18 December 2016

Aristotle's "before and after" & quantum gravity

Aristotle's famous and fateful definition of time reads:
"Time is the number of movement with regard to before and after" 
(o( xro/noj      a)riqmo\j kinh/sewj kata\ to\ pro/teron kai\ u(/steron e)stin, Phys. IV xi 219b2; vgl. auch De Caelo I ix. 279a15)
This hermeneutic cast of time remained in force throughout Western history without question until Heidegger's thinking put it into question in 1927 with the publication of Being and Time. His treatise shows that this "arithmetic" clock-time is a "vulgar" derivative of an originary time which provides the answer to the question concerning the "meaning of being" (die Frage nach dem Sinn des Seins). This gives us something to chew on philosophically that has so far been neglected, not only in analytic philosophy, not only throughout modern science, but even in Heideggerian scholarship. I won't go into the details of this neglect here (cf. however A Question of Time).

Instead, here is a simple observation that apparently has not been made throughout the two-and-a-half millennia separating us from Aristotle: Aristotle's definition is viciously circular. The simplest things are hardest to see. To define time as the number of movement/change with regard to "before and after" presupposes that "before and after" — which themselves are temporal determinations — are already understood. The tradition has invariably focused on the number of movement, that is, on the clock, no matter whether this clock is taken to be a sun dial measuring the sun's regular return to the same longitude each day or the frequency of electronic transitions in a caesium 133 atom. The temporal "before and after" are tacitly presupposed.

As any philosopher worth his or her salt knows, philosophy's job is to unearth the tacit presuppositions on which any (philosophical) thinking is implicitly based, thus making them explicit, visible. This is how philosophy progresses, namely, by moving backwards into the tacit presuppositions. With Heidegger, philosophical thinking has moved backwards into the most elementary phenomena possible: being and time — phenomena that are taken for granted by everyone and every philosophy and every science, thus in their questionability invariably overlooked.

Without always already (a priori) understanding before and after, and the now in between them, we would not be human beings. Aristotle also famously said, and modern science agrees, that only that which is now exists all. All that is before was and is no longer. All that is after is not yet. For modern science what is 'now' are the sensuous data it collects with its detection instruments of all kinds and of all degrees of sophistication, right through to the Large Hadron Collider in CERN and the planned LISA laser interferometer in outer space for detecting the long-sought gravitational waves. 

Without presupposing before and after, it would be senseless, for instance, to talk of a Big Bang, of an expanding universe, or any other competing variant thereof. After all, ever since Aristotle, physics has been the science of ta\ kinou/mena , i.e. of that which can move/change.  Mathematized physics has long since laid claim to the title of the fundamental science on which all other sciences are based, from chemistry, biochemistry right through to neuroscience and the scientific quest for cracking the phenomenon of so-called consciousness, which seems — misguidedly — to be holy grail for today's science. 

One of the two most promising approaches to the long-sought-for theories of quantum gravity, along with string theory, is loop quantum gravity associated with the names Carlo Rovelli, Lee Smolin and Abhay Ashtekar . In his most enlightening 2004 book, Quantum Gravity Rovelli commendably provides many philosophical side-reflections, including on meanings of time. Apart from the first meaning, the "time of natural language" with its "existence of memory and expectations", all the other meanings of time listed up to the penultimate one — including "time-with-a present, ...  thermodynamical.... Newtonian ...special relativistic ... cosmological... proper... clock... parameter time" (p.60) — are one-dimensionally linear.

With the identification of 4D space-time with the gravitational field in loop quantum gravity, the former vanishes and along with it parametric time with respect to which all motion in the electromagnetic and gravitational fields is infinitesimally or discretely differentiated — in favour of a covariance in changed measurements in measuring instruments, including clocks. Time becomes just another measurement read off an experimental apparatus and thus surreptitiously remains counted clock-time. 

Rovelli calls this final meaning "no time", "the idea about time underlying every theory in which there is no fundamental notion of time at all" (ibid.). What this "underlying" "idea about time" is or could be Rovelli does not say. In truth, he merely hides the traditional conception of counted clock-time in the mathematics. 

