Technological evolution

We need a measure of technological sophistication.

Technology changes through history, and technological sophistication is closely related to scale and societal eigenmode.

The internet, for example, makes possible and is made possible by the high scale of the modern world.

• It should be obvious that the internet makes the modern world possible. Consider the direct impact on many businesses if their web and email facilities were suddenly shut off, and consider the indirect impact on many others.
• As for the modern world making the internet possible, imagine a group of, say, a hundred idealists who decide to cut themselves off on a desert island. Could they produce or maintain all the familiar internet facilities like Google, Amazon and Wikipedia? Obviously not. Even if they took this technology with them, they would soon fall behind what was happening in the outside world, where thousands, even millions, of people are continually advancing the relevant services and underlying software.

In order to talk comparatively about technological change, we need a uniform way of describing the degree of sophistication of any given technology. This has to be applicable to everything from a stone axe to a Saturn V rocket and beyond.

Technological sophistication reflects four factors relating to the creation of an artefact instantiating that technology:

1. The sophistication of the inputs or precursor processes and materials.
2. The amount of effort needed for preparation (e.g. assembling the materials in one place).
3. The amount of effort needed for actually producing the artefact.
4. The amount of skill required.

The higher the skill, the higher the effort of preparation and production, and the higher the sophistication of precursors or inputs, the greater the sophistication of the technology.

• A crude stone axe requires no input except a stone, which is about as unsophisticated as one can get, and minimal preparation. It may take some skill but this is relatively easily acquired, and the process of production may involve only a few minutes of effort.
• A space rocket has very sophisticated inputs, including specialist plastics and alloys, complex microelectronics, and a large ground-based infrastructure for mission control. Preparation and production may take many years of effort by many people, and they will be drawing on an extensive education, from kindergarten through university to specific on-the-job training.

We can reduce the four factors to a common form by considering them in terms of time resources (also known as effort), i.e. the number of people involved in each activity multiplied by the amount of time each person contributes. Specifically, we define technological sophistication as equivalent to total time resources to produce the artefact:

t = tm + tp + ts +

∑ i

ti

where

t	= total time resource to produce artefact ( ≡ technological sophistication)
tm	= time resource for actually making the artefact
tp	= time resource for preparation
ts	= time resource for skill acquisition
ti	= total time resource to produce input i ( ≡ technological sophistication of input i)

Technological sophistication therefore has units of person-seconds (or equivalently person-hours, person-days, person-years, whichever is most suitable). Note that technological sophistication is a characteristic of an artefact, not of a society or of a period in history.

Technological sophistication can be thought of as the amount of time it would take one person, starting from scratch, to manufacture the artefact in question, including all its precursors and materials. If the artefact were, for example, a Saturn V, the person would have to begin by learning basic geology and making a spade or pick in preparation for mining the ore to produce the metal from which the rocket's parts would eventually be constructed. The technological sophistication of the rocket could amount to many human lifetimes.

The actual time resources going into the creation of an artefact are not, in general, equal to the theoretical time resources used in the above definition of technological sophistication. This is because few artefacts are made starting from scratch. Instead, effort is amortised over many artefacts.

• For instance, once a digger is available for mining ore, it can be used on many projects, not just to produce the one Saturn V. The time resources absorbed by producing the digger are in reality shared across many projects, and the Saturn V is responsible only for a small fraction of that effort.
• Similarly, if multiple copies of an artefact are produced, the effort for skill acquisition, and possibly some of the preparation, does not need to be repeated. The skill acquisition and preparation time resources per artefact are therefore a fraction of what they would be for just one artefact.

Nevertheless, it makes sense to define technological sophistication as if one were starting from scratch while producing only enough of everything to manufacture one final artefact, even though that does not happen in practice. It is this definition that gives the truest account of what goes into making an artefact.

• Consider writing a letter on a computer versus writing it with quill pen and parchment. The effort involved in each case may be about the same (e.g. it could take an hour to produce the letter either way). This is also true of preparation (switching on the computer, trimming the quill pen) and skill acquisition (learning to type, learning proper calligraphy)--the effort may be about the same in each case. Even the time resources devoted to the inputs might be similar if the time to build a computer is about the same as the time to prepare a piece of parchment from animal skin. Therefore, if we considered only the actual time resources going into the modern and medieval letters, there would seem to be no difference in technological sophistication. However, there obviously is a big difference in technological sophistication, which is reflected in the fact that a lot more effort and knowhow went into the development of the modern computer than ever went into the development of parchment and quill pens. This is what our definition of technological sophistication captures by assuming one starts absolutely from scratch.


• Consider also that one person probably could produce a parchment letter from scratch (e.g. starting by tanning the goatskin and mixing soot and egg white to make the ink* etc.). However, to make a computer starting from scratch (i.e. beginning at the level of mining the ore) would take a lifetime, or probably several lifetimes. The time resources going into a computer are so high that, to make computers feasible/affordable, the time resources have to be amortised over many units, both for the final artefact and for the components from which it is built. This industry can only survive if it is done on a large scale, serving a large customer base. In this respect, medieval society was neither populous nor connected enough to support computing, and parchment-based letter writing technology was all that was feasible.

*This is merely illustration, not an accurate description of how to make medieval ink.

To demonstrate this definition of technological sophistication, I will calculate the changing sophistication of cutting tools, from the stone age onwards.

I cannot provide absolutely accurate values of technological sophistication, especially for the more complex technologies. This would require a vast amount of research. The figures given below are only estimates. My main purpose is to show the definition of technological sophistication in practice.

The first cutting tools used by humans were made of stone (=lithics). The tools of the palaeolithic and mesolithic (old and middle stone ages) can be classified into five lithic modes, reflecting increasing levels of sophistication (see Grahame Clark, World prehistory: a new outline, 2nd edn [1969]). The cutting tools of the neolithic (new stone age) were of higher sophistication again. After this came the successive increases in sophistication of copper, bronze and finally iron or steel tools.

---

Mode 1 stone tools involve the creation of a cutting edge by the application of a few sharp blows from another stone. This requires skill, but not much effort, and little attention is paid to the final form, which is rough and ready. The tool may either be the stone or one of the flakes chipped from it. Sometimes the tool is 'retouched' by chipping off a few small flakes to restore a cutting edge after it has been blunted or broken in use.
Mode 1 stone tools: typically prepared with just a few blows, ad hoc in size and shape

Mode 1 tools were already in use with early hominids in Africa, 2.5 million years before the appearance of modern humans. Some of the tools used by Australian aborigines, who are fully modern humans, continue to belong to this most basic category.

