The Historian Atheist II

The Historian Atheist


Patterns of wave interference
Interference patterns from two wave-sources. Patterns whose workings was latter imposed on other ‘wave-like’ systems due to similarity.

In the last post we discussed philosophy as science’ cohesive force. In it we saw how philosophy formed and defends many of the axiom’s and assumptions the other sciences incorporate. Among these assumptions is one that accepts the existence of patterns in reality. Series of events that when abstracted show relative or even absolute similarity to each other.

The laws of physics is one way of poring these patterns into models from which they can be reduced no further, the minimal valid description of reality. We can assume that the patterns thus far identified are not the entire set of patterns that exist out there. In fact until we have a final grand unifying theory of everything we will not be sure if there aren’t still patterns that escape us.  In contrast, until you have a law-model that has been tested and reproduced independently you cannot state for certain that you have identified a pattern at all.

Sometimes a pattern is not obviously the result of a series of events in time: the spots on a leopard, the pattern of tree-branches. Sometimes patterns are visually obvious yet mathematically inscrutable: the wave shapes in the sand on the shorelines, the unexpected regularity of certain cloud-formations in the early hours of the morning. Sometimes the patterns are only mathematically observable: highway traffic, cellular phone-traffic during and after business-hours.

I have always been fascinated by how models for patterns that are made in one field of science are sometimes transferred to entirely other fields based on the similarity of the pattern. For example everything that was found out in the field of fluid-dynamics regarding the wave function, wave propagation and interference patterns was transferred onto electro-magnetism. Purely on the basis of mechanics this was entirely unjustified: with electro-magnetism the wave-analogy is not through a medium but through a vacuum.

Even the ‘wave-ness’ of the phenomenon is not  unambiguous since electro-magnetism needs to model ‘signal-instances’ both as a wave as well as a particle and acts as either in different experiments. And yet it was the interference pattern of light-“waves” that was used in the last great discovery of this decennium: gravity waves.

While with fluid-dynamics we have a very good idea of the interactions of the particles (in this case water-molecules) that play in the creation of the wave, and how for example viscosity influences the phenomenon. For light traveling through a vacuum the formation of the wave is more a post-factum observation. We don’t know why it acts like a wave and all conclusions that are pressed onto light, coming from fluid-dynamics, are done so purely on analogy of pattern and not the result of a prediction from an underlying theory.


If I define the field of ‘History’ as ‘the study of reality along the time-dimension’, which is not a stretch in any sense, I feel justified to conclude it has a lot of commonalities with physics. After all physics’ descriptions of reality are rarely void of time-elements. Nor is history described with the assumption that the laws of physics were suspended.

If we encounter an old description of a siege in Chinese documents which contains an ill-defined measure of distance but it also contains a distance over which cannon was able to fire, physics can help us gain a very good estimate of that measure of distance. A lot of physics was also involved in figuring out how the Egyptians could build constructions that held height-records until the late 19th century.

In closer regard the differences between history and physics seem to be the traditional methods of approach, the timespan and the manner of description. Physics will use current sources mostly created by the scientist himself, very short timespans and exact, quantitative descriptions. History will use any available source, most often not created for the purpose and incomplete, very long timespans and probabilistic qualitative descriptions. However, as we will see in a moment, both use patterns and both can transfer conclusions from one pattern onto another based on the similarity of the patterns.


When dealing with our young siblings or when venturing onto the job-market we have all been confronted with the way things change constantly. Our children behave differently. There is always another skill or technology or methodology one must learn in order to stay employed.  Even ‘change’ itself seems to have changed since it seems today everything changes so much faster than it used to.

And yet the observation of “Panta Rhei”, “everything flows” is attributed to a certain Heraclitus, Greek philosopher in a book by Plato from 402 B.C.E. ‘One never steps into the same river twice’. So it seems that the fact that everything changes is a pattern throughout history that, while it itself has changed in scale, has been around for some time without at least changing so much as to completely disappear.

