11 May 2020

Movement as capitalist gainful game

(The following is an excerpt from a work in progress.)

In previous chapters various kinds of movement have been discussed at length and from various angles. A proper consideration of the kind of movement appropriately called power interplay and struggle requires, as investigated in the preceding, the introduction of whoness as a mode of being vis-à-vis traditional whatness. Movement within whoness is in general that of mutually estimative power interplay in which, in the first place, human beings themselves mutually estimate each other’s value, their worth in one respect or another. Such a mutually estimative interplay reflects back onto things themselves insofar as they are mutually valued in exchange, thus becoming owned commodities, here comprising both goods and services. Such movement is basically that of trade, commerce, mercantile activity, whose historical origins are ancient, well documented and narrated in economic histories. Money as a mediator of commodity exchange and insofar as a reification of commodity-value itself is also historically ancient, albeit as yet not predominant. Reification as a socio-ontological category of things, as well as the ontology of that kind of movement called exchange, is already inaccessible for any historical telling, including any purported dialectical-historical narrative.
Among others, the Greeks knew of two techniques or arts that distinguish themselves from the paradigmatic art of making called τέχνη ποιητική, namely, τέχνη κτητική and τέχνη χρηματιστική, i.e. the art of acquiring property and the art of making money, respectively. Both involve essentially the movement of exchange (μεταβολή), whereby μεταβολή, interestingly and crucially, ambiguously signifies also simply ‘change’ that can be understood productively. The movement of exchange, however, is a movement sui generis that, as a mode of being, differs from the movement of change initiated from a single origin (ἀρχή) as a productive power (δύναμις) for such change. Hence Aristotle’s definition of δύναμις as ἀρχή μεταβολῆς. Despite the millennia-long tradition of forcefully pressing the ontology of exchange into the mould of the ontology of productive change, thus ostensibly gaining predictive power over movement via efficient causality, the ontology of exchange has to be considered in its own right as homeomorphic with the ontology of mutually estimative power interplay of whoness, if only because the commodities exchanged are either the expenditure of powers and abilities (services) or the products thereof (goods) and are necessarily valued. Behind any valuation of goods in exchange there is always the estimation of the expenditure of human abilities exercised (as well as natural powers exploited), via exchange, for the benefit of others. (The estimation of natural powers as the gifts of nature, along with the appropriation of parcels of land or water as property requires a separate investigation.)

Both the art of acquiring property and the art of making money, however, imply a striving for ‘more’ in property or money, respectively, and thus a quantitative aspect. The movement of exchange then fails in one sense if a ‘more’ does not come from it. The ‘more’ or surplus is quantified in terms of money itself or money-value, since money is the reified or ‘thingly’ universal equivalent of everything of value, thus enabling their uniform valuation in a social (who-)measure sui generis that has to be distinguished from any physical (what-)measure. Money therefore embodies, apparently in itself, a power, namely, the power to acquire something of value, including the labouring power of individuals that is put productively to work by and for the benefit of the acquirer. Such augmentative movement of reified value to produce a surplus mediated by the necessary exchanges to acquire means of production and labour power is the prototypical movement of capital whose simplest formula is the movement of money to more money mediated by production, a social movement sociating both things and people, whats and whos. If the resulting surplus of all the required value interchanges is negative, i.e. a loss, then the movement has failed in a certain sense and its continuation is in put into doubt.
Although a circuit of capital proceeds from an initial advance of money-capital to purchase the required means of production and labour power, the money-capital or its bearer, the capitalist entrepreneur (who may be a natural person or an incorporated company), is not the sole origin of this movement because it requires multiple value interchanges with other players in the circuitous value movement: the suppliers of means of production, the workers/employees themselves, the lenders of money-capital, the owners of land, the purchasers of the end-product. These four kinds of figures are the basic players in this gainful game of value-augmentation each striving for their characteristic share of the resultant reified value in the form of wages, interest, ground-rent, leaving a residue of profit for the entrepreneur. All the various kinds of players are involved in mutually estimative power interplays with one another over gaining their respective kinds of income, in which uniform category the differences in the income-sources are disguised, more than often, conveniently so. Whether the income-outcomes of the countless various power interplays are fair or not depends on the current historical state of play of the power interplays, ranging from periods of relative all-round mutual satisfaction through to bitter and bloody power struggles among the players. The outcomes of power interplays over earning income in any given society in a given time are in any case uneven: fair, middling or downright unfair.

