…or is the whole notion of an infinite set a paradox?
Since a set is by definition a defining of a boundary, whenever we talk about sets which are infinite we are talking about a boundary containing unbounded contents. Such a boundary makes it necessary that boundary-making itself is presumed to be outside of things being bound, i.e. it is taken as axiomatic that boundary making is part of a theory which does not change anything except our own understanding.
Things get murky however, when we consider time an infinite set. In Zeno’s Paradox of the Tortoise and Achilles, for example, the idea of an infinite set is used to trick us into thinking that motion is impossible. The logic is that for something to move one unit of distance, it must first move an infinite number of smaller distances. We can reverse this logic, however, and say that to divide one distance into an infinite number of smaller distances in the first place would take an infinitely long time if we had to actually make those measurements in some way, provided each measurement takes a non-zero amount of time.
Here is the difference between the map and the territory. Actually moving across a distance is a ‘territory’; a concrete reality. The idea that there is some number of points in which could be measured along that distance is a theoretical abstraction. When we apply the abstraction of infinity to the reality of concrete phenomena, we get paradox. The tortoise’s lead appears to always be getting smaller and smaller, but is still a nonzero fraction of the total distance ahead of Achilles, no matter how much faster Achilles is. What distracts us is that we are taking our own measurement for granted. Yes, it’s true that each measurement at time t will find the tortoise ahead of Achilles if we keep giving the tortoise a fraction of his original head start after calculating Achilles position, but infinity doesn’t end at that measurement. Infinity means not only that there will always be a measurement where the tortoise is ahead, it also means that there will always be an interval after the measurement where Achilles overtakes the velocity challenged reptile. In short, an infinite set means that the set always will extend beyond itself.
The physical allegory of the infinite set is a universe of stars and galaxies which expands into an infinity of empty space. But can emptiness really envelope things or is it the expansion of things which exists on its own without any envelope? Is the assumption of empty space really a projection of our own intellectual expectations of set-making? I think that it is important to see that Einsteinian spacetime calculations would work the same either way. Spacetime need not be a literal container of mass-energy, if mass-energy is already entangled at superliminal rates. It makes it easy to think of General Relativity as referring to a spatiotemporal entity (a ‘reference mollusk’ as Einstein called it, or a Minkowski space), but the reality may be that spacetime is nothing more than the influence that the entangled consensus of mass-energetic relations has on itself. This way, no envelope of infinite emptiness is required around the Big Bang, and the vacuum can leave its quantum contents behind to revert to a true void. The vacuum energy gets turned inside out…it’s not inside of spacetime, it’s inside of relativity, i.e. universal perceptual entanglement.
Eastern and Western Eternity
If the Western view of time is an unlimited set of (limited) moments, then eternity is purely conceptual – the perpetually incomplete ‘set-hood’ of that set. The Western sense of eternity is also of perpetually filling itself with more and more clock ticks. Eastern mystics have promised instead that the fundamental truth of nature is the antithesis of that: A timeless connectedness of all things, or a universal connectability (The Force, Field, Love*, God) from which all ‘things’ are seemingly detached. Such a detachment is described as an illusion or temporary masking of underlying unity which remains eternal and pervasive. From the Eastern view, it is not space and time which contain all phenomena, but rather times and spaces are emergent dissociations within the grand phenomenality.
With the advent of General Relativity, the pendulum of Western thought began unknowingly to swing Eastward. Eternity came to be seen as a universal 4D manifold which distorts rates and lengths of physical processes. The distortions are understood to be relative to frames of reference; they are the ‘appearances’ of each frame to any other rather than a fixed physical property common to all frames. Frames themselves are, like the tortoise, given an unfair advantage of inheriting our ignorance of the nature of perception. Physics has attributed a frame-making capacity from a purely theoretical warrant, a warrant which magically acquires real powers of perceptual transformation (Lorentz contraction/dilation) which define the universe.
Some will complain that inertial or Galilean frames have nothing to do with perception, that they are tied only to linear velocity, however this takes velocity relations for granted in the same way that infinite sets take sets for granted. Here is where Relativity and QM completely agree. They both hinge on the concrete physical fact of measurement as the relation between properties such as space, time, position, and momentum. The measurement is a thing that separates the uncollapsed theoretical wave from the concrete wave-effects which are common to matter.
