# Historical cycles in the last 5000 years

• F

#### faustolevantesi

I am trying to find a mathematical model in order to pattern cycles in human history.
I know, the idea of historical cycles is controversial, but my attempt may not be worthless.

My cycles are made up of two phases, an "UP" phase (curve heading upward) and a "DOWN" phase (curve heading downward).
Here's my current hypothesis:

I am not a historian, but I am seeking someone who could give me an opinion about this hypothesis.
Are these periods somehow meaningful to you?
Do they fit the main trends in the demographic, economic, technological, political, social and cultural history of the last 5000 years?
At least for the Near Eastern, Mediterranean and European areas?

Thanks

• #### Kirialax

Why is 713 such a low point?

• F

#### faustolevantesi

Why is 713 such a low point?
That's exactly what I want to know.
Does 713 CE correspond to the darkest point of the dark ages in Western Europe?
The information I find on the Internet is sometimes quite generic and even contradictory, as far as pre-modern history is concerned.
But any opinion is welcomed.

• #### Kirialax

That's exactly what I want to know.
Does 713 CE correspond to the darkest point of the dark ages in Western Europe?
The information I find on the Internet is sometimes quite generic and even contradictory, as far as pre-modern history is concerned.
I can't speak about western Europe, but the Umayyad caliphate was an economically and intellectually active force in the Mediterranean at that time. You might want to take a look at Garth Fowden's Before and after Muhammad: The First Millennium Refocused (Princeton: Princeton University Press, 2013).

• #### NordicDemosthenes

I am trying to find a mathematical model in order to pattern cycles in human history.
I know, the idea of historical cycles is controversial, but my attempt may not be worthless.

My cycles are made up of two phases, an "UP" phase (curve heading upward) and a "DOWN" phase (curve heading downward).
Here's my current hypothesis:

View attachment 20999

I am not a historian, but I am seeking someone who could give me an opinion about this hypothesis.
Are these periods somehow meaningful to you?
Do they fit the main trends in the demographic, economic, technological, political, social and cultural history of the last 5000 years?
At least for the Near Eastern, Mediterranean and European areas?

Thanks
Interesting. I will admit to a certain a priori skepticism, but it's brave of you to try!

Which kind of input data have you put into the model, and how does your model look? What is the function, mathematically speaking? How do you measure cultural/political/social progress?

Demography and economy are, while difficult, at least technically straight forward. I'm curious how you're doing it.

As for how the model looks right now... it's not completely nonsense, if you accept certain "miscalculations" by 100 years or so as well as various somewhat strange interpretations.

1920 B.C. as a specific date means nothing, but the first minoan palaces date somewhere to

I'd also date the Bronze age collapse (1262 B.C.) a century later, but it's debatable. I have a problem with the slope of the curve though (more on that later).

As for 769 B.C. being a new low-point (and therefore the start of an "upside") this time seems to coincide extremely well with the first recorded Olympiad (so well done on that - my congratulations). There might be something to it, although it feels weird to say that there was continuous decline up until that point. Same thing with the downward trend from 563 to 522. Why? Because of the Persian conquests? Or because of tyrannies in Athens? I'm not sure I see it.

I think 713 as a date is rubbish, but somewhere between the 7th and 8th centuries as an end to the worst of the European dark ages seems about right to me. As @Kirialax pointed out though, other parts of the Mediterranean world looked quite different.

So my overall judgement is 3,16 at this point. Not great, not terrible.

My biggest problem with your model is how you slope some of the curves. Looking at this from a more humanistic, historical and non-quantitative perspective (although I'm training to be an economist so I'm not total **** at counting) I find it hard to quantify an absolute extreme point at the convex side of the curve (i.e. the low points). Let's take 1262 B.C., the Bronze Age collapse. In your model this is a low point. Well... why? Surely it should be a high point instead. From where I'm sitting things should get worse rather than better after a collapse, and so the curve should slope downward. That is at least how I see things. (Of course, you could see 933 as the start of the collapse instead, but then you really shouldn't have both cycles in your model, as the magnitude for the Bronze Age collapse is much greater).

Anyway, as I wrote - I'd be curious to know how you compute these things...

Last edited:

• F

#### faustolevantesi

Interesting. I will admit to a certain a priori skepticism, but it's brave of you to try!

Which kind of input data have you put into the model, and how does your model look? What is the function, mathematically speaking? How do you measure cultural/political/social progress?

Demography and economy are, while difficult, at least technically straight forward. I'm curious how you're doing it.

As for how the model looks right now... it's not completely nonsense, if you accept certain "miscalculations" by 100 years or so as well as various somewhat strange interpretations.

1920 B.C. as a specific date means nothing, but the first minoan palaces date somewhere to

I'd also date the Bronze age collapse (1262 B.C.) a century later, but it's debatable. I have a problem with the slope of the curve though (more on that later).

