A New Theory of Time: X-tention is Simultaneously Discrete and Continuous

Time has been conceived mainly as either discrete or continuous, but not widely as a simultaneity of the two. I would like to articulate a new theory of time in which time is reconceived as a ‘raw material’ whose natural state is both discrete and continuous. This is a “middle third” position that extends Husserl’s theory of internal time consciousness by being a new form of time in the middle between and connecting retention-protention (which are continuous) and recollection-expectation (which are discrete). What I am naming X-tention is this middle kind of time, existing in a primordial state that is simultaneously discrete and continuous, with the capacity to solidify into either in the case of a specific situation. Time could be analogous to another fundamental physical element, light, which exists in a superposition state of both particle and wave before collapsing into one or the other per observation.

Husserl's theory of internal time structure 
In The Phenomenology of Internal Time Consciousness (1893-1917), Husserl expounds his theory of the structure of time. His core claim is that any present-now moment is comprised of three elements. There is a primal impression, the pure perception of the present now, plus a link to what this perception retains of just-recently past-now moments (retention) and what it anticipates of quickly-upcoming future-now moments (protention). Husserl distinguishes between two kinds of memory, primary memory as retention and secondary memory as recollection. Retention does not break continuity with the present-now moment; it is the part of a temporal object that contemplates its pastness and allows the present to emerge from the temporal background. Recollection does break continuity with the present; the current moment is interrupted to recall and re-represent past memory. Husserl’s theory is depicted in Figure 1.

Figure 1.

A new middle third form of time: X-tention
Retention-protention is continuous; recollection-expectation is discrete. Recollection and expectation are piled-up snapshots of discrete past moments and imagined future events. When brought to mind, they are reproduced in a new present-now flow, but exist prior to recall or replay as un-presented discrete elements. The structure of the present-now moment, on the other hand, is a continuous flow of the intentional unity of primal impression and retention-protention. How far the retention-protention horizon extends is unclear. It might only encompass the most immediate recent-pasts and near-futures surrounding the primal impression of the present-now moment, or it might extend to include all previous and future experiences in the realms of recollection and expectation. I posit the conception of a middle third form of time, X-tention, to sit respectively between recollection and retention, and protention and expectation. My addition to Husserl’s theory is illustrated in Figure 2. Whereas protention and retention are continuous, and recollection and expectation are discrete, X-tention as the middle form of time is simultaneously discrete and continuous.

Figure 2.

X-tention: a superposition of raw time collapsible into discreteness or continuousness
X-tention as the middle third conception of time is conceptually similar to light’s wave-particle duality. Like light, the idea is not that time is an either/or kind of a thing. Light is not the kind of thing that is a particle or a wave, light is the kind of a thing that is more fundamentally not either, and may behave like a wave or particle depending on the situation. Likewise, the nature of time could be that it is fundamentally a kind of a thing that is more malleable in its core state, and that may behave as discrete or continuous based on the situation. X-tentive time thus exists as a possibility space where time is simultaneously discrete and continuous, a superposition of the possibility of both until collapsed into a reality situation of one or the other. The metaphor is that of Schrödinger’s cat, which exists in a quantum superposition state of being simultaneously both dead and alive until an observer looks into the box and the state collapses into one or the other. With X-tention too, it is possible to “look into the box,” i.e.; force the superposition state of dual time possibility to collapse into a reality instance of either discreteness (recollection-expectation) or continuousness (retention-protention). The possibility state collapses into one determination or the other. Since time is a function of the intentional act of meaning, for Husserl, in the case of time, “observing” would be applying an intentional act of meaning. Applying an act of meaning, in the sense of directing intentionality toward an object or objective, would collapse the potential time instance into either retention-impression-protention (continuous) or recollection-expectation (discrete).