Since Rovelli does not tell us anything about a deeper conception of time, let's provide the answer, which can come from a serious engagement with and critique of Heidegger's thinking. This "fundamental notion of time" is hidden in the "before and after" in Aristotle's definition, which he nowhere explicates  Before and after name two dimensions of ecstatic (Latin meaning literally out-standing) time to which, along with the now of the third dimension, the present, into which human existence stands out. Only through belonging to this three-dimensionally stretched time are we humans human beings who understand the world with our minds. Time and mind are identical in a hermeneutic cast as time-mind. 'Was' and 'will be' no longer name dimensions in which entities do not exist, but in which they presence and 'are' in two distinctive modes of absence. Absence is itself a mode of presence in which entities that purportedly 'are not' exist, that is. are — for the human mind. 

This 3D time is genuinely three-dimensional, that is, not one-dimensionally linear and thus confined to a notion of succession. Hence events occur to the human mind with maximum degrees of freedom in which the three temporal dimensions remain continually and 'simultaneously' open to mental leaps. Being mental and thus non-physical, such leaps are not subject to the relativistic absolute limit of the speed of light. 

Moreover, the mind is not on the 'subjective' side of time-mind, and time is not on the 'objective' side. If time were solely objective, it would be 'in itself', an sich, separate from mind like a Kantian Ding an sich. If time were merely subjective, as it is in Kant's transcendental ego, it would be merely 'for us', für uns. In truth, time-mind is an-und-für-sich, neither inside (in so-called consciousness) nor outside (in the so-called external world), but pre-spatially no-where in an identity of time and mind, of Zeit und Geist, in a way consonant with Hegel's identity of subject-object in the Idea, which is likewise an-und-für-sich.

Since all modern, mathematized physics, including the most advanced theories of quantum gravity, is duty-bound to make predictions, thus calculating motion, it must remain unquestionably committed to a notion of linear, successive, 1D time, even when it deals in quantum-mechanical "transition probabilities". Hence the three-dimensionality of time-mind must be truncated for the sake of mastering movement calculatingly. Modern science remains in denial regarding its deep-seated tunnel vision. Why? Because its essence (Wesensbestimmung) is the will to calculating, effective power over movement and change of every conceivable kind

Hence it comes as no surprise that all the modern sciences, starting with physics, and through to the social sciences of economics, psychology, sociology, etc. are all positivist, i.e. based on empirically observable 'facts' to the exclusion of any purported 'transcendent' dimension. Aided and abetted by analytic philosophy, scientific thinking firmly keeps the lid on the ontological difference and denounces any attempt to re-open it. However, modern science and analytic philosophy come too late in closing the lid, because all human being implicitly understands three-dimensional time by virtue of always already understanding 'before' and 'after' and 'now'. None of these dimensions is a being, but is to be found by descending into the ontological difference between being and beings first discovered by Greek philosophy, and then even further into this 3D-time itself AS the clearing that enables beings of all kinds to presence and absence AS what and who they are for our hermeneutically imbued human minds. This explicit uncovering of the open clearing of 3D-time is the task of thinking for our age. Its fourth dimension resides in human being's standing-out (ex-sisting) into this temporal clearing and therefore can be called mind. Mind and time belong intimately together.

On the other side of the divide, so-called Continental philosophy is impotent in the face of the positivist onslaught because — with the rare exceptions of those few who to date have taken Heidegger's world-shattering message of Being AND Time seriously — it is just as clueless about the ontological difference as are science and analytic philosophy.  Continental philosophy has a penchant for merely literary gestures and an aversion against mathematics and mathematized science, and also against conceptual thinking. Thus it is merely an opposed rhetorical position, appealing to those with similar prejudiced proclivities, without providing true insight into the originary time underlying the ontological difference. It is this insight into the temporal clearing that poses the genuine historical challenge to positivist science and its allied, subservient analytic philosophy.

Further reading: A Question of Time and 'The End of Science and the Beginning of Wisdom'.