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	None	0
Skill acquisition	Ten minutes to pick up the basic technique, though performance would improve with practice	600
Preparation	5 minutes to select a suitable stone and hammer stone. Any kinds of stone lying around would be suitable, provided they were of reasonable size and shape.	300
Manufacture	1 minute to knock off a few chips	60
TOTAL		≈ 1000

---

Mode 2 stone tools require at least twice as many blows as a Mode 1 tool, and they are made to take a definite, standardised, symmetrical form, that of the classic hand axe. Instead of chipping with another stone, a soft implement of wood, antler or bone is typically used, often with pressure flaking, to provide fine control over the shape. The removed flakes are not used.


Mode 2 stone tools: chipped all the way round with a soft hammer (wood, bone) to achieve a definite symmetrical form, requiring at least a dozen blows

Mode 2 tools were in use with pre-human hominids from about 1.5 million years before the emergence of humans. The technology developed in Africa and was carried into Europe and Asia by the pre-human hominids that colonised these regions from around 1 million years ago. Again, Mode 2 tools have continued in use with the Australian aborigines.

-- Key innovation --

Specialised ancillary tool (wood etc. hammer); aim of producing a repeatable, pre-conceived form.

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	The bone/wood/antler flaking tool needs to be sourced and prepared, cutting it to the right length and maybe shaping it a bit. Perhaps twenty minutes.	1200
Skill acquisition	It should be possible to get the technique (from sourcing the stone and flaking tool to the design of the axe) in an hour.	3600
Preparation	A more specific size, shape and type of stone is required. Going to a likely site and selecting a suitable stone might take about half an hour.	1800
Manufacture	More blows are required and more careful attention, in order to get the symmetrical shape. Perhaps 5 minutes.	300
TOTAL		≈ 7000

---

Mode 3 stone tools involve the Levallois technique, in which a stone core is first carefully prepared and then a single large flake is struck off from it with a sharp blow. In contrast to Mode 2, where the shape emerges gradually, allowing some trial and error, this technique requires a thorough understanding of how flint fractures and an ability to picture in advance the flake that will be produced. Preparation of the core requires a hundred or more shaping blows before the final blow that removes the flake. However, the precise shape of the flake is not particularly standardised.


Mode 3 stone tools: struck with one movement from a carefully prepared core, requiring around a hundred preliminary blows along with the expertise and imagination necessary to envisage how the stone will fracture at the last critical blow

Mode 3 tools are associated with the near-human Neanderthals and were in use from about 200,000 years ago. The first modern humans also sometimes used Mode 3 tools, and indeed the Australian aborigines have never used anything more than Mode 3.

-- Key innovation --

Extensive preparatory work during which finished item is not apparent.

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	Again a special tool is used for flaking. To prepare it: twenty minutes.	1200
Skill acquisition	A period of practising more basic techniques would be needed to develop the necessary understanding of stone's characteristics. One 8-hour day.	28,800
Preparation	Special types of stone, similar to Mode 2, would be required. Fetching time: 1 hour	3600
Manufacture	A long period of shaping the stone is required before striking off the final product: 10 minutes	600
TOTAL		≈ 35,000

---

Mode 4 stone tools are based on long, narrow blades with two sharp edges. These are struck from a core whose preparation is more complicated than for Mode 3, requiring some 250 blows with a bone rather than stone hammer, but then yielding five times as many tools from one block of stone. Blades are also versatile. For example, one edge may be blunted, to create a scraper, or the blade may be shaped into a burin, which has a sharp point and can be used to gouge holes in other materials.

Mode 4 stone tools: struck successively from a prepared core, having long sharp edges and possibly further shaped into specialised tools such as the burin (right), used for drilling holes

Mode 4 tools came into use among fully modern humans at the beginning of the Upper Palaeolithic, i.e. G 1 (c. 50,000 years ago). Whereas Mode 3 tool users stuck to stone almost exclusively, blade tools are associated with equal numbers of tools made from bone and antler. Only modern humans used Mode 4 tools, but not all modern humans used them, since the Australian aborigines and some extinct cultures of Southeast Asia never did.

-- Key innovation --

Preparatory work to produce savings downstream as many blades can be mass-produced from one core; creation of tools to make tools (e.g. burin is used for making holes in bone/ivory to produce needles).

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	Again a specialist hammer: twenty minutes	1200
Skill acquisition	Much practice is needed for genuine competence: two 8-hour days	57,600
Preparation	Greater care is needed in selecting the best stone (flint or similar). This might take a day (8 hours) to fetch. In reality, stone might be traded so that people would not have to find it themselves, but this is the sort of efficiency saving we ignore in the calculation of technological sophistication	28,800
Manufacture	The preparation of the core requires 250 blows and the blade is further refined after being struck: 25 minutes	1500
TOTAL		≈ 90,000

---

Mode 5 stone tools consist of microliths, i.e. small flakes of around an inch long, or less. They come in many precise forms, including triangle, rectangle, rhombus, trapezium, crescent and leaf-shape. They are not complete in themselves but belong to composite tools, such as knives, sickles, spears, harpoons and arrows, with several microliths being fixed into a bone or wooden handle or shaft using resin and possibly some kind of fibre.


Mode 5 stone tools: tiny microliths, chipped into precise shapes and stuck into wooden or bone handles/shafts, using resin and fibre, to produce composite tools such as an arrow (left, with trapezoid head) or harpoon (right)

Mode 5 tools appeared in Africa and India around G 475-875 (40,000-30,000 years ago). By G 1275-1675 (20,000-10,000 years ago) they were in use almost everywhere. There was, however, much more variation than for Modes 4 and below, with groups only a hundred miles apart favouring different shapes and styles of microlith. The greater sophistication of Mode 5 technology is also apparent from the way they were associated with simple 'machines' multiplying human muscle power, namely the bow and the spear thrower, both of which were in use by G 1475 (15,000 years ago, the bow may have been in use much earlier).

-- Key innovation --

Complex composite tools, themselves part of compound systems (e.g. bow and arrow).

