## The Church-Turing Thesis and the Asymmetry of Intuition

### 23 November 2012

Friday

Alonzo Church and Alan Turing

What is the Church-Turing Thesis? The Church-Turing Thesis is an idea from theoretical computer science that emerged from research in the foundations of logic and mathematics, also called Church’s Thesis, Church’s Conjecture, the Church-Turing Conjecture as well as other names, that ultimately bears upon what can be computed, and thus, by extension, what a computer can do (and what a computer cannot do).

Note: For clarity’s sake, I ought to point out the Church’s Thesis and Church’s Theorem are distinct. Church’s Theorem is an established theorem of mathematical logic, proved by Alonzo Church in 1936, that there is no decision procedure for logic (i.e., there is no method for determining whether an arbitrary formula in first order logic is a theorem). But the two – Church’s theorem and Church’s thesis – are related: both follow from the exploration of the possibilities and limitations of formal systems and the attempt to define these in a rigorous way.

Even to state Church’s Thesis is controversial. There are many formulations, and many of these alternative formulations come straight from Church and Turing themselves, who framed the idea differently in different contexts. Also, when you hear computer science types discuss the Church-Turing thesis you might think that it is something like an engineering problem, but it is essentially a philosophical idea. What the Church-Turing thesis is not is as important as what it is: it is not a theorem of mathematical logic, it is not a law of nature, and it not a limit of engineering. We could say that it is a principle, because the word “principle” is ambiguous and thus covers the various formulations of the thesis.

There is an article on the Church-Turing Thesis at the Stanford Encyclopedia of Philosophy, one at Wikipedia (of course), and even a website dedicated to a critique of the Stanford article, Alan Turing in the Stanford Encyclopedia of Philosophy. All of these are valuable resources on the Church-Turing Thesis, and well worth reading to gain some orientation.

One way to formulate Church’s Thesis is that all effectively computable functions are general recursive. Both “effectively computable functions” and “general recursive” are technical terms, but there is an important different between these technical terms: “effectively computable” is an intuitive conception, whereas “general recursive” is a formal conception. Thus one way to understand Church’s Thesis is that it asserts the identity of a formal idea and an informal idea.

One of the reasons that there are many alternative formulations of the Church-Turing thesis is that there any several formally equivalent formulations of recursiveness: recursive functions, Turing computable functions, Post computable functions, representable functions, lambda-definable functions, and Markov normal algorithms among them. All of these are formal conceptions that can be rigorously defined. For the other term that constitutes the identity that is Church’s thesis, there are also several alternative formulations of effectively computable functions, and these include other intuitive notions like that of an algorithm or a procedure that can be implemented mechanically.

These may seem like recondite matters with little or no relationship to ordinary human experience, but I am surprised how often I find the same theoretical conflict played out in the most ordinary and familiar contexts. The dialectic of the formal and the informal (i.e., the intuitive) is much more central to human experience than is generally recognized. For example, the conflict between intuitively apprehended free will and apparently scientifically unimpeachable determinism is a conflict between an intuitive and a formal conception that both seem to characterize human life. Compatibilist accounts of determinism and free will may be considered the “Church’s thesis” of human action, asserting the identity of the two.

It should be understood here that when I discuss intuition in this context I am talking about the kind of mathematical intuition I discussed in Adventures in Geometrical Intuition, although the idea of mathematical intuition can be understood as perhaps the narrowest formulation of that intuition that is the polar concept standing in opposition to formalism. Kant made a useful distinction between sensory intuition and intellectual intuition that helps to clarify what is intended here, since the very idea of intuition in the Kantian sense has become lost in recent thought. Once we think of intuition as something given to us in the same way that sensory intuition is given to us, only without the mediation of the senses, we come closer to the operative idea of intuition as it is employed in mathematics.

Mathematical thought, and formal accounts of experience generally speaking, of course, seek to capture our intuitions, but this formal capture of the intuitive is itself an intuitive and essentially creative process even when it culminates in the formulation of a formal system that is essentially inaccessible to intuition (at least in parts of that formal system). What this means is that intuition can know itself, and know itself to be an intuitive grasp of some truth, but formality can only know itself as formality and cannot cross over the intuitive-formal divide in order to grasp the intuitive even when it captures intuition in an intuitively satisfying way. We cannot even understand the idea of an intuitively satisfying formalization without an intuitive grasp of all the relevant elements. As Spinoza said that the true is the criterion both of itself and of the false, we can say that the intuitive is the criterion both of itself and the formal. (And given that, today, truth is primarily understood formally, this is a significant claim to make.)

