Technology System Version 5.1

[Mark_Everson]

Richard:

Yes, I Know we had it b4... just embarassed I didn't think of using it to solve the current issues.

[Mark_Everson]

Richard:

I'm sorry to be giving you such a hard time, but Level 2 is Not acceptable for an interface approach IMO. It might work with agriculture as you described... but even this has a weak link. The Player is interested in Food for the people. They generally won't care if it comes from the land or the sea nearly as much. Now food is So important that we could easily justify the player needing to do extra work in this one case, but I think the problem is very general.

I went back and found Numerous examples where the player would be stupified as to Where To Start Looking using a Level 2 interface! For example:

Airplanes--- Fluid Dynamics 35%, Engines 50%

How in the hell is the player supposed to know where to look??? Maybe 5% of players would guess to look in Fluid Dynamics, and maybe 25% would look in Engines. That is the sign of a Poorly-Thought-Out interface.

In my Thematic approach there would be links to airplanes in each of Military, Economic, and Communication and Transportation (think we need the latter for the interface) and it will be right there where they expect it.

We could, as a compromise have both sorts of interface. But I am sure as I ever am of anything, that the thematic one will be the one used by virtually all players. However if we can identify the level of things that go into a thematic interface, and keep it down to a two-step menu for the main areas, then I will be happy. By two-step I mean you go to the tech screen and select 1)Economic Model; and then 2)Food Production. If the player wants to go down further into specifics (Fishing, Husbandry, Farm Landscaping, Farm Tools and Machines) then they can.

I really do think that your approach to the organization is more rigorously correct from a taxonomic standpoint! But this is primarily a Game, not an exercise in pedagogy.

[Richard Bruns]

This is the first part of Tech System 5.2 It contains updated equations and an analysis of the system. The actual tree will come later, after I can get everyone's techs and try to compile them. Sometime soon, I will also finish writing up my analysis of application factors and other issues regarding game mechanics and interface.

These conclusions were reached after a lot of number crunching and thought, but there may still be mistakes. Feel free to check my math and logic. I have probably included more than is necessary, so if you are not directly involved with the tech tree you can skim a lot of this.

Symbols, Definitions, and Axioms:

k: This 'imaginary variable' represents the quantity of knowledge in a certain tech that your civilization has. It may have a number after it when multiple techs are used (k1, k2). It will not be tracked in the programming, but it helps the math a lot. It will always disappear from the final formulas, however. k is defined so that k=1 represents a minimum workable knowledge of some field. k is never allowed to be below one; it simply disappears if it drops below one. kn will be used to signify the knowledge level on a certain turn.

dk: This is the change in knowledge in any one turn.

T: This is the tech level of some specific tech. It may have a number after it when multiple techs are used (T1, T2). Also, Tn and Tn+1 will be used to represent the technology level on one turn and the next turn. T is defined so that T=100 represents the highest publicly known level of technology as of January 1, 2000. A doubling of k is always represented by a T increase of 10.

Ts: This is the level that a tech starts at. If T falls below Ts then the technology is lost. This number will be determined by historical research; we will analyze the history of a tech and determine how many times it has doubled in the course of history. For example, if knowledge has doubled six times the tech starts at Ts=40. Ts will never be less than zero.

Axiom 1: k=2^((T-Ts)/10)

Corollary 1: k=1 when T=Ts

RP: This represents the Research Points that are invested in the growth of technology.

m: This represents the effectiveness at which RP's are converted into knowledge (k). Discounting helper technology change, there is no reason for this to change over time.

b: If no RP's are spent on a technology, this is the amount the tech changes in one turn. If b is zero, the tech level will not fall. b should change over time, increasing as k increases

c: This determines what percentage of current knowledge can be lost in one turn.

Axiom 2: b=ck

Assumption: On any one turn, the tech increase should be directly proportional to the amount of RP's spent. I don't think that any diminishing returns are needed here because there is no real evidence of diminishing returns for research. In fact, hiring more researchers at one time often creates synergy that gives research more quickly. The sum of these two influences (assuming diminishing returns exists) can be approximated by a linear relationship.

