A response in a philosophical dialogue
I'm afraid we are very far apart. You yourself name the crux: "we
disagree on the question of time" which I do
not at all see as "a primary property of the extant
domain" whereas you regard it as "an
artefact of the existence of matter-energy" which provokes me to pose the question: What does "existence" mean here?
The incompatibility between our conceptions, in truth, lies much deeper, for each of us conceives two entirely different temporal phenomena and name them by the same name simply as 'time'. If my concept of genuinely three-dimensional time "invokes Heideggerian suppositions", then your conception of one-dimensional time (compatible with "matter-energy") invokes Aristotelean preconceptions. Why? Because the conception of time that reigns today (with various nuances) is thoroughly Aristotelean. No thinker before Heidegger has ever escaped the gravitational pull of the Aristotelean casting of time.
Aristotle's conception of (linear, one-dimensional) time is lifted from his ontology of efficient, productive movement (based on a simple, everyday phenomenon like carpentry), which is itself linear. The very concept of energy that you so willingly accept as foundational and adhere to is taken originally from Aristotle's concept of _energeia_ (his own neologism), the middle term mediating between _dynamis_ (potential) and _entelecheia_ (lit. having-in-the-end-ness). Newton thoroughly mathematized this ontology, which is to be found also in Kant's Urteilstafel (the table of judgements for understanding that serve as its logical rules).
Because this conception of one-dimensional time is lifted from, i.e. derivative of a (specific) kind of movement, it is not and cannot be originary and in truth misses the phenomenon of time entirely. Therefore all Western (and today global) conceptions of time conceive it as a kind of movement that, of course, can also be counted off. Hence the most vulgar concept of clock-time that is indispensable for mathematized physics. The predominant kind of movement investigated by physics is change of place, _kinaesis kata to topon_ or loco-motion, to which all the modern (mathematized) physical sciences reduce any kind of movement. Why? Because change of place is most amenable to mathematization via the real variable t.
The Aristotelean conception of (one-dimensional) time is also spatialized, derived as it is from movement as change of place. Hence spatialized conceptions of time reign supreme today without question, with time even being conceived as derivative of (motion in) space. This is entirely consistent with the Aristotelean conception of (one-dimensional) time. Even Hegel spatializes (1D) time in his Naturphilosophie, and Einsteinian relativity theory conceives time as the motion of light (electromagnetic radiation) through space.
The linear time of Aristotelean ontology of (efficient, productive) movement goes hand in hand with the linear temporal connection of cause and effect. Without the conception of efficient causal movement, implicating the en-erg-eia or at-work-ness of a power (_dynamis_), there would be no modern science at all, be it natural or social. The causal nexus is the lifeblood of modern science, even when it becomes frayed and fuzzy, and has to resort to statistical methods based on mathematical probability theory, as in statistical mechanics or quantum dynamics.
By contrast, what you call "Heideggerian suppositions" derive from the study of a completely different phenomenon whose rudimentary outlines Heidegger discovered in the early 1920s studying Kant's Kritik der reinen Vernunft in his pursuit of the question: What does being itself mean? Heidegger's reading homes in on the Einbildungskraft (power of imagination) that mediates in the KdrV between sensuousness and understanding. The three temporal dimensions in their rudiments can be discerned there under the names of apprehension. reproduction and recognition.
This uncovering of rudimentary originary time in the power of imagination leads to a fundamentally alternative conception of time as genuinely three-dimensional, i.e. the three temporal dimensions are independent of each other and not linearly dependent. Moreover, this conception of 3D-time is prior to any kind of movement, i.e. not derivative of any kind of movement. Rather, 3D-time enables (free, independent) movement of all kinds, whereas a particular kind of efficient-causal movement allows a (derivative) conception of 1D-time to be lifted off it, as Aristotle originally did.
Only the conception of three-dimensional time (a phenomenon with which we are all intimately acquainted, if only we paid attention to it) allows an alternative ontology of movement that is basically incalculable, unpredictable, uncontrollable, 'non-linear' in a genuine sense and is thus free. It is the ontology of interplay that involves not cause-effect relations at all, but rather mutual estimation in power plays of various kinds.
This ontology is fitting for a social phenomenology of whoness. Why? Because all sociation (Vergesellschaftung) is a movement of mutual estimation that is always also a power play, play between and among powers emanating from different sources rather than a single source, as it is in the Aristotelean ontology of movement. Without this ontology of interplay, I assert, there is no possibility of approaching and appropriately conceptualizing whoness as distinct from whatness, for the play of mutual estimation among whos eludes the grasp of the will to power over movement. Only within three-dimensional time is there the possibility of freedom of movement, hence of freedom per se.
The old, traditional conception of one-dimensional time, on the other hand. is contained in a truncated way within the conception of genuinely three-dimensional time only as a special, highly restricted case.
You may ask: Why are the three dimensions of time independent of each other?
Because the mental imagination has the power to hip-hop
haphazardly throughout the openness of 3D-time, from one
temporal dimension to another, without regard to following any
physical movement in space. That's the way the mind moves, focusing on
this and that. Such mental movement may be illogical, irrational
for traditional conceptions, but it is in general an entirely coherent
3D-time is prespatial. It provides the openness for any extended, physical entity to take a spatial place and present itself to the mind, and also for non-physical, non-spatial entities such as mathematical ones (e.g. complex imaginary numbers) or fantastic products of the imagination, to presence and absence. The mind can only understand entities insofar as they presence and absence within the 3D-temporal openness which represents the finite limits of human beings' experience. Entities exist only insofar as they stand-out into this ec-static temporal openness in which they essence (verbally, comprising presencing and absencing). 3D-time thus enables all sorts of movement (including physical movement and mutually estimative interplay) in the world, and the mind can only see any movement as such because it is endowed with temporally triple vision that sees 'simultaneously' or all at once into the three temporal dimensions.
Further reading: A Question of Time and