By Andrew Hennessey - (1976, 1999, 2013)

The Human Race for the past 12 millennia since the last ice age have been locked into the most basic set of patterns of growth and decay - as the following model will show.
The idea that there are peaks and troughs in civilisation, rises and falls of empires, wars, renaissances, dark ages and space ages we are all familiar with. What might give us a hard time however is that all our intellectual posturing, industrialisation and politicising has only aped in terms of social evolution the most basic tribe of gorillas with their unprotected supply of bananas.
In 1976 just after leaving school I first started exploring the idea of biological cycles and exponential doubling – by devising a simple model of what I called ‘Peaks and Troughs in Civilisation.’
Replete with many hefty assumptions it predicted that civilisation began about 12 or 15,000 BC and then collapses into a stone-age-like trough in the 21st Century just shortly after the first criteria for hi-tek are fulfilled in the various ages on display.
The model assumes that there are – as there are for less sentient life-forms, environmental restrictions to infinite doubling and that civilisation spreads and radiates from a common root in Indo-Asia (V.G Childe, 1936). It also assumes that there is an end-based-telic tendency in social growth that fulfils itself most when enough socially atomic components merge and constantly are acted upon and are doubled without triggering environmental limitations.
All the numbers can be produced on the cheapest 8 digit calculator  The model at its most fruitful and displaying its most advanced technologies shows 99999999 and at its most socially primitive 1.1111111
The doubling effect X2 acting on smaller numbers eventually results in a crash and a halt modelled by the calculator overflow which then results in the numbers being reset and a loss of several powers of 10.
It can be easily said that this primitive reductionist model is merely a toy full of arbitrary associations – yet two things are known: the approximate start date of this model of Civilisations produce – i.e. the end of the last ice age – approximately 12,000 BC and the fact that the first instance of a highly evolved technology is in the 20th century. The last glacial period, popularly known as the Ice Age, was the most recent glacial period within the current ice age occurring during the last years of the Pleistocene, from approximately 110,000 to 12,000 years ago
All the iterations therefore between 12,000 BC and 2000AD, the 20th Century represent or postulate the state of social growth and evolution of mankind in the millennia prior to the 20th century.
Generally speaking the peaks and troughs in the model represent a continuous wave of social growth and changes in social fabric and interaction in space and time from the Indo-Asian hub to its various peripheries e.g. Western Europe.
But what can a few impoverished numbers tell us about the highly complex social fabric of human society over many millennia ?
How can such a simple generalism and reduction provide accurate insight ? Yet the model refers to exponentially growing volumes within finite constraints.
The numbers 0-9 represent a scale of increasing social investment in social fabric subject to natural doubling without constraints and limitations, but these are imposed by an overflow which represents local  energy debt and subsequent disintegration of evolutionary aspects of civilisation with time.
Starting at 1.1111111 in 12000BC the first instance of 99999999 with fabric sustaining a complex investment of natural powers and product is in the 20th Century. If this social model is true, then mankinds social fabric is not governed by beliefs or politics or intelligence or creativity but by the basic constraints on energy and resources externally imposed by the environment.
It is probably true to say that the shape of the cycle of peaks and troughs are the same with every population of any species in the natural world.
It is true to say though that with the wholesale adoption of free energy – this natural model of mankind is superceded – mankind would then break freely from the cycle of depletion.
Thanks to Martin Lowe, 1997, for the Basic Code – for Peaks and Troughs in Society. The model does not address human sophistry but models a general tendency of biological life to exponentially increase and then be constrained by physical factors such as predators or lack of resources in the environment. Its classification within the Philosophy of Science is an Instrumentalist model after Pierre Duhem. Duhem's views on the philosophy of science are explicated in his 1906 work The Aim and Structure of Physical Theory,
For Duhem the highest test of a theory being a natural classiļ¬cation is when it becomes a 'prophet for us', that is, when it predicts novel facts ...
The idea is based on a very simple piece of mathematics which produces peaks and troughs over a period of time.

When analysed - those peaks and troughs seem to correspond in time to the ancient civilisations of the Northern hemisphere starting around 10,000 BC [as predicted by the new datings of the Sphinx etc], through Sumeria, Egypt, Greece, Rome, troughs at the dark Ages and Peaks at a maximum tech for the first time around 2000 AD - then, as predicted by the latest research into Mayan calendars and prophesies - a massive trough after the year 2000 AD !!!!!! ????
It doesn't have to mean the end of civilisation though - [2013AD] for this pocket calculator only represents the resources of our planet - and if other planets and other resources were added to the equation Now - the destiny of the Model will Definitely Change.

