on it. The ensemble of a semon with its offspring, its offspring’s offspring and so on, in addition to their many interactions with each other, constitutes a cohesive whole called a system.

A system is a semon whose molarity is distributed across multiple entities, rather than a single one. So, in a sense, a system is simply a semon with some additional structure imbued.

The term itself is charged by decades of association with notions found on several different disciplines, most notably mathematics, physics, biology — not to mention its own field of research: the interdisciplinary area of ‘Systems Science’. But since we don’t find them to be necessarily in conflict with our own, we choose to employ it anyway. The one concept that most resembles our own take on the term though is that of a quasicategory, as in Category Theory. There are of course countless forms a system can assume — and its configuration will ultimately define things like what sort of behavior is admissible or how expressive it is -, the only properties able to distinguish between them being either their locus or order. A pure semon is itself a system, but only of the most uninteresting kind: no inner structure, no features, no behavior. However, once it’s divvied up, all sort of interesting phenomena start arising in response to the ‘space’ suddenly made available by its partitioning — though all the elements remain rooted at the original synod, through which any system-wide influences must travel. A system’s synod is its invariant, or identity element.

Within a system, semonic value is preserved, and all transformations must obey the Principle of Coherence. It is then, by virtue of definition, that any system within our perspective will always be of the closed kind. This though does not preclude that they can’t interact or even influence each other’s evolution; matter-of-factly, most of what determines the outcome of a system has as its source external factors — like the boundary conditions it is subject to, equilibrium requirements and entropic pressures -, and not internal ones. One should also remember that all systems are themselves subsystems of other systems (with the exception of the prima synod), and are hence as contingent as their own strata.

Systems of every kind share these general properties, but we often fail to recognize them in the bigger, messier ones that constitute our immediate experience because we tend to aim the focus into their epiphenomena (like the symptoms of a disease) instead of the underlying elements and their invariants.

But let us consider for a while the case of quantum mechanics, the discipline which concerns itself with the study of the submicroscopic world. The usual interpretation for the odd and counterintuitive phenomena observed at those smallest scales, dubbed “Copenhagen Interpretation”, states, for instance, that until observed, a quantum system has no objectively defined parameters, falling to the observer (who’s defined as ‘any system interacting with it’, even something as fortuitous as a random photon) the job of ascribing, through the measurement process, a specific value to it. Before that happens, they argue, the system is nothing more than a cloud of endless possibilities, none of them truly actualized. The so-called “measurement problem”, of how exactly that happens and what’s the true state of the quantum system prior to it, lies at the heart of many paradoxes plaguing the field.

Under Synesism, however, an undisturbed quantum system is merely the actual (not just potential) ensemble of all possible outcomes, or a undivided semon. Through measurement, we are effectively upsetting the system by interacting with it (remember the Principle of Coherence), and hence forcing it into partitioning, so that it can be apprehended by us. The question that puzzles physicists is what happens to all the other values associated with the system that weren’t selected after the measurement, as their sudden disappearance would seem to imply they didn’t even exist in the first place. But we know that a partition is merely a superficial phenomenon, and though it may seem to break the semon apart it’s simply chiseling it, never actually severing the link from the offspring to the synod, but only to each other. So much so that, despite all the indeterminateness associated with which outcome the system will choose (as is the case with beta decays), its overall evolution is wholesomely and deterministically given by the associated wavefunction. In our perspective, the wavefunction is the very operational description of a semon and its behavior in a quantum language (in this case, with each quantum system corresponding to a semon), while the manifest entities — be them waves, particles or aggregates — are the partitioned forms it assumes. The semon itself can’t be said to correspond to any of them, but to a much more fundamental entity: the quantum field, a multidimensional gauge bundle from which every other constituent of our physical reality arises as an excitation of its ubiquitous and continuous character.

