Late on Time

As topological manifold, time explains our world emerging

Marcus van der Erve
Nov 22 · 10 min read

Physicists may be less well positioned than one would think when it comes to establishing the true nature of time.

The conception of time that rules their thinking is conditioned, even constrained by their never-ending endeavor to sustain a massive network of interdependent equations, in which time plays a primary role, as variable.

As they lock onto the role of time in this network, they inevitably lock out (if not, struggle with) time-related perspectives from “outside”. Or, to put it bluntly — paraphrasing Sabine Hossenfelder, they tend to get “lost in math”.

But even under the protective cover of this network, time is not free from its demons.

  • Interpretations of our world, dependent on “the observer” as they are, show time slowing down for those that travel close to the speed of light.
  • Equations go wacko when going back to time’s ultimate zero, to what is assumed to be the beginning our Universe.
  • At quantum levels, where chance predictions rule our observations, the arrow of time may point at the archer.
  • Although crucial to the establishment of a moving object’s future position, time fails to hint at the state of its evolution.

What’s worse, in the vexed pursuit for equation consistency, variables such as time and force have evolved into near-physical phenomena, far from the bare predictive parameters that Newton and Leibniz once envisaged.

Force has turned into “the force” and time has gyrated into some basic clockwork that produces ultimate ticks (or, as scientists financed by the Templeton Foundation might like us to believe, “divine ticks”).

Physicists seem to have forgotten that, even to Schrödinger, force was but a hindsight “measure” of a difference in “free energy” rather than something physical— I explore an example involving osmosis here.

I argue that a more complete picture of time also hinges on a sociological perspective.

As part physicist, part sociologist, I stumbled over time decades ago when studying corporate-development paths. In a nutshell, I saw stunning parallels between companies but, at the same, many duration differences.

The explanation of why these parallels sustained irrespective of the clockwork that is used to time a company’s evolution led me onto a long path of inquiry. Eventually, I published my findings in one book and my journey in another.

My interest in “time” was rewarded, even recently, by publications on the topic by physicists with whom I had shared my work. To me, this suggested that the question of time is still waiting to be answered.

Probably because of the reasons sketched above, I failed to find in these publications the enlightening insights that had served me so well, insights that, in my opinion, might serve physicists too.

So, here they are, in short.

Time as Topological Manifold

When studying the development paths of individual companies —at a local level, I noticed that, for some companies, this path appeared to lead across rather flat regions with just a few bends here and there.

As a result, these companies not only covered distances in a relatively short time but could also sustain their travels more easily, not hindered by life-threatening roadblocks.

The path of other companies, however, appeared to lead through rough mountainous terrain with hairpins, cliffs, and elevation differences. Their journey would often be cut short as they got stranded on the side of the road.

At a global level, all these companies travelled through similar stages, in which “organizational conditions” changed predictably from stage to stage. Not much in these stages hinted at their journey at a local level.

My observations, thus, revealed two puzzling duration-related views:

  • the local view, which exposed path- and timing-related differences, and
  • the global view, which showed parallels between organizational conditions.

When pondering how I could marry these two duration perspectives, I turned to the mathematics of geometric differences and parallels. In effect, the idea of a topological manifold appeared to unify the local and global perspective.

The Earth, for one, is a topological manifold. At a local level, its surface varies from planes to mountainous terrains, river beds, and oceans. At a global level, seen from space, it unifies these differences into a smooth whirling globe.

With the above duration-related differences in mind, I realized that time (even Minkowski’s spacetime) is a topological manifold too.

At a local level, time presents itself as “clock ticks,” of which the quantity may differ from case to case. At a global level, it unfolds as a whirling stage-driven phenomenon, each stage with common organizational conditions.

Time at a local level

At a local level, time involves the kind of clock ticks that we all are familiar with. It is the ‘t’ that physicists use to calculate the position, velocity, or acceleration of an object. Time ‘t’ doesn’t reveal the specifics of company development, other than the duration of energy transformation.

Then what are these “clock ticks” of time ‘t’ really about?

Before we invented clocks, we would measure our journeys in terms of “days travelled”. To get from A to B, for example, we might travel by camel or by sea. By camel our journey might take ten days while, by sea, it might take only five. So, if duration was an issue, we would choose to travel by sea.

We could make this comparison only after translating two totally different means of transportation across contrasting surfaces of the Earth (desert and sea) into one regularly repeating phenomenon such as the Earth’s rotation.

Of course, when you run a marathon, your arrival time and that of your competitors in terms days would not suffice. You’d like to know the hour, minute, second, or even split second. This is why the invention of the pendulum clock by Christiaan Huygens was such a breakthrough.

Huygens concocted a regularly repeating pendulum to divide our days into small equally-sized bits of time. This way, people, in Huygens’ days, could compare more accurately the duration of their journeys by translating each journey into his pendulum-clock ticks first.

By now, also Huygens’ clocks no longer suffice. We want to measure the most minute events that take place in much less time than the blink of an eye. So, to compare ever-shorter events, we seek phenomena that produce ever-shorter regularly repeating clock ticks.

The following sums up what time ‘tat a local level (local time) is about:

  • It arises only after translating the duration of events into time slices of some known regularly repeating reference phenomenon.
  • It is not fundamental because we choose the reference phenomenon that regularly repeats itself (Earth rotation, pendulum swing, light wave, etc.).
  • It is “objective” when we compare different events with one and the same regularly repeating phenomenon.
  • It is “subjective” in that we, as observers, choose the regularly repeating reference phenomenon. This is why time may appear to pass either fast or slow—several books have been written about this “magic” experience.