It goes on with more peaks and troughs into the future.

It predicts a big dip in Civilisation circa 2000 AD just like the Mayans did and they had access to greater processing power.

1. Intro to the Doomsday calculator
2. The code in BASIC
3. The assumptions
4. The metaphysics of the numbers

The Doomsday Calculator.
It is based on a very simple piece of mathematics which produces peaks and troughs over a period of time.

All the numbers can be produced on the cheapest 8 digit calculator
When analysed - those peaks and troughs seem to correspond in time to the ancient civilisations of the Northern hemisphere starting around 10,000 BC [as predicted by the new datings of the Sphinx etc], through Sumeria, Egypt, Greece, Rome, troughs at the dark Ages and Peaks at a maximum tech for the first time around 2000 AD - then, as predicted by the latest research into Mayan calendars and prophesies - a massive trough after the year 2000 AD !!!!!! ????

It goes on with more peaks and troughs into the future.

The peaks and troughs are numbers on a scale of eg. 1-8 produced by the simple maths - and 1 would be a hunter gatherer and 8 would be a high tech society.

[there is a detailed interpretation of the model which you can see below.]

The mathematics in the model also have mileage because it is based upon a very simple law found operating in all of nature and the cosmos. The Exponential function X2

Examples in the world
  • The number of microorganisms in a culture will increase exponentially until an essential nutrient is exhausted. Typically the first organism splits into two daughter organisms, who then each split to form four, who split to form eight, and so on.
  • A virus (for example SARS, or smallpox) typically will spread exponentially at first, if no artificial immunization is available. Each infected person can infect multiple new people.
  • Human population, if the number of births and deaths per person per year were to remain at current levels (but also see logistic growth). For example, according to the United States Census Bureau, over the last 100 years (1910 to 2010), the population of the United States of America is exponentially increasing at an average rate of one and a half percent a year (1.5%). This means that the doubling time of the American population (depending on the yearly growth in population) is approximately 50 years.[1]
  • Many responses of living beings to stimuli, including human perception, are logarithmic responses, which are the inverse of exponential responses; the loudness and frequency of sound are perceived logarithmically, even with very faint stimulus, within the limits of perception. This is the reason that exponentially increasing the brightness of visual stimuli is perceived by humans as a linear increase, rather than an exponential increase. This has survival value. Generally it is important for the organisms to respond to stimuli in a wide range of levels, from very low levels, to very high levels, while the accuracy of the estimation of differences at high levels of stimulus is much less important for survival.
  • Genetic complexity of life on Earth has doubled every 376 million years. Extrapolating this exponential growth backwards indicates life began 9.7 billion years ago, potentially predating the Earth by 5.2 billion years.[2][3]
  • Avalanche breakdown within a dielectric material. A free electron becomes sufficiently accelerated by an externally applied electrical field that it frees up additional electrons as it collides with atoms or molecules of the dielectric media. These secondary electrons also are accelerated, creating larger numbers of free electrons. The resulting exponential growth of electrons and ions may rapidly lead to complete dielectric breakdown of the material.
  • Nuclear chain reaction (the concept behind nuclear reactors and nuclear weapons). Each uranium nucleus that undergoes fission produces multiple neutrons, each of which can be absorbed by adjacent uranium atoms, causing them to fission in turn. If the probability of neutron absorption exceeds the probability of neutron escape (a function of the shape and mass of the uranium), k > 0 and so the production rate of neutrons and induced uranium fissions increases exponentially, in an uncontrolled reaction. "Due to the exponential rate of increase, at any point in the chain reaction 99% of the energy will have been released in the last 4.6 generations. It is a reasonable approximation to think of the first 53 generations as a latency period leading up to the actual explosion, which only takes 3–4 generations."[4]
  • Positive feedback within the linear range of electrical or electroacoustic amplification can result in the exponential growth of the amplified signal, although resonance effects may favor some component frequencies of the signal over others.
  • Heat transfer experiments yield results whose best fit line are exponential decay curves.
  • Economic growth is expressed in percentage terms, implying exponential growth. For example, U.S. GDP per capita has grown at an exponential rate of approximately two percent since World War 2.