The latter seeming paradox is linked to another pattern we all know to exist in history: ‘History repeats itself‘. We have all, on the big and the small, encountered ‘déjà vue’ instances where we clearly recognise a series of events to be similar to another at a different time.

  1. A charismatic person is elected to power thanks to the hope and belief of his fellow people. After a time the habitude of power warps the morality of the person which results in his abuse of it and the disillusionment of the electorate.
  2. A war is started, initially with universal conviction that it will be short, well-worth it and winnable. After what seems like forever all parties come to regret their initial naiveté and invest in the war only because losing it is, with a small margin, the worst option of two very bad propositions.
  3. A small community builds a more egalitarian society based on absolute altruism, the skills and dedication of some. With the success of the community its size gets bigger and it is infiltrated by less altruistic, less skilled and less dedicated elements, sometimes even rising to power. The gains of scale crumble, society-wide satisfaction turns sour, and after a period of repression the egalitarian society collapses to individuals where the most successful are those that combine talent with ruthlessness.

So it seems we recognize two contradictory concepts about history simultaneously, the first ‘that everything is constantly changing’, the second ‘that history is often repeating itself’. On the face of it, these two patterns, the ‘history-changes’ and the ‘history-repeats’ are contradictory to each-other: if everything is constantly changing it is not possible for history to constantly repeat itself.

However it is important to realise, when we take a step back, that ‘history-repeats’ is actually a meta-pattern on the overseeing level that tells us something about other patterns in history on the tactical level. This means that ‘history-repeats’ does not suggest that we will tomorrow circle back to the 60’s or even recreate those years ad-verbatim ‘leather, “grease” and Jane Fonda included’. It means that throughout history we will see patterns repeating themselves and one of the most prevalent patterns is that, on the tactical level, everything constantly changes.


Time-series in phase-space

Phase-space example
Example of a simple phase-state diagram in which the different states of a system are plotted.

If we were to register all the measurements that describe the present, the temperature, air-pressure, the position of every living and dead object, we could model this to be a point of histories’ time-series. By making such an abstraction of reality we are able to detect patterns on another level and compare things with each other which would otherwise remain entirely separate concepts. The 3-D graph in which we could plot these time-series would be called a phase-space:

In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space.

Plot of a pendulum
Progression showing how the movement of a pendulum is differently plotted in a time-series compared to a phase-state diagram.

Now let us review some examples of what history would look like given different patterns:

If all measures/dimensions would be the same for all time (if history disallowed for any change at all), history could be described by a straight line in our phase-space. This would perhaps seem rather boring to you but in fact it is endlessly fascinating since already we stumble on an unintuitive question we otherwise might have missed: why is everything not in a static state of equilibrium?

There is really nothing about the fundamental forces that in principle prevents an alternative history where 3 million years after the Big Bang processes come to an equilibrium and we never evolve to begin with.

However we know this isn’t the case, we know the plot can’t be a straight line because of the manifest changes we see everywhere and all the time.

We also know that the plotted line can’t intersect itself because we have no example of two distinct moments actually being the same moment (albeit with separate pasts and futures). From a-far this would look a little like the loops of the strings we tie our shoes with, roughly a bow-tie-shape: two distinct curves meeting at a point but separate in every other way.

Complex phase space
Example of a much more complex plotting in a 3-D phase-space.

We also know that the line is not interrupted: each point on the curve is the result of the previous point on the curve in a (on the macro-scale) deterministic relation. (Although we must allow for Time itself to possibly be a discrete quantity, which would make the plot less a line and more a collection of points separated by distances of zero-length.)

This deterministic relation also prevents the plot from just being random scatter. We will come back to this phase-space type of modelling history after we have discussed non-linear systems and strange attractors.


Non-linear systems and chaotic dynamics

Strange attractor art
Drawings based on non-linear mathematical formula give us visuals of strange attractors.