The above observation can be formulated as a general principle such that the intuitive can grasp all of the intuitive and a portion of the formal, whereas the formal can grasp only itself. I will refer to this as the principle of the asymmetry of intuition. We can see this principle operative both in the Church-Turing Thesis and in popular accounts of Gödel’s theorem. We are all familiar with popular and intuitive accounts of Gödel’s theorem (since the formal accounts are so difficult), and it is not usual to make claims for the limitative theorems that go far beyond what they formally demonstrate.

All of this holds also for the attempt to translate traditional philosophical concepts into scientific terms — the most obvious example being free will, supposedly accounted for by physics, biochemistry, and neurobiology. But if one makes the claim that consciousness is nothing but such-and-such physical phenomenon, it is impossible to cash out this claim in any robust way. The science is quantifiable and formalizable, but our concepts of mind, consciousness, and free will remain stubbornly intuitive and have not been satisfyingly captured in any formalism — the determination of any such satisfying formalization could only be determined by intuition and therefore eludes any formal capture. To “prove” determinism, then, would be as incoherent as “proving” Church’s Thesis in any robust sense.

There certainly are interesting philosophical arguments on both sides of Church’s Thesis — that is to say, both its denial and its affirmation — but these are arguments that appeal to our intuitions and, most crucially, our idea of ourselves is intuitive and informal. I should like to go further and to assert that the idea of the self must be intuitive and cannot be otherwise, but I am not fully confident that this is the case. Human nature can change, albeit slowly, along with the human condition, and we could, over time — and especially under the selective pressures of industrial-technological civilization — shape ourselves after the model of a formal conception of the self. (In fact, I think it very likely that this is happening.)

I cannot even say — I would not know where to begin — what would constitute a formal self-understanding of the self, much less any kind of understanding of a formal self. Well, maybe not. I have written elsewhere that the doctrine of the punctiform present (not very popular among philosophers these days, I might add) is a formal doctrine of time, and in so far as we identify internal time consciousness with the punctiform present we have a formal doctrine of the self.

While the above account is one to which I am sympathetic, this kind of formal concept — I mean the punctiform present as a formal conception of time — is very different from the kind of formality we find in physics, biochemistry, and neuroscience. We might assimilate it to some mathematical formalism, but this is an abstraction made concrete in subjective human experience, not in physical science. Perhaps this partly explains the fashionable anti-philosophy that I have written about.

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## Ecological Temporality and the Axes of Historiography

### 4 November 2012

Sunday

In my last post, Axes of Historiography, I mentioned in passing that a more detailed and comprehensive schematic taxonomy of the axes of history could be obtained by interpreting the axes of historiography in terms of ecological temporality. This post will be my first attempt to sketch this in barest outline. What follows is sufficiently complex that it may of of little practical use, even of little practical intellectual use in terms of thinking things through, nevertheless the impulse to elaborate is there.

Here are the categories of historiographic methodology that I formulated in Axes of Historiography:

● nomothetic synchrony

Law-like interaction of all elements within a broadly-defined present

● ideographic synchrony

Contingent interactions of all elements within a broadly-defined present

● nomothetic diachrony

Law-like succession of related events through historical time (especially “deep time”)

● ideographic diachrony

Contingent succession of related events through historical time

Keeping this in mind, with its very sketchy distinction between the synchronic and the diachronic scope of the present, respectively, consider a more detailed breakdown of temporal scope. In my post ecological temporality I distinguish five levels of temporality from the personal lived experience of micro-temporality flowing from the punctiform present to the greatest sweep of history that I call meta-temporality:

●Micro-temporality: The temporal setting in which the individual lives; immediate “lived” time and individual time consciousness, as well as the finest grained temporal structure of non-conscious events.

●Meso-temporality: Relations between micro-temporalities or connections between immediate temporal contexts.

●Exo-temporality: Links between a temporal setting in which the individual does not have an active role and the individual’s immediate temporal context.

●Macro-temporality: The historical era in which individuals live, linking into a single history the exotemporal structures that lie outside immediate temporal experience or fine-grained temporal interactions.