6.4.1 Contradictoriness of the elementary exchange-movement

In what sense are the power interplays played out in the capitalist gainful game contradictory? As a kind of movement, albeit sui generis, power interplay partakes of the contradictoriness inherent in all movement as the ‘at-once-ness’ of presence and absence pertaining to all transition, an ‘at-once-ness’ that is seen by the mind’s temporally triple vision (cf. Chap. 3 above). But what is special or idiosyncratic about the contradictoriness of those movements that can be called mutually estimative power interplays?
Just as a carpenter’s making of a table can serve, and has served, as the simple paradigm for the productive movement of τέχνη ποιητική, the paradigm of the sale of wares on the market may serve as the elementary paradigm for, and even kernel of, the socio-ontology of the intricate web of power interplays constituting the gainful game. The simple paradigm of the art of making, on which the Aristotelean ontology of productive movement is based, has ‘blossomed’ into the onslaught of the modern sciences and technologies in striving to master all movement in the world, whereas the simple paradigm of commodity exchange has ‘blossomed’ into the untrammeled gainful game that today is unleashed globally with oft devastating effect. The socio-ontology of the paradigm of commodity exchange, however, has to date never been explicated, nor the fundamental difference in its ontology from productive movement made clear.
To start with, an elementary exchange between two parties mediated by money is idiosyncratic in the sense of being its own mixture (ἰδιοσύνκρασις) of two different movements proceeding from two different origins or starting-points (ἀρχαί), viz. the buyer and the seller. These two movements are in two different, indeed, opposed directions, but intertwine and depend on each other if they are to reach their respective destinations, i.e. each movement negates the other but also positively includes it. The seller aims at getting rid of, i.e. absencing, the good in his or her possession in favour of gaining, i.e. presencing, money in his or her hands, whereas the buyer aims at gaining possession, i.e. presencing, a good that is good for something or other, useful and therefore a use-value while at the same time handing over, and thus absencing, the purchase price in money, from his or her possession. Each party as a starting-point of the transaction has an opposed but interlocking, dovetailing, complementary intention in mind, namely, complementary to the other party’s intention. A successful, mutually satisfying transaction reached by agreement represents the Aufhebung (resolution) of the contradiction between two opposed movements. It is attained, if at all, through each party estimating the value of what the other party has to offer and, crucially, coming to an agreement (if the one party, say, appropriates the other’s good by force or cunning, the contradiction has not been resolved but only exacerbated).
The buyer assesses the value in use of the good on offer (which may be either a consumer or productive good) in relation to how much it costs, whereas the seller assesses the price at which he or she is willing to part with the commodity good, whereby this assessment includes an estimation of the margin of profit made or whether the expenditure of his or her own powers in producing the good in question is adequately compensated, i.e. valued, by the prospective purchaser. Insofar there is a formal parallel between the productive movement of making something and the completion of an exchange transaction: the contradictoriness inherent in the movements is resolved in attaining an end (τέλος), either in the finished product or in the finished, agreed transaction. Otherwise, however, the ontologies of these two different kinds of movement differ, as is apparent already in the necessity of two different ἀρχαί having to reach agreement, to strike a deal, on their mutual estimations. For instance, a carpenter can finish making a table and be satisfied with the result of his or her productive activity, but its sale requires the independent value-estimation of the table by another, namely, the prospective buyer and also that this buyer and the carpenter reach agreement with each other.
Whether the resolution of the contradiction between two opposite but complementary movements in a completed transaction is mutually satisfactory for both parties is entirely open, just as is whether a transaction comes about at all. In contrast to productive movement, neither party (ἀρχή) to the potential transaction has power over its eventual outcome, even though each may have definite intentions, such as the buyer or seller having envisaged (mentally) a fixed acceptable price range in advance. Despite best efforts, for instance, the seller cannot activate an efficient cause on the prospective buyer to effect a sale. Market conditions outside the control of either buyer or seller also set boundary conditions within which any transaction can be completed. A glut or scarcity of a certain good on the market may force transactions on one of the parties that are entirely unsatisfying, e.g. sale at a loss or purchase at an exhorbitantly high price. The mutual estimation of the values involved in the transaction then does not lead to a mutually satisfying resolution of the opposed movements with the consequence that the exchange, depending as it does on the mutual agreement of two parties, may not take place at all, or only begrudgingly on the part of one of the parties, who is in need. Exchange interplay therefore requires the two players (buyer and seller) to see not along one-dimensional, linear time in terms of cause and effect, but to envisage or imagine various future possibilities residing in the potential transaction during the course of bargaining and haggling (insofar as it occurs) over its terms. The movement called exchange is thus beset with an inherent uncertainty that must be situated in open three-dimensional time rather than predicted effectively along a time-line.
The simple paradigm of the buying and selling of wares can be easily modified to consider services which are a kind of ‘liquid’, not yet solidified, objectified good. The purchaser is not purchasing a finished good, but hiring a worker’s labour power to provide a certain service. In this case, the seller offers his or her own powers and abilities to the prospective purchaser to provide a service of whatever kind to him or her. The service-provider is then paid a wage for expending his or her own labour power for the other’s benefit. The interchange that comes about may or may not be mutually satisfying and is in any case likewise not under the control of either party, in particular insofar as external market conditions set boundary conditions for the transaction, but also simply because it requires an Aufhebung in an agreement. There is an asymmetry when the hirer of labour power is an entrepreneur and the service-provider is an employee earning a livelihood who has scarce or no reserves to play for time in the transaction. On the one side there is then a small or large or huge company with considerable financial power; on the other a worker of some kind seeking employment whose stand in the power interplay may or may not be strengthened by membership in a workers’ union that enhances bargaining power. In any case, a shift of the balance of power in the gainful game results when corporations face employees in the power interplays of the gainful game.
A given transaction is only one move in the more encompassing gainful game of earning income. It must be complemented by others to weave the complex fabric of the income-earning lives of many players. This applies especially for the enterprise player who, as the co-ordinator of productive collaboration, must complete countless transactions for purchasing means of production, hiring labour power and selling finished products in the circulation process of capital. The gainful game is enabled first and foremost by the reification of value in money that serves as the indispensable medium lubricating the game’s movement. Reified value is thus the medium of sociation bringing the players together, all of whom are striving for reified value in the form of the four characteristic incomes or hybrids thereof. Any talk of capitalism that is ignorant of reified value as the medium in which the gainful game is played — and this includes all of today’s economic theories(*)  — has failed to understand what it is.