Why is a middle third position of time needed? 
It may well be queried why a middle third position of time might be needed. How is it that Husserl did not more explicitly connect the two time regimes? Likewise, while other subsequent thinkers of time such as Heidegger and Derrida have critiqued many aspects of Husserl's theory, they essentially adopted wholesale the time structure of continuous retention-impression-protention and discrete recollection-expectation. However, I think that the discrete and the continuous are too disjoint, and do not seem to connect closely ontologically, methodologically, or practically to each other. Even just the posited structure of time as a binary “either-or” state is an indication that these might not be the only states, or that like light, the more foundational nature of the phenomenon is such that discreteness and continuousness are merely proximate behavioral dimensions of a more profound underlying phenomenon. Conceiving of time as simultaneously both discrete and continuous might also more closely correspond to the real-life phenomenological experience of time, which can seem to be both simultaneously snapshot and flow in the course of lived experience. Moreover, this is congruent with the Husserlian project of phenomenology, describing “how” things are experienced, not “what” is experienced. In summary, the concept of the middle third term of time, X-tention, is simultaneous time duality, where one of time’s properties is discreteness versus continuousness. "Raw time" or "pure time" exists simultaneously in a superposition of both states before an intentional act of meaning collapses it into one or the other state. X-tention can be seen as a perdurant (e.g.; temporal object-based) temporality of complexity because indeterminacy (as non-determinacy) is a key property. A temporality of complexity is important as we are now starting to have the understanding and technological tools to approach reality in the more nuanced manner of complex systems (non-linear, dynamic, emergent, open, unknowable at the outset, interdependent, self-organizing) as opposed to situations of simple linear causality.

Matter, energy, and light vs. space and time
I am positing the case of light wave-particle duality as a metaphor, not necessarily as justificatory grounds for my conjecture of a middle third designation for time. Just because duality is true for light does not mean that duality would be true for time. For one thing, matter, energy, and light are one class of physical phenomena, while space and time are another. Matter, energy, and light are ‘what is there,’ while space and time are the composition of the background. It is not that light is grounds for time, but it could be that many or even all physical phenomena ultimately turn out to have a property of duality or multiplicity. At small enough scales, many phenomena in physics might have a duality or multiplicity of states and behaviors, or more broadly indeterminacy as a general property that collapses from possibility to actuality per certain conditions. The presence of an observer is also a dynamic that is not yet fully understood. Matter, energy, and light are inter-translatable per Einstein’s equivalency of E=mc², and thus perhaps all subject to wave-particle duality in some sense.

Physics: Scientific formulations of time as simultaneously discrete and continuous 
The conceptualization of time as simultaneously discrete and continuous is an under-explored notion in the philosophy of time, but is enjoying some degree of investigation in physics. One interesting paper notes that information is a quantity which is both discrete and continuous, where time and other physical phenomena might be reconceived as simultaneously discrete and continuous with an information theoretic formulation. The specific calculation involves Shannon’s sampling theory, which is essentially scaling any ‘analog’ phenomenon down to a digital’ formulation, and translating between the two. Another theory, loop quantum gravity, also holds that time might be simultaneously discrete and continuous at small enough scales, like the smallest scale, the Planck length (1×10⁻³⁵ m). Nanotechnology, the precise placement of atoms in positional nanoassembly as a comparison for example, takes place at the (1×10⁻⁹ m) scale. At the Planck scale, fundamental building blocks of spacetime might be composable like Legos into different spacetime fabrics, such as those of “regular” baryonic matter, dark matter, and dark energy.

More information: Temporality of the Future

Magic Blockchains, but for Time? Blocktime Arbitrage

There is no doubt that blockchains are a reality-making technology, a mode and means of implementing as many flavors of our own crypto-enlightenments as we can imagine! This includes newer, flatter, more autonomous economic, political, ethical, scientific, and community systems. But not just in the familiar human social constructs like economics and politics, possibly in physical realities too like time. Blocktime’s temporal multiplicity and malleability suggest a reality feature we have never had access to before – making more time.

Blocktime: A General Temporality of Blockchains
Blocktime as blockchains’ own temporality allows the tantalizing possibility of rejiggering time and making it a malleable property of blockchains. The in-built time clock in blockchains is blocktime, the chain of time by which a certain number of blocks will have been confirmed. Time is specified in units of transaction block confirmation times, not minutes or hours like in a human time system. Block confirmation times are convertible to minutes, but these conversion metrics might change over time.

Blocktime Arbitrage
One key point is that the notion of blocktime, as an extension of computing clocktime more generally, creates a differential. Blocktime and human time already exist as different time schemas. A differential suggests that the two different systems might be used to reinforce each other, or that the differential could be exploited, arbitraging the two time frameworks. Through the differential too is the way to ‘make more time,’ by accessing events in another time trajectory. The conceptualization of time in computer science is already different than human time. Computing clocktime has more dimensions (discrete time, no time, asynchronous time, etc.) than human physical and biological time, which is continuous. Clocktime has always been different than human time. What is different with blocktime is that it builds in even more variability, and the future assignability of time through dapps and smart contracts. For example, MTL (machine trust language) time primitives might be assigned to a micropayment channel dapp as a time arbiter.