If we decide that it is vitally important to include diminishing returns, then I could change the equations. But I really don’t think that this has to be modeled here. Higher tech levels already require a lot of upkeep, so a diminishing returns scheme here would penalize the player twice for making emergency investments.

Axiom 3: dk=m*RP-b

Corollary 1: dk=0 when RP=m/b

h: This determines the effect that a helper technology or vital technology has on the technology or application it influences. It may have a number after it when multiple techs are used h1, h2).

Note: Suppose Tech A influences Tech B. Then, if Tech B is a sub-field of Tech A, then Tech A is a vital tech. Otherwise, Tech A is a helper tech.

H: This combines the effect of all helper and vital technologies.

Formula Derivations:

Base Tech Change Formula:

Given Axioms 1-3, I derived the tech growth formula as follows:

k=2^((T-Ts)/10)

ln(k)=.1*(T-Ts)*ln(2)

T-Ts=10*ln(k)/ln(2)

T=10/ln(2)*ln(k)+Ts

Every turn:
Tn+1=f(kn+dk)

Tn+1=10/ln(2)*ln(kn+dk)+Ts

Tn+1=10/ln(2)*ln((2^((Tn-Ts)/10)) +dk)+Ts

Tn+1=10/ln(2)*ln((2^((Tn-Ts)/10))+(m*RP-b))+Ts

Tn+1=10/ln(2)*ln((2^((Tn-Ts)/10))+(m*RP-(c*k)))+Ts

And Finally:

Tn+1=10/ln(2)*ln((2^((Tn-Ts)/10))+(m*RP-(c*(2^((Tn-Ts)/10))))+Ts

By the way, it looks a lot better when you write it on paper

Notes: This equation does a good job of modeling tech growth, and it only needs the intuitive variables c and m defined. I have tested it extensively using a calculator program. It works well when c=0.1 and m=0.01. With those two values, the a tech with Ts=0 has the following properties, assuming no helper techs:

At tech level 1, the tech needs 11 RP to sustain itself and increase a minimal amount. Anything less will result in the tech going down to zero. If 30 RP per turn is given to the tech, it will rise as follows: 1, 3.39, 5.24, 6.73, 7.95, 8.96, 9.82, 10.55

At tech level 10, the tech needs 20 RP to counteract tech loss and stay constant.

At level 20, the tech needs 40 RP to counter tech loss.

RP needed continues to double every time the tech level raises ten points.

This equation cannot be manipulated by fluctuations in spending. A spike in spending followed by a period of minimal spending will give slightly worse results than that same amount of RP’s spread out evenly.

At this point I should comment on the amount of RP’s generated by your civ. Assume that there would be about 150 Level 3 techs in ancient times and they would be about 20 levels above minimum. I am ignoring the Level 1 and 2 techs because their helper effect will cancel the RP needed to keep them up. This will be explained later. I am also ignoring the effects of helper techs here. So an ancient civ would need to generate 6000 RP’s to prevent tech loss. I know that seems like a lot, but otherwise the numbers are too imprecise at the level of the individual tech.

Let’s consider a sample ancient civ to give context to this RP production. Suppose that the small Snurb Empire has ten simple agricultural provinces. RP’s are generated by each of those provinces, and also by trade within my empire and contact with the neighboring tribes. In addition to this, my capitol has a library, university, theatre, and forum. I am working on building some roads and fortifications as well as maintaining an army to defend myself.

Note that these numbers are just meant to be examples. Exact values will have to be determined by playtesting.