Returning to the subject of the ‘missing stuff’ that results from the measurement process though, it is necessary to recall the nature of and exact description of what a partition actually represents; we’ve seen that it’s an inflicted degree of separability (or in the language of physics: noncommutativity), but what shape does it assume? The most usual one we know of is that of spatiotemporal separation, with the speed of light acting as a fundamental limit for the rate of physical interactions within the universe (but not TO the universe, as we now know space itself actually expands at much higher speeds than that of light traveling inside it). But the very act of measuring something entails that both the system being measured and the observer must coincide to the same coordinates in time and space, otherwise their interaction wouldn’t even be possible. This then begs the question: if at t — 1 the system allotted for a much greater variety of values, where could they possible have gone that they appear to instantaneously vanish after the measurement? Our intuition requires that they be, at the very least, found transposed to some other coordinates set, but there’s no physical indication of that either.

The answer lies in supposing, as did Hugh Everett III in the 1950’s, that each time a measurement is performed the universe ‘branches’ into two or more causally disconnect timelines, each with their very spacetime housing its own specific outcome, while overall respecting the unitarity of the wavefunction and preventing any sweeping-under-the-carpet of its quantum numbers (keep in mind this is a DIFFERENT unitarity than the one we adopted as axiom a while back).

Many people object the so called ‘Many Worlds Interpretation’ of quantum mechanics, as it became known, mostly on aesthetic or experimental grounds — they worry it needlessly multiplies the number of entities in the theory and that it defies falsifiability by positing all these extra universes we could not possibly hope to get any direct evidence of. My answer to them, in which I echo the thoughts of people like Max Tagmark and Sean Carroll, is that though it apparently demands a lot to be added into our conceptual baggage for understanding the quantum domain, it actually really doesn’t — all the elements are already present in the usual formalism! From the Schrödinger Equation that governs the wavefunction and necessarily inhabits an infinite-dimensional setting called the Hilbert Space (and where, different than classical physics’ phase space, multiple outcomes are actually simpler to describe than just one), to the fact that the unitarity of the system is always preserved (the central tenet of the discipline itself), everything in the quantum formalism naturally leads to this interpretation. Indeed, to get away with breaking the superposition, competing interpretations have to add all these extraneous and ad hoc features to the theory, like dynamical collapse or hidden-variables models. Bare-bones quantum mechanics (ie, just assuming the evolution of the Schrödinger equation to be unitary) is a much more elegant description of reality — once we give the proper interpretation of what the math’s telling us.

Not only that, but theoretical physicists working on the field’s fringes (in areas such as cosmology, particle physics and high-energy physics) have been observing an odd convergence in the last decades: most of the models they work on, specially their dearest ones, seem to either require or imply the existence of parallel universes as a consequence of their formalism. From cosmological inflation to M-theory (which, should be noted, is more of a framework or ‘umbrella term’ than any single theory), the existence of worlds other than our own is an increasingly natural thought to most physicists, as denying it would mean scrapping the models they’ve be piecing together for over a century now with incredible success. Plus, it does help answering some hard questions about our universe, like: why some forces are stronger than others, why the three generations of particles if the overwhelming majority of its constituents comes from the first one, why there seems to be a phenomenological gap in the high-energy spectrum, why the universe contains features much larger than anything that could possibly arise from the big bang — not to mention the nagging question of ‘what was there before the big bang?’. And though this may be the most controversial issue arising from one’s full acceptance of Synesism, I believe there is more than enough evidence to assert its justifiability beyond a reasonable doubt.

But back to theory: suppose now Everett is right and every time a system is measured the decoherence prompts the emergence of a new spacetime for each of the previously possible outcomes. We’ve already established that our universe (and presumably any other) is a closed system, which means that after it’s been created, its contents should remain within the bounds of the system. How do we reconcile that with the superposition of quantum states?

The apparent contradiction is solved once we consider what these quantum states actually represent. First of all, we should bear in mind that the scales of our physical world are not the scales of the Worldtree and its basal sema. A simple way to visualize the relation between the two is to say that, while the Worldtree is built in an up-down kind of direction, the elements of physical reality are somewhat perpendicular to them, arranged in a left-right one; the two do have a correspondence, albeit not of a direct kind. In the case of quantum mechanics, the science of the smallest scales of physical reality, the objects of its study are actually those dealing with the most general phenomena in our experience — in other words, a much deeper order of the Worldtree and, hence, reality. This means that, for example, more than one “spacetime” may be embedded into a single entity such as a semon — and, in fact, when a quantum system decoheres, it’s as if the infinitely many spacetimes it contains in potentia within itself were splitted along its offspring, such that while they share a common origin, they’re no longer interchangeable (ie, become noncommutative).