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	The inputs are finished stone blades (the microliths). I will assume these have the technological sophistication calculated above for Mode 4 (90,000). Another input is string, for which I will conservatively assume a technological sophistication of 8 hours	118,800
Skill acquisition	Training is needed in sourcing resin, carving a stick to the right size and shape, and hafting the microliths to it. 8 hours	28,800
Preparation	Obtaining the resin and a suitable stick (the string and microliths are already available, having just been made). Half an hour.	1800
Manufacture	Carving the stick and attaching the microliths. Half an hour.	1800
TOTAL		≈ 150,000

---

Neolithic stone tools involve the imposition of a preconceived shape on a piece of stone. This is either by minutely detailed chipping, to create arrowheads and daggers, or by polishing, to create axes and hammers. In both cases, the form transcends the material of which it is made, in the sense that the object's function, rather than the behaviour of stone, is the primary driver. One is looking at an object that happens to be made of stone, rather than at a stone that has been hacked into a useful shape.


Neolithic stone tools: (not to scale) standardised forms determined by the intended function rather than by the properties of the stone, and involving either minutely detailed chipping to create arrowheads (left) and daggers (centre left), or polishing to create axeheads (centre right) and socketed axe-hammers (right)

Neolithic stone tools: (continued) a neolithic polished axehead, and the tool as it would have been used

The beginning of the Neolithic, and hence of tools like this, is synonymous with the beginning of farming around G 1600 (10,000 BC). The technique of polishing axeheads was perhaps suggested by the technique of grinding corn between two stones, where the stones became smooth as they rubbed against each other.

This technology emerged first in North Africa and the Middle East, and later in Europe, Asia and the Americas. It continued after the invention of metalworking, among people who could not afford or obtain metal tools. The above dagger dates from around G 1940 (1500 BC) and seems to have been inspired by bronze weapons.

Besides their practical purpose, polished axeheads had value as a medium of exchange and store of wealth. The clip below is of a hoard of axeheads found in a burial mound in Brittany, France, and shows they must have been produced in huge quantities.

-- Key innovation --

Form determined by function rather than by properties of underlying material.

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	A suitable block of stone would need to be prepared as a grinding platform (8 hours). Animal hide would need to be obtained (by hunting) and prepared for binding the axe in a tool (4 hours). An initial set of stone tools would be needed for the carving and cutting tasks associated with these and subsequent activities (assume sophistication of Mode 4 tools: 90,000 person-secs).	133,200
Skill acquisition	The basic grinding/polishing technique could be picked up quite easily, although to create sharp, smooth and symmetrical axes would require longer practice. 2 hours	7200
Preparation	The hide is assumed available. Other parts to be sourced and fetched are: the stone to be polished, resin for gluing it in the handle, the handle itself, and one or more abrasives (sand) to be used in polishing. Total: 1.5 hours	5400
Manufacture	The stone would be roughed out by chipping then polished by rubbing against the platform, using successively finer abrasives to get the final smooth surface (1 day). It would then be mounted in the handle (1 hour).	32,400
TOTAL		≈ 180,000

---

Copper tools are made either by beating the solid metal into shape or by melting it and casting it in moulds. In a very few places, such as parts of the North American Great Lakes, copper can be taken from the ground in virtually pure form. However, most of the time it has to be extracted from an ore by heating. It thus requires an extra stage of transformation compared to the shaping of a stone. Yet unlike a stone, the molten metal can be cast into arbitrary forms, and once a mould has been produced, identical copies can be turned out one after the other. Copper is also less brittle than stone and, if broken, can be melted down and recast. Since copper is not nearly as common as stone, the widespread use of copper requires long-distance exchange between producers and consumers. Typically, the ore is refined close to the mine location then transported in the form of standardised ingots.

Copper tools: the metal is either beaten into shape with a hammer (e.g. spearhead, left; note the groove round the hammer stone for attachment of a handle), or molten and cast in a mould (e.g. axehead, right); the resulting copper tool (centre, reconstruction) can be neater and more compact than its stone equivalent

Copper tools: (continued) this is a classic oxhide ingot of the ancient copper trade; the ingot is 27 inches by 16 inches (70 cm by 40 cm) and weighs around 82 lb (37 kg); it is a convenient shape for carrying by two people
Copper and gold were the first metals to be worked by humans, beginning in ancient Iraq around G 1760 (6000 BC). Copper was in common use in Europe and Egypt by G 1860 (3500 BC). The reconstructed copper axe above belonged to Ötzi, the man from G 1870 (3300 BC) whose body was found in an Alpine glacier in G 2080:16 (AD 1991). Copper chisels were used in the building of the Giza pyramids around G 1900 (2500 BC). This 'copper age', also known as the chalcolithic (chalcolithic = 'copper-stone'), technology does not seem to have reached sub-Saharan Africa until G 1960-1980 (1000 - 500 BC).

The discovery of copper metallurgy is related to the invention of pottery, which meant that people were already experimenting with heating earthy materials in a fire. Pottery, in turn, could have been suggested by the practice of heating stone tools to give them strength; this may have led people to experiment with the effects of heat on other materials.

-- Key innovation --

Transformation of raw material (ore) whose properties are not those of the finished product.

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	One input is the copper ore. This requires developing some knowledge of geology (4 hours), and then the actual location and extraction of the ore (8 hours). A set of stone tools would be needed for this (assume Mode 4: 90,000 person-secs). There is also a need for a pottery crucible and charcoal for the fire: assume 8 hours to make these.	162,000
Skill acquisition	It is necessary to understand the construction of a cast and the melting and pouring of the copper. 12 hours.	43,200
Preparation	The copper must first be produced from the copper ore. 8 hours.	28,800
Manufacture	A mould has to be made, then the copper poured. After the copper is removed from the mould, it requires tidying up and polishing. For this: 12 hours. Finally, the object needs to be mounted in a suitable manner: 4 hours.	57,600
TOTAL		≈ 290,000

---

Bronze tools are made from a mixture of typically 90 percent copper and 10 percent tin or arsenic. The metals are molten together and cast in a mould. Bronze is much harder than pure copper, and can hold a sharp edge. Tin-bronze is superior to arsenic-bronze, which therefore tends to be found only in early or less developed bronze industries. However, tin is even rarer than copper, so a tin-bronze industry presumes a well-developed trade network connecting the point where the ore is mined and refined with the regions where the bronze artefacts are to be produced.