6.4.2 Metaphysical eeriness of the gainful game

Although the gainful game seems motivated by the willed and willing strivings of its many and various players to earn income, and thus seems to be the result of the collective action of countless subjects, its core movement is far removed from any underlying human subjectivity. The core movement is namely the augmentative movement of reified value itself as capital, a seemingly eternal circular movement that draws all the players into its complexly intertwined and unforseeable movements of the countless circuits of individual capitals that the capitalist entrepreneurs and their agents, the executives, attempt to tame and manage profitably. Insofar, the will to earn income in competitive struggle is that of an unseen metaphysical will acting behind all the players’ backs: the will to play the gainful game per se. The players themselves, including even the powerful entrepreneurial players, are not the subjects of a game initiated by them and under their collective control; rather they are the pawns in a competitive game that comes over them like a stroke of fate. Each player may be out for modest or obscenely immodest success in earning income, but the game’s rules of value-augmentation are set by the overall, all-subsuming movement of reified value itself as capital willed by none of the players. Only within and underneath this overarching movement of total capital do the various players play out their individual gainful power interplays.
The metaphysical eeriness of the capitalist gainful game remains hidden to all the players caught up in it. They do not see the gainful game ontologically as such, but at most only pre-ontologically and explain it in merely ontic terms, i.e. in terms of facts, putative causes, historical narratives. This entails that the gainful game cannot be overcome historically by any collectivity of subjects, traditionally named as the working class, who are ostensibly destined to become historically an association of free producers consciously sociating and controlling the fruits of their labours. Such a projected overcoming of the capitalist gainful game is called socialism that is ruled out socio-ontologically, not merely, say, by historical experience of failure. A compromise between the gainful game and such a conscious sociation of the subjects via democratic power struggle in politics, where the state is supposed to tame excesses of the gainful game, is called social democracy. Its aim is to reform some of the asymmetries of the class power struggles by making the superior state power serve wage-earners. Neither of these political overcomings (Aufhebungen) relying on power struggle among humans conceived as a collectivity of subjects, however, is in the light of an insight into the socio-ontology of the gainful game, including its mysterious metaphysical, ‘theological’ will to gain ever more in the dimension of reified value. This hidden god of the gainful game, to whom all income-earners bow, could be called, in accordance with the Greek πλεονεξία (the striving for more, for a greater portion, for profit, for advantage, for superiority, etc.) Pleon Exia. Insofar, such collective political struggles for liberation from the gainful game are illusory. A socio-ontological insight into the gainful game would shed an entirely different historical-hermeneutic light on the world, recasting it as a world in which the alternative sight of fairness of mutually estimative power interplay were visible and in play, in which the blindness of being merely caught up in the gainful game as players of various sorts is meliorated. Overcoming blindness through a soberly enlightened eye on the capitalist gainful game is an historical precondition for any freedom whatsoever. Such freedom could be exercised in historical time by stepping back from an all-too-close entanglement in the machinations of the gainful game.
The boundless will to gain more in the gainful game is wedded to and intertwined with the absolute will to power over all kinds of movement and change in the set-up (Gestell), a metaphysical god I have named Willy P.,  the absolute will to power over all kinds of movement. Willy P.(**) and Pleon Exia are intimately related, but they are different, the former being an excessive outgrowth and dissemination of the ontology of productive movement derived from the innocent paradigm of τέχνη ποιητική, whereas the latter is an hypertrophic exaggeration and universalization of the socio-ontology of exchange interplay derived from the likewise initially innocent paradigm of τέχνη κτητική, the art of acquiring. When the obfuscating veil of the medium of reified value is stripped away, it can be seen ontologically that at the gainful game’s core lies the estimation and valuing of what human abilities and powers can do for each other on a basis of mutuality, along with an estimating and esteeming of the Earth (see below).

