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THE COMING DARK AGE
Newsletter
December, 2003
1. INTRODUCTION
Happy new year to all readers. This month's edition describes a problem
in dark age theory, which is intended as a challenge for readers with
mathematical skills.
Past editions of the newsletter are at the following address:
http://www.darkage.fsnet.co.uk/Newsletter.htm
I welcome all comments, suggestions and contributions, especially the
latter. Please forward this newsletter to anyone you think might be
interested.
Marc Widdowson
2. PROBLEMS IN DARK AGE THEORY #1 - SELF-COUNTERVAILING FUNCTIONS
Dark age theory recognises three key variables, corresponding to the
political, economic and social sides of life. These are referred to as
(political) integration, (economic) organisation and (social) cohesion.
For example, historians writing about past civilisations frequently
note that, when the given civilisation is in decline, it DISINTEGRATES
into multiple independent regions. We can therefore say that a
civilisation which is on the way up experiences integration (bringing
previously separate regions into one large political entity, such as
the Roman empire), while a civilisation which is on the way down
experiences disintegration (splitting up again into many smaller
political entities). So we may recognise a great civilisation by its
high level of integration, and we may recognise dark ages by their
almost total disintegration. It follows that we can tell whether our
own civilisation is moving towards or away from a dark age simply by
asking whether it is tending to become more or less integrated. Similar
comments apply for the concepts of organisation and cohesion.
Dark age theory suggests that integration, organisation and cohesion
affect each other. However, this occurs in a complex way, so that the
three variables never settle down but are continually fluctuating up
and down. It is this continual fluctuation that we recognise as the ups
and downs of history.
E Lorenz analysed a similar situation when he was studying models of
the earth's weather systems in the 1960s. He modelled the atmosphere in
terms of three variables (representing things like pressure,
temperature and density) and he produced a set of equations describing
how the rate of change of each variable depended on the current values
of the three variables. He found that these equations generated the
kind of fluctuation now referred to as 'chaos', where the three
variables neither reached equilibrium nor oscillated smoothly but moved
up and down in a very irregular manner. Of course, this is very much
what the weather actually does and that is why it is so unpredictable.
Returning to history, we should have a similar chaotic dynamic among
the three variables that characterise societies. The question is, what
form should we give the equations that connect the rates of change of
these variables to their instantaneous values. In terms of symbols, if
we use x, y and z to stand for integration, organisation and cohesion,
we should have equations of the following form:
dx/dt = f(x,y,z)
dy/dt= g(x,y,z)
dz/dt = h(x,y,z)
The question is then, what should the functions f(x,y,z), g(x,y,z) and
h(x,y,z) look like?
Consider the way that organisation depends on integration. A more
intuitive way of describing integration is as 'governmental power' and
a more intuitive way of describing organisation is as 'wealth and
commerce'. What history shows us is that a strong government helps to
promote wealth and commerce - for example, the law and order created by
the Roman empire, not to mention the Roman roads, made it much easier
to conduct trade throughout the Mediterranean and led to a commercial
boom. In other words, 'governmental power' reinforces 'wealth and
commerce', which is to say that integration reinforces organisation.
On the other hand, a strong government can also be bad for wealth and
commerce. This is because strong governments may take too much out of
the economy in terms of tax and they may also inhibit the technological
innovation that promotes economic growth. For example, the printing
press was seen as a potentially subversive invention by governments in
Europe and by the Ottoman empire, and these regimes were all keen to
ban it. However, the relatively weak European rulers failed to enforce
the ban, whereas the more powerful Ottoman emperors succeeded. The
result was that, while Europe came on in leaps and bounds, the Ottoman
empire remained economically backward. Thus, 'governmental power' can
undermine 'wealth and commerce', which is to say that integration can
undermine organisation.
Now consider the way that integration depends on organisation. A
wealthy society tends to produce a strong government (while a poor
society produces a weak government) - consider, for example, how the
power of the US government results from the enormous wealth it has at
its disposal. In other words, organisation reinforces integration.
