Fractals and Time, PART I,2,3 & 4 : Unfolding, Timeless Time, and Holography

[ënagualí~ᏉLAᗪἇ ኔጡ።]

Fractals and Time, PART I: Unfolding, Timeless Time, and Holography..

Fractals have a bad rap for a good reason –  a lot of really cheezy, new-agey stuff has been written about fractals. But fractals are mathematical objects with rigorous applications that need to be separated from the fluffy stuff done in their name.

So it was with a great degree of trepidation that I approached Keri Welch’s dissertation, A Fractal Topology of Time, just completed at the California Institute for Integral Studies, which I hadn’t heard of before, but which sounded quite new-agey. But someone with strong cred in my book recommended it, and mentioned some of the concepts, and they sounded promising.

Well, let me just say that the work done in here is top notch, and really worth reading. Welch largely combines the work of three theorists – French theoretical cosmologist Laurent Nottale, German fractal researcher Susie Vrobel, and the inimitable Roger Penrose – to develop the most rigorous account of the potential relation between time and fractality that I’ve seen to date. This work is really a full on mixture of physics and philosophy, and seems to me to succeed in its endeavor.

While Welch does provide some context in regard to the philosophical tradition, and describes in detail at points certain concepts by Bergson, Husserl, and Whitehead, this is largely a work of philosophy of physics. The implications of her work in relation to continental theory and speculative realisms these days is not developed. But it hits me that there’s a LOT of potential here.

What follows is a summary and sketch of what that might look like. First, though, I need to explain what is meant by ‘timelessness’ in contemporary quantum physics discourse, because her task, as she articulates it, is to use fractals to show how “time can be generated from timelessness.” The rest of this post will do this set-up work, the next post will explain Welch’s work itself.

But first, here’s a bibliography that gives a sense of where I’m getting the claims I make in the next section:

– The End of Time: The Next Revolution in Physics, by Julian Barbour

– Before the Big Bang: The Prehistory of Our Universe, by Brian Clegg

– In Search of the Multiverse: Parallel Worlds, Hidden Dimensions, and the Ultimate Quest for the Frontiers of Reality, by John Gribben

– Timeless Reality: Symmetry, Simplicity, and Multiple Universes, by Victor J. Stenger

– About Time: Einstein’s Unfinished Revolution, by Paul Davies

A Timeless Universe?

What might it mean for time to be fractal? Firstly, we need to specify whether the time described is subjective or objective, and for Welch, the theories of Nottale, Vrobel, and Penrose allow us to think both, as well as potential relations between the two.

Welch distinguishes three levels of time familiar to all physicists, if not explicitly differentiated as such – linear time, reversible time, and timelessness. Linear time is the time that flows, in which A precedes B, and causes create effects who follow them in time, but there is no reverse causality.

However, many physicists have argued that many quantum phenomenon become comprehensible once we imagine the possibility of bi-directional or reverse causality. That is, unless causes and effects line up both forwards and backwards in time, an event won’t occur. Such an approach solves the apparent physical contradictions brought to light by famous quantum experiments such as the EPR experiment, or quantum erasers.

Now if quantum phenomenon experience a ‘smearing’ of spacetime, and if our universe likely started with a Big-Bang-like event of some sort, then it seems likely that the entirety of our universe was squished into an incredibly small, dense packet of condensed spacetime in which quantum rules, such as superposition, time-reversal, spatial spreading, and self-interference apply.

From such a perspective, it might not be absurd to wonder if perhaps all possible universes that could emerge from the Big-Bang were all present, superimposed, condensed in time and space, and that our universe is simply the unfolding of one of these within the ‘extended’ (to use a Whiteheadian term) existence of spacetime which we know as existence in our universe.  Of course, there’s no way to know if the universe is not in fact pursuing all of these simultaneously (a multi-verse interpretation of the cosmos), and if quantum ‘decisions’ create paths that leap between these or split and recombine these (‘multiple-worlds’ interpretation of quantum mechanics).

Some have even argued that our universe is a large hologram. Holograms don’t encode a 3D image in a 2D plane (ie: a photograph), but rather, the difference between a reference rays directed straight at a plane of glass and a rays directed from a multitude of angles at that glass after hitting an object. From this differential encoding, a hologram can reconstruct the virtual image of a 3D object from a 2D imprint.

From this we may begin to question – might not our whole universe not actually have left that original quantum state of the Big-Bang? Perhaps all we see is a 4D simulation of what is encoded in a smaller number of dimensions within a quantum superposition of the ‘Big-Bang’, without the expansion actually having to occur?