It is reasonable that my provinces would generate a base average of 400 RP each and split most of it among the techs relating to basic activities of that province. Any techs relating to farming, daily living, and simple crafts are thus supported, as well as social techs and arts. The advanced capitol city makes 1000 extra RP’s that give extra support all the basic sciences and arts. My trading activity generates 700 RP’s and supports transportation, economics, and some production techs. The basic operation of my government and centralized religion makes 500 RP’s for techs related to government and management, literacy, social technologies, and arts. The building of the roads and forts generates another 500 for engineering, masonry, and construction techs. And the maintenance of my army gives me 300 RP for military techs. So I have 7000 RP’s, even when I am spending nothing directly on tech and am not considering my tech gains from contact with the surrounding tribes. 6000 of these would go to keeping the tech at its current level, and the remaining would go to advancement of the techs.

As I continue to develop my civ, the RP production will naturally grow. Those roads and forts will make travel and trading easier and safer, so there will be more RP generation in that area. As the provinces become more developed, they will generate more RP’s. My government will have to get bigger and do more, so I get more RP’s from that. And as I expand my territory, I come in contact with new people and use my military and diplomacy more. My tech should grow at a healthy rate.

Note that most of the RP’s are used for specific things. The player would only have control over a small portion of the province RP generation and a larger proportion of the RP’s generated by the advanced cities. Everything else counts as RP’s that come from building or doing something, so they are assigned automatically.

For this we can use a system similar to what Hrafnkell suggested in the earlier tech thread. Every tech has a few tags like Farming or Military attached to it. But rather than have the prevailing social conditions multiply the RP’s like Hrafnkell proposed, the social conditions actually make RP’s that go to techs with the proper tag. So an agricultural province generates RP’s that are automatically used to support a certain kind of technology. Call these tagged RP’s. In addition, the province generates general RP’s. These do not have a specific use and can be sent to anything. If the player does not reassign them they go to the same thing the tagged RP’s go to.

Government operation also generates tagged RP’s, as do military upkeep, building projects, and so on. The biggest source of untagged RP’s will be cities with libraries and universities.

Helper Tech Effect Formula and Consequences:

The best way to model the effect of helper and vital technologies is to have them alter the amount of RP’s spent on a certain technology. This is the most realistic way of representing the helping effect of other techs, and it is easy to work with.

The consensus has been that helper techs and vital techs should have a multiplicative effect, based on their level. If a tech has more than one helper tech, they all multiply the RP’s by some level So:

H=1+(h1k1*h2k2* . . .)

dk=m*H*RP)-ck

This seems reasonable at first, but it can create big problems. I will illustrate:

Consider a tech tree with a single level where the techs are helper techs for each other. Each technology aids several other techs, and is in turn aided by several different techs. This situation is similar to what could happen to Level 3 techs in our tree of we put a lot of helper connections between them. Also assume that RP’s are spread equally among all techs and all techs have the same m value.

Now, to simplify things, assume that each tech helps and is helped by only one other tech. The dynamics are still about the same, but the connection is easier to imagine (a giant ring). Now, imagine that the number of techs decreases steadily, keeping the same connection structure. Eventually you get to the point where there are only two techs that help each other. Now, this system is basically the same as the large ring. It simply is smaller.

For a further degree of simplification, consider a situation where there is only one tech and it is a helper tech for itself. This will behave the same as a system with two identical techs that are helper techs for each other, and it serves as an easy mathematical representation for the big cross-linked system.

So we have a situation where dk=m*(1+hk)*RP-ck

Let’s plug in some numbers and see what happens. Let m=0.01, h=0.2, and c=0.1. All of those are reasonable values for the constants. Suppose that on a certain turn k=4.

We can find out how the presence of the helper tech affects the break-even point; the point at which there is no tech loss and no tech gain.