(*) Marx’s critique of political economy in his mature writings is the exception insofar as the so-called value-form analysis offers the kernel of a viable social ontology of capitalism based on a well-developed concept of reified value.

(**) For the character called Willy P., see my novel, The Land of Matta.

Further reading: Capital and Technology: Marx and Heidegger.
Social Ontology of Whoness.

02 May 2020

Perplexities of quantum mechanics

 The following is an excerpt from a work in progress.

3.4 Quantum-mechanical movement 

The advent of quantum mechanics as the successor to classical Newtonian-Galilean mechanics through the work of famous physicists such as Einstein, Heisenberg, Schrödinger, Dirac, Born and Bohr has been hailed by many physicists as an exquisite testament to the power of the human mind to unravel the mysteries of nature. It also gives rise to perplexing paradoxes. To quote just one of these enthusiastic quantum physicists, “Quantum mechanics is the greatest, the most profound of revolutions in our modern view of the physical world. Even for experts, acheiving a deep conceptual understanding of quantum mechanics can be an elusive goal.” (Bowman 2008 p.172)  Wherein lies the deeply paradoxical and downright confusing nature of quantum physics expressed in figures of thought such as quantum indeterminacy and the dual nature of quantum entities as both particle and wave? Are they ultimately paradoxes of the mathematized mind’s own making? Let us investigate the matter.
The basic entity of quantum physics is neither a particle, as in Newtonian physics, nor a force field, as in Maxwellian physics, but a dynamic quantum state that is expressed mathematically as a ket-vector in some linear vector (Hilbert) space of discrete finite, discrete, countably infinite or continuous, uncountably infinite dimensions with complex, rather than real scalars. These dimensions are purely mathematical, as a rule not (conceived as) physically spatial. The ‘dynamic’ in dynamic quantum state refers to the character of a quantum state as being in movement toward another quantum state under the impetus of a δύναμις, i.e. a power or force. A major consideration of quantum mechanics is thus what it calls the ‘time-evolution’ of a quantum state along linear real time, t, that can only be precalculated i) by conceiving an operator (the Hamiltonian) operating on the given quantum state and ii) by employing the infinitesimal differential calculus to solve (partial) differential equations in t that govern the movement. To this calculative end, the quantum state absolutely must be conceived (i.e. interpreted) as a real-infinitesimal state in a present instant of time along a real continuum of instants.
This present quantum state, in turn, is conceived as the prepared starting-point for an experiment set up to register the outcomes of movements of the quantum state to compare them with theoretical predictions. These possible outcomes are in the plural, that is, at least two and no longer one, as in classical physics. They may be discretely many, infinitely many but still discrete, or infinitely many in a continuum (such as a single, linear, spatial dimension). These multiple possible or potential outcomes are said to be, i.e. conceived as being, contained in the present quantum state which therefore must be in some sense a superposition of multiple potential quantum states, each of which could render a single observational outcome when measured in the future. Measurement itself is conceived mathematically as the operation of an observable-operator on the present quantum state, a multidimensional ket-vector. Whereas the present quantum state is conceivable mathematically by the physicist as a superposition of present alternative, as yet undecided, ambiguous, future physical states (say, of spatial position, linear momentum, angular momentum), the observable generated by the operation of the observable-operator on the quantum state is a certain, definite data-result recorded in a future present of the completed experiment.
Unlike the situation in classical mechanics, where experiments are repeated to ensure that the outcome of the experiment gives the same result within a margin for experimental error as quantified by mathematical statistics, thus allowing efficient causal inferences to be drawn within a statistical margin of error, the outcomes of quantum mechanical experiments repeated many times reveal a well-defined, distributed statistical pattern of multiple outcomes that can be plotted to show a regularity in their spread. The physicist tries to achieve a calculable grasp on this observed regularity by means of the mathematics of probability, which, having arisen in the 17th century with mathematicians such as Pascal, is today a well-established, highly sophisticated branch of mathematics. Like all mathematics, however, probability mathematics, too, can only operate on given mathematical entities in a mathematical ‘space’, mapping them to another single mathematical entity in another ‘space’, or to multiple entities forming a mathematically amenable probability distribution whose various parameters, such as expected value and standard deviation, can be calculated from the given data. Once these parameters have been experimentally ascertained and calculated, the road is clear for being able to reliably precalculate the outcomes of given quantum experiments with certain mathematically known probabilities and thus within statistical margins of error.