I submit that measurement itself is only the superficial way of understanding what is going on behind SR, GR, and QM. What makes measurement possible – all measurement – is an intrinsic relatability or sense which pervades all of physics. It is only parsimonious to assume at this point that this relatability is identical to the awareness which underlies our own conscious experience.
As it stands now, theoretical physics must resort to a kind of dualism where the idea of an ‘observer’ is somehow presumed separate from conscious observation. Any deviation from this premise is taboo and treated with antipathy. The Western imagination has been captured by positivism, so that all legitimate phenomena begin with an assumption of being separable from phenomenology. This unfortunately leaves phenomenology itself orphaned from physics, and the purest contents of conscious experience orphaned from legitimacy. We turn to the idea of “emergence” to reclaim some semblance of coherence, but emergence itself is no more physical or derivable from logic than consciousness itself.
Relativity applies to instantaneity as well as simultaneity.
To further bridge the Einsteinian notion of eternity with the Eastern one, I suggest a relativity of instantaneity. We can see from time lapse photography, for example, that different rates of exposure present nature at speeds of time. If we had nanobots we could surely step down our own body motions so that we could interact remotely with nanoscale objects at scales and speeds which would not be possible to us on the macro scale.
We can also see how the ocean appears to slow to a crawl when seen from the air. Interestingly, the trails that boats make in their wake appear to flow against a solid background of standing ocean waves.
In this photo you can’t see it, but next time you are flying over the water, notice how the narrow wake tracks which cross-cross the static ocean shimmer with movement. I’m curious about the physics of this – is it the distance of the plane or the speed which averages out the speed of water, and then the motion of the boat which makes some of the speed visible? Some kind of phase-cancellation?
It is this kind of transformation which I’m referring to as the relativity of instantaneity. The scope of the instant depends on perspective, and physics, having no preferred perspective, can have no way to define any separation between instants or any set which unites them. In this way, emergent properties themselves emerge from perception.
East vs West
I suspect that both views of time are reflections of the perspective from which they emerge. Eastern or Empathizing psychologies focus on the unity of categories in the category-making mind itself while Western, Systemizing modes focus on impersonal categories, the origin of which is seen as irrelevant. As the two modes have grown apart, they are no longer able to locate each other without distorting them into a straw man. The Western mind sees the Eastern view as an overestimation of our own presence (including the present moment) while the Eastern mind sees the fatal flaw of the Western effort to deflate the presence of the now and its presenter. Interestingly, the antipathy flips in the assignment of blame, with the Western skeptic taking personal umbrage at the individuals who they see as peddlers of ‘woo-woo’ superstition and postmodern ‘word salad’. By contrast, the Eastern mystic sees the Western resistance as a function of impersonal forces of spiritual immaturity. This dynamic of projection and inversion is a good place to study the lensing of consciousness. The model which I propose suggests that studying how people argue will show that fundamentalist positions on either side will have more in common with each other neurologically than there will be differences. From there we can begin to map the blind spot of the Western approach as it cascades down through academic policies, experiment design, and finally economics, and politics.
The Western approach is intrinsically bottom up in that it begins with a collection of external particulars and then extrapolates generalities and universal laws. Scientific thought is an analytic introspection which is intended to generate a synthetic ‘extraspection’. Our naive, introspective sense of the present time is as Edwin Schrodinger and Ken Wilber point out is “the only thing that has no end”. Meaning that we literally cannot locate within the present any beginning or ending. Only memories within the present which seem to explain things outside of the present can be found:
“We dissipate our energies in fantasy mists of memories and expectations, and thus deprive the living present of its fundamental reality and reduce it to a “specious present”, a slender present that endures a mere one or two seconds, a pale shadow of the eternal Present.”