For those of you who are not introduced to the concept of the butterfly –effect, a bit of a misnomer if you ask me, let me summarize. In the early days of developing computer-models for weather-prediction one of the findings was that small differences in the rounding of the numbers that were put into the system made very radical differences between different models after a few days.

This was later quoted as that a ‘difference of a butterfly-wing flap in the input could result in a difference of a hurricane at the outcome’. At no point was this intended to mean a butterfly could be ‘amplified’ into a hurricane, but nevertheless that is regretfully how it is most often understood.


The reality is that non-linear systems’ sensitivity to initial conditions (or changes therein) is just one part of what makes a chaotic system. They must also show topological mixing, meaning that, if you take a cube of the phase-space of arbitrary size eventually (after mathematically infinite time) at least one point must map to any other randomly chosen cube of equal size. More visually stated: it must be like you put a die in you paint and stir it very-VERY- well.

Finally, if the system has periodic orbits (meaning the graph shows quasi circular constructs) these must be allowed to be arbitrarily close to each other. This means there must not be a reason why two phase points of such circular constructs can’t be as close together as possible, with the exception of being the same point.

Lorenz Attractor
The Lorenz attractor. One of the first mathematical attractors found and a good ‘basic-model’ for history. In it we find see evidence for sensitivity for initial-conditions as at certain points the graph veers wildly off to another ‘platform’ of stability. We see evidence of ‘platforms of stability’ as the graph at many places makes curves that are arbitrarily close together. As only an attractor is shown there is no topological mixing.


Not all chaotic systems have periodic orbits. Gas molecules in a bottle may be susceptible to initial conditions and ‘mix-it-up’ pretty good, there is no indication that it goes through cycles of similar states. In fact most chaotic systems are just boringly increasing entropy in every part of its system.

The reason that some chaotic systems are interesting is because they show fractals; Patterns of order that develop in one part with a greater offset of disorder in all the other parts. Sometimes all it takes is a random number generator, a mathematical formula and a finite number of iterations for such a pattern to emerge. Order that comes from a system of disorder.


The point I am getting at, my core thesis here, is that based on a similarity of patterns, history is a chaotic system including the tendency for strange attractors. This would explain why the early universe did not condense into a steady state equilibrium: while it is not an impossibility, in a non-linear system the chance is smaller than tossing a coin and finding it landed exactly on its edge.

It also would explain why history doesn’t repeat itself exactly: for the time-series of history to curl back on itself and traverse its own past would mean ‘hitting’ a target of the same size of the steady state equilibrium universe from the first example.

Another reason is that traversing its own past would be ‘de-facto’ time-travel and given determinism rules on the macroscopic scale this should result in the same future, resulting in an endless loop. Still, given the length of time history has, I believe the probability for time being circular would be rather high if it had not been for quantum uncertainty.

Let me argue the similarity of history with non-linear systems using some examples:

During most of it, history has sensitivity for initial conditions: Assume we are able to go back in time and move a chair in the past. This is the historical equivalent of a butterfly-wing flap since by itself, in most histories the future with the chair at position ‘A’ or the chair in position ‘B’ will be exactly the same. But it could also be that the chair being in position ‘B’ is what makes Napoleon Bonaparte do a clumsy fall, break his neck and it ends up changing the history of Europe as profoundly as it ever could.

History also shows considerable mixing: if we take a snapshot of the world at the one moment and make a collection of slightly different histories (or variation-points in our phase-space) by changing something in random places all over the world; the outcomes of these alternative histories will eventually be arbitrarily far from each other without anyone being able to predict the outcomes.


However we also observe that certain parts of history are profoundly insensitive to initial conditions. If you go back in time and kill a person on board the Titanic, you are doing much worse to history than just moving a chair, but you have a good chance that the result will only be that this person dies a few minutes earlier than would have been the case.