With no helper tech:

dk=m*RP-ck=0

RP=ck/m=40

With helper tech:

dk=m*(1+hk)*RP-ck=0

m*(1+hk)*RP=ck

RP=ck/m*(1+hk)=22.22

So the helper tech has drastically decreased the number of RP’s required to maintain the tech level. Tech will also rise a lot faster. This is exactly what helper techs are supposed to do, but the system breaks down rather quickly:

Suppose that 100 RP were spent on the tech.

dk=0.01*(1+0.2k)*100-0.1*k

dk=1+0.2k-0.1k

Thus dk=1+0.1k with no increase in RP’s spent! Without the helper tech, dk would have been 1-0.4, or 0.6. The tech level would have gone from 20 to 22.01. But with the helper tech, the knowledge level will increase without bound for 100 RP a turn. On the first turn, dk is 1.4, and the tech level goes form 20 to 24.33. After that, the tech increases as follows: 27.95, 31.10, 33.91, 36.49, 38.87, 41.11, 43.22, 45.24 . . . This rate of change will not slow down. Without helpers, tech growth would have stopped at a tech level of 33.22 because the tech upkeep at that level would be 100 RP’s. But with this system of helper techs, 100 RP will be enough to make the tech level rise to without limit.

The same kind of thing could happen in a cross-linked system of 200 techs if 100*200, or 20,000 RP were put into the system per turn. All of the tech levels would skyrocket!

For the simple system, it is easy to calculate the point at which the tech will start its infinite increase. We find RP such that the gain from the helper tech is equal to tech loss. At this point, there is no RP penalty for higher tech levels. And at higher RP values, the rate of tech rise will increase as k increases.

H*m*RP

=(1+hk)*m*RP

=m*RP+hk*m*RP

so: dk= m*RP+hk*m*RP-ck

If the last two terms are equal, the tech will always rise by m*RP.

hk*m*RP=ck

h*m*RP=c

RP=c/(h*m)

(m=0.01, h=0.2, and c=0.1)

In this example, RP=50. k will always rise by .5, no matter what the tech level is. The tech level will rise more slowly as k increases, but k will still be increasing, regardless of the tech level. And if the RP input increases any more, then dk will increase as k increases.

A similar thing would happen in a cross-linked system of 200 technologies if 10,000 RP were put into the system. All of the techs, serving as helper techs for each other, would constantly rise at a rather rapid rate. And remember that 10,000 RP’s is not a lot. It is almost within the grasp of my small Snurb Empire.

Here we get to the major flaw in this system. For all practical purposes, tech loss drops out of the equation and helper techs instead create tech gain! At a certain (low) number of RP’s, the sum of the helper techs effect will cancel out the RP drain from tech loss, so knowledge generation remains constant for all tech levels. This cannot be prevented by changing the constants. For any c/(h*m), there will be an amount of RP that will result in unchecked growth. If h were set low enough to prevent an advanced modern civ from making unchecked growth, the helper techs will have almost zero effect in ancient times.

Hold that thought while we consider the Level 1 and 2 technologies. These technologies have no direct effect on applications; their sole purpose is to act as vital and helper technologies for the Level 2 and 3 techs. Given that job description, the helper effect of these technologies must be greater than the RP loss due to upkeep of those technologies. Otherwise they are simply a drain on the RP pool. The previous helper tech formulas will serve nicely here; if you spend enough RP’s on things that Level 1 tech help, then the upkeep of the techs will be repaid. And as Level 1 and 2 techs do not generally support each other, there will be no problem with unlimited tech rise.

In earlier discussion, we agreed that the difference between helper and vital techs would simply be the magnitude of the h constant for that tech. But we have seen that that is not possible. For any h value, a system of techs that help each other has the possibility to rise without bound. So I propose that the formulas for helper and vital techs be differentiated. Vital techs would retain the formulas described above so that their benefits outweigh their upkeep, and helper techs will use a formula that eliminates the possibility of an infinite tech rise. Taking the square root of knowledge will work well, and it would be reasonable. We can assume that helper techs can only help so much, and at a higher knowledge level they cannot provide as much benefit. So:

H=1+(h1k1*h2(k2)^.5*. . .)

Where k1 is the knowledge level of a vital tech and k2 is the knowledge level of a vital tech. We cannot leave k in the formula for H, however. k will not be counted in the game; it simply made the math a lot easier. So H in terms of tech level is:

H=1+(h1(2^((T-Ts)/10))*h2(2^((T-Ts)/10))^.5*. . .)