This orthodox conception of the dynamic quantum state as a superposition of multiple possible quantum states upon measurement in a given instant must give rise to controversy because it is regarded as sacrosanct under the law of non-contradiction, that a present physical state cannot be in two or more states simultaneously. Simultaneity hence becomes a major stumbling block engendering paradoxes, confusion and denial among physicists. (Multiple simultaneous future potentials, however, provide the key to circumventing this apparent logical impasse.) To avoid this controversy over simultaneity, that is mostly regarded with disdain by physicists as ‘metaphysical’, some quantum physicists (e.g. Ballentine 1998) have proposed the statistical interpretation of quantum mechanics in which the focus is solely on the mathematically manageable statistical outcomes of quantum experiments in ‘real’ data, without bothering to concern themselves with the interpretation of the unseen ‘inner workings’ of the prepared quantum state. The quantum state is said to merely be a vector of probabilities for the observed ranges of experimental outcomes. The observable-operator can be represented as an operation on a complex linear combination of the set of the operator’s eigenstates spanning the ket-vector space that results in a weighted linear combination of the possible eigenvalue outcomes of the experiment. The weights are given by the modular squares of the expansion coefficients of a quantum state in the chosen eigenstate basis; they are interpreted as the mathematical probabilities in a probability distribution of observable outcomes.
For many a quantum physicist, this interpretation is highly appealing, since it avoids and apparently dissolves many of the perplexing conundrums of quantum indeterminacy and duality. However, does this statistical interpretation hold water phenomenologically? It proceeds from two implicit fundamental ontological-metaphysical pre-conceptions: i) that a dynamic physical state of any kind can be conceived as a state ‘frozen’ in a given now-instant and ii) that the physical state itself is objectively disjunct from any observer-subject who can only observe by registering physical data-signals received from any physical event in four-dimensional space-time (x, y, z, t). That is to say, any physical state is only instantaneous in time t, and any physical observation is likewise only a reception of physical data by the observer-subject’s senses, no matter whether they be assisted by sophisticated apparatuses such as various kinds of modern microscope or telescope or not.
These ontological-metaphysical preconceptions do not stand up to phenomenological scrutiny. Why not? Because they are based on misconceptions of the mind, time itself and therefore of physical movement, all of which are intimately interwoven. For modern mathematized physics there is no mind, nor can there be, because it operates from within an implicitly presupposed metaphysics of subject-object in which the observer-subject is endowed with an interior consciousness that is hooked up to the exterior world via sense-organs. These sense-organs are able to receive sense-data from the separated, external, objective world and process them internally through the intellect that itself is conceived as some kind of individual process ‘inside’ (mainly the brain) with many secrets yet to be deciphered by neuroscience. A dynamic physical state in the external world is conceived to ‘exist’ quite independently of any individual subject of consciousness who may or may not be observing it in any particular instant. Physical movement of any kind, quantized or not, is purportedly one ‘objective’ thing; its perception by an individual subjective consciousness quite another.
If there were no individual human consciousnesses around, this way of thinking prescribes, there still would be objective physical movement galore. But for whom? For what? For movement to ‘be’ it must present itself as such-and-such to and be understood as such-and-such by an understanding mind. This mind is not an internal individual consciousness, but a necessarily shared understanding in which all that occurs is understood or misunderstood in one way or another in a given historical time. Such a shared mind for understanding occurrences in the world as such-and-such is not merely the slave of the senses and the sense-data they deliver at the speed of light in the present. If it were, there would be no understanding of the world and its movement at all. Movement ‘exists’ only for a shared mind that understands it, conceives it as such-and-such, and this understanding must encompass, i.e. must mentally see, all three temporal dimensions at once to see that movement comes from a dimension of past and proceeds into a dimension of future. Movement is always underway toward, even when the final destination is seen mentally only indistinctly, without any reliable, definite prediction or is entirely unknown. The destination of a movement must be mentally in view for movement to be, i.e to present itself and thus presence in the mind, as movement at all. The destination may be completely obscure and unknown, but it is still a destination-in-mental-view as an εἰδος, an eidetic ‘look’ that is necessarily non-physical. There can never be a purely physical movement; it must be also ‘meta-physical’ in the sense of presenting itself to a mind that must be able to see temporally all at once in three dimensions.
