I'm thinking about how to model an ecosystem of recursively self-improving computer programs.  The model I have in mind assumes finite CPU cycles/second and finite memory as resources, and that these resources are already allocated at time zero.  It models the rate of production of new information by a program given its current resources of information, CPU cycles, and memory; the conversion of information into power to take resources from other programs; and a decision rule by which a program chooses which other program to take resources from.  The objective is to study the system dynamics, in particular looking for attractors and bifurcations/catastrophes, and to see what range of initial conditions don't lead to a singleton.

(A more elaborate model would also represent the fraction of ownership one program had of another program, that being a weight to use to blend the decision rules of the owning programs with the decision rule of the owned program.  It may also be desirable to model trade of information.  I think that modeling Moore's law wrt CPU speed and memory size would make little difference, if we assume the technologies developed would be equally available to all agents.  I'm interested in the shapes of the attractors, not the rate of convergence.)

Problem: I don't know how to model power as a function of information.

I have a rough model of how information grows over time; so I can estimate the relative amounts of information in a single real historical society at two points in time.  If I can say that society X had tech level T at time A, and society Y had tech level T at time B, I can use this model to estimate what tech level society Y had at time A.

Therefore, I can gather historical data about military conflicts between societies at different tech levels, estimate the information ratio between those societies, and relate it to the manpower ratios between the armies involved and the outcome of the conflict, giving a system of inequalities.

You can help me in 3 ways:

• Tell me why this is a bad idea.
• Tell me some better way to relate information to power.
• Gather historical data of the type I just described.

If you choose the last option, choose a historical conflict between sides of uneven tech level, and post here as many as you can find of the following details:

• Identifying details: Year, opponents involved, name of conflict
• Number of combatants on each side
• Duration of the conflict
• Outcome of the conflict
• Identification of technological advantages of either side, especially ones that proved key (this can include non-material technologies, such as training or ideologies)
• How long the side with a technological advantage had possessed that technology at the time of the battle
• Estimation of the tech levels of each side in terms of a "standard" Western-Equivalent era (WE) attached to the most-advanced "Western" nation of the time (or in the conflict), and the facts used to make these estimates.  (We might trace the WE timeline starting with Sumeria, then Egypt, Greece, Rome, etc.  If enough datapoints are available for the 2 societies involved to model their information growth, they need not be mapped to WE.)

For example:

• Battle of Agincourt, English vs. French, October 1415.
• English combatants: Given as 5900, or 8000
• French: Given as 20,000-36,000, or 12,000
• Duration: 3 hours
• English win; 4,000–10,000 French dead, with up to 1,600 English dead
• Most historians identify the English longbow as the key technology responsible for the English win (reference needed).  The English longbow was used at least as early as 1346.  However, the Wikipedia article on Agincourt, as well as this site, indicate that the crucial technology was not just the longbow, but the use of palings (long stakes driven into the ground to protect bowmen from cavalry).  A third key innovation of the English was being dedicated to winning battles rather than to fighting for glory; the French disdained longbows as unchivalrous, and were given to drawing up battle plans that would give them personal glory in the retelling rather than battle plans that would win (described briefly here, and in more detail in a book, I think "A Distant Mirror" by Barbara Tuchman.)  This may be why the French deployed their archers behind their cavalry, where they were unable to take part in most of the battle.
• I assign the French a tech-level of 1346 WE, based on this being the date when the English first used the longbow heavily in a major battle.

Using the two dates 1415 and 1346 leads to some tech-level (or information) ratio R.  For example, under a simple model assuming that tech level doubled every 70 years in this era, we would give the English a tech-level ratio over the French of 2, and then say that the tech-level ratio enjoyed by the English produced a power multiplier greater than the manpower ratio enjoyed by the french:   P(2) > 30000/5900.  This ignores the many advances shared by the English and French between 1346 and 1415; but most of them were not relevant to the battle.  It also ignores the claim that the main factor was that the French had heavy armour, which was a disadvantage rather than an advantage in the deep mud on that rainy day.  Oh well.  (Let's hope for enough data that the law of large numbers kicks in.)

After gathering a few dozen datapoints, it may be possible to discern a shape for the function P.  (Making P a multiplying force that is a function of a ratio assumes P is linear, since eg. P(8) = P(8/4)*P(4/2)*P(2/1) = 4*P(2); the data can reject this assumption.)  There may be a way to factor the battle duration and the casualty outcome into the equation as well; or at least to see if they correlate with the distance of the datapoint's manpower ratio from the estimated value of P(information ratio) for that datapoint.

(I tried to construct another example from the Battle of Little Bighorn to show a case where the lower-level technology won, but found that the Indians had more rifles than the Army did, and that there is no agreement as to whether the Indians' repeating rifles or the Army's longer-ranged single-shot Springfield rifles were better.)