-Ken Wilber, No Boundary
It seems clear to me that the Western view is dominated by the specific function of the intellect, which is to isolate problems and analyze them sequentially. Using the intellect to analyze itself, we conflate mental kinds of functions with nature in general and have learned to mistake this map of our own map-making for the territory. Because the Western mind identifies with itself rather than with the consciousness behind thought, it inverts our own existence into a ‘specious presence’. First an orphaned soul in an Enlightened machine, then a self-modeling semantic mechanism, the personal presence has now been so aggressively deflated that many insist that it has no existence at all.
If the Western view overlooks the magnitude of significance of the present in its modeling of time, the Eastern view overlooks the overwhelming influence of non-human scales of the present in the universe. The human scale of ‘now’ is overly preferred, so that the Western half of the universe, with its bottom up chains of causality, can be discounted irrationally (hence the woo-woo). This means that the vital and important contributions of science and technology can be dismissed by the Eastern approach, thus losing all credibility with Western thinkers. The sentiment that thoughts create reality is straw-manned to imply that human thoughts create all reality, when the truth is that human influence may be both more powerful and less powerful than we imagine.
Coming Together Over Time
I propose that the way to transcend the problematic notions of time in both the Western and Eastern modes is to see time as the “most common sense” through which eternity ‘pretends’ to be each moment, and how the eternal moment pretends to its own eachness. Time is what limits the unlimited and opens the limited to the possibility of the infinite.
Because the Western view of time has resulted in an all-but-insignificant present, it has contrived an all-but insignificant subjective conscious presence to act as an almost-disposable timekeeper. The ‘observer’ in physics is naught but a convergence of particular coordinates…coordinates which themselves are only defined by there own axiomatic coordination. The cosmos appears as an unorchestrated orchestration…an autoverse rather than universe.
The Eastern view inflates the present and the subjective presence to the absolute extreme, so that the cosmos appears as an unfalsifiably teleological monolith. This infuriates the Western mind, hearing soft-headed homilies of ‘There are no coincidences’ and ‘Everything happens for a reason’ to justify pre-scientific superstition. This would be a solipseverse rather than a universe – a universe which fits into single self. Monotheism splits the difference, with a Unisolipse – a single God self who is not us, but who is like us and can help us and care about us.
What I propose is that each of these models fall out naturally as reflections from a sense-based foundation. The true universe is an orchestration of (orchestration-unorchestration) of perceived qualities and conditions. A paratheistic or ambitheistic society of self-elaborating experiences.
*Love to me seems more human-centric or mammal-centric to me, but I think that Love could be better understood in this context as the most recent form of empathy or sense. Sense allows wholes and parts to partially disconnect and reconnect with the whole.
If we compare two sense modalities, such as seeing vs hearing, we can get a hint of what it might mean for spacetime to be orthogonal to experiential time. Think of the primordial nature of time not as a coherent parameter to be measured, but instead we can see the possibility of time as emerging from experience. A temporal sense which is driven by tempo. Fugues of dream-like, non-orientable perceptual gestalts, with sequential qualities emerging from semantic intensities. If this kind of time were a tent, the tent poles would be significant moments – aesthetically saturated occurrences which resonate into re-occurrence through their cosmological nobility.
For human beings, with a relatively huge psychological bandwidth, we we would experience this prototype to spatialized-time as chronologically ambiguous. Call it a mytho-poetic Dreamtime, collective unconscious, or primordial qualia; a condition where characters and their stories are fused together. The hero makes the journey, and the journey makes the hero. Splitting this atavistic tempo into space and time is the mirroring of unseen perspectives. The hero and journey are polarized into subjects and objects. I would imagine on a pre-biological level, this would be more like position and momentum – less metaphor and more semaphore.
Once the primitive experience takes on a divided perspective there would be opportunities for a sense of hierarchy. Simpler, semaphoric ‘times’ and more developed, metaphorical times are residuated within a densely realized middle ‘place’ as repeating cliches or themes. To broker between these experiential threads, an intermediary sense is used to define boundaries and relations in simple, literal terms. Spacetime, or spatialized time serves to reign in a worldly epoch, and segregate it from the quasi-timeless and quasi-spaceless epoch. The division of fact from fantasy recapitulates the division of space and time, object and subject, body and mind. The reality of space, body and mind is, in the absolute sense, the child of pansensitivity or transrealism. In the local sense, that relation is flipped, and the body is presented as the parent of the subjective mind.