It is in the senses listed above that has had many theorists entertaining the possibility that timelessness could exist in our universe beyond the smearing of spacetime seen in quantum phenomenon. Julian Barbour has in fact worked to show what a ‘timeless’, fully spatialized model of the time of the universe might look like. Barbour imagines a quantum superposed state in which every possible universe that could emerge from such superposed state exists as a branch in that state, and that some of these states would include false ‘memories’ or embeddings of some states within others. Our consciousness of the world actually moving through time could simply be a flashing between these states in a way that gives the illusion of movement. Since memories are built into our sense of the world, each snapshot would feel like it had history, even if it didn’t, and even if these slices didn’t come in order. We wouldn’t in fact know the different between a random fluctuation between possible universes and linear progression, for the illusion would be there. While a reeeeeaaal stretch (and in some ways similar to Descartes’ ‘evil god’ argument), at least it seems to me, there is no way in fact to disprove such an approach.

But perhaps we don’t need to look quite this far to find examples of timelessness in our world. The simple photon can take care of that for us. Photons move at the speed of light. Since moving at the speed of light compresses spacetime, what would it be like to be a photon?

We know that as one approaches the speed of light, the world around one seems to stop moving, time slows down and screeches to a halt, and space spreads out really long in the direction of one’s movement. In fact, in one’s direction of movement, one’s sides would become so long and spread out that anything in front or behind you would start to shrink in size, until your sides become lines and eventually a blur and then sheet stretching from one’s front to one’s back. As one approaches the speed of light, one’s environment congeals, for in fact, you have, in a sense, left spacetime for timelessness.

Why then do we see photons? Because we keep smacking into them! Matter and light interact on a regular basis. As a photon smacks into matter, it adds energy to the atom it hits, and is often then kicked back out, but at a modified frequency. The angle and frequency/color of the light as it keeps being smacked around in this sense is precisely what our eyes are sensitized to read.

But what would it be like if you were timeless, like a photon, yet also sentient? Of course, we cannot know, but we can speculate. What would a photon ‘see’ of all this? Since all space is opaque to something moving at the speed of light, and since this entity moving at the speed of light exists outside of time, and since a photon is a quantum particle in which superposition of states is possible, it doesn’t seem unlikely that every interaction that the photon has with matter, and those periods outside of time, are layered one on top of the other, at the same ‘out of time’. In a sense, this spatializes time.

Of course, photons often have short lives, for a photon which hits an atom is not necessarily the same photon emitted by that atom shortly thereafter. But there is also no way to be sure that all the photons in the universe are not in fact multiple appearances of the same photon! For in fact, if any photon is outside of time, how would it appear to us, creatures within time?

We can find an analogue by imagining how a 2D line creature would sense the presence of an entity which could navigate a third dimension (something explored in many of the versions of Edwin Abbott’s Flatland). A 2D creature would see a 2D friend of theirs vanish and appear somewhere else, as if they’d jumped in and out of existence, and went missing for the time in between. But for us in the third dimension, there was no vanishing, just our 3D figure had ceased being sliced by the 2D world of the ‘flatlanders.’

So it is with a photon. If photons are truly outside of time, and have a markedly different relation to space, might it be that there is simply one photon, that jumps in and out of our spacetime, just as a 3D figure seems to jump in and out of 2D space? Some scientists think this could very well be the case. We already know that the phenomenon of ‘gravitational lensing’ allows for multiple copies to appear when gravity warps spacetime so that light rays bend around it, giving the impression to our eye that there are many copies of what is ultimately one. What if gravitational lensing has a more radical analogue at work in regard to photons, seemingly multiplying copies of one photon throughout spacetime? If gravity can make copies of images, might extreme gravity make copies of entities, particularly those which are themselves light?

This further explains why some have argued that it is possible that our whole universe is simply the illusion of movement within a super positioned quantum state. We are simply ‘reading’ the hologram, which results in the sensation of ‘moving’ through time, in the manner described by Barbour, within quantum fluctuations in this superposed state.

Welch begins her argument by attempting to describe how it might be that time could emerge from timelessness. And she uses fractals to do this.

Fractals and Time, PART 2: Spacetime Smearing and Crystalline Time.

What follows is Part II of series on the relation between fractals and time.

Before we get to the specifics of how time might be considered a fractal, we need to get a specific sense of how quantum phenomenon relate to time.