This has decisive consequences for the conception of a dynamic quantum state which cannot be properly conceived as an instantaneous state in a present now-instant. Why not? Because, as dynamic, the quantum state includes also its connection to a future state, or rather, multiple possible future states mathematized as probabilities that may be quantified and confirmed by frequency proportions of measured empirical data. This connection to the future lies in the very conception of a quantum state which is a conception for the encompassing, shared historical human mind (and not for the individual human consciousness of an observer-subject). At the very least, therefore, the conception of a quantum state must admit, upon unearthing its as yet hidden, suppressed, implicit presuppositions, the double temporal vision that can see conceptually a present state together with multiple possible future states. In other words, the very conception of a quantum state, adquately conceived, cannot be that of a purely present state at time t but must be temporally spread, which in itself poses a perplexing conundrum for any mathematization of the dynamic situation. Any possible future state, by definition, cannot be sensuously present for the senses, but this is no deficiency at all. Rather, the sensuous observations of experimental data are an impoverished act within an overall conception of what the quantum-physical experiment is supposed to predict or confirm, namely, a preconceived, mathematized theoretical result.
The perplexing paradox of Schrödinger’s cat is such only by virtue of conceiving the indeterminacy of a quantum state as a present, instantaneous state in which two or more physical states exist ‘simultaneously’ in the same instant; prior to physical-sensuous observation by an observer subject, the cat is said to be in a limbo of being simultaneously dead and alive, which is, within this construction, paradoxical, contradictory, impossible. The dead-or-alive status of the cat, however, refers only to possibilities that are set up experimentally so as to be mathematizable as 50:50 probabilities for the release of the poisonous gas that kills the cat. The release, in turn, depends on which of two equally likely paths a prepared photon in a strictly controlled experimental set-up will take. The ambiguity is said to ‘collapse’ on observation. This dynamic situation is on a par with leaving it to the toss of a coin whether a cat will be killed by some automated mechanism triggered by heads or stay alive if the outcome is tails. The tossed coin in its indefinite spinning movement contains both heads and tails as potential future outcomes of the toss, neither of which is present-as-actualized during the toss. Nevertheless the possible future outcomes are present (in the mind of anyone conceiving the experiment or watching it from within some preconception or other) as futurally absent. Futural absence, however, is a kind of presence, i.e. of existence.
Analogous considerations pertain also to the Stern-Gerlach experiment often employed to illustrate the indeterminacy of the finitely discrete spin ½ angular momentum in which a particle (a silver atom in the original 1922 experiment; cf. Bowman 2008 p. 102) with a magnetic moment proportional to the spin passes through a magnetic field that generates a force deflecting the particle in one of two directions (up or down), depending upon whether the quantum spin is positive or negative. Whereas the particle with its spin in flight cannot be physically observed, its deflection up or down, as a macro movement, can be, from which the particle’s spin, positive or negative, is inferred. The physically observed deflection registered by a detector makes sense within the framework of a precisely preconceived experiment in which the particle’s motion is (conceived as) influenced by the magnetic field due to the magnetic moment generated by the spin angular momentum. This spin must therefore be preconceived by the physicist’s mind as a quantum superposition of two eigenstates of the pertinent spin quantum state of the particle, the two eigenstates corresponding to two alternative eigenvalues, either of which can be experimentally observed. The experimental observation is thus strictly preconceived and preinterpreted in line with the mathematized theory which says that a moving particle of the kind experimented with can assume one of two opposite states that can be physically seen on coming to rest in a detector, just like a tossed coin is possibly in one of two equally likely states, either heads or tails, on coming to rest somewhere on the ground. While in motion, the spin state is as yet physically unobservable and insofar indeterminate for the observing mind. This does not entail, however, that, as long as the particle is in motion, it is in both spin states ‘simultaneously’ in the same instant. Rather, it has the potential to assume one of these states in the future and the particle’s spin-influenced motion has been precisely preconceived mathematically as indeterminate, wavering between two possible outcomes.