 Computer technology

  • Processing power of computers. See also Moore's law and technological singularity (under exponential growth, there are no singularities. The singularity here is a metaphor.).
  • In computational complexity theory, computer algorithms of exponential complexity require an exponentially increasing amount of resources (e.g. time, computer memory) for only a constant increase in problem size. So for an algorithm of time complexity 2x, if a problem of size x = 10 requires 10 seconds to complete, and a problem of size x = 11 requires 20 seconds, then a problem of size x = 12 will require 40 seconds. This kind of algorithm typically becomes unusable at very small problem sizes, often between 30 and 100 items (most computer algorithms need to be able to solve much larger problems, up to tens of thousands or even millions of items in reasonable times, something that would be physically impossible with an exponential algorithm). Also, the effects of Moore's Law do not help the situation much because doubling processor speed merely allows you to increase the problem size by a constant. E.g. if a slow processor can solve problems of size x in time t, then a processor twice as fast could only solve problems of size x+constant in the same time t. So exponentially complex algorithms are most often impractical, and the search for more efficient algorithms is one of the central goals of computer science today.

In Basic, the code for the Peaks and Troughs model is;

for n=0 to 300
print n,x
if x>99999999 then x=x/10000000
next n

The peaks and troughs are numbers on a scale of eg. 1-8 produced by the simple maths - and 1 would be a hunter gatherer and 8 would be a high tech society. There is a detailed interpretation of the model which you can see below.


Answers to peer reviewed scientific criticism.

1. The model IN NO WAY depends upon the number of digits being fixed -your choice could be arbitrary. e.g. 8, 9 or 10 etc
2. the 'doubling effect' chosen to act upon those digits is to a certain extent also arbitrary - though something akin to 'fibonacci' and the doubling trends seen in nature was preferred.
3. The only fixed requisite was a mathematical 'overflow' to simulate population extinction upon exhaustion of resources.
4. The maximum criteria for this model occurs in an obvious way.
5. I don't make claims for a direct 1 to 1 correlation of data.
6. It predicts according to its own criteria

here's the philosophy of the science


These are the philosophical assumptions upon which the Peaks and Troughs Model is founded. [there are 6]

Lemma 1. Atoms [numbers] when acted upon by a unifying and generating
principle (natural power law) combine to form complexes of varying

Lemma 2. In Analogy, Humanity acts on simple atomic components
to form complexes of great magnitudes - artefacts capable of
eventually evolving advanced technological society.

Lemma 3. The Doubling, exponential power law most seen in nature from plant cells to fibonnacci exponentials, and in demography represents, generally, tendencies in all natural growth and the behaviour of natural systems. e.g. in crystal growth, the doubling effect on surface area enables a doubling of available bonding sites for its ions.

The simple exponential X2 has been chosen to model this doubling effect though it is recognised that some natural functions that are exponential in tendency are attenuated by the intrusion of some other contextual factors. [ie. The pure maths of growth and doubling are interfered with by the chaos of the natural world]

Lemma 4. There are various constraints on exponential growth
ie. When the resources run out chaos follows. [lack of resource, raw material, competition, and exceeding the parameters of the umbrella under which growth occurs, exposes the process of growth ie. growing system to direct competition or entropy/breakdown]

Lemma 5. The fixed limits of the model depict the capacity of different magnitudes of chaos outside of the civil umbrella to degrade growth.

In reality, the 'Fixed Limits' of this simple model would themselves be variable, as each and every system is a context and umbrella of some other, and each is in flux to some extent.
It is the shaping power of restriction which helps to perpetuate the evolution of artefacts with time. [cf. Darwinism].

Lemma 6. An artefact is a tool which enables the energies of the context to be competitively accessed. It is a product of an energy transaction between two systems occurring in such a way as to facilitate easy energy exchange and access. Along the lines of least resistance. It makes it possible to fulfil the most potential with the least energy expenditure. [most benefit for least cost]
Such an artefact can be a tool, lever, a well-travelled goat track, or the route of an electrical discharge.