●Meta-temporality: The whole of metaphysical history in which the individual and other lesser temporalities (Meso-temporality, Exo-temporality, and Macro-temporality) are embedded, and the temporal scope at which ideas unfold in history.

As I explained in Metaphysical Ecology Reformulated and Ecological Temporality, I derived this quinquepartite schema from a modification of Urie Bronfenbrenner’s conception of biosocial ecology.

Using ecological temporality to define the scope of time, and using the axes of history to define the methodology used to study a given scope of time, there are twenty permutations of historical study, as follows:

● Micro-temporal nomothetic synchrony

Law-like, predictable interactions of all elements across the immediate lived present of the individual

● Micro-temporal ideographic synchrony

Contingent, unpredictable interactions of all elements across the immediate lived present of the individual

● Micro-temporal nomothetic diachrony

Law-like, predictable succession of related events in the immediate lived present of the individual

● Micro-temporal ideographic diachrony

Contingent, unpredictable succession of related events in the immediate lived present of the individual

● Meso-temporal nomothetic synchrony

Law-like, predictable interaction across micro-temporalities or connections across temporal contexts of micro-temporalities

● Meso-temporal ideographic synchrony

Contingent, unpredictable interactions across micro-temporalities or connections across temporal contexts of micro-temporalities

● Meso-temporal nomothetic diachrony

Law-like, predictable succession of related events in relations between micro-temporalities or connections between temporal contexts of microtemporalites

● Meso-temporal ideographic diachrony

Contingent, unpredictable succession of related events in relations between micro-temporalities or connections between temporal contexts of micro-temporalities

● Exo-temporal nomothetic synchrony

Law-like, predictable interactions of all temporal elements across temporal settings in which the individual does not have an immediate, active role

● Exo-temporal ideographic synchrony

Contingent, unpredictable interactions of all temporal elements across temporal settings in which the individual does not have an immediate, active role

● Exo-temporal nomothetic diachrony

Law-like, predictable succession of related temporal events linking temporal settings in which the individual does not have an immediate, active role and the individual’s immediate temporal context

● Exo-temporal ideographic diachrony

Contingent, unpredictable succession of related temporal events linking temporal settings in which the individual does not have an immediate, active role and the individual’s immediate temporal context

● Macro-temporal nomothetic synchrony

Law-like, predictable interaction of all elements across the historical era in which individuals live

● Macro-temporal ideographic synchrony

Contingent, unpredictable interactions of all elements across the historical era in which individuals live

● Macro-temporal nomothetic diachrony

Law-like, predictable succession of related events through historical time

● Macro-temporal ideographic diachrony

Contingent, unpredictable succession of related events through historical time

● Meta-temporal nomothetic synchrony

Law-like, predictable interaction of all elements across the temporal scope at which ideas unfold in metaphysical history

● Meta-temporal ideographic synchrony

Contingent, unpredictable interactions of all elements across the temporal scope at which ideas unfold in metaphysical history

● Meta-temporal nomothetic diachrony

Law-like, predictable succession of related events through the temporal scope at which ideas unfold in metaphysical history

● Meta-temporal ideographic diachrony

Contingent, unpredictable succession of related events through the temporal scope at which ideas unfold in metaphysical history

This looks and sounds too complicated to be of much help in illuminating any understanding of history, but if you take the time to think it through, you may see some virtues in this.

How can it make any sense to speak of micro-temporal synchrony when I have been characterizing synchrony in terms of a broadly defined present, while the micro-temporal is by definition narrowly defined? This is a matter of taking a present just large enough to be larger than the narrowest interpretation of micro-temporality (which would be the punctiform present), but not so large as to encompass the next level of temporality, that of meso-temporality. So micro-temporal ideographic synchrony would be something like situational awareness, while micro-temporal nomothetic synchrony would be those things in your immediate environment (perhaps those events within the lived experience of one’s own mental life) that you expect to happen because of the predictable regularities of experience.

It takes a little effort and a little sympathetic interpretation to make the whole structure work, but when it is interpreted charitably not only is the whole a coherent and systematic structure, but it actually eliminates some ambiguities by stretching out the boundaries of temporal categories until they abut neighboring categories. For example, the upper bound of micro-temporality stretched upward and outward by a synchronic interpretation abuts the lower bound of meso-temporality stretched downward and inward by a synchronic interpretation. Thus there is a certain usefulness for this schema, and it is not merely a theoretical indulgence.