As for 769 B.C. being a new low-point (and therefore the start of an "upside") this time seems to coincide extremely well with the first recorded Olympiad (so well done on that - my congratulations). There might be something to it, although it feels weird to say that there was continuous decline up until that point. Same thing with the downward trend from 563 to 522. Why? Because of the Persian conquests? Or because of tyrannies in Athens? I'm not sure I see it.

I think 713 as a date is rubbish, but somewhere between the 7th and 8th centuries as an end to the worst of the European dark ages seems about right to me. As @Kirialax pointed out though, other parts of the Mediterranean world looked quite different.

So my overall judgement is 3,16 at this point. Not great, not terrible.

My biggest problem with your model is how you slope some of the curves. Looking at this from a more humanistic, historical and non-quantitative perspective (although I'm training to be an economist so I'm not total **** at counting) I find it hard to quantify an absolute extreme point at the convex side of the curve (i.e. the low points). Let's take 1262 B.C., the Bronze Age collapse. In your model this is a low point. Well... why? Surely it should be a high point instead. From where I'm sitting things should get worse rather than better after a collapse, and so the curve should slope downward. That is at least how I see things. (Of course, you could see 933 as the start of the collapse instead, but then you really shouldn't have both cycles in your model, as the magnitude for the Bronze Age collapse is much greater).

Anyway, as I wrote - I'd be curious to know how you compute these things...
No, my model is not the result of a calculation (or regression analysis) based on actual data. As you said, it's pretty impossible to have precise data about socio-cultural events.
Instead, my method was trial and error, I made many hypotheses about possible mathematical patterns and then verified how well (or how badly) each of these patterns fitted my own knowledge of historical facts.
My present model has three main characteristics:
• it is cyclic, because it is made up by a succession of phases of two opposite kinds; the dualistic nature of these two phases, these two “zeitgeists”, has not been totally defined yet. The expanding phase (UP phase) is associated with an increase in population, material production, technical inventions, literacy and individualism. The contracting phase (DOWN phase) is associated with a decrease of the above through wars, famines, pandemics and catastrophes, which incidentally leads to an increase in scientific discoveries and intellectual feats that will be applied in the following expanding phase.​
• it is evolutive, because each phase has not the same duration of the previous one, but half (or double) the duration of the previous one. The fact that the duration of successive phases tends toward zero adds a further dimension to the repetitiveness of a simple biphasic cyclic model, insofar as it provides an element of progress (or regress) toward the future (or the past).​
• it is fractal, because each phase can be subdivided in further subcycles according to the same mathematical law. This entails that the interpretation of any moment in time must take into consideration the trend of the curves in many levels of the fractal.​
I have not yet found the exact mathematical function that best describes the expanding (or contracting) phase, but the curve may be similar to a tangent function or a logit function. It is constrained between two vertical asymptotes and has an inflection point at half its duration. This means that the trend of a phase varies widely with time.

The expanding phase starts in an “explosive” way, then it slows down gradually until it almost stops expanding at all, but it immediately resumes expanding gradually and ends up in a hyperbolic expansion.

The contracting phase starts in an “implosive” way, then it slows down gradually until it stops contracting at all, but immediately resumes contracting gradually and ends up in a hyperbolic contraction.

Mathematically, each vertical asymptote corresponds to a singularity. Of course, singularities seem to be absurd in a sociological or historical context because no human event can be "infinite"... Therefore, I propose that its meaning must be understood considering the fractal nature of the function, these singularities are not absolute, but relative, somewhat “smoothed” by the superior level of the fractal.
For example, the trough point at 1262 bce. According to my hypothesis, at this point the Bronze Age Collapse was planted with the first seeds of the following Iron Age. Maybe just when the destruction of Bronze Age cities was at its peak, somewhere in the Syro-Hittite states a smith started producing iron with the new methods, and maybe some phoenician merchant started using the proto-canaanite abjad to facilitate his trade. Of course it took a couple more centuries before ferrous metallurgy and alphabets were noticeable to archeologists and historians, but it all may have started at that precise moment.

• #### deaf tuner

Question : what is the finality of Your model?

• F

#### faustolevantesi

Question : what is the finality of Your model?
Finding a mathematical relation between historical events will prove that causal determinism governs the world.
Or to which extent it governs the world.
Or course, any such model wouldn't be only descriptive, but also predictive...
And this will raise all sorts of speculations about the relationships between determinism and free will.

• #### deaf tuner

Finding a mathematical relation between historical events will prove that causal determinism governs the world.
Or to which extent it governs the world.
Or course, any such model wouldn't be only descriptive, but also predictive...
And this will raise all sorts of speculations about the relationships between determinism and free will.
Thank You.

1. Isn't "governing" a bit axiomatic?
2. Shouldn't be "determinism and randomness" before bringing free will in equation, or maybe "determinism, randomness and free will"?

Rodger

• F

#### faustolevantesi

Thank You.

1. Isn't "governing" a bit axiomatic?
2. Shouldn't be "determinism and randomness" before bringing free will in equation, or maybe "determinism, randomness and free will"?
1. Quantum mechanics and general relativity govern the physical world: are they axiomatic?
2. Sure, but I always thought of randomness as a special kind of determinism...