Time has not been future-specifiable before, in the way that it can be assigned in blocktime smart contracts.

Temporality as a Smart Contract Feature
Time speed-ups, slow-downs, event-waiting, and event-positing (a true futures-class technology) could become de rigueur blocktime specifications. Even the blocktime regime itself could be a contract-specifiable parameter per drop-down menu, just like legal regime. Temporality becomes a feature as smart contracts are launched and await events or changes in conditions to update contract states. Time malleability could itself be a feature, arbitraging blocktime with real time. An example of a time schema differential arising could be for example, a decentralized peer-to-peer loan that is coming due in blocktime, but where there have not been enough physical-world time cycles available for generating the ‘fiat resources’ to repay the loan. 

Blocktime Standards
In blocktime, the time interval at which things are done is by block. This is the time that it takes blocks to confirm, so blockchain system processes like those involving smart contracts are ordered around the conception of blocktime quanta or units. This is a different temporal paradigm than human lived time (whether Bergsonian doubled duration (the internal sense of time passing) or external measurable clocktime). The human time paradigm is one that is more variable and contingent. Human time is divided and unitized by the vagaries of human experience, by parameters such as day and night; week, weekend, and holiday; seasons; and more contingently, crises, eras, and historical events.

Since blocktime is an inherent blockchain feature, one of the easiest ways to programmatically specify future time intervals for event conditions and state changes in blockchain-based events is via blocktime. Arguably, it is easier, and more congruent and efficient, to call a time measure from within a system rather than from outside. It could be prohibitively costly for example, to specify an external programmatic call to NIST or another time oracle. Possibly the emerging convention could be to call NIST, including as a backup, confirmation, or comparison for blocktime. Currently, blockchain systems do not necessarily synchronize their internal clocktime with NIST, but the possibility of a vast web of worldwide smart contracts suggests the value and necessity of external time oracles, and raises new issues about global time measurement more generally. Especially since each different blockchain might have its own blocktime, there could be some standard means of coordinating blocktime synchronizations for interoperability, maybe via a time sidechain for example.

Novel Temporalities of Computing (Discontinuous) and Big Data (Predictive)
First computing clocktime made time malleable through its different discontinuous forms. Then machine learning and big data facilitated a new temporality, one oriented to the present and future, instead of responding to just the past. There was a shift from only being able to react to events retrospectively after they had passed, to now being able to model, simulate, plan, and act in real-time as events occur, and proactively structure future events. The current change is that blockchains and particularly smart contracts add exponential power to this; they are in some sense a future reality-making technology on steroids. Whole classes of industries (like mortgage servicing) might be outsourced to the seamless orchestration of blockchain dapps and DACs in the next phases of the automation economy. While Bitcoin is the spot market for transactions in the present moment, smart contracts are a robust futures market for locking in the automated orchestration of vast areas of digital activity.

Blockchain Historicity: Computer Memory of Human Events
Blockchain logs are a human event memory server. Blockchains are already event history keepers, and now with blocktime have even more responsibility as the memory computer of human events. It is now possible to think in terms of blockchain time sequences, in the anticipation and scoping of future events and activities, as blockchain reality unfolds, as opposed to human time scales and events. For example, there are normal human time sequences, like a one-year lease agreement. Other sequentiality is based on human-experienced conditions like ‘the park is open until dark,’ which makes little sense in a blocktime schema. There are time guidelines that vary per lived experience in human realities. Likewise, there could be analogs in lived experience in blockchain realities. Different events could mark the historicity of blockchains, for example, the time elapsed since the genesis block, and other metrics regarding number, amount, and the speed of transactions. In cryptophilosophy, Hegel, Benjamin, Holderlin, and Heidegger’s conceptions of historicity and temporality might be instantiated in the blocktime paradigm, where, in ecstatic temporality, historicity is the event from the future reaching back to present now (Heidegger, Being and Time, 474).

Related Crypto-philosophy Talk: Swan, M. “Bergson’s Qualitative, Kant’s Time and Imagination, and Blocktime Smart Contracts.” Spatiality & Temporality Conference. 11-13 December 2015. Warsaw, Poland.