When we deal with quantum mechanics, it’s rather like we’re dealing with the mainframe of a huge computer, where all the electrical inputs are flowing and the low-level operations are coordinated to ensure that at the high-level (like your monitor) the effects are as desired. Remember how we said previously that models like the worldtree (a simple, binary tree) are a gross oversimplification of matters? This is where their ineptitude becomes glaringly obvious. In the real world, whenever a semon partitions, it’s literally a new dimension that is being created in its innards — like in our birthday-cake-slicing example, the empty space that constitutes the boundaries of the slice is not in the case of a basal semon actually physical empty space, like a vacuum, but more like a new degree of freedom; its physical correspondence might be that of spatial or temporal separation (even the big bang itself, or the 4-dimensional manifold in which our universe unfolds), but it could also be of some more abstract category. Entanglement is just one of those kinds of instances — a bond which is neither space or timelike, but of material causality (where ‘materiality’ refers of course to molarity). That’s made possible because when a semon partitions, the two offspring are not side-by-side to each other like the Worldtree graphic would make us believe, nor are they any more distant, necessarily, from others of the same order than they are from their own siblings. In reality, every semon is adjacent to countless others at any given time, with the respective orders determining their immediate vicinity — lower-ordered sema naturally being better “connected” in the network than higher-order ones. This is further proof of the limited illustrating power our “2-dimensional, 2-degree Worldtree” provides, though it serves well-enough as an introductory model; just consider how, on an ordinary graph with no cycles, a single edge can connect no more than two points, while on a hypergraph, a ‘hyperedge’ can connect much more than that (note that, whereas an ordinary edge is usually drawn as a straight line between two vertices, a hyperedge is depicted as a curve that wraps around three or more vertices). It’s a hard thing to visualize, since these things actually inhabit an n-dimensional space (with n corresponding to the order of the system, but whose dimensionality is not of a physical but mathematical nature), but on many levels it resembles a jigsaw puzzle — as in: the boundaries of one piece are also the boundaries of all its adjacent pieces. It isn’t the space of our everyday experience but, rather, something akin to a phase space, in which the semonic value is represented by one axis and the relative structure (ie, after partition-caused decoherence) of the system the other. The intuition one must keep at all times, though, is that there’s no one-to-one correspondence between an action in a worldtree setting and one in physical spacetime, but at most a nonlinear one — sema can twist and bend (not themselves of course; the systems they compose. Sema themselves are never moved), and it’s this multidimensional tensorial quality of theirs that gives rise to our large-scale experience of inhabiting a smooth, continuous manifold, and not the other way around. Spacetime, despite seeming such an important thing to take into consideration when investigating the fundamental nature of reality, has at most a secondary part in the action; it’s by no means an element of ultimate reality, but a mere emergent property or epiphenomenon of this ethereal fractal.

In the case of entanglement, the distances between the particles involved couldn’t be of a lesser importance: the ‘influence’ that instantaneously affects one if the other has its state upset taps on something deeper and much more fundamental than spacetime — their shared ancestrality in the Worldtree. Just like in our jigsaw example, if we somehow redraw the lines separating two pieces, we can’t expect to have just one of them change as result; both their states will be affected and the board dynamics at that juncture will have to accommodate that, regardless of whether they’ll remain together or be scrambled with others later on.

The same happens in the case of superposition and the measurement phenomenon: though we may assume that after a system is created it severs the bonds it had with all the other members of the family, this is never the case; there’s no possible chasm that’s deep enough to completely detach a semon from the rest of the Worldtree. That’s why Synesism is a monistic philosophy. What remains closed in a closed system is merely it’s semonic value; when a semon from said system partitions — the process we know as decoherence -, what’s actually splitting is the spacetime that wraps around it. That’s how they can continue to influence each other, even if on opposite edge of the galaxy or separate universes altogether.