Smearing. In the time after a quantum particle vanishes from view and becomes a potential particle, the range in which this particle may appear expands, based on the speed of this particle, which is the speed of light for photons, slower for heavier particles. This range may be thought of as a sphere (which may be distorted by curvature in spacetime) which expands in size over time until that potential is localized by means of an interaction. If a test particle is shot into the spacetime area in which a potential is located, there are some sub-areas in which it is more likely that the original particle will emerge and actualize in relation to the test particle. Much of this is determined by the trajectory of that particle in relation to the event in which it last appeared. We cannot be sure that the particle which emerges on either side of a potential is the same particle, and in fact, if all potentials might not be in some sort of communication. We do know, however, that the previous interaction impacts the forthcoming one. Furthermore, as quantum eraser experiments have now proven, forthcoming events also impact the ways in which a potential may actualize, for quantum potentials interfere with themselves differently over multiple trials depending on events which occur after both interactions on either side of a quantum potential have occurred. Quantum particles act as if causality not only flowed forward in time, from cause to effect, but also effect to cause. This is why they may be described to exist within a reversible sort of time, for there is no way to know if the particles are actually going backwards or forwards in time, particularly because the only way to distinguish quantum particles going forward in time from those going backwards would be a shift in spin.

In this sense, it is meaningless to say that quantum potentials exist in time in the manner that quantum particles do. Likewise, because quantum particles may actualize anywhere within a given spatial location, if in differing probabilities, we cannot say that these potentials are localized in any particular place within that given area. It is in this sense that we say that in a given spacetime area, determined by a spheroid shape and in relation to external measures of spacetime, that for a given quantum potential within that spacetime area and between quantum events, that spacetime in the traditional sense does not exist, but rather, is smeared, and that, furthermore, it is as if the particles themselves were, as in a sense, smeared across the spacetime area in question.

What is it that determines the probability to which a quantum potential might actualize within its relevant spacetime area? If we are dealing with a static particle detector, the more direct a path between the emission of a potential and the detector, the more likely the particle will actualize there. Quantum randomness, either caused by micro-influences from the potential’s context or some other unknown source, has manifested in these experiments such that over multiple trials, there is only probability, not certainty, as to where that particle will land. If we shoot a test particle into a spacetime area relevant to a quantum potential, there is a higher probability of the two potentials actualizing as an event on a path which is the most direct between the two potentials, as based on their trajectories when they were emitted.

For the reasons listed above, many have suggested that a quantum potential ‘explores’ all paths within its spacetime area, but explores with more strength those which are more direct. Were quantum potentials to exist in time, it would be as if the quantum potential would run through all paths, forewords and backwards in time at the same time, each path taking the same amount of time to traverse, and such that the potential would run through the most direct paths more frequently, making it more likely that if disturbed it would show up in the direct paths rather than others. If we can imagine this to occur, but not progressively in time but statically at the same time, we have a sense in which it seems quantum potentials exist.

Crystal. Such a state, while static and outside of time, nevertheless changes, and here we will employ the term used by Whitehead, ‘advance’, for this sort of development which occurs in states which seem to be outside of standard forms of time. Quantum potentials advance because the size of the spacetime area in which a particle may actualize increases over time. In this sense, the smeared area of spacetime, or the smearing of the particle as potential in spacetime, increases over time as perceived outside the potential in question. As a spacetime potential expands as it advances, each new added area, and the time associated with it, recalibrates the entire set of probabilities within the quantum potential, both forwards and backwards in time, and if we think of separate paths off the most direct ones as sideways, then we can say in many directions in spacetime at once.

This is why some researchers have referred to this sort of time as spatial, while others have put forth a fractal model to describe such phenomenon, and both describe aspect of what is at work in quantum potentials. We will describe this sort of spacetime, following Gilles Deleuze, as crystalline. For like a crystal, a quantum potential grows from a germ, namely, a quantum event which emits a potential. The potential then grows, in all spacetime directions, in a manner which is both determined by that germ and the medium, or context, within which that germ finds itself, as well as some degree of randomness.

As exponents of the fractal metaphor have argued, it seems that quantum potentials exhibit fractal properties at multiple levels of scale, similar to the manner in which cells of a crystal repeat at multiple levels of scale. As with crystals, as quantum potentials advance, they increase in spacetime area in a manner in which each new increment is mediated by the shape of the crystal as a whole, and this is due to the fractal iterative structure  at work in both part and whole. As with holographs, the whole is represented, if in mediated form, within each of the parts, in a manner similar to the iterative nature of crystals. And just as light is refracted when it enters a crystal according to the manner in which the whole is enfolded in its parts, so it is that the whole of a quantum potential is enfolded in all the parts (otherwise it could not advance at its edges), if differently and more intensely at some points than others, thereby leading to the refraction of probability states in a manner analogous to that of light. It is in this manner that quantum potentials advance in a crystalline manner, even if they do so in a manner which exceeds traditional definitions of space and time.