With spacetime, the tent of pansensitive experience is normalized on one end, so that even though the ‘tent poles’ of significance and memory remain as defining the contours of the tent on top, all are now evened out on the bottom. The more primitive, ‘physical’ types of experience have lower amplitudes of significance compared to our experiences, so their variations are collapsed into mere statistical anomalies from our perspective. Our view of their physical time is a mechanical average, generic and lacking any tent-pole significance. Reducing experience to a single quantitative dimension of repetition and duration is the ultimate spatialization of time. With all privacy flattened to be available for public inspection, subjectivity is disenchanted and nomenalized. The figurative and the literal switch roles and the heroes journey is reduced to mere coordinates in a phase space.
The mistake we make is to import this bottom-level generic time into our own high-level proprietary frame. In the most ‘objective’, absolute sense, time radiates from experiential significance as memory and foreshadowing. Time circulates within experience like rhyme does through a poem. Substituting that raw animation for the expectation of rigorous clock-time is not a neutral act. It is an assumption about the universe which cascades through the psyche and civilization, improving and automating our exteriors while our interiority languishes in perpetual angst. Liberation from spacetime literalism might help us find a new way of tapping into larger, more intuitive senses of place and time.
How would you define it?
I propose a new way of describing time, which I find clearer and more explanatory than others.
Time is an abstraction which refers to a general property of experiences which are remembered or recorded as having occurred in a either an irreversible linear sequence, or a repeating sequence (cycle). In my view, time is inherently phenomenal (private, experiential) rather than physical (public, structural), not just because of time dilation under Relativity, but for the more axiomatic reason that time requires memory. Without memory, there can logically be only one eternal moment. It could be repeating forever or be following a pattern or have no pattern and nothing could tell the difference. Time…is experience, or a quality of experience through which private memory can map to public structure. I suggest that time can be understood as taking on three different modal scopes:
I. Micro-phenomenal: This is clock time. Physics. Looking at the development of time keeping, we can see that early devices exploited natural processes which were either continuous and invariant, such as the flow of water or sand into a container, or which cycled reliably, such as a shadow on a sundial. Mechanical clocks offered a marriage of the two, whereby an underlying linear or oscillating effect such as an unwinding spring’s tension or a pendulum’s swing would advance the teeth of a system of gears, one by one.
Each tick/tock is an precisely measured event which is, as much as possible, uniform and generic. As technology has improved, we have refined the clock to a pinnacle of pure abstraction. Both the indivisible and divisible power of nature has been abstracted electronically. A perpetual electrical current drives generic switches to compute a digitally coded readout. Satellite networks deliver synchronized atomic time. Each microsecond like the last, and even though global adjustments to clock or calendar can be made arbitrarily by central authorities, we feel that this kind of time is the ‘real time’.
II. Phenomenal Time: This is natural time. Idioms like ‘time flies when you’re having fun’ or ‘it was the longest night of my life’ reflect that our ordinary sense of time also dilates and contracts through emotional states. Significant events and experiences seem to stand out in our autobiographical memory as not only more timely, but more timeless as well. We claim them, intentionally or unintentionally, as our own. This kind of time is narrative. “I woke up, I ate breakfast, I went to the store”, etc.. There is a story which has a shape – beginnings, middles and ends. It is not just generic oscillation or monotonous duration or arrow of increasing entropy, but a proprietary sequence of participation. This is the kind of time that we might say ‘seems like’ it is real.
If you think of how a story works, the more of the story is told, the more the information entropy decreases. By the middle of the story, we know the characters, the setting, the plot, etc. The number of possible ways the story can continue is relatively limited (even if it is still potentially unlimited in an absolute sense). The significance, however, of the remaining bit of the story is increasingly augmented. If the story is good, you want to hear the end of it, even if you are pretty sure that you know how it will turn out.
After the story ends, it would seem that there is no entropy left. The story has been told in its entirety. In reality, however, the meta-story has just begun. The memory of it survives, creating new opportunities to be applied figuratively in one’s life, as well as sharing it socially and seeing it retold, dramatized, and celebrated in culture as myth.