The next step in this exposition of ecological temporality and the axes of history would be to produce a particular, concrete example of each of the twenty instances of historical thought outlined above in order to intuitively illuminate the idea of each category. I don’t have that many examples to hand at the moment, however, so I will save that effort for another time.

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## The Origins of Time

### 30 November 2011

Wednesday

The Construction of Ecological Temporality

A Genetic Account of the Origins of the World

The ontogeny of time

The emergence and development of temporal consciousness — that is to say, the origins of individual time, the ontogeny of time — begins in the individual, but the early experience of the individual is that of an individual embedded in a temporal context. The individual’s internal time consciousness is constructed in a temporal context that I will call the reflexive experience of time.

Children — at least those children allowed a childhood, which is not always the case — live most in the world of meso-temporality, mostly because they have not yet learned not to trust, and so they feel free to express the spontaneity of their inner time consciousness as though by reflex. Reflexive experience of time, in which there are few if any barriers between the micro-temporality of the individual and the meso-temporality of the immediate social context of the individual, embodies an absolute innocence.

In a condition of innocence, everything that occurs is new, so that time is densely populated with unprecedented events. Every hour and every day brings novelty. As we age, every hour and every day brings more of the same — the same old same old, as we say today — and so it is little surprise that we don’t notice the passing of this undifferentiated sameness. For the young, time flies by unnoticed, and because the passage of time is unnoticed it has the quality of timelessness.

As we age, time flies by all the faster.

Later, in our maturity, we have the ability to appreciate episodes of innocence that we could not have appreciated in our younger years — thus following the well-worn idea that youth is wasted upon the young — there is another sense in which youthful experience makes the fullest use of time and yields a density of experience that we cannot experience in later life.

G. B. Shaw was the one who first said, “Youth is wasted on the young.”

The time consciousness of youth, driven by the stream of novelty that is the result of innocence, sharpens and enlarges the smallest events, and thus we see young children sobbing over a ice cream cone that has dropped to the ground, which leaves us, as adults, largely unmoved. We shrug our shoulders and move on. Would that we could experience life with such intensity that an ice cream cone were worth a flood of tears.

There is a sense in which it is counter-intuitive to speak of the intensity of experience of children, since the halcyon days of youth are usually not thought to consist of intensity but rather of carefree indolence, but in the sense outlined above, the innocent lead lives of greater intensity than the jaded.

Innocence wrings every last drop from the passing of time, so that in a condition of innocence there is no moment that is wasted. In maturity, the greater part of time is wasted, until, as Shakespeare noted, having wasted time, time wastes us.

Developmental temporality: the role of play

Developmental psychologists have had much to say about the child’s initial encounters with a recalcitrant world that does not answer to its whims. This initial phase of socialization is also the first loss of innocence, and the first compromise of reflexive temporality. As the consciousness of temporality progresses in the individual, the individual comes to understand that they can cultivate a Cartesian privacy in which fantasies will not be interrupted by the recalcitrant world. Thus reflexive temporality gradually gives way to imaginative temporality, and the spontaneity of the child is displaced from the immediate expression of inner promptings to the inner expression of these promptings by way of imagination. Thus play emerges, and the imaginative temporality of play allows the individual to further develop the inner time consciousness of Cartesian privacy.

Erik Erikson's stages of psycho-social development is one well-known developmental theory.

Play, however, also makes possible a re-discover of reflexive temporality when the childred discovers other children and begins to play with them. The shared, social temporality of play, especially when adults are not present to puncture the illusions generated by imaginative time consciousness, can again converge onto a purely reflexive time consciousness when the child feels free to express their spontaneity among peers who share the form of time consciousness common to this stage in the development of childhood.

Pieter Bruegel, detail from Children's Games, 1560, Oil on oak panel, 118 x 161 cm, Kunsthistorisches Museum Wien, Vienna

Play, too, is eventually compromised, as conflicts inevitably emerge from games played with peers, so that the life of the child exhibits a dialectic of shifting between reflexive time consciousness and imaginative time consciousness, which is a shift of the focus of spontaneity from outer life to inner life and back again to outer life. It is the dialectical process that contributes to the further development and reinforcement of an inner time consciousness of Cartesian privacy, which becomes a haven for the individual, wounded by encounters with an unsympathetic world.

Games among children often result in conflicts, and these conflicts teach us early in life that the world is usually not responsive to our will.