Bronze tools: an alloy of copper and tin, bronze is strong than either and capable of carrying a sharp edge; varying sophistication is evident in both the amount of metal used and the complexity of the shape to achieve a given effect, here ranging from the flat axe (far left) to the same with small flanges that hold it more firmly in the handle (centre left), to the palstave axe with an attachment loop and shaped mounting area separate from the blade (centre right), and finally to the fully socketed axe (right)

The earliest bronze-working societies were in the areas of modern Turkey, Syria and Iraq, beginning around G 1860 (3500 BC). Bronze was in use in China by G 1912 (2200 BC), in north-western Europe by G 1930 (1800 BC), and in India and Egypt by G 1940 (1500 BC). In the Americas, metalworking, with gold, silver and copper, began around G 1980 (500 BC), and copper-silver and copper-gold alloys appeared around G 1993 (200 BC). Arsenical bronze did not appear until around G 2040 (AD 1000), and classic tin-bronze was only introduced by the Incas around G 2060 (AD 1475), shortly before the Spanish conquest. American pre-Columbian metalwork tended to consist of decorative and prestige objects, rather than tools or weapons.

Arsenic often occurs naturally in conjunction with copper, which would have facilitated the discovery of arsenical bronze and perhaps suggested the possibility of experimenting with other adulterating metals.

Styles of bronze artefacts evolved continuously, tending to become both more efficient and more mass produced in their appearance, as illustrated in the following clip.



I have participated in a couple of bronze-making workshops run by Dave Chapman. The first was to make a leaf-shaped sword based on one in the Pitt-Rivers museum; this was cast in a stone mould. The second was to make an early bronze age-style axehead, using the lost-wax technique.

Replica leaf-shaped bronze sword cast in stone mould
Replica early bronze age axehead made using lost-wax technique

-- Key innovation --

Combination of raw materials to produce substance not found in nature.

-- Sophistication estimate --

Factor	Discussion	Time resources (person-seconds)
Inputs	For the ores, geology knowledge is required - more than for copper as there are now two metals involved, so 6 hours. For locating and mining the ores, two 8-hour days. Again there is a need for a set of stone tools (assume Mode 4: 90,000 person-secs), and for a pottery crucible and charcoal for the fire (8 hours).	198,000
Skill acquisition	Similar skills are needed as for copper, but now two metals are involved. Assume 50 percent more effort: 18 hours.	64,800
Preparation	The metals need to be separately refined from their ores: 12 hours	43,200
Manufacture	The actual melting and pouring of the bronze takes relatively little time, but there is much work first in creating the mould into which the metal will be poured and then in cleaning up and polishing the object after it has been removed from the mould. For this, two 8-hour days. Finally the object needs to be mounted in a suitably carved handle: 4 hours.	72,000
TOTAL		≈ 380,000

---

Iron tools are usually made from iron combined with small amounts of carbon (up to about 2 percent), and possibly with other elements, to create various kinds of steel. In terms of hardness and sharpness, decent bronze can actually be superior to an average piece of iron. On the other hand, deposits of iron ore are relatively common, which means that, compared to bronze, the technology is less reliant on far-flung trade networks, and this makes it cheaper. Iron has a higher melting point than bronze (around 1500°C compared to 1000°C), so that refining or casting it requires more sophisticated furnaces and handling equipment. However, the metal can be worked at lower temperature in a forge. A sword, for example, can be made from a bundle of rods heated and hammered together -- the metal becomes soft enough to take on a new shape, but does not actually melt. Iron can also be welded. This involves causing two pieces of metal to fuse by the local application of intense heat.


Iron tools: made from a metal that is widely available but only melts at high temperature (although becoming soft enough at lower temperatures to be worked in a forge); iron is usually mixed with small amounts of carbon, and sometimes other elements, to create various steel alloys; iron and steel remain in common use for a wide range of tools; here are shown an axehead of around G 1980 (500 BC) from the Black Sea region (top left), a replica Roman sword (left), a Roman axe (centre), a modern axe (right), and a chainsaw (bottom right)

Iron was first produced in the period after G 1920 (2000 BC), in India, the middle east and east Africa, but this was only in small quantities and as a kind of novelty. Around G 1960 (1000 BC), iron came into widespread use, overtaking bronze as the material of choice for tools and weapons. This occurred first in the middle east and Mediterranean countries from Egypt to Italy. In central Europe, iron technology took off 10 g later, i.e. around G 1970 (750 BC), and in north-western Europe 10 g later still, i.e. around G 1980 (500 BC). Iron technology also became fully established in sub-Saharan African in this same period, G 1960-1980. Africa was unusual in that iron and bronze came into use there at around the same time, instead of a lengthy bronze age preceding the take-up of iron. Iron was not known in the Americas until after the Columbian contact (G 2060:17 = AD 1492).

The addition of carbon to iron, to make steel, was a fairly natural development, since carbon would previously have been used in bronze casting, where it prevents a skin forming over the molten metal. The carbon came from charcoal (85-95 percent carbon), which is obtained by heating wood in the absence of oxygen and burns at the high temperatures needed for melting metal. In a primitive foundry, with a charcoal fire force fed by bellows, there would be plenty of carbon dust floating around in the air, and early metallurgists probably could not avoid it getting into the mix.

Over the generations, the technology of iron-making has evolved in several ways. One goal has been to allow iron to be handled in larger quantities, while another has been to adjust the amount of carbon and other elements so as to produce iron/steel with varying qualities (in terms of melting point, malleability, rust-resistance etc.) suitable for performing varying tasks. One major innovation, the Bessemer process, was made only just over 6 g (150 years) ago, and iron-making patents continue to be taken out to this day. Steel remains important, although plastics and sophisticated composite materials are increasingly dominant.

-- Key innovation --

Iron-making was perhaps not as revolutionary as some earlier transitions between lithic modes or the first use of metals, but the development of the high-temperature furnace was a breakthrough.

-- Sophistication estimate --

Factor	Discussion	Time resources (seconds)
Inputs	A knowledge of geology is required: 4 hours. To obtain the ore (more widely available than copper ore): 4 hours. Also required are a crucible and high temperature furnace, along with charcoal fuel: two 8-hour days. Tools are needed to mine the ore and construct the furnace, for which assume a bronze package: 350,000 person-secs.	436400
Skill acquisition	The necessary skills include producing the high temperatures for melting iron, handling the molten metal, and understanding how carbon or other ingredients affect the metal's properties: 20 hours.	72,000
Preparation	The iron has to be smelted from its ore: 12 hours.	43,200
Manufacture	The work involves creating a mould, melting the iron, and polishing the cast object into a finished product: 2 days. Finally, it has to be mounted: 4 hours.	72,000
TOTAL		≈ 625,000

---

Summary

The following table summarises the technological sophistication of different types of cutting tools and the times at which they first appeared.