3.4.1 Non-commutability of operators and quantum indeterminacy

To recapitulate and extend the above discussion, I shall first give an orthodox interpretation of quantum indeterminacy in terms of the non-commutability of Hermitian operators on a complex Hilbert ket-vector space. A quantum state as a dynamic physical set-up or situation is a generic concept for everything physical in the world and, as such, supersedes the older basic physical concepts of particle and force-field. It is not localized in a particle, but is an entire physical-dynamic situation situated 3D-spatially, with this spatiality being captured by the notion of a spread-out wave with phases captured mathematically by complex-imaginary exponents of the Eulerian exponential number, e. (The conception of a 3D-temporal quantum situation would break with the strictures orthodoxly laid down by quantum physics as a predictive science, as discussed further below.) Mostly, however, a quantum state is carefully preconceived, designed and set up in line with a mathematized theory to experimentally interrogate the kinetic behaviour of (usually) sub-atomic (but also atomic or molecular) quantum entities conceived as quantum states to empirically validate or invalidate the theory. The aim is to gain a law-like, mathematically precalculative grasp on the movements of relevant quantum entities. What can be observed of quantum states is determined by operators on the ket-vector space operating on, i.e. transforming, such ket-vectors into the canonical state of a superposition of distinct eigenstates (represented mathematically as eigenvectors) associated with the eigenvalues of the given operator. Any state is then expressible as a complex-linear superposition of a chosen orthonormal basis of eigenvectors, usually for some observable. In line with a proposal by Max Born, the squared magnitudes of the complex coefficients in such an expansion are interpreted as the probabilities of obtaining each eigenvalue upon (future) observational measurement by the observable operator. Upon measurement, the quantum state must assume just one of its eigenstates (as prescribed by the mathematics of linear vector spaces employed) with its associated eigenvalue that is constricted to be a real number by stipulating that the observable operator be Hermitian. Any subsequent measurement of this eigenstate will reproduce only this one eigenvalue-measurement (a fundamental postulate of quantum mechanics).
To grasp the dynamics of the quantum state, however, observational measurements of more than one observable dynamic parameter are required. For instance, it is not sufficient to observe only the spatial location of a quantum state. Since physics is concerned with dynamics, i.e. with movement, the linear or angular momentum of the quantum state, for instance, must also be measured and accounted for theoretically. Momentum, be it linear or angular, as a dynamic parameter like spatial position, is also conceived as a superposition of multiple potential eigenstates of momentum. The same quantum state can therefore be represented also as a complex linear superposition of momentum eigenstates in a chosen orthonormal basis, say, of position. Once a position measurement has been carried out on the quantum state and it has irrevocably entered a single position eigenstate, its representation as a superposition of momentum eigenstates remains hovering in a multiplicity of potential momenta eigenvalues that may be actualized upon measurement, each weighted with the probabilities of the squared coefficients of the momentum expansion of the quantum state in the position basis. Hence repeated measurements of the momentum will result in a statistically manifested probability distribution, i.e. in an indeterminacy of measurement.
The repeated measurement of one observable, say, spatial position, of a carefully prepared quantum state will result in a spread of position measurements (real eigenvalues) whose spread, as calculated by standard deviation, can be reduced, thus increasing the precision of the position measurement in terms of probability by narrowing the spread of the distribution. For each of these repeated position-measurements, however, the quantum state is in different superpositions of another, interrelated dynamic parameter (standardly employing the example of the famous Schrödinger wave equation): linear momentum, which, upon its measurement, displays an ever greater spread as seen in the wider spread that is quantified by a larger standard deviation of the measurements. That is, the momentum measurement becomes less precise, the greater the precision (probability confidence) of the position measurement. This is the nub of Heisenbergian quantum indeterminacy: observable-operators do not commute; their order matters. The increased precision in measuring one observable parameter of a quantum state is paid for by less precision in measuring another. This is a general feature of non-commuting operators of a complex linear ket-vector space, not just of position and linear momentum nor of Hermitian observable-operators generating real measurements.
Position and (linear) momentum, as well as their commutator relationship to one another, are all quantized in quantum physics. They also remain conceived as continuous. How so? Both position and linear momentum are conceived as observable operators on a Hilbert vector space whose elements are ket-vectors of superposed quantized eigenstates of position or momentum. This Hilbert space, however, is conceived as infinitely dimensional with the infinity being an uncountable one of the real continuum. Hence both the operators, position and linear momentum, are continuous, represented by continuous functions. The relationship between position and momentum is also quantized by their non-zero commutator containing the Planck constant that keeps them apart. The probability distributions of both position and momentum on observation are again both continuous in vector spaces of continuous-infinite dimensions and are both continuously variable, but their joint spread cannot be made arbitarily small by repeated measurement, being held discretely apart as they are by the Planck constant. Hence a duality of discreteness and continuity holds sway in this quantized mathematization of a basic physical phenomenon, namely, motion itself in terms of position and momentum. It is one particular manifestation of the famous and notorious wave-particle duality of quantum physics.