III. Metaphenomenal Time: Carl Jung famously wrote about the Collective Unconscious, and synchronicity. Experiences which some consider delusional or paranormal. Meaningful coincidences, prophetic dreams, a symbolic language of recurring characters and sagas called archetypes. This is eternal time. Time wound around itself in such a way that some essential, iconic reduction of all that has happened or might happen is in some sense ‘always still here’ and in another sense ‘never really anywhere’.
This is not mystical babbling to me, it is literally the physical reality of what the universe is and what (or who) it does. We have no trouble thinking of eternity in the Platonic sense, as ideal geometric forms or mathematical relations, but because we ourselves are immersed in human phenomena we do not see ourselves as being composed of similarly eternal recurrences.
Because there is no hard line between I, II, and III, all time is actually nested within all three contexts. This can help explain how intuition could work to allow people to sometimes pick up on feelings from a larger scope of time. Events that have great significance especially could theoretically cast a shadow from the III range to the II, so that from the II perspective, it is precognitive.
“The greater part of operating causes in nature are simultaneous with their effects, and the succession in time of the latter is produced only because the cause cannot achieve the total of its effect in one moment. But at the moment when the effect first arises, it is always simultaneous with the causality of its cause, because, if the cause had but a moment before ceased to be, the effect could not have arisen…. The time between the causality of the cause and its immediate effect may entirely vanish, and the cause and effect be thus simultaneous, but the relation of the one to the other remains always determinable according to time.” (Kant, 1787, The Critique of Pure Reason)
As the crickets’ soft autumn hum
is to us
so are we to the trees
as are they
to the rocks and the hills.– Gary Snyder
Diogenes was called Kynos — Greek for dog — for his lifestyle and contrariness. It was from this word for dog that we get the word Cynic.
Diogenes is also said to have worked minting coins with his father until he was 60, but was then exiled for debasing the coinage. – source
In comparing the semiotics of CS Pierce and Jean Baudrillard, two related themes emerge concerning the nature of signs. Pierce famously used trichotomy arrangements to describe the relations, while Baudrillard talked about four stages of simulation, each more removed from authenticity. In Pierce’s formulation, Index, Icon, and Symbol work as separate strategies for encoding meaning. An index is a direct consequence or indication of some reality. An icon is a likeness of some reality. A symbol is a code which has its meaning assigned intentionally.
Baudrillard saw sign as a succession of adulterations – first in which an original reality is copied, then when the copy masks the original in some way, third, as a denatured copy in which the debasement has been masked, and fourth as a pure simulacra; a copy with no original, composed only of signs reflecting each other.
Whether we use three categories or four stages, or some other number of partitions along a continuum, an overall pattern can be arranged which suggests a logarithmic evaporation, an evolution from the authentic and local to the generic and universal. Korzybski’s map and territory distinction fits in here too, as human efforts to automate nature result in maps, maps of maps, and maps of all possible mapping.
The history of human timekeeping reveals the earthy roots of time as a social construct based on physical norms. Timekeeping was, from the beginning linked with government and control of resources.
According to Callisthenes, the Persians were using water clocks in 328 BC to ensure a just and exact distribution of water from qanats to their shareholders for agricultural irrigation. The use of water clocks in Iran, especially in Zeebad, dates back to 500BC. Later they were also used to determine the exact holy days of pre-Islamic religions, such as the Nowruz, Chelah, or Yalda- – the shortest, longest, and equal-length days and nights of the years. The water clocks used in Iran were one of the most practical ancient tools for timing the yearly calendar. source
Anything which burns or flows at a steady rate can be used as a clock. Oil lamps, candles, can incense have been used as clocks, as well as the more familiar sand hourglass, shadow clocks, and clepsydrae (water clocks). During the day, a simple stick in the ground can provide an index of the sun’s position. These kinds of clocks, in which the nature of physics is accessed directly would correspond to Baudrillard’s first level of simulation – they are faithful copies of the sun’s movement, or of the depletion of some material condition.