Which simplifies nicely to:

H=1+(h1(2^((T1-Ts1)/10))*h2(2^((T2-Ts2)/20))*. . .)

Where T1 is the level of a vital tech and T2 is the level if a helper tech.

The RP input needed to cancel tech loss for a helper tech is now:

h*k^.5*m*RP=ck

RP=ck/(h*k^.5*m)

RP=ck^.5/(h*m)

In terms of Tech level:

RP=c(2^((T-Ts)/10))^.5/(h*m)

RP=c(2^((T2-Ts2)/20))/(h*m)

So there is no longer the possibility of an infinite tech increase. RP needed increases exponentially with the tech level. Note that this will not make tech research too difficult. The helper techs usually have other purposes aside from helping, so the RP gain from helper techs is a free bonus. Vital techs, which usually have the sole purpose of helping other techs, will provide more RP benefit than their RP upkeep cost.

So what does everyone think?
[This message has been edited by Richard Bruns (edited February 24, 2000).]

[Krenske]

Richard,
You don't have a calculator somewhere back in your family tree do you.

I see the reasoning and it appears quite sound.

[Richard Bruns]

LJG wants to add diminishing returns to tech spending. This can be done nicely by raising the number of RP's spent to the power of 0.99. This produces small diminishing returns at about 5000 RP's and it would not be too hard to implement. I personally don't think that we need to do this, but it remains an option. What do you think?

[Krenske]

So how will that work?

Is this it. Point 1 = .99^1 = .99
point 2 = .99^2 = .98
.
.
point 50 = .99^50 = .60
.
.
point 200 = .99^200 = .13

Actual points added equals the sum of all results.

This seems very processor intensive, It may be quicker to just say the first 100 points are worth 1 each the next 100 are worth .9 etc.

I'm not sure I like the diminishing returns bit at all but I think there should be a minimum at some point. Maybe we could use a number of levels of intensity for a civ based on SE factors regarding the rate of research within the civ. If 10% of research on one item then as normal. Each point over that is at 66%, each over 50% of total research is at 33%.

Hang on that's confusing let me put it another way.

% of research into an area	value of each point less than threshold
10	100
50	.66
100	.33

How is that?

[Krenske]

Richard,
The game "Spaceward Ho" has a very good spending and technology system that worked on diminishing returns. The sliders worked in a reverse exponential way. As you moved a slider all the others compensated but the -ve changes associated with small alterations at high level +ve changes were severe. (going from 8 to 9 in weapons research dropped the levels in the other areas from 3 to 1) Obviously some logarithmic factors were in use. The original MOO operated similarly but I don't think there was a diminishing returns factor.

It is a fairly quick system to use and if we were to limit the techs to just 10-12 tags then this could be a usefull distribution system. We can even include certain minimums etc based on social and governmental factors. We could actually have two sets of bars, one is just a indicator of use related research,( research gained within a field by the users eg. Farmers generating points towards farming.) The second set is the government spending sliders. We could apply the diminishing returns factor to both or either set.

[Mark_Everson]

Richard:

I think there's something wrong there... in your analysis that the helper techs cannot work as advertised.

At the root of it, I believe, is your formula for the helper tech contribution. It is because you assume a helper tech Always helps, and never hinders progress in an area. If you remove this bias in your formula then the problem will go away. Realistically, helper techs should only be "ahead of the curve" half of the time on average. Also it looks like you are plugging in numbers way outside the normal range of applicability of your formula. For instance for the case where you showed that the helper tech example is broken, even the "well behaved" Tech advances from 20 to 22 in one turn!!! So Clash is going to be a 50-turn game is it? That's what I would expect if you can get 2% of the way to modern technology in a single turn. Of course, I have just glanced at that part of the doc so I may have it wrong...

[Lord God Jinnai]

One quick thing here, very minor but imporatant. the minimum level of knowledge should be at .01% not 1%. This is to make sure all levels of doubling are equal since otherwise 1%-10% has 9% points inbetween while everything after is FE 10.01-20% had 9.99% points inbetween. Whether this is reprented by K or not, it needs to be mentioned.