All throughout the dialectic of early time consciousness, however, the experience of the child is still marked by innocence, and it is the process of the degradation of innocence that brings about a fully mature time consciousness (if, in fact, this does develop, and its development is not arrested by trauma).

The degradation of innocence and the emergence of mature time consciousness

The degradation of innocence comes about from cumulative experience. Cumulative experience can only be experienced as cumulative with the development of memory, so that the emergence of robust memories is central to the emergence of fully mature time consciousness. However, it is the same process of the emergence of memory that degrades innocence. Memory demonstrates to us the non-novelty of our spontaneity, and as the spontaneity of our internal promptings loses its novelty, it also begins to lose its interest.

As we age, and the depth and breadth of our experience grows, preserved in an improving memory, and our opportunities for experiences of innocence decline proportionately until our capacity approaches zero and we no longer expect or even hope to directly experience innocence again. In the lives of many adults it is their relationships with children that yield whatever vicarious experiences of innocence for which they still retain hope, and so they take pleasure in seeing the world anew through the eyes of another, but there is a melancholy to this because one knows in one’s heart of hearts (as subtle as the distinction may seem to be) that there is a difference between immediate and vicarious experiences of innocence.

And yet (and despite), when we are surprised by an authentic experience of innocence later in life, beyond the bounds of youth, we now experience it from a perspective of maturity, and both its rarity and our capacity to appreciate it make the experience all the more precious. When we are young, everything is new to us, and experiences of innocence are common; experience narrows the scope of innocence until any such experience appears as something completely unexpected, but when it does occur we have the maturity to appreciate the experience that we did not possess in youth.

It is the same innocence that is behind the very different time consciousness of youth compared to maturity. Everyone knows that as you age, time seems to pass ever more quickly, until it flies by and the years scarcely make any impression in their passing. This stands in stark contrast to feelings of endless summers from our childhood that seemed to go on forever, as well as anticipating and waiting for holidays that seemed to take forever to arrive.

The time consciousness we associate will full cognitive modernity is a product of cognitive maturity.

Keeping secrets and Cartesian privacy

Another aspect of the child’s encounter with a recalcitrant world not obedient to his or her wishes is the discovery of the power of secrets. The youngest children, immersed as they are in meso-temporality and observing few if any boundaries between internal spontaneity and external expression, cannot keep a secret. Even if they make an experiment of it, and older children try to let them in on a secret, they will usually blurt it out, and as a consequence are considered untrustworthy. …

The shared confidences of older children, however, especially confidences that exclude adults and their alien forms of time consciousness, become an object of envy for the younger child, who wants to become “grown up” in order to share in these confidences. Thus the younger child makes a conscious effort of will to cultivate inhibitions on his or her spontaneity. Older children will continue to test the younger children for the trustworthiness in keeping secrets, at the behest of the pleading of younger children, initially with small secrets and eventually with larger secrets. When these secrets are successfully kept, the child passes the test, and in passing the tests passes another threshold of maturing time consciousness.

The experimenting and testing of secret-keeping trains the child in the development of his or her Cartesian privacy, which becomes a faculty consciously developed by the individual as an exclusively private reserve from which the world entire. The child discovers that not only may adults be excluded, but that other children can also be excluded from this realm of Cartesian privacy. In this perfectly private space of conscious, purely interior micro-temporal consciousness takes root and begins to grow, and as it grows it contributes progessively more to constitution of individual consciousness.

Shared time, social time, and the world as we find it

One of the most mysterious aspects of personal chemistry between individuals, and that which is perhaps the conditio sine qua non of friendship (whether Platonic or romantic), is the simple fact of shared time. Friendship has its origins in childhood play, but its possibilities are deepened by mature time consciousness. We are able to be friends with those with whom the common passage of time is enjoyable. Play is the first expression of joy in shared time. In adolescence, the shared time begins to take on a more intellectual form as shared time becomes primarily shared conversation. In contemporary colloquial English, this is called “hanging out” or simply “hanging.”

I suspect that everyone, or almost everyone, has experienced among their interaction with acquaintances the fact that, with some combinations of individuals, the two or more parties in question mutually enjoy the passage of time together, while among other combinations of individuals, the two or more parties find the common passing of time together to be irritating, unpleasant, or otherwise unfulfilling. The former is a welcome kind of chemistry, while the latter is an unwelcome (but also inevitable) kind of chemistry.