The idea that end-based evolutionary changes in thought and artefacts take place in human social evolution was researched by V G Childe in the 1930’s.
This idea is substantiated by V G Childe’s famous work ‘the urban revolution’ in 1936.
Childe first discussed the Urban Revolution in his 1936 book, Man Makes Himself, and then his 1950 article in the journal Town Planning Review brought the concept to a much larger audience. In that paper, he presented a 10-point model for the changes that characterized the Urban Revolution:
  1. Large population and large settlements (cities)
  2. Full-time specialization and advanced division of labor
  3. Production of an agricultural surplus to fund government and a differentiated society
  4. Monumental public architecture
  5. A ruling class
  6. Writing
  7. Exact and predictive sciences (arithmetic, geometry, astronomy, calendars)
  8. Sophisticated art styles
  9. Long-distance trade
  10. The state
Although sometimes interpreted as a model of the origins of cities and urbanism, Childe's concept in fact describes the transition from agricultural villages to state-level, urban societies. This change, which occurred independently in several parts of the world, is recognized as one of the most significant changes in human Sociocultural evolution. Although contemporary models for the origins of complex urban societies have progressed beyond Childe's original formulation, there is general agreement that he correctly identified one of the most far-reaching social transformations prior to the Industrial Revolution, as well as the major processes involved in the change.
Thus at a higher level of material organisation/ and civilisation, artefacts appear to be more developed.

The following model is intended to demonstrate the 'Crystallisation of civilised products into more and more sophisticated artefacts'.

It reduces things down to how doubling effects accumulations and growth with time.

It depicts the capacity of the umbrella of resources under which man operates i.e. the minerals and resources, soils and harvest as the capacity of an eight digit calculator to square a row of numbers.

The powers of the numbers most cheap calculators can hold as : 10 to the power of 8.
It depicts the fabric the stuff we then make throughout history - the numbers which represent these resources as being raised to various powers or levels of crystallisation (sophistication of artefacts and their systems).
These powers of numbers represent the structure and mechanics of the evolving civilisation - where the quality of the fabric (high numbers) indicate a significant degree of refinement, crafting and social and evolving principle whilst using the available resource base.

The exponential generative power law that drives the model - which represents the constant application which provides the cohesion necessary for social expansion.
The overall picture is one of structure building up, overstepping its limitations and deteriorating or degrading to more chaotic states, and the complete picture is not unlike the growth format 'real' History was alleged to have taken from the fall of fabled epochs etc

In order to calibrate the results to determine any meaningful correspondence with real archaeological data it is assumed that the 20th

Century was the first period in time to significantly fulfil the maximum criterion for the model.
We invented PC computers, high-technology and jets in the 20th century.

This makes the start date somewhere in the region of 12000BC – just after the last ice age.

The 'Peaks and Troughs' model demonstrates the way in which social fabric is built and invested in by using as its basic bricks - powers of numbers - where 10 to the power 1 is the most basic, and 10 to the power 7 is the most invested.
Let the capacity of the umbrella or environment/resource base under which we grow be represented by the capacity of an eight digit calculator to cope with the exponential function x2 acting upon an eight digit number.

For the purposes of the model, Man will operate upon/start with the most basic and low powered significant number that is representative of an eight digit system ie. 1.1111111 - well we've just been created and just been flooded out.

This represents the primal unit of useful environmental possibilities open to early Man. Eg. Fire, flint and stone and the odd buffalo and cave.

Optimal use of the environment/resource base will be realised in the context of the model when a number less than or equal to but not exceeding the capacity of the eight digit display is attained.
Ie. Double up as much as possible without triggering the overflow
As the numbers build up as we work away - we must make sure that we don't hit the overflow - overstretch our resources or our little society will crash as quickly as a windows 95 operating system.

The number of digits (8), is deemed sufficient  to illustrate the fluctuations of diverse factors, but is up to a point arbitrary ie. the same model could employ 9 or 10 digits but not much fewer than eight in order to retain an aspect of diversity.

Basically a 6-10 or plus any number of digits calculator display can do this - it doesn't have to be an eight digit display  - the number is arbitrary.

As Man's constant growth and drive maximises etc. applies itself to the digits of the resources, a successfully used resource base is represented by a high numerical power. The assumption is that for social, population and technical growth, Man tends to act with or upon smaller units to construct and invest time in larger units, converting resource base into socio-economic fabric and artefacts.

In this respect, Man's use of power law logistics is as mechanistic as any unintelligent system in the Cosmos. ie. Our growth is mathematically similar to any beast or plant.