3.4.2 Paradoxes of a quantized mathematization of the physical world

The complications of non-zero commutators for dynamic variables such as position and linear momentum for their precalculation is just one perplexing consequence of the quantized mathematization of the physical world. Another, intimately associated one is the observed phenomenon of wave-like interference of particle-like quantum entities, as in the well-known double-slit Gedankenexperiment, and the resultant ambiguity of particle-wave duality forced on quantum physicists attempting to theoretically precalculate the movements of quantized entities.
The introduction of physical quanta was first imposed on theoretical physics by the breakdown of a mathematized description of electromagnetic radiation in terms of continuous, real mathematical functions. Planck proposed the famous Planck constant, h, to quantize energy levels in an atom as discrete multiples of the finite frequency f of the radiation emitted: E = h.f. This theoretical move was made to avoid the consequence of infinite energy levels for continuously increasing, high-frequency (ultraviolet) radiation emitted from an idealized black body. From then on, the quantization of physical entities such as photons and electrons had to be taken into account mathematically. The first physical phenomenon to be quantized was light itself, the absolute physical motion of relativity theory. Electromagnetic light waves had to be conceived mathematically as quantized into photons, which are for physics tiny packets of pure motion, i.e. pure energy with massless momentum.
Hitherto, since the inauguration of mathematized physics in the 17th century with Galileo and Newton, physical entities and parameters had been uniformly treated as continuous real variables whose variability over linear time could be handled calculatively by the infinitesimal calculus. This required the mathematical physicist to imagine (conceive) that any physical entity, including space and time themselves, could continuously approach a zero-dimensional point-limit to make it amenable to the infinitesimal calculus of differentiation and calculation. Even after the quantization of mathematized physics, the predictive calculation of the movement of quantized entities (as quantum states) still had to employ differentials with respect to continuous, linear, real time, t, to maintain any sort of precalculative grip on physical movements of all kinds. Other classical variables, however, notably position and linear momentum, lost their imagined continuity to a discrete quantization. As we know from high school maths, classical mechanics operates with continuous time and continuous space to derive continuous velocity v at an instant in this continuous, linear time. A physical thing in this classical mechanics is conceived as composed of point-mass particles with linear momentum m.v in a continuum of matter whose motions can be precalculated by the application of three simple, Newtonian, mathematical laws of motion.
In quantum physics, these basic physical variables, position and linear momentum, lose (and also retain) their continuity with the consequence that they must be conceived mathematically as a complex-imaginary superposition of many different quantized states rather than the unique state calculated by differentiation and integration of continuous real position and continuous real momentum. Each possible physical state of position and momentum must then be quantized, and thus rendered precalculable, by the mathematical probabilities of an operatoe rather than unique solutions to differential equations. The calculative hold of mathematized physics on physical motion and movement is thus both weakened and maintained. Since quantum phenomena are endlessly repeated in nature, the stochastic quality of their movement in linear time can be easily coped with by means of probability calculus. This is sufficient for practical purposes, especially since all mathematized modern science, both natural and social, has to take into account experimental errors by employing quantitative stochastic-statistical methods. Hence, in a sense, all modern science has to calculatively cope with the indeterminacy of all movement.
Thus, despite the set-back of forced quantization, modern quantum physics remains true to the Pythagorean insight into numbers as a secret key to the world and also to the Galilean edict that the laws of nature are written in the language of mathematics. The wave-particle duality in ‘our’ (i.e. the mathematical physicists’) ‘picture’ of the physical world is ultimately a reflection of the duality in mathematics itself between (originally arithmetic) discreteness and (originally geometric) continuity, the countable infinity of the rational numbers and uncountable, irrational infinity of the continuum. Already the Greeks grappled with the irrational non-commensurability of certain real numbers of the continuum. The forced quantization of continuous, linear time itself, that is indispensable for calculating and thus predicting physical movement, would be a last bastion to fall in defending the mathematization of the world by the modern sciences. This last bastion could never fall due to any conceivable physical experiment, but only as a consequence of how time itself is conceived by our shared historical mind, that is, how time itself is hermontologically cast as what it is. This task of undermining the conception of linear, real time, however, is not and cannot be the concern of physics or any of the other modern sciences for the simple reason that the raison d’être of science ever since the Greeks has been to predict movements and thus enhance the hold of the unbridled will to power over movements of all kinds. 

Further reading: Ballentine, Leslie E. Quantum Mechanics: A Modern Development World Scientific Publishing Co. Pte. Ltd., Singapore 1998.
Bowman, Gary E. Essential Quantum Mechanics Oxford U.P., New York 2008.
Eldred, M. Movement and Time in the Cyberworld De Gruyter 2019