Fractals and Time, PART 3: Unfolding, Timeless Time, and Holography.

Unfolding. Building on the work of Laurent Nottale, Susie Vrobel, and Roger Penrose, theorist Keri Welch has recently proposed a fractal model of time which integrates a wide series of sources to produce a unified account of how “time emerges from timelessness.” The hypotheses which follow build upon what has just been presented to describe, explain, and at times elaborate upon Welch’s notion of a fractal model of time, the ramifications of which sync in many senses with the network logical project. Under unusual conditions, such as the curved space present at the imagined start of the universe, or within a black hole, a quantum potential would not necessarily advance, and in this manner, we can imagine a state which is truly static yet distributed in terms of space and time. Many have argued that our universe emerged from a state precisely like this, a crack which opened in the crystal, so to speak. What’s more, there is currently no way to know whether our entire universe exists within a massive black hole, and some researchers have argued that black holes in our universe each lead to other universes ‘inside’ them.

Theorists have largely been loathe to speculate how it might be that time could unfold, so to speak, from the timelessness of such a state. Since quantum potentials seem to exist in a manner in which each part is mediated by the whole, such that the intensity of the quantum potential at a given point depends on the whole of the potential in relation to its contexts, it would seem that the advance of a quantum particle comes about from the integration of new spacetime contexts into the whole of the potential even as this new whole is folded into each of its new parts, if more intensely at some parts than others.

Based on this, some researchers have argued that fractal shapes such as the Mandelbrot set can provide some clues. As one zooms into a given area of a two dimensional plot of a Mandelbrot set, each level of zoom leads to more detail, to an infinite degree as one continues to zoom. The layers of detail that one will encounter are all iterations and enfolding of the fundamental Mandelbrot pattern into itself, such that the whole is contained in an enfolded manner in all its parts, and yet depending on which area of the plot where one begins one’s zoom, the patterns one will see will be fundamentally different. Most Mandelbrot sets are color coded to describe degrees of inclusion/exclusion from the set, and here we see analogues to degrees of intensity, just as the zoom is analogous to the concept of advance, such that the zoom within the Mandelbrot set from any given point can be seen as analogous to the advance of the whole as perceived from one particular location within the whole as that whole advances. Because our eyes lack the resolution to distinguish incredibly small or large distances, it seems that new shapes appear and vanish as we zoom into the Mandelbrot set, even though these shapes are always there, and merely unfold as our zoom proceeds.

All of this is generated from an equation, a relation which is itself static and outside of time, but one which iterates differently depending on how it enfolds within itself. If we imagine something like a Mandelbrot set in three dimensions, and imagine the zoom on a particular location as the movement of a location through time, we see the manner in which it may be possible for a static, timeless relation (the equation) to refract itself in a manner which is fractal and holographic in the manner of quantum potential, but in a manner which appears to be progressively unfold differently at each location even as the whole unfolds. This unfolding is nevertheless taking place within timelessness, for there is actually no progression within a Mandelbrot set, only an increase in resolution and zoom as produced by a computer program as we expand our resolution at one particular location. But in a perfect Mandelbrot set, one not iterated by a computer but existing fully formed in spacetime, this unfolding process does not produce anything new, but simply unfolds what is already there.

If a three dimensional Mandelbrot set were to expand in size dramatically, and a particular location were to stay where it is and have the folded Mandelbrot ‘matter’ expand unfold around it as the whole expanded it, it would likely ‘experience’ something like we experience zooming into a Mandelbrot set, if in four-dimensions. And if this location is occupied by a sentient observer with memory yet limited resolution, this observer would likely experience this expansion as something similar to moving in time. This is because the expansion of the Mandelbrot matter around it in all directions would be perceived as a the zooming we have described, but one which occurs from all sides.

It is in this manner that a timeless relation, the Mandelbrot set, can give rise to what can only be described as change in four dimensions, or the experience of three dimensions of space and one unfolding dimension of time, in a manner which iterates differently depending on the location within this expansion, yet in a manner which always reflects the whole. And in fact, all fractals have a germ, which some researchers have called a fractal’s ‘prime.’ It is not unreasonable to say that The differential unfolding of a multi-dimensional prime could, in theory, give rise to spacetime in the manner described above, as both container and contained, giving rise to time in the process.