[Richard Bruns]

Mark: In the example where tech rises two points, the RP input was more than it should have been. I was pointing out what would happen if too many RP's were put into the system. Without helper techs you get a small spike and then tech growth slows down, but in the old system tech levels rose to infinity.

Quotes:
---
Without the helper tech, dk would have been 1-0.4, or 0.6. The tech level would have gone from 20 to 22.01. . .

Without helpers, tech growth would have stopped at a tech level of 33.22 because the tech upkeep at that level would be 100 RP’s
---
I don't see how it would work to have helper techs penalize research progress sometimes. Could you explain what you were thinking of?

LGJ: You have k confused with the tech level. k=2 represents twice as much knowledge as k=1 and k=4 represents twice as much knowledge as k=2. It is a linear scale, not a logarithmic one like the tech levels are.

Krenske: No, it would be RP^.99 this will be about equal to RP until you get to really high levels in the modern era. I don't think that this is really needed, however. The tech loss already penalizes players for being too advanced; diminishing returns would penalize players twice for emercency spending.

[Mark_Everson]

Richard:

BTW lots of good work!

On the 'helper' techs hindering. Consider:

Economics with helpers Mathematics, Social Sciences.

Current levels
Econ 60%
Math 12%
Social Sciences 60%

In your formula you get a Bonus for the Abyssmal level of Math. In reality your Math should be Preventing you from ever getting far above say 30% in Econ. Essentially as soon as Math is needed to advance economic theory the whole thing should come to a grinding halt .

IMO the helpers' contribution should be its knowledge level Relative to the current tech or some such. In that case Math would impose the huge penalty it should on Econ progress.

That's my view of it anyway.

Richard and LGJ:

One more issue I'm wrestling with. It seems to me that the kind of actions that prevent tech backsliding are essentially different from those that result in actual innovation.

Maintaining tech is mostly an issue of using it, and maintaining education levels (for modern mostly). It really requires only a pale shadow of what you need to innovate.

Adding to tech requires a host of other things, most of which are heavily influenced by the society in question. Among these are: contact with new ideas, availability of capital, limited levels of corruption, an innovative cast to society, and many other things we have talked about before.

It seems to me we may be making our modelling life harder, and getting skewed results by taking care of tech maintenance and innovation with the same flavor of RPs.

Thoughts?


[This message has been edited by Mark_Everson (edited February 25, 2000).]

[Richard Bruns]

This post continues Tech System 5.2 with an analysis of the Application Factor, as well as some discussion about technology tags.

Application Factor

After running the numbers on this, I have found that the current exponential model should be tweaked a little. The current equation works as follows:

Symbols:

T: This is the tech level of some specific tech. It may have a number after it when multiple techs are used (T1, T2).

h: This determines the effect that a technology has on the application it influences. It may have a number after it when multiple techs are used h1, h2). That number will correspond to a certain technology number.

R: This is the tech level required for an application. It may have a number after it when multiple techs are used (T1, T2). That number will correspond to a certain technology number.

L: This is the longevity of an application, a number between 0 and 10 that determines how long an application should be around before it will have to be replaced.

E: A factor that multiplies the power or effectiveness of an application.

Equations:

RTL = (h1*(T1-R1) + h2*(T2-R2) + ...)/(h1+h2+...)

E = (1+ L/10) ^ (RTL/10) when RTL is positive or zero.

E = (10+RTL)/10 when RTL is negative.

The RTL will be zero if all techs are at the required value, so E will be 1. After that, the application effectiveness rises based on the RTL and L. If L were equal to ten, then the E would rise just as fast as the tech level; the application would never become obsolete.

Let ka be 2^(RTL/10).

This system does not work well for lower L values. One thing that I think should happen is that the effectiveness of an application should initially rise slightly faster then the knowledge level (ka) increases. This simulates the fact that new things have a lot of room for improvement, and will improve quite a bit after they are introduced.