  1. Dear Michael,
    your account is very interesting, and is in touch with the recent manuscript:
    Heidegger’s Being and Quantum Vacuum:
    A dialogue between Martin Heidegger and a theoretical physician unveils the striking relationships between the philosophical concept of Being and the experimentally detectable quantum vacuum. We provide an account of long-standing theoretical issues, such Being, Entity, Existence and the unique role of the human Thoughts in the world, and expound their possible physical counterparts.
    see: http://vixra.org/abs/1612.0280

    Concerning Rovelli, his "underlying" "idea about time" is the following: he provides an explanation of the VERY microscopic world not in terms of strings as usual, but in terms of the so called "quantum gravity". In the quantum world, differently from our macroscopic world, the concepts of time and cause/effect do not hold anymore: a quantistic event is called "time-symmetric", meaning that the arrow of time can proceed both in what we call the "future" and in the "past".

    1. Thank you for the comment and link. Quantum vacuum is still a physical entity, of course, albeit a minimum one. Insofar, it is incomparable with being itself, which should not be confused with entities, i.e. with beings.

      The so-called "arrow of time" then points in both temporal directions from the present and is thus still linear, one-dimensional, albeit now bi-directional?

      It should be noted that, as that which enables movement/change and is thus prior to it, 3D-ecstatic time itself in unmoving. In fact, in its identity with mind, time-mind itself is not physical at all. Nor is it meta-physical in the sense of 'beyond the physical, sondern rather 'pre-physical', prior to all that is physical and thus movable/changeable.

  2. For me, all these fascinating ideas revolve around the possibility of being aware of them. Starting from that awareness, I find its matrix in my sense of my embodied personal presence. Question, can that awareness (consciousness) be regarded as the first, non-instrumentally mediated perception? Can its matrix of body be regarded as the primary instrument of observation - still in a direct intimacy with the world, not yet producing perceptions processed into computable form? Sorry, this is all amateur thinking. I'll stop here: 'time' as I am personally aware of it is the space I live in, while the 'time' told my clock is trip line cutting through that space, that I keep falling over.

    1. Thank you, Jonathan. If you think about it, personal awareness consists not only in a sense of your own embodied personal presence, but in your being stretched 'simultaneously' into past and future in your mind e.g. with what happened yesterday, what you plan or expect for the next couple of months, etc. Moreover, your awareness of your present situation only makes sense within the context of the three-dimensional stretchedness of your personal existence. We perceive the world 'all at once' in its temporal 3D expansiveness, merely hopping mentally effortlessly between the three temporal dimensions in often haphazard ways, not merely sequentially, linearly.

      Of course, to 'be here' in this time-mind identity, you need your body and in particular your brain. But the brain is merely the physical organ (tool) used by the mind for thinking. Even though, of course, you have personal opinions, personal views, the ideas you have are historically shaped by the times in which you live. Insofar, your opinions are only particularizations and you belong to this historical time-mind of an age and share your ideas per force with many others, even though they may seem to be your 'very own'. Very, very rarely is a new thought thought, and this is the realm and task of philosophy.

  3. However, a recent claim suggests that brain activity might occurr in... four,and not three spatial dimensions!
    Towards a fourth spatial dimension of brain activity:

    1. Interesting. The abstract says, "Our thoughts [NB: NOT merely our 'brain patterns' ME] exhibit [...] the unique ability to connect past, present and future events in a single, coherent picture as if we were allowed to watch the three screens of past-present-future 'glued' together in a mental kaleidoscope."
      The article claims that this is an accomplishment of the brain, a physical organ. with "brain functions embedded in a[n] imperceptible fourth spatial dimension."
      Why should this ostensible fourth dimension be spatial?
      Isn't it in truth 4D-time-mind that is being addressed here (the fourth dimension being that human being itself is embedded in time-mind)? Time-mind understands all three usual temporal dimensions 'simultaneously'; no need for sophisticated torus topology. Time-mind is not physical at all, and beyond the reach of the physical sciences, including neuroscience, which is concerned only with the physical brain and its ancillary organs. In ignoring the issue concerning the (pre-physical) nature of time itself, modern science is on a wild goose chase after so-called 'consciousness'.