Technology	Sophistication	Appearance
Mode 1	1000	Pre-G 1
Mode 2	7000	Pre-G 1
Mode 3	35,000	Pre-G 1
Mode 4	90,000	G 1
Mode 5	150,000	G 500
Neolithic	180,000	G 1600
Copper	290,000	G 1760
Bronze	380,000	G 1860
Iron	625,000	G 1920

This chart shows growth of technological sophistication over time, based on the above table:



While these figures for technological sophistication are rough and ready, it is not surprising to see the kind of accelerating growth shown in the chart.

To make the numbers easier to write, it will be helpful to introduce some abbreviations. Thus, 90,000 person-seconds = 90x10³ ps = 90 kps, where ps is short for person-seconds and kps is short for kilo-person-seconds, i.e. 1000 person-seconds; similarly we can have Mps (mega=10⁶), Gps (giga=10⁹) and Tps (tera=10¹²).

---

To conclude, I want to make two final points:

• Only modern humans have used tools with sophistication 90 kps and above (Mode 4 lithics and higher). However, this does not mean modern humans only use tools above 90 kps. Humans continued to use Modes 1-3 lithics alongside more sophisticated tools, while some groups, like Australian aborigines, did not use anything higher than Mode 3. On aborigine tool-making, see R. Foley and M.M. Lahr, 'Mode 3 Technologies and the Evolution of Modern Humans', Cambridge Archaeological Journal, 1997, 7(1): 3-36; A. Brumm and M.W. Moore, 'Symbolic Revolutions and the Australian Archaeological Record', Cambridge Archaeological Journal, 2005, 15(2): 157-175.
• The adoption of a more sophisticated technology does not mean the abandonment of less sophisticated ones. At most, less sophisticated technologies become rarer over time, as more sophisticated ones are taken up. However, a relatively simple technology, such as a hammer, can be well adapted to its purpose and remain in widespread use despite massive growth of technological sophistication in other areas. Thus lower mode lithics continued alongside higher ones, neolithic tools continued alongside bronze, and bronze continued alongside iron. In principle, an astronaut landing on the moon could still pick up a pebble to fashion a Mode 1 tool for a purpose like prising open an equipment canister.

Scale and competition

In The Dynamic Society, Graeme Snooks stresses the importance of the demand for as opposed to the supply of ideas in driving technological change. In other words, necessity is the mother of invention.

A society's technology is wrapped up with its other characteristics in an eigenmode. An invention like writing should be seen not as a lucky discovery but as an inevitable concomitant of a particular level of social development. Inventing writing is not really that hard. It comes into existence in a high-scale society because such a society cannot function without some means of recording information. It is not fruitful to ask whether writing causes or is caused by a given scale. They go hand in hand, that is all it is meaningful to say.

To extend the point to a recent, familiar example, the internet is associated with an increase in the scale of global society (we can get in touch with more people, more easily). The conventional view would be that some boffins invented the internet, and scale increased as a result. However, it could equally be argued that the development of the internet was driven by the needs of governments and businesses struggling to deal with increases in social scale. We have all heard of inventions like Leonardo's helicopter that languish in limbo because they are 'ahead of their time', showing that merely coming up with an idea is not enough. With the internet, people only invested in it because it filled a real technological gap. Again, the eigenmode concept says we do not need to choose between these opposing viewpoints, i.e. as to whether the internet led to increased scale or increased scale led to the internet. The internet and increased scale both caused each other, while the precise steps by which this came about would not tell us much even if we knew what they were.

I say all this because Snooks's observations have made me think again about geographical influences on technological development, and how I may have been insufficiently rigorous when discussing this in an earlier post.

Thus, I previously put up the following diagram, as part of an explanation of why development first took off in the more centrally located regions of the world's landmasses.

The argument was that more centrally located regions had higher scale, i.e. higher social interactivity, because there were more people within shorter range than was the case for societies around the periphery, and this higher scale meant a higher level of technological development. (I went on to explain that as technology, especially sea-going technology, evolved, it changed which societies counted as central and thus changed which regions had the highest scale and were the most advanced.)

While I continue to stand by this argument, I may have been misleading in implying that it was the flow of ideas from neighbouring societies that was the critical factor stimulating the development of the centre.

What I now want to emphasise is that all we can really say here is that high scale (i.e. proximity of large populations, due to the central location) meant there was societal development and complexification. The details of how this happened are not critical. It may be that centrally located societies were stimulated by the strong flux of ideas reaching them from all the surrounding societies. However, Snooks would argue that the important thing was the pressure exerted on the central societies by their neighbours. In his view, the central societies, with so many close rivals, had to struggle harder to survive compared to the more isolated, peripheral societies, and it was this intense competition that stimulated or compelled them to develop. As before, it is fruitless to get into a debate about which of these viewpoints is correct. Probably both aspects played a part, and there may be other factors or mechanisms as well.

It is not my intention to provide a full review of Snooks's book, which is one of a series in which he sets out laws of history. However, it is worth saying that I do not agree with his assertion that the demand for ideas was the only issue, while for the most part I found his book pretty confused and simplistic.

• Snooks presents his theory as describing biological as well as sociological evolution. This, to me, is a red herring. (It is, however, surprisingly common. Kenneth Boulding does this in Ecodynamics, as does Stuart Kauffman in At Home in the Universe and also arguably Richard Dawkins with his concept of gene-like social memes). Yes, there are superficial analogies between biological and sociological phenomena - e.g. the Roman empire was born, lived and died - but they disappear on close examination - e.g. the Roman empire did not actually 'die', nor was it really 'born'. Biology and sociology exist on quite different levels and need their own conceptual tools. On the sociological side, which is what I am concerned with, we need to use the ideas of politics, economics and cultural anthropology, not the ideas that make sense in biology.


• Snooks argues that the lack of development of the Australian aborigines was because their isolation meant they were not exposed to significant competitive pressure. (Felipe Fernández-Armesto takes a similar view in Pathfinders [p. 11], where he describes the aborigines as "the 'dropouts' of 50,000 years ago, opting out of worlds of change in order to settle a new continent, where they could maintain a traditional way of life".) However, one could ask why the aboriginal tribes did not compete with each other; it might be thought that being cooped up in a small continent could even have increased competitive pressure. Elsewhere, Snooks introduces the notion of 'funnels of transformation', which are narrow regions like Mesoamerica and the Middle East, where many peoples passed through, creating pressure for development. Australia, apparently, had no such funnel. There is something in this, but why do certain geographical conformations have this funnelling effect? Snooks does not really address this. However, it emerges naturally from the 'scale' concept and the idea that sophisticated social mechanisms are needed to deal with intense interaction among close-packed populations connected by short lines of communication.