This exponential model does not allow for such improvement. In fact, E will always be lower than ka unless L is ten. This means that the ideal of diminishing returns will not be achieved. In fact, low L values will hardly ever produce any returns; E will always be about 1.

The dynamics of my old linear system worked very well for the period shortly after the tech was discovered. E rose more rapidly than ka at first, but soon got into diminishing returns. At ten tech levels above the invention of the application, E was equal to ka. At twenty tech levels above invention, E was 3 while ka was 4. At that point the application was considered obsolete, and a new thing would be invented to replace it. For tech levels below invention, the old system acted the same way as the current one does. The problem with that system was that it was not very flexible and did not consider longevity.

To get a better description of this system, look at the first post in the Technology System 5.1 thread.

I have found that the strengths of the two systems can be combined by literally adding them together. So:

E = (10+RTL)/10 + L/10 ^ (RTL/10) when RTL is positive or zero.

E = (10+RTL)/10 when RTL is negative.

My old system is a special case (L=0) of this new equation.

For values close to the invention point (R1, R2, . . .) the linear term predominates, producing the short term rise in E and then the diminishing returns. But in the long run, the exponential term and the L value have more effect. If L=10 there are no significant diminishing returns and E will always be slightly higher than ka.

To see how L affects this system, we can look at how it affects two points. The break-even point is defined as the RTL when E=ka. At that point, the application has the same value that it would have if it were rising at the same rate as the knowledge level. Before this point, the application effectiveness is greater ka to represent the rapid increase of the effectiveness of something after it is introduced.

The next point is the obsolescence point. At that RTL value, the E value is three-fourths of the ka value. This is about the time that a new application should appear to replace the old one. Note that this thing does not stop working at this point. In fact, it works better than it ever did before. But the rate of its increase is not a lot lower than the rate of tech increase. The thing has been improved about as much as it can, and a new application will be better than it is.

This chart shows how L affects the break-even point and the obsolescence point. B and O are in terms of the RTL.

L; B; O
10; never; never
9; 44.6; 70.46
8; 35.05; 49.76
7; 29.53; 41.14
6; 25.56; 35.76
5; 22.24; 31.86
4; 19.63; 28.77
3; 17.15; 26.19
2; 14.80; 23.59
1; 12.46; 21.90
0; 10; 20

As you can see, this allows for a wide range of application lifetimes while keeping good diminishing returns dynamics.

Technology Tags:

So far, each technology has the following numbers attached to it:

Ts, the tech level it starts at.
m, the effectiveness of RP’s in advancing the technology.
c, the percentage of the knowledge (k) that can be lost in one turn. This determines the difficulty of tech upkeep.
T1 and v1, T2 and v2, . . ., the vital technologies that affect this technology, and the numbers that determine how much they affect it.
T1 and h1, T2 and h2, . . ., the helper technologies that affect this technology, and the numbers that determine how much they affect it.

These numbers are all that are needed to determine the mathematics that drive the tech advancement, but they are not enough to describe the technology from a player interface or AI perspective. To describe the technology’s primary effects and usefulness, tags will have to be added to the technology.

These tags will correspond to the things that need to be done in the civilization. I can think of the following tags:

Cash Flow
Control
Exploration / Movement
Food
Happiness
Health
Infrastructure
Military
Production
Pure Science
Standard of Living

Obviously this list will have to be altered, but those work for a start.

Each technology will be labeled with all of the tags with a number attached to each tag. That number tells how important that tech is to that activities related to that tag. Zero would mean useless and 10 would mean that the tech is extremely useful.

Let this number be called Z. Z stands for, “I’ve already used up all the good letters so I’m picking something more or less at random.”

A player who really doesn’t want to mess with the tech tree can simply order cash put into one of those tags. The research will be divided among the technologies based on Z values, with higher numbered tech getting more of the RP’s.

I don’t know how exactly how multiplayer games will work, but if there is a time limit and you have to deal with some other crisis, then this would be a big help.