Yet a rich populace is also harder to control because it has the
resources to resist domination. Similarly, the European governments who
saw the printing press as subversive were actually right. The
dissemination of knowledge that printing made possible led to demands
for democratisation, and eventually to things like the French
revolution. In other words, 'wealth and commerce' can undermine
'governmental power', which is to say that organisation can undermine
integration.
Putting all this together, if we want to model how integration depends
on organisation, say, we have a contradictory situation. One set of
considerations tells us that organisation tends to increase
integration, but another set of considerations tells us that
organisation tends to decrease integration. Therefore, the function
that relates the change of integration to the level of organisation
should sometimes give a positive value and sometimes give a negative
value, presumably depending on other factors. As we have seen, the same
applies for the effect of integration on organisation.
I won't argue it here in detail, but it can be shown that similar
findings apply to the other combinations of variables. That is,
integration and cohesion both increase each other and decrease each
other, and organisation and cohesion both increase each other and
decrease each other.
I said that whether, say, organisation increases or decreases
integration depends on 'other factors'. What could these other factors
be? In the equations indicated above, we only have the three variables
x, y, z (integration, organisation, cohesion) and the additional
variable of t (time). It would be desirable to keep our model simple,
not introducing any more variables, so the way that dx/dt (the change
of integration) depends on y (the level of organisation) should be
influenced solely by x, y, z and t or a subset of these. The same
applies for all the other combinations, i.e. how dx/dt depends on z,
how dy/dt depends on x etc.
The problem for dark age theory is to find a set of equations that can
satisfy these requirements. That is to say, if dx/dt = f(x,y,z) then
this should indicate that the contribution of y can sometimes be
negative and sometimes positive, depending on the values of the other
variables, and so on and so forth (for the contribution of z to dx/dt,
the contribution of x to dy/dt etc.). [To be strictly correct, if t can
influence whether y has a positive or negative effect, I should write,
dx/dt = f(x,y,z,t).]
To add to this broad requirement, there is another fundamental
requirement, which is that the way that dx/dt depends on x, y, z and
possibly t should be historically plausible. In other words, and this
is obvious really, we ought to have a good reason for writing the
equations in a particular way, which is to say it should be based on
our understanding of how history actually works.
I like to add three other requirements. These are simply based on my
aesthetic prejudices, and it may be found that they are inconsistent
with the requirement for historical plausibility, in which case they
will need to be jettisoned. Firstly, I would like the way that dx/dt
depends on y to be independent of t, and preferably dependent solely on
z. (Similarly for the other combinations, e.g. dx/dt should depend on z
in a way that depends solely on y, and dy/dt should depend on x in a
way that depends solely on z etc.) Secondly, I would like the three
equations (for dx/dt, dy/dt and dz/dt) to be of identical form, with
only the roles of the variables changing. This implies that g(x,y,z) =
f(y,z,x) and h(x,y,z) = f(z,x,y). Thirdly, I would like x, y and z to
be limited to the range 0 to 1 (this is perhaps not just prejudice -
there is some reason for thinking that a society cannot be more than
100% integrated, i.e. integration = 1, or less than 0% integrated, i.e.
integration = 0).
One final requirement is that when we solve the equations, whatever
they might be, we should find that they result in chaotic behaviour,
just like Lorenz's model of the atmosphere. This is on the basis that
history is actually seen to be a chaotic process, like the weather,
with no regular cycles but with continuous fluctuations of differing
amplitude. If we can do this, we will have produced a simple
mathematical model of historical change, and it will exceed Blaha's
model in richness because it incorporates political, economic and
social variables.
To give the idea, a possible form for the equations might be
dx/dt = y (0.5 - z) + z (0.5 - y)
dy/dt = z (0.5 - x) + x (0.5 - z)
dz/dt = x (0.5 - y) + y (0.5 - x)
For example, the first part of the first equation above says that
organisation has a positive effect on integration when the cohesion is
below 50% and a negative effect on integration when the cohesion is
above 50%.
However, experimentation with this particular model does not yield
convincing results and the equations are also dubious on theoretical
grounds.
This then is the problem I would like to set readers of this
newsletter: develop a set of equations that fulfil the above
considerations and produce history-like fluctuations.