There are also obvious cases of asymmetry, when one party to the shared passage of time finds the experience rewarding, while another party to the same shared temporal frame of reference finds the experience unrewarding or even odious. Here the temporal frame of reference is identical, but the subjective experience of that shared time is sharply distinct. Such are what Shakespeare called the pangs of despised love.

In my post ecological temporality, in which I developed Urie Bronfenbrenner’s bio-ecological model, specifically expanding and extending the ecological treatment of time, I distinguished levels of temporality parallel to Bronfenbrenner’s distinction between levels of bio-ecology. Thus what Husserl called internal time consciousness I called micro-temporality, and the interaction of micro-temporalities begets meso-temporality.

Meso-temporality is social time, and another way to refer to social time would be to call it shared time. An isolated individual experiences the micro-temporality of internal time consciousness, and simply by being present in an environment experiences a rudimentary level of meso-temporality from the necessary interaction of an organism with its environment (the minimal form of rudimentary meso-temporality involves interaction with an inert environment, as, for example, knocking on a door).

Shared time is facilitated by secret-keeping. The young child who cannot yet keep a secret says things openly that impair social relationships. As children learn more above the social environment in which they find themselves, they learn, under penalty of social exclusion, what must be confined to Cartesian privacy, and what may be openly and freely shared. To blurt out socially inappropriate assertions with no concern for boundaries of privacy — both one’s own privacy as well as the privacy of The Other — is to commit a social faux pas and to risk social exclusion. Being envious of social inclusion, children make an effort to train themselves in the boundaries of polite expression, and in so doing they are forced to cultivate a consciousness of the Cartesian privacy of The Other, which is another important threshold on the way to mature time consciousness. The recognize the Cartesian privacy of the other is to recognize the internal time consciousness of The Other. Thus one’s own emerging micro-temporality is placed in the context of the other’s inferred micro-temporality, which together and jointly constitute social time.

The social time or meso-temporality that emerges from a common temporal frame of reference for two or more individuals possessing internal time consciousness is perhaps distinct from that meso-temporality emergent from the micro-temporality of internal time consciousness in the context of an inert, non-conscious environment. Thus meso-temporality may take a variety of forms. Meso-temporality simpliciter may be taken as the interaction of a micro-temporal agent with its environment. When that environment includes other micro-temporal agents and agents join in common action (or common inaction, for that matter), this is social time or share time. Thus social time is a subdivision of meso-temporality.

The minimum condition for social time is two conscious individuals. Two micro-temporalities functioning in a common frame of temporal reference constitutes the first and simplest level of shared time, though shared time can be augmented with the addition of more conscious individuals and can grow until, for spatio-geographical reasons, a common frame of temporal reference is not longer possible. This meso-temporality that exceeds a common frame of temporality is meso-temporality of a higher order of magnitude, and thus constitutes exo-temporality. The interaction of meso-temporalities yields exo-temporality, which is the usually setting for “history” as this is usually understood. Herodotus and Thucydides write on the level of exo-temporality: the interaction and intersection of particular communities over space (a given geographical region) and time (a given period of history).

Returning to the interaction of micro- and meso-temporalities, we can see from the very different responses that individuals have to shared social time that this “functionality” in a shared temporal frame of reference can function in different ways for different individuals. Even when the shared temporal frame of reference is identical, the micro-temporality of consciousness usually remains clearly distinct from the shared time. That is to say, consciousness usually enjoys Cartesian privacy. This is the point of departure of Husserlian internal time consciousness.

The exceptions to Cartesian privacy occur when an individual agent, even having previously cultivated a sense of Cartesian privacy in the childhood dialectic of reflexive time and imaginative time (which perhaps only becomes possible in the context of fully mature historical consciousness), becomes so fully embedded in a meso-temporal frame of reference that they experience no boundaries between themselves and the other agents present. In shared social time one may be so comfortable in the presence of others that one is as spontaneous in interacting with them as one may be spontaneous with one’s own thoughts in private. This constitutes a (temporary) recovery of the reflexive time consciousness of early childhood.

One way to express this is that a particular subdivision of shared social time is when individuals participating in a common meso-temporal frame of reference experience in common what psychologists call “flow states”, such that the individuals in question can no longer distinguish between their internal time consciousness and the meso-temporality of shared time: the barriers of the self come down, and the individual is lost in the shared world. This would be a particularly intimate form of social time, and is possibly the necessary condition of love. Possibly.