These tags would also make the AI smarter and easier to program. Normally, the AI would just make everything grow about the same rate. But if there is a problem, then the computer can invest in technologies based on the Z values for the tag that the computer needs to improve. So if the computer is having chronic problems with rebellious provinces, it invests in Happiness and Control technologies.

Tags have another purpose. Aside from determining where RP’s should go, they also define where they came from. Certain activities will generate tagged RP’s that are automatically spent based on the Z value attached to that tag. For example, an agricultural province would generate RP’s that are tagged for Food. Those RP’s are assigned to technologies with the Food tag.

A preliminary idea for distribution or RP’s would be to give each tech a percentage of the total RP spent as follows:

For every tech, raise 2 to the power of Z/2 and then subtract one. Call this the Y value.

Add up all of these values to find the X value.

Each tech gets a percentage of the total RP’s spent equal to Y / X.

The only problem with this that I can think of is that it might use up too much processor time. If so, is there anyone who knows what mathematical operations take the least amount of time to process? I could try to redo the formula to use those.

[This message has been edited by Richard Bruns (edited February 25, 2000).]

[Richard Bruns]

I forgot to include this before:

When splitting RP's among tagged techs, some preference should be given to techs that are lagging behind. Not only will these techs be easier to gain and keep up, but they are also the techs that are probably holding things back.

So there should be a temporary adjustment of the Z term for techs that are behind. If Z is not zero, then it should be increased by one for every five tech levels that the tech is behind the average tech level of your techs with nonzero Z values for that tag.

[Richard Bruns]

Mark: I'll think about your relative helper tech influence idea and see what I can come up with. It seems like it should work.

I'd have to disagree with you about the dichotomy between upkeep and gaining tech. All of the things that you mentioned for innovation also play a part in upkeep. And don't forgat that tech gain is not necessarily innovation. A large part of it is a simple improvement on something currently being used. Constant use and improvement is the main thing that makes tech rise IMO.

Consider Medieval Europe. That had little trade or economic activity and were not an educated society, and yet there was a constant and steady improvement in farming, manufacture, and many other skills during this time period. The techs rose simply because they used them a lot.

And as a practical matter, I think that having two different types of research would be more trouble and confusion than it is worth.

[Mark_Everson]

Richard:

LOL on the 'Z' comment

I think the tag stuff looks good! I think we might possibly need a sub-tag system under it, especially for the AI. But what you have will definitely be sufficient for demo 5. I'm sure one of the other model leaders will speak up if something big has been missed.

I hate to be a wet blanket, but there is a big problem with your effectiveness equation:
E = (10+RTL)/10 + L/10 ^ (RTL/10) when RTL is positive or zero.
The trouble is for nonzero L when RTL equal 0, you get E = 2 instead of 1 as it should be! I'm not too worried about this, because I think we can come up with a decent formula using a polynomial fit or something if worse comes to worse.

Any thoughts on the "relative helper tech influence idea"? I had one that I think I'll pass on and see what you think about it. I'll go back to the example that I used in my immediately preceding post. So we have Economics which depends on Math and Social Sciences. My idea is to just to use a simple formula similar to the old effectiveness formula (your earliest one) to get the Current Difficulty of researching a technology. The Current Difficulty formula will oscillate to both sides of zero, and is on the same basic scale (percent in technology level) as the RTL formula.

This is Not well thought out. It is more in the way of a thought starter. I may not have covered all the bases, but I think this is enough to get the general idea across.

So we would have something like the helper tech modifier to research progress is...
H = (10+ CD)/10
there would be a minimum value of H of something like 0.05 to stop this expression from going negative.

Symbols:
T: This is the tech level of some specific tech. It may have a number after it when multiple techs are used (T1, T2).
h: This determines the effect that a technology has on the application it influences. It may have a number after it when multiple techs are used (h1, h2). That number will correspond to a certain technology number.
O: This is the tech level offset applied to a particular helper tech. It may have a number after it when multiple techs are used (O1, O2). When the offset is positive it means that the particular helper tech involved doesn't require as high