To conclude, local time ‘t’ doesn’t hint at the developmental state of an organization. Yet, as duration, it does indicate that energy might have been transformed. This suggests that there may also be a thermodynamic face of time.

Time at a global level

When a cell divides into two and when these divide again and again, the ensemble of cells soon starts behaving like a complex system. This means that the ensemble behaves in an unpredictable, nonlinear way, based on how the cells deal with one another and the influences from outside as a whole.

In fact, each cell, being at another location, interfaces with a slightly different environment. This essentially produces a division of labor that is location-inspired because each cell is condemned to specialize in dealing with the challenges and opportunities in the environment that it faces.

Of course, the behavior of a cell in the ensemble is entangled with the behavior of adjacent cells. So, a growing ensemble of cells essentially self-organizes on the back of a division of labor and behavioral entanglement.

Interestingly enough, this agrees with the two axes of self-organization in human ensembles that I identified in my doctoral thesis of 1993. I took this idea further in a recent article, in which I discuss the socioeconomic and thermodynamic origin of the so-called “division-cohesion paradox” and how this paradox can be put to use to improve the agility of organizations.

Crucially, neither the division of labor nor the entanglement of behaviors is static. Both are bound to wax and wane due to developments outside.

As engineers know, when plotting two pendulum-like phenomena (such as sines and cosines) on an oscilloscope, their swings combined generate a cyclic phenomenon that goes round and round. The same happens when you plot the division of labor and behavioral entanglement this way.

In the crosshairs of the axes for the division of labor and behavioral entanglement, four stages emerge — shown by different colors in the diagram. These colors mark the changing conditions as the division of labor progresses, followed by the entanglement that it entices, when the size and complexity of the ensemble grows (and, eventually, declines).

These conditions have been found to apply across companies. Some of these, such as the varying sensitivity to inside and outside events and the coupling and decoupling of internal activities, also apply to other kinds of organization.

The physical chemist and Nobel laureate, Ilya Prigogine, observed how in a thin layer of liquid, which is heated from underneath, the moving molecules start shaping into an organization. Behaving chaotically at first, they eventually follow orderly paths to transport heat to the surface more efficiently.

Intriguingly, the orderly motion of the molecules produces a honeycomb-like structure (of so-called Bénard cells) at the surface of the liquid. At the center of each cell, molecules rise to the surface to shed their heat as they travel to the edge of a cell where they are sucked down to the bottom again.

This is not just a hiccup of nature. Across our planetary system, this process sustains conditions that are also essential to life on Earth. The granules on the surface of the sun, the Earth’s 20-odd tectonic plates, and the high- and low-pressure weather pattern, to name just a few, all depend on it.

Thermodynamic face of time
Prigogine’s research focused on thermodynamics, the transformation of energy from, say, heat to motion. He measured in how far the orderly motion of molecules improved the dissipation of heat at the surface of the liquid.

Global time, therefore, is the thermodynamic face of time because it shows the stages of how non-living and living phenomena develop to transform energy by some form of orderly behavior among the objects, players, or actors involved.

The difference between living and non-living phenomena, in this respect, is that non-living phenomena are entirely dependent on external events. For example, when the heat underneath the liquid in Prigogine’s experiment is turned off, the orderly behavior of the molecules collapses almost instantly.

Living phenomena, from bacteria to humans and human organizations, carry a surplus of energy (through their metabolic system, for example) to sustain their orderly behavior long enough to find another source of energy (food) or, when it comes to companies, another product-market combination. This takes place typically during the first and second stage of global time.

In Prigogine’s experiment, it may appear as if the orderly behavior of molecules collapses almost instantly when the heat is turned off (or arises when the heat is turned on). This does not mean that the rise and decline of orderly behavior skips a few stages of global time.

Rather, it shows that the time slices of local time are not small enough to register the duration of these global-time stages.

In fact, the rise of orderly behavior in living and non-living phenomena always cycles through the four stages of global time but not always slow enough for us to notice it.

Then again, in a recent article about the rise of our successor species, the duration of the stages of global time varies from 40,000 years (stage 1) and 10 years (stage 2) to probably longer than 40,000 years (stage 3).

The following sums up what time at a global level (or global time) is about:

  • It arises when we look out for stages of repeated orderly behavior development where or when the external conditions conditions appear to be right.
  • It is fundamental in that it traces the way nature fosters the development of orderly behavior in four distinct stages, no matter their duration.
  • It is “objective” in that it necessarily hinges on the inclination of nature to improve the efficiency of energy transformation by orderly behavior — I explore the thermodynamics behind this in more detail here.

In sum, global time is the thermodynamic face of time and the four stages of orderly behavior development, duration independent as they are, are universal.


Because we choose the regularly repeating reference phenomenon that determines our sense of duration, it can be said that local time is a human clock. Global time, on the other hand, is nature’s clock. We read it by tracing the different stages of orderly behavior development.

The world of physics would benefit if it opens up to the idea of global time because it helps identify, predict, and manage the emerging realities that shape our world.


Societal Cycles

Marcus van der Erve

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Societal Cycles

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