Refraction. Is there any evidence that our universe is something like this? Researchers have noticed that the visible universe expands relatively uniformly over time. This is both because space is expanding, but also because older light has more time to reach us. Because it takes time for light to reach us, not only are we looking out in space when we peer into space, but also in time. This has lead some to argue that we are surrounded by the past, enfolded in it, from all sides. For in fact, the most ancient light we can observe comes at us from all sides. For when we peer out at great distance in any direction from earth, we see quasars, young galaxies in the process of formation, relics from earlier times in our universe.

In addition to this, however, we also are bathed, as is every part of the universe, from what we can tell, with a semi-randomly dense energetic medium known as the Cosmic Microwave Background Radiation (CMBR). The fact that it is basically uniform implies that all the universe was in fact originally at the center, a fact which would make sense if expansion from a Big Bang came from everywhere, leading to whatever is far away to seem distant in spacetime. The semi-uniformity would imply that small fluctuations in this expansion of the early universe lead to the clumping of matter and energy into galaxies, at least after a period of intense expansion which largely flattened space itself.

There therefore seems to be evidence to support the notion that our universe is expanding and expanded in a manner similar to what we have just described. If the universe is then fractal in the manner of a three dimensional Mandelbrot set, we might experience something like an unfolding of time from the expansion of a previously quantum state. That said, it does not seem that space is expanding around us in a visibly appreciable manner. Many have argued that the ‘arrow of time’ experienced by humans is the result of the flow of energy in the universe, from high concentrations to low concentrations, with all human processes moving along this flow like leaves floating on top of water moving along in a river. But what grounds the very flow of energy in anything like a flow, a movement in something we have called time, may be due to something like the expansion of a fractal quantum state of the sort we have just described. And since, as many researchers have argued, it seems that the most primordial stuff in our universe is in fact a sort of quantum foam, one which exhibits fractal levels of detail the further one zooms into it (which is equivalent to the degree of energy one uses, hence the need for massive accelerator's to view smaller and smaller particles in order to see what particles may have existed in the extremely condensed conditions of the early post-Big Bang universe), it does not seem unreasonable to argue that our universe is in fact the result of a differential unfolding of interfolded forms of the same fundamentally fractal and holographic material.

Developments in string theory seem to provide a way to link quantum foam with particles, providing a mediating state, for string theory may explain the ways in which that of which the foam is composed could complexify into vibrating patterns which give rise to the particles encountered in the world. From such a perspective, the universe may in fact be simply a vibrational pattern which folds and unfolds within itself in a manner which is timeless in and of itself, yet gives rise to the experience of time for those within it.

Fractals and Time, Part 4: Light, Matter, and Memory.

Light. Such a perspective can be more fully fleshed out if we examine the peculiar temporal state of light. Many researchers have argued that light exists in fact outside of time, and that what we see is simply the manner in which the interactions of light with matter keep dragging light into spacetime, and in the process, expanding one photon into what appears like many.

As an entity approaches the speed of light, all that which is around one seems to speed up in time, and all that is aligned with the movement approaching the speed of light increasing in length (giving rise to the lines of light which many sci-fi fictions imagine travelers would see instead of point-like stars). At its breaking point, as one hits the speed of light, all space going in the direction of one’s travel would become infinite, destroying any ability to see in front or behind one, as one’s sides literally swallow one’s front and back, all time outside one would become infinitely fast, and one’s own time would appear infinitely slow to those outside.

What would it be like for an entity moving at the speed of light when it ‘encounters’ matter? When a photon hits matter, it may bounce off at a different angle, or may be absorbed, such as what happens when a photon makes an electron jump in level to excited state. When the electron falls back down to its original state, it releases a photon, and this also travels, as do all photons, at the speed of light. What would a photon, if it could experience, experience of these interactions? Photons would continually jump between timelessness and moments where they are jerked back into time.

From the perspective of a timeless, moving photon, these moments in time could not be said to be before or after each other, for these terms become meaningless when one hits the speed of light and is truly outside time. So all the separate moments within time can be thought of as existing ‘at the same time’, or ‘smeared across spacetime’, within the timeless existence of a single, undivided photon, which then appears in many spacetimes at once across the universe. It is for this reason that famed physicist John Wheeler suggested that it may be possible that all photons in our universe are actually multiple appearances of one photon, refracted into many by the process of being ‘expanded’ into spacetime by means of interaction with extended matter.