In fact, one of the sad and depressing facts about history is that much of history has been filled with layers of inconsequential people impacting little else but generations more of other inconsequential people. People whose suffering elicited no change and whose short lives could have been impacted, shortened or prolonged with impunity since any change would have been absorbed and compensated by an equilibrium pattern within history. These are the ‘strange-attractors’ of history. We can repeat some examples we already discussed: war, corruption, famine and disease.


If you feel like it seems there are no ‘good’ strange attractors to history: You are not wrong. There is even a good reason for that. ‘Strange attractors’ are in fact ‘islands of relative stability’ within a system, it therefore requires that none of the elements that determine them are in a highly instable state.

As I’ve discussed in earlier posts: entropy always wants to increase and to reduce entropy requires effort. Since it is easier to become corrupt than to be incorruptible, since it is easier to start a war than to continue finding compromise for peace, since it is easier to get contaminated than to get rid of disease, because of this there is no “good” stability-platform. In a perfect world there would exist a platform of equilibrium where everybody is happy. Since this isn’t possible, life, mathematically speaking, sucks!


It is not possible to show that history has “arbitrarily dense periodic orbits”. The point is that there is no reason, if history repeats itself, that the outcomes can’t resemble each other arbitrarily close. Hypothetically so close as to be indistinguishable from one another with only the date being different.

This means that far from being on a road to ever increasing prosperity there are potential futures that lead us back to the Dark Ages. In fact one recipe is trivially easy to conceive: if we don’t teach any of our kids anything in the next 25 years, within one century the global population would be reduced by 90%, with maybe 2-3% able to read and agriculture again being the basis for economics, provided we still remember how to do agriculture. More popular but sort-like Hollywood scenarios might involve nuclear-apocalypse or diseases.


In conclusion

If there is a root of truth to what I have said here let me add some consequences: when faced with a choice the easier solution tends to be the morally worse one. It also means there is no such thing as a ‘wasted effort’, only effort whose consequences haven’t become clear yet.

If we were to conclude, based on these similarities in meta-patterns, that history is a chaotic system this ‘predicts’ [explains] much of what we encounter: the fact that Order is by far outnumbered by Disorder; The far reaching self-similarity of our reality: moons orbiting planets, planet orbiting stars, stars orbiting black-holes; but also: events in history resembling each-other despite the difference in time, place or scale.


The ordering properties of chaos, as build into the fundamental forces that actually shaped our universe are just another reason why ‘God’ is an unnecessary hypothesis. And despite all the effort that the religious put into ‘getting up and getting to mass/mosque’ I would maintain that being a theist is the lazier and thus tends to be the more immoral of the two world-views.

There are several reasons for this: the fact that ‘God did it’ reduces science to a hobby one can choose not to pursue. ‘God did it’ also is an easy explanation that requires little effort to be understood. Rational explanation however, requires so many infinitesimally small pieces of the puzzle and a strong maintained effort to be understood and verified.

The atheist worldview is also a lot harder because due to a lack of ‘reason for being here’ there is no ‘right’ or ‘sufficiently good’ state for the world to find itself in. The atheist must admit the world is not as it should be, and continuously try to make it better.

The theist can fall back onto the idea that the world as it is, if he fails to make it better, must eventually be so because God willed it to be so. Far be it from them to try to foil God’s own plan, right?


In the next and final part of this series we will combine the first post of the series with this post. We will consider, in a philosophical way using knowledge and uncertainty, the inevitable future of Artificial Intelligence. We will see if the notion -that history is a chaotic system- can shed new light on this.

Discussing A.I. is relevant both from a humanitarian worldview as an atheistic one since it transects history with an encounter with a non-human consciousness. It is also relevant because despite access to all information several well-known and intelligent people seem to have radically different opinions about what our future with A.I. will look like.

I can only observe for a technological evolution that is arguably more significant than the invention of the atomic bomb, that we seem disturbingly ill-prepared and (on average) revoltingly indifferent as a species. It will be my attempt to reduce both in a modest way.

See you in the next post.



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