• Snooks refers repeatedly to 'The Industrial Revolution', which seems to play a large role in his thinking. I find this especially surprising when he himself points out, for example, that sixteenth century growth rates, i.e. two centuries before the 'industrial revolution', exceeded those of any other period bar the 1950s and 1960s. (And he notes high growth rates at other times as well.) The 'industrial revolution', in the sense of a special period in history when technological change suddenly became dramatic, is an illusion. Industrial development during this part of the eighteenth and nineteenth centuries grew seamlessly out of what had gone before, and it was then just the latest twist in the ongoing acceleration of technological evolution. The term 'industrial revolution' originally arose as a pun, jokingly implying that, while France and other countries had political revolutions between about 1750 and 1850, Britain had an industrial revolution. The concept then stuck. It seems that people have a weakness for such explanations of history that assign special significance to particular periods and 'turning points'.

Despite my above criticisms, I would still recommend reading Snooks's books. His work has made me more aware of the issue of demand-side versus supply-side explanations of the evolution of ideas, and indeed of the fact I may have lazily slipped into naive, supply-side explanations myself. He also makes other worthwhile points, such as that co-operation and competition are both necessary in an economy. However, I have reservations concerning his overall model. It is not that it is necessarily 'wrong' in a straightforward sense, but I think it is too vague and impressionistic to be any real use as a theory of history.

Specific coastline and development

Sea transport was more efficient than land transport throughout most of the development of civilisation - from the late neolithic or early bronze age until today. Coastal areas had higher scale, and were more populous and more advanced than inland regions.

Therefore, other things being equal, regions with a large amount of coastline for a given landmass developed faster and further. Europe benefited from this, since it is a relatively small continent with a long, convoluted coastline. By contrast, Africa and Asia, with smoother, more rounded shapes that encompassed a much bigger area, were at a developmental disadvantage.

We call the ratio of a region's coastline to its surface area, the specific coastline. Values of the specific coastline for various regions are as follows:

Region	Specific coastline (km-1)
Europe	4.1 x 10-3
Asia	1.7 x 10-3
Africa	1.0 x 10-3
Western Europe	6 x 10-3

Source: N Rashevsky Looking at history through mathematics (Cambridge, MA 1968) pp. 132-3.

The advantage of Europe, especially western Europe (excluding Russia and Poland), is clear. Its high specific coastline helped it to develop faster than other regions during the last half-millennium of ocean-going transport. This advantage has diminished with the growth of land and air transport, and will all but disappear as humanity transitions to a space-based economy.

Europe - specific coastline = 4.6 x 10^-3

Asia - specific coastline = 1.7 x 10^-3

Africa - specific coastline = 1.0 x 10^-3

Europe appears even more advantaged when we consider the specific river coastline (ratio of total river length to area). For Europe, this is 9 x 10^-3 km^-1, compared with 1 x 10^-3 km^-1 for China, and 5 x 10^-4 km^-1 for India. Europe's total coastline (river and sea) is nearly ten times that of China or India (Rashevsky Looking at history through mathematics p. 133).

The Mediterranean and development

I will now discuss the pattern of world development with respect to the model introduced in my last post. You can use the program supplied in that post to reproduce the following discussion and experiment for yourself.

Set up a simple model of the Mediterranean region as shown below.

This uses the default terrain types, representing land, river, coast and sea, as well as the surrounding ocean.

The layout depicts the Mediterranean sea, surrounded by Europe, Asia and North Africa. The regions bordering the sea are designated as coast. The Nile and Tigris-Euphrates river valleys are also represented. However, the main body of Africa is not included, leaving North Africa and the Nile valley as an isolated strip. This represents North Africa being isolated from the rest of the continent by the Sahara desert. (One could include some 'desert' terrain to represent this, but it is easier just to leave the southerly regions as impassable 'ocean'.)

See the diagram below, with red labels showing the terrain types, and white labels showing the geography.



The aim of this experiment is to demonstrate two aspects of historical development:

1. The Nile valley benefited from both its central location and the ease of movement afforded by the river.
2. As (marine) technology improved, the advantage shifted from the river valleys to the regions bordering the sea, especially the Italian peninsula sticking out into the middle of the sea.

We need to make sure the various terrain types have the appropriate properties of habitability and traversibility. The ones we will use are supplied as the default values in the program.

Land, river and coast are assumed to have the same habitabilities. The only difference between them is that coast and river have traversibilities that are respectively 20 and 40 percent higher than that of land. Sea has a habitability of zero, and initially a traversibility of zero. However, when technology reaches a high enough value, the traversibility of sea switches to a value much higher than that of land. The traversibilities (and habitabilities) of land/river/coast do not change at all with technology. This reflects the notion that, over the period we are interested in, roughly 3000 BC to 1 BC, although movement on land improved somewhat, the really significant change was the opening up of sea transport.

Having set up the topography as above, click the button to populate all regions.

Check the Verbose box, to get a display of the status of each region (you may need to move the land to the middle of the map display, so you can see it in verbose mode).

Press Step, to calculate the scale of each region. Compare 'Italy' with the 'Nile delta' (the region of river adjacent to the 'Mediterranean'). You should find that the Nile delta has a higher scale and consequently higher potential technology than Italy (specifically, 0.41 for the Nile delta, 0.142 for Italy, see below).



Now press the Run button and allow the simulation to run till the values for each region have pretty much stopped changing. You should find that Italy has overtaken the Nile delta (potential technologies of 1.739 for Italy, 1.489 for the delta, with both regions probably having reached their potential). The diagram below shows how the development levels of the different regions (Italy, Egypt, Mesopotamia [i.e. Tigris-Euphrates], Levant [i.e. coastal strip at east end of Mediterranean]) change during the run.



Obviously, this model is very crude in terms of the values assumed and the way we have laid out the topography. However, it demonstrates the basic points referred to above: that, with respect to development, Egypt had an initially favoured position and that this advantage shifted elsewhere as technological growth changed the sea from an insulator to a conductor of human interaction.

What happens in the simulation is that, as technology grows (in Egypt and elsewhere), it passes the level that opens the sea up to marine transport. At this point, the regions bordering the Mediterranean receive a boost in scale and in technological potential. For Italy, being surrounded by sea was previously a disadvantage but now becomes an advantage.

If you want to follow the detailed steps by which this change comes about, pause the simulation, click on Clear Population then Populate All again, and just press Step repeatedly.