But what about matter? Why does matter experience time? One phenomenon which may shed some light on this is that of gravitational lensing, in which the image of one stellar body appears multiple times due to the way in which a massive body’s gravitational pull distorts the light coming towards earth. Gravitational lensing explains the way in which one image can become several due to the effects of gravity on light. If gravity can multiply the images of matter due to the interaction of matter with light, it would seem that truly extreme gravity, like that of the Big Bang, would infinitely multiply the image of matter, till it was in fact everywhere, holographically projected.

Conversely, what if the matter we observe is simply the unfolding of what was originally distributed throughout an early, compacted quantum state? If the original matter were ‘smeared’ across space in a quantum state, the its unfolding may give rise to something like the extended state we observe today. From such a perspective, matter and light begin to seem like two sides of the same coin, with matter dividing light from itself, just as matter increasingly localizes as gravity decreases. And since the emission of photons from matter gives rise to the energy that powers, producing the energy that gives rise to all the rhythmic mechanical and biological processes which allow organisms to gain a sense of the flow of time, might it not be the intersection of matter and light, rhythmically pulsing between time and timelessness, which gives rise to the flow of time?

Layering. Can memory be accounted for by fractal processes? Some theorists have argued that just as time can be concieved as the expansion of a fractal space, such an expansion would be percieved by an observer as not an outfolding but an infolding. This would only be furthered by the flow of energy which is layered on top of the expansion of what is, giving rise to a second level echo of this infolding.

It is in this manner that even though the expansion of the universe is proceeding rather slowly relative to our present state, the flow of energy which emerged therefrom is not. These energetic processes give rise to the material clocks which found the biological clocks whose cojoined rhythms give rise to the experience of lived time. Humans live within a constant influx of energy from the sun, and yet that influx is continually fighting against the general tendency of all that is to disintegrate due to the collective forces of entropy. Only the constant influx of energy keeps complex systems in a state which maintains and/or increases in complexity. The forward pulse of material and biological evolution, which produce the clocks which produce our sense of time, have been themselves put in motion precisely by the energetic flows of energy from the sun which counter the continual pull of entropy.

Such a movement of time could occur in this way no matter if energy is flowing into or out of a system, so long as the general direction of the system as a whole which sets the clocks, so to speak, follows one direction at a time. Memory occurs when experiences which have occurred are layered into those which continue to unfold.

If we conceive of a local experience of time as the progress of a line which is zooming into a larger three dimensional fractal, and energetic flow as echoing these processes, we can imagine memory as the layering of a primary set of experiences into those which follow, in the manner in which a prime layers into itself in a fractal. Primary experiences describe the general shape of not zooming into a fractal, but rather, zooming out of a fractal, with original experiences feeling more distant, yet ever layered into the wider and wider experiences which come.

Memory in this sense can be conceived of as an inside out mirror image, like a Klein bottle, of the fractal model of spacetime which we have previously described. While such a fractal would have a start, as these memories continue to enfold themselves, they give rise to echoes in a wide variety of permutations, each refractions of the original. If each of these primaries are nevertheless refractions of an aspect of a fractal, holographic whole, then in a sense all the memories that ever existed could be produced by the complex in folding of an incredibly complex yet ultimately timeless pattern. From such an experience, the repetition of primaries in memory would give rise to cycles in memory whereby recognition could develop, and from this it would be possible to establish relations to objects, cycles within objects, and ultimately time metrics.

Lived time, however, would feel more dense or less dense depending on the degree to which recalled memories were enfolded into a present moment, or the present were experienced relatively free of such detailing. The experience of images fading and arising from memory may then be more an effect of the limited resolution of the human brain, even though all experience is laden through and through with memory, if in differing degree. Such memory can be thought of simply as an enfolding of the past in the present, and anticipation within the present as the fantasized projected mixture of such memories to imagine possible future states. And if, as some researchers have argued, the looping of dopamine around certain circular channels in the brain provides us with a basic internal clock, then the ratio of the density of memory compared to this internal cycle could give rise to the sensation of the stretching or condensing of time experienced by humans in a wide variety of situations.

[Ametrine -(MHZ)]

Thank you, Vlada. 

[ënagualí~ᏉLAᗪἇ ኔጡ።]

Your welcome Ametrine..:)

[Ametrine -(MHZ)]

:o)