Staying within this same agricultural era of civilization, we can understand the birth of currency in the same way. Trading of everyday commodities could be indexed with concentrated physical commodities like livestock, and also other objects like shells which had intrinsic value for being attractive and uncommon, as well as secondary value for being durable and portable objects to trade. In the same way that coins came to replace shells, mechanical clocks and watches came to replace physical index clocks. The notions of time and money, while different in that time refers to a commodity beyond the scope of human control and money referring specifically to human control, both serve as regulatory standards for civilization, as well as equivalents for each other in many instances (‘man hours’, productivity).
In the next phase of simulation, coins combined the intrinsic and secondary values of things like shells with a mint mark to ensure transactional viability on the token. The icon of money, as Diogenes discovered, can be extended much further than the index, as anything that bears the official seal will be taken as money, regardless of the actual metal content of the coin. The idea of bank notes was as a promise to pay the bearer a sum of coins. In the world of time measurement, the production of clocks, clocktowers, and watches spread the clock face icon around the world, each one synchronized to a local, and eventually a coordinated universal time. Industrial workers were divided into shifts, with each crew punching a timeclock to verify their hours at work and breaks. While the nature of time makes counterfeiting a different kind of prospect, the practice of having others clock out for you or having a cab driver take the long way around to run the meter longer are ways that the iconic nature of the mechanical clock can be exploited. Being one step removed from the physical reality, iconic technologies provide an early opportunity for ‘hacking’.
|physical territory > index||local map > icon||symbol > universal map|
|water clock, sand clock||sundial/clock face||digital timecode|
|trade > shells||coins > check > paper||plastic > digital > virtual|
|production > organization||bonds > stock||futures > derivatives|
|real estate||mortgage, rent||speculation > derivatives|
|genuine aesthetic||imitation synthetic||artificial emulation|
The last three decades have been marked by the rise of the digital economy. Paper money and coins have largely been replaced by plastic cards connected to electronic accounts, which have in turn entered the final stage of simulacra – a pure digital encoding. The promissory note iconography and the physical indexicality of wealth have been stripped away, leaving behind a residue of immediate abstraction. The transaction is not a promise, it is instantaneous. It is not wealth, it is only a license to obtain wealth from the coordinated universal system.
Time has entered it’s symbolic phase as well. The first exposure to computers that consumers had in the 1970s was in the form of digital watches and calculators. Time and money. First LED, and then LCD displays became available, both in expensive and inexpensive versions. For a whole generation of kids, their first electronic devices were digital calculators and watches. There had been digital clocks before, based on turning wheels or flipping tiles, but the difference here was that the electronic numbers did not look like regular numbers. Nobody had ever seen numbers rendered as these kind of generic combinatorial figures before. Every kid quickly learned how to spell out words by turning the numbers upside down (you couldn’t make much.. 710 77345 spells ShELL OIL)…sort of like emoticons.
Beneath the surface however, something had changed. The digital readout was not even real numbers, they were icons of numbers, and icons which exposed the mechanics of their iconography. Each number was only a combinatorial pattern of binary segments – a specific fraction of the full 220.127.116.11.18.104.22.168. pattern. You could even see the faint outlines of the complete pattern of 8’s if you looked closely, both in LED and LCD. The semiotic process had moved one step closer to the technological and away from the consumer. Making sense of these patterns as numbers was now part of your job, and the language of Arabic numerals became data to be processed.
Since that time, the digital revolution has shaped the making and breaking of world markets. Each financial bubble spread out, Diogenes style, through the banking and finance industry behind a tide of abstraction. Ultra-fast trading which leverages meaningless shifts in transaction patterns has become the new standard, replacing traditional market analysis. From leveraged buyouts in the 1980s to junk bonds, tech IPOs, Credit Default Swaps, and the rest, the world economy is no longer an index or icon of wealth, it is a symbol which refers only to itself.
The advent of 3D printing marks the opposite trend. Where conventional computer printing to allow consumers to generate their own 2D icons from machines running on symbols, the new wave of micro-fabrication technology extend that beyond the icon and the index level. Parts, devices, food, even living tissue can be extruded from symbol directly into material reality. Perhaps this is a fifth level of simulation – the copy with no original which replaces the need for the original…a trophy in Diogenes’ honor.