The lost paradise of reflexive time

Why do we seek ideal love? We seek ideal love because it is the temporary recovery of the lost paradise of the purely reflexive temporality — unmindful of boundaries, unmindful of a distinction between self and world, unmindful of any barrier to absolute spontaneity and freedom of expression, unmindful of any social constraint risking social exclusion. Love is the reminder of what we have lost in coming to mature time consciousness, even while knowing what we having gained in terms of cultivated micro-temporality, memory linked both to immediate micro-temporality and enduring self-identity, and an awareness of history and our personal place within history.

Moreover, ideal love in the context of mature time consciousness can exceed or surpass the lost paradise of early childhood’s reflexive temporality, because ideal love can accommodate an authentic awareness of the beloved as other, as possessing its own Cartesian privacy and its own micro-temporality. To love the other in full awareness of their otherness is a more profound species of shared social temporality, and with this profundity comes depth of feeling that did not exist and could not exist in childhood. It has been said that a woman’s heart is a ocean of secrets, and perhaps we need not even superadd a qualification of gender to this poetic truth. Shared secrets, withheld from the rest of the world, can be among the most powerful form of shared social temporality, and it is the power of these experiences that moves us (i.e., we experience the sublime) and thus generates profound awareness of the other and depth of feeling in one’s relationship to The Other.

However, love disappoints more often than it satisfies, so that our tentative reaching out to the world in search of love becomes an experiment that is disconfirmed more often than it is confirmed. And even when love satisfies, it rarely endures. Some retreat within themselves, when the pangs of despised love are too powerful, while others, unable to forget the ideal of the lost paradise, continue to seek, and are in rare moments rewarded for their efforts.

The phylogeny of time

The origin of non-human time, of objective time, is the proper concern of the phylogeny of time. Of course, ontogeny and phylogeny are intimately interconnected, and we may even speculate on a temporal recapitulation in which temporal ontogeny recapitulates temporal phylogeny, but I will not pursue this further in the present context.

In terms of the origins of time, or, rather the origins of human time consciousness, interaction with other agents within an environment — i.e., meso-temporality — almost certainly preceded the emergence of self-aware micro-temporality, just as meso-temporal interaction almost certainly preceded those larger temporal formations such as exo-temporality and macro-temporality.

Macro-temporality emerges even later, in terms of specifically human macro-temorality. Before humanity knew itself as a whole (on which cf. the quote from George Friedman that I cited in Humanity as One) we did not know ourselves as a whole either in space or time. It is only with the emergence of human self-knowledge of our species as a whole in time that macro-temporality emerges, and this cannot happen until a fully naturalistic account of human origins emerges with Darwin.

The internal time consciousness of Cartesian privacy emerges from cognitive modernity, much as does historical consciousness. There is a sense in which internal time consciousness is historical consciousness of the self, while historical consciousness is the internal time consciousness of history. Both represent temporal consciousness of a greater order of magnitude than the interactions of meso-temporality. This is another interesting idea that I will not pursue further at present, but which deserves independent exposition.

Cosmological and relativistic time

Objective conceptions of time rooted in mathematics, physics, cosmology, and the natural sciences can be formulated without reference to human time, much less to the structures of micro- and meso-temporality that constitute the greater part of the ordinary business of life. However, science, as a human undertaking, retains its relevance to the human agents who are responsible for the constitute of objective, natural time.

In fact, we run into difficulties when we attempt to formulate a doctrine of time too far removed from human experience, precisely because human experience has been responsible for science, and the truths of science must ultimately be redeemed in human experience.

One is immediately put in mind, in this context, of Newton’s famous formulation from his Principia:

“Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.”

Newton implies that human measures of time such as “an hour, a day, a month, a year,” are untrue, because only mathematical time is true time, but Newton’s categories of “relative, apparent, and common time,” are in fact quantitative measures of time in natural history which can be studied and defined with the utmost precision by natural science. Time measurements of a day, a month, and a year are rooted in astronomical events that constitute some of humanity’s first and earliest scientific knowledge. Had Newton gone in the other direction in the litany of apparent time, listing instead “an hour, a minute, a second, …” he would have approached the punctiform present and therefore the ideal limit of micro-temporality.