    2. Let's say that in judiciously evading the issue concerning the (I claim: pre-physical) nature of time itself, modern science is on a wild goose chase after so-called 'consciousness'. It is judicious, because in this way physical science maintains its hegemony, including that of the experimental scientific method essential to all physical science as THE criterion of 'truth'. But the issue concerning the nature of time is eo ipso not accessible to testing by any experiment whatsoever. Rather the question concerning the nature of time is an issue challenging philosophical thinking today, whose essential task it is to think through the most elementary of phenomena, thus unearthing the unjustified presuppositions made by modern, mathematized, experimental science.

  4. Is the brain multidimensional?
    There are two different ways to define and assess brain dimensions. Indeed, the term dimension may reflect either
    a) functional relationships of brain activities, or
    b) anatomical connections between cortical areas.

    a) The first approach takes into account the dimensionality of the neural space. Connectivity and complex network analyses of neural signals allow the assessment of the complex dynamics of brain activity, providing a novel insight into the multidimensionality of various neural functions’ representations (Kida et al., 2016). From a dynamical system perspective, one would expect that brain activities are represented as, for example, some scalar quantity measured at different brain locations (say N locations) at different points in time. Then one could describe nervous dynamics as trajectories and/or manifolds in a N-dimensional phase space (Lech et al., 2016). Mazzucato et al (2016) demonstrated that stimuli reduce the dimensionality of cortical activity. Clustered networks, such as default mode network, have instead a larger dimensionality, because the latter grows with ensemble size: the more neurons are recruited, the more the dimensions (Mazzucato et al, 2016). Apart from giving insights in neural dynamics in the canonical three dimensions (space, time, and frequency), complex network analyses are also able to evaluate other functional dimensions, e.g. categories of neuronal indices such activity magnitude, connectivity, network properties and so on (Kida et al., 2016). It must be taken into account that dimension reduction and symmetry breaking display close relationships, so that symmetries are correlated with changes in functional dimensions in the brain. Indeed, a key feature of dynamical approaches is that the dynamics they predict are characterized by nonequilibrium phase transitions, and therefore breaks of symmetries (Scholz et al., 1987). Many studies emphasized how different levels of behavioral dynamics’ organization take place in neural ensembles. To make some examples, Jirsa et al. (1998), focusing on the cortical left-right symmetry, derived a bimodal description of the brain activity that is connected to behavioral dynamics, while Jirsa et al. (1994) demonstrated that, when an acoustic stimulus frequency is changed systematically, a spontaneous transition in coordination occurs at a critical frequency, in both motor behavior and brain signals.

    b) Concerning the second approach to brain dimensionality, it has been recently suggested that brain trajectories, at least during spontaneous activity, might display four spatial dimensions, instead of three (Tozzi and Peters 2016a). Brain symmetric states display dimensions higher than asymmetric ones, so that, in this case, the space of interest does not refer to dynamical neural spaces, but to detectable physical cortical locations. In such a vein, Stemmler et al. (2015) proposed that animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales. Combining population vectors at different microscopic dimensions predicts indeed neural and behavioral correlates of multiscale grid cell readout, that transcend the known link between entorhinal grid cells and hippocampal place cells. While the spatial activity of a single grid cell does not constitute a metric, an ensemble of hierarchically organized grid cells does provide instead a distance measure (Stemmler et al., 2015). In our paper, the mapping of trajectories from high dimensional manifold to lower dimensions refers to both the above described definitions of dimensionality.

    1. What is a dimension? Etymologically it derives from Gk. _diametreo_ 'to measure through, to pass through, to traverse' (Liddell & Scott), a spatial signification. Mathematics abstracts from this physical meaning to obtain a conception of dimension as a continuum of variables that are independent of other variables, likewise in a dimension that can be traverse continuously. Mathematically there can be many, even an infinity of countably or uncountably many, in a mathematical 'space' (e.g. vector space, Hermitian space). The abstract dimensionality of a mathematical space has only a tenuous relationship to physical space that can be passed through. The quantum physicist Sakurai warned against the dangers of getting lost in the mathematical models of quantum physics, thus losing touch with the physical interpretation of the mathematics -- an hermeneutic task.