The eight digit ceiling that the operation of the function takes us to (ie. all the possibilities of growth that can occur under the umbrella of the resources) is the point where the demand for resources to invest in the socio-economic fabric overrides the capacity of the environment to provide, and development is halted by the limitations of the resource base. ie. We use it all up and crash.

The ceiling could be defined as the most socio-economic fabric attained, produced and manufactured as a result of competitive investment - where demand for growth does not outstrip the capacity to supply.

The higher the powers benchmark left at the overflow, the more successful and technological the society as it Fell. - where the most successful result at calculator overflow is 9.9999999

At this stage, the overflow has been reached and the growth of numbers on the display has been systematically deteriorated or knocked-back by a constant in the calculator which is representative of the disintegrative properties of an overloaded system, the entropy of which tends to disintegrate the larger system down to more basic but logistically sound smaller systems and levels of organisation. Demand outstrips supply.

eg. a Rural agronomy can return to Barbarism.
The anarchy that follows overpopulation and collapse of supply in terms of this Mechanistic model, can be defined as 'units of production with no capacity to sustain the evolution of socio-economic fabric'
At this stage, the re-application of Mans' driving power law constant either maintains or betters levels of the past, or the fabric of civilisation deteriorates further, taking the level of numerical growth or 'socio-economic integrity' with it.
The remnants or 'husk' of accrued evolution - the failed society, remains as a number related to that which it once was - and is then redeveloped.
At intervals determined by environment and resource there will be periods of optimal numbers or fabric - these are peaks in Civilisation.
The following narrative is a rough guide to the semantics/reasoning behind the interpretation of the power levels of the numbers -generally speaking, each power level represents an increasing level of sophistication of artefact, information, technology and social fabric.

1.0000000 ... The population groups into a society. eg. Nomadic
10.000000 ... The Society is coherent eg. Barbarism.
100.00000 ... A Coherent society may organise to develop the use of resources eg. Agronomy/trade
1000.0000 ... An efficient use of resource base provides security for the organised society eg. technical specialisation - mining

10000.000 ... A materially secure civilisation attempts to expand by developing its understanding of science and natural resource.
100000.00 ... From a materially secure base, the expanding civilisation with an understanding of some science and technology attempts to negotiate the pitfalls of supply and demand as it attempts to exploit its environment -

1000000.0 ... A civilisation attempts to compensate for economic variation from an unpredictable environment, and will with proper co-ordination of its massive energy demands, develop competitively.

100000000 ... With evolved understanding of economic and natural laws, the civilisation manipulates the capacity of the environment, physics, cosmology ans metaphysics/abstraction to produce secure excesses to fuel huge areas/avenues of expansion (needed to maintain fabric, investment and supply) electricity etc

The latter category - 10 to the power of 7 (10000000) has as its definition 'an evolved civilisation with secure excesses to fuel avenues of expansion'. There are, ten possible values of 10 to the 7 - these are defined below as general tendencies towards prowess of information systems, capital and technical achievement. These are very rough semantic guidelines.

1-30000000 ... Profit tends to be inactive in the exploration of natural laws to any extent.

... The cost and benefit of developing the tools of expansion are considered in civilisations political interest.
... Profit is invested in research and actions which maintain civilisations expansion using natural laws and systems uncovered.
4-60000000 ... The agencies of research are providing insights into improvements in the use of excesses.
... The manipulation of natural laws and efficient information systems which maintain and preserve the excesses of expansion is politically desirable in the interests of civilisation.
... The profitable political and economic use of natural laws and of effective administration is uncovered.
7-99999999... The control of natural laws and information is institutionalised in the interests of expansionist policies.
Profit from excesses is channelled into agencies which are developing control of natural systems which are providing a technological and economic coherence to the evolution and expansion of the civilisation.
.. The laws of nature, science and information are on tap for politically desired directions in civilisations evolution


The results show the peaks and troughs of Egypt, Greece & Rome, the Dark Ages, the climb of the Renaissance and the Hitek of the 20th Century and shortly thereafter a calamitous plunge from the heights of high tek literally back to the stone age.
This 2013AD plunge was predicted by the Mayans.

If, however, resources are introduced from other planets or scientific and technological revolution e.g. Tesla free energy - then the ‘deterministic’ picture can be made to change.


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