Despite the relativity of simultaneity that isolates us from the temporality of other dynamic systems independent of our own, there is a sense in which human temporal categories seem to me to retain their relevance throughout the cosmos today — at very least, just because human beings are an interested party in the universe at present — in a way that I do not feel human temporal categories to be relevant to very early cosmological history or to the far flung future of cosmological history.

One way to formulate this would be to put it in the context of the divisions of cosmological history propounded in The Five Ages of the Universe. We live today in the Stelliferous Era, i.e., the Age of Stars. Before the Stelliferous Era came the Primordial Era, which includes the Big Bang, expansion, inflation, and consists in large part of subatomic particles that have not yet congealed into familiar elements and structures. After the Stelliferous Era come the Degenerate Era, the Black Hole Era, and the Dark Era, after the stars have burned themselves out and the cosmos goes dark again. This is a classic scenario of cosmological eschatology based on heat death due to entropy.

Human measures of time seem meaningless at the quantum and subatomic scale of the early universe, and these same measures seem equally meaningless at the vast time scales of the universe as it steadily runs down in entropic heat death. Yet, at the present, anthropocentric time scales seem relevant to the universe entire as we know it today (relevant, though not by any means necessary or even privileged), although most of the universe is beyond any meaningful relation to specifically human time, and will remain so.

One justification for the feeling (which I readily admit is my own prejudiced intuition, and I claim no validity for it beyond that) that anthropocentric temporal categories apply throughout the Stelliferous Era is that life as we know it is possible throughout the Stelliferous Era, while life as we know it is not possible during the Primordial Era or during the Degenerate Era or after.

The possibility of life as we know it throughout the Stelliferous Era means the possibility of other species emergent from other solar systems, other planets, other biospheres, and other sentient species emergent from a parallel biological context, functioning according to the same natural laws that govern our world, our bodies, and our minds, means that an approximately anthropocentric (although technically xenocentric) time consciousness exists elsewhere in the Stelliferous Era, and is perhaps pervasive throughout it.

Objective micro-temporality

Although the categories of human time seem irrelevant to either the earliest stages of the universe immediately following the big bang, and perhaps also to the largest structures of space andtime, the “cosmic soup” of the early universe is recognizably a form of micro-temporality, even if it is not microtemporality at the same level of human micro-temporality. Moreover, the micro-temporality of pre- and sub-atomic particles prior to the precipitation of universe from the coalescence of ordinary elements is another paradigmatic instance of meso-temporality: the particles interact, and they can only come together and coalesce into the world we know and love by coming together.

The temporality of the early universe thus closely parallels the temporality of the ontogeny of time in the individual, in so far as the individual’s micro-temporality is always constituted jointly by the meso-temporality of the shared milieu in which the individual finds himself or herself. The micro-temporality of the individual particles of the early cosmic soup is crucially dependent upon the milieu of interacting particles, which is a meso-temporal milieu.

Larger structures of cosmological time — objective exo-temporality, objective macro-temporality, and objective metaphysical temporality — only come above in the fullness of time — lots of time — as the universe matures and new spatio-temporal structures emerge. As novel physical structures emerge, there necessarily emerges an interaction of these larger structures with smaller structures and with other larger structures, and these interactions of ever-increasing size produce the higher levels of objective ecological temporality.

Closing speculation

As ever-larger temporal structures emerge from a universe consolidating its structure, and ever-larger temporal structures emerge from the maturation of human consciousness, these objective and human forms of ecological temporality converge. It would be very difficult to demonstrate a close parallelism between the micro-temporality of consciousness and the micro-temporality of fundamental particles, but in the increasingly more comprehensive temporal categories of ecological temporality the chasm between the two becomes less marked.

At the level of macro-temporality, it is not difficult to see the convergence of human time and objective time, since human life and human civilizations are shaped by macroscopic forces such as geography, and geography is a local expression of cosmology. A human civilization that emerges from its planet-bound condition and asserts itself on a cosmological scale would constitute human beings living on a macro-historical level, and to do so would demand the emergence and cultivation of macro-temporal consciousness.

It may be only at the level of metaphysical temporality (which I also call metaphysical history) that there can be a full convergence of human time and objective time, so that that two ultimately become indistinguishable and therefore one. This may be the ultimate telos of civilization: to establish an identity with the universe at large.

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I have had a little more to say on the above in Addendum on the Origins of Time.

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