• You may like to create more realistic representations of world topography, including additional terrain types, and experiment with different values for traversibility and habitability.
• You could also extend this simulation to model the later shift of advantage from the Mediterranean to the Atlantic rim, once technology growth opened up the ocean.

Italy is not the only land sticking out into the Mediterranean. Greece also does so, and the development of civilisation there preceded that on the Italian peninsula. This reflects its greater proximity to the original centres of civilisation in the near east. See the map below.

View Larger Map

Experimentation with development

This program is for exploring some of the ideas in my last post. (Scroll down for explanation.)

(No program? See only a red X? You need to install the Java Runtime Environment (JRE). Click here.)

The above program allows you to investigate how scale and development depend on topography.

The idea is that you can create a land-mass with a particular shape and give it a certain population. This allows you to see how scale varies at different points of the land-mass. Higher scale results in greater development of technology, which permits a larger population and greater ease of movement. Since scale depends on population size and ease of movement, this creates a positive feedback. Having set up your land-mass and initial population, you can run a simulation to watch how things develop.

In the program, the world is divided into a grid of square regions. You create your land-mass by 'painting' different shapes (e.g. oval, rectangle) and different types of terrain (e.g. land, river) on the grid. Similarly, you 'paint' the population on the regions. You can add your own terrain types, and, for each terrain type, define the habitability (maximum population) and traversibility (ease of movement) as a function of technological level. Initially, all regions are set to 'ocean' (pale blue colour).

The traversibility of terrain depends on the technology of the source region. Suppose a region X has a given population. This population contributes to the scale of surrounding regions. To work out X's contribution to the scale at region Y, we have to take into account the difficulty of movement from X to Y, which means taking into account the traversibility of each region between X and Y. In performing this calculation, we use the technological level of X to determine all the traversibilities (i.e. not the local technological level of each region). Conversely, when working out Y's contribution to the scale at X, we use the technological level of Y to work out the traversibilities of the intervening regions. The idea behind this is that a region's ability to project itself depends on its own technology not on the technology of the receiving regions. E.g. America's ability to influence, say, Nigeria depends on American technology (internet, TV, airlines) not on Nigerian technology.

To familiarise yourself with the program, try the following (you may want to open a copy of this window so you can follow these instructions and view the program at the same time):

1. First, we need to activate the applet (program). Click anywhere in the program box to do this. The program has controls at the top, and a display area where you can set up land-masses by painting terrain onto the different regions.

2. To see the regions clearly, click on the check box labelled Grid (top right). You can move the display around by dragging with your mouse, and zoom in/out with your scroll wheel.

3. To create an island in the shape of a rectangle divided into 9 regions with terrain type 'land', do the following:
a. Click on the radio button labelled Rectangle (top left).
b. Click on the button labelled Paint (top centre).
c. Make sure the adjacent drop-down box says Land. If not, select it from the list.
d. Draw a 3x3 square in the middle of the display area by clicking and dragging the mouse. If you make a mistake, click the button Clear Terrain (top right) and try again.

4. To set up each region with an initial population of 100, do the following.
a. Edit the field labelled Population to read 100 instead of 1000 (left hand side of control panel).
b. Click the button labelled Populate All (left of control panel). Dots should appear on the square island. The size of the dot in each region represents the size of the population in that region. (If you want, you can add population to one region at a time, by clicking the Paint button next to the population field, then clicking on the relevant region.)

5. To see the status of a given region of the island, right click on it, and select Region Information from the popup menu. A dialog box will appear with the relevant information. 'Population' is self-explanatory. 'Potential' represents the potential scale generated by all the populations in surrounding regions; the potential generated by each population depends on its size, how far away it is, and the ease of movement between the two regions. 'Scale' is the potential scale multiplied by the population of the region in question; e.g. a large population in region B generates a large potential scale in region A, but, if there is nobody in region A, the actual scale of region A is zero. 'Technology' represents the technological and institutional sophistication of the region; this can reach a maximum level that is a function of the region's scale. 'Habitability' represents the maximum number of people the region can support, given its technological level. Finally, 'traversibility' represents the ease of movement across the given type of terrain. In this case, you should find that the region's population is 100, the habitability is 1000, the traversibility is 0.1, and everything else is 0. Click ok to get rid of the dialog box. If you check the other regions, you will find that they are the same.

6. Now let's look at scale.
a. Click the button labelled Step. This performs one iteration of the simulation and results in the scale of each region being calculated as a function of the populations of surrounding regions.
b. Now click on different regions of the square island and view the Region Information again. Where is scale highest? Where is it lowest? Why is this? You should find that scale is highest in the centre, lowest at the four corners, and intermediate in the remaining regions. This reflects the fact that the central region is overall closest to the other regions, while the corner regions are overall furthest away.

7. Next let's simulate the growth of population and technology. The assumption is that population grows asymptotically towards the level set by the region's habitability, while technology grows asymptotically towards a level that is equal to the region's scale.
a. Select the checkboxes labelled Population and Technology. These variables will now be updated at each iteration of the model. (This feature means you can choose independently whether or not to simulate the growth of population and/or technology, making it possible to isolate one factor and see how it behaves.)
b. Click Step, then inspect the information for each region. You will find that the population of each region has grown by the same amount, but technology has grown to different extents depending on the scale of each region.
c. Let the simulation continue until the populations have just about reached the maximum habitability, which is currently 1000. Rather than repeatedly clicking the Step button, you can click the Run button to do this automatically. The slider to the right of the button controls the speed. Move the slider to the left for the simulation to run faster. (If the simulation seems to freeze, move the slider right to slow it down.)
d. When the centre region's population is say 999.99 (check the region information, as above), click the Run button (now labelled Pause) to pause the simulation. Check all the regions. You will find that the technology in each region is virtually equal to the region's scale, and is therefore highest in the centre, lowest at the corners. The actual values should be about 0.429 for the centre, 0.217 for the corners, and 0.317 elsewhere. If you click Run again, these values will change little, as population has pretty well reached its maximum everywhere.