      Arturo, in your paper 'Towards a fourth spatial dimension of brain activity', you and your co-author, Peters, propose in connection with this "fourth spatial dimension" that, "Our thoughts exhibit [...) the unique ability to connect past, present and future events in a single, coherent picture as if we were allowed to watch the three screens of past-present-future 'glued' together in a mental kaleidoscope."
      How is it that the three usual temporal dimensions are here conceived AS spatial dimensions? And why is the fourth dimension "gluing" them together also treated AS a spatial dimension? What justifies the interpretation of time AS spatial? Is not thereby hermeneutic violence done to the phenomenon of time itself -- for the sake of scientific calculability?

      In relativity theory the justification for spatialization of time is provided by setting up an equivalence between clock-time and the absolute motion of light (electromagnetic signals). But is clock-time the ultimate, primitive time?

      The phenomenon of time has long since been geometrized and mathematized in science, and geometry, as Aristotle shows, performs an abstraction from physical bodies in their places to geometrical figures in their positions. Geometrical visualizations of abstract configurations in mathematical physics remain highly prominent and favoured, but in all this, the question concerning time and its spatialization is studiously evaded. This is not merely an accidental oversight.

      A clarification of the nature of time itself has everything to do with the question concerning the nature of the mind and its relationship to the brain, but these issues are diligently skipped over in favour of developing highly sophisticated mathematical models of the brain whose relationship to the mind or so-called 'consciousness' remains obscure or worse: taken for granted as already clarified.

  5. Dear Michael,
    from Ernst Mach on, the concept of time is deeply changed. Indeed, our universe, after Einstein, is made of four dimensions (three spatial and one temporal), inextricably glued together in a framework of Lorentz transformation. Therefore, the time of Aristotle does not hold anymore.
    Our apprach suggests the brain made of FIVE dimensions: apart from the "classical" four (spacetime), we add a further SPATIAL dimension, that elucidates the brain activity in a "simple" way. We also demonstrated (manuscript under review) the presence of such a spatial further dimension. See here for further details:


    1. Dear Arturo,
      I agree that by tying together the linear dimension of time to the three proper spatial dimensions, Einstein "deeply changed" the conception of time - above all the Newtonian conception of absolute time, which, in Einsteinian relativity, become relative time, that is, time relative to a subject-observer in his or her reference frame. This is also very different from Aristotle's conception, but also the same, for relativistic time remains one-dimensional, i.e. linear, and also countable, i.e. measurable by some kind of clock, whether it be a sun dial or, today, a caesium clock (witness the role of clocks in Einsteinian relativity theory, be it is special or general). In this fundamental sense nothing has changed. One-dimensional time is spatialized in relativity theory hermeneutically AS the absolute motion of light (electromagnetic radiation, or even gravitational radiation).
      In the abstract to your recent paper, you "suggest that several brain activities, such as mind-wandering and memory retrieval, might take place in the functional space of a four dimensional hypersphere". Memory-retrieval and mind-wandering (including into the future), however, are clearly temporal phenomena, so why do you designate a fourth SPATIAL dimension, alongside a one-dimensional temporal dimension? Why not explore the possibilities of a genuinely three-dimensional, phenomenally experienceable time instead? Such a 3D-time is no longer straight-jacketed by linear, countable, and therefore, mathematically calculable time. The postulation of a "four dimensional hypersphere" introduces a differentiable manifold, but physics ostensibly is interested in understanding the physical world experienceable by us human beings. Or is it today more interested in esoteric mathematical models?

  6. The confusion, I think, arises from the definition of time you gave: time, according to the current tenets, is NOT three-dimensional: it is a FOURTH dimension correlated with THREE SPATIAL dimensions.

    1. Dear Arturo,
      This is not at all a case of "confusion", but of clear-sightedness into an alternative. The current tenets of today's established science are simply established orthodoxy. Why not question this orthodoxy? Modern science refuses to do so. And yet, since 1927, with the publication of Heidegger's 'Being and Time' an alternative has been on the table that today's scientists continue to ignore -- or thoughtlessly reject, if they ever bother to stray beyond the mental strictures of their mathematical models.
      I think that broadening the horizon to 3D-time would help today's thoroughly mathematized science understand better its fitting place. Note that I am a mathematician by training.