8. The next thing to learn is how to set the traversibility and habitability for a given terrain type.
a. Make sure that Land is selected in the drop-down list and look at the table labelled Terrain Types. The first row should read Technology=0, Traversibility=0.1, Habitability=1000. This means that, for a technology level of 0 or above, the traversibility and habitability of 'land' have the values indicated.
b. Click in the second row of the table, in the column labelled Technology, and type 0.4. Then edit the values in the second row under Traversibility and Habitability to be 0.15 and 1000 respectively. This means that, for a technology level above 0.4, the traversibility of land is now 50 percent higher, 0.15 instead of 0.1. This represents the fact that a certain level of technology brings innovations like the road, horse-and-cart or motor-car, which allow people to get around more easily.
c. You can also change the colour assigned to a terrain type, by clicking on the coloured rectangle labelled Colour, and create a completely new type of terrain, by clicking on the button labelled New. We won't do either of these in this case.

9. Now let's see what difference it makes that a higher technology level produces a higher traversibility.
a. Step the simulation once then check the information for each region. You should find that the scale and technology level of the central region are the same as before, around 0.429. However, the scale of the four side regions should be found to be higher, around 0.356, while the technology level has also increased, to around 0.321. Similarly, the scale of the corner regions should have increased to around 0.235 and their technology level to around 0.219.
b. What is going on here? Well, the technology level of the central region is above 0.4, so for this region the traversibility of Land is higher than before, 0.15 instead of 0.1. This means its contribution to the scale of surrounding regions declines more slowly with distance, so their scale is higher than it was. However, the technology of other regions is below 0.4, and for them the traversibility of Land has not changed. Therefore their contributions to the scale of the central region are also unchanged. Overall, the scale of the central region remains the same, but the scale of all the surrounding regions has increased. (Note that a region does not contribute to its own scale.) This increase in scale of the surrounding regions means their technology is beginning to increase towards the level allowed by the new scale.
c. Click the Run button and allow the simulation to run for a while, then check the regions again. You should find that the situation has stabilised with the technologies of the surrounding regions at the new higher level corresponding to their scale.

10. Now we will allow technology to increase habitability as well. This will create the situation where the technology of all regions goes above 0.4.
a. Pause the simulation. Go back to the Terrain Types table, and change the habitability in the second row to 1500. This represents the fact that a higher technology level produces innovations like farming tools, which allow more people to survive on the same area of land.
b. Step the simulation and check the region information. You should find that things are much the same as before, but the population of the central region has increased slightly, to move towards the new, higher habitability.
c. Continue stepping the simulation and keep a careful eye on the scale of all the regions. You should find that their scale is increasing. The growing population of the central region is making a growing contribution to the potential scale of its neighbours, and hence to their actual scale. The potential scale of the central region remains the same, since the neighbouring populations are unchanged, but its actual scale is increasing in line with the increased population. And as scale increases in each region, technology level follows.
d. Run the simulation for a while, until it reaches a new steady state. Check the state of the various regions. You should find that the technology level of the central region is now around 1.480, while that of the side regions is around 1.101 and that of the corner regions is around 0.773. You should also find that the population of all regions is around 1500.
e. What has happened? Well, the growing population of the central region increased the scale of the surrounding regions, until eventually the side regions broke through the 0.4 barrier. This increased their traversibility and habitability so they made a much greater contribution to the scale of the central region, and its technology grew accordingly. Both they and the central regions also increased the scale of the corner regions to the point at which they too broke through the 0.4 barrier, further enhancing the scale and technology of the other regions. The result was a great increase in technology and population all round.

You should now know the way the program works, and be able to experiment on your own. Some final points to note are:
a. Rather than drawing a rectangle, you can draw an ellipse, line or single cell. Lines have to be drawn from left to right. (Yes, my program is a bit rough, but it does the job, I hope.)
b. If you want to explore the effects of a coastline, it can be tedious to paint the coast manually (changing regions from land to coast). The Outline button can do this for you automatically.
c. The Verbose checkbox causes the grid to be displayed zoomed in, with the details of each region written in. This is convenient if you want to follow the changing numerical values. On the verbose display, P=population, T=technology (maximum possible technology shown in brackets), t=traversibility (at T=0), h=habitability, p=potential scale, s=scale. The pair of numbers at the top of each cell are its co-ordinates (column, row).
d. Each iteration of the simulation involves 3 sub-steps: calculating scale, technology, and population in that order. There is also a sub-step for calculating migration, but this is currently not modelled and does nothing. You can perform one sub-step at a time by clicking the Sub-step button. The next sub-step to be performed is shown in the box to the left of the button.

I will finish with some technical details of the model. In the next post, I will discuss how the above program can be used to illustrate the relative historical roles of Egypt and Rome.

Technical details...

The model involves 3 calculations--scale, technology and population--and a set of constants.

(1) Scale calculation

I take each region (square) in turn and calculate its contribution to the potential scale of all the other regions. Firstly, I set the potential of each region to zero. For each region, the algorithm is then as follows:

a. Call the source region the region now being processed.
b. Set working_potential of the source region to be equal to its population.
c. Set the current region to be the source region.
d. Let current_potential be the working_potential of the current region. Consider each region to north, south, east and west of the current region, in turn, as the target region. If the target region has already had its working_potential set during processing of this particular source region, do nothing (this occurs if potential has been propagated to it by another route, and stops potential being propagated back the way it came). Otherwise, calculate propagated_potential as current_potential x traversibility / (traversibility_threshold + traversibility), where traversibility is the traversibility of the terrain type of the target region given the technology value of the source region (note, not the current region or target region). If propagated_potential exceeds a fixed threshold_potential, set the working_potential of the target region to be equal to propagated_potential.
e. Consider each region whose working_potential was set at the last step, in turn, as the current region, and go back to step d.
f. Once there are no more regions whose working_potential has been set but not propagated to its neighbours, add the working_potential of each region, except the source region, to its potential. Set all working_potentials back to zero.

The above is repeated, taking each region in turn as the source region. The result is a total potential for each region. The scale of each region is then calculated as simply the product of its potential and its population.

(2) Technology calculation

For each region, I calculate delta_technology from the formula, delta_technology = time_step x technology_growth_rate x (technology_constant x scale^technology_exponent - technology). Here, scale^technology_exponent means 'scale raised to the power of technology_exponent'.

The new technology of each region is then calculated as technology + delta_technology.

(3) Population calculation

For each region, I calculate delta_population from the formula, delta_population = time_step x population_growth_rate x population x (habitability - population). In this formula, habitability is the habitability of the region's terrain type given the region's current technology.

The new population of each region is then calculated as population + delta_population.

(4) Constants

I used the following values for the various constants introduced above:

traversibility_threshold = 1
threshold_potential = 10^-6
time_step = 0.1
technology_growth_rate = 1
technology_constant = 1
technology_exponent = 1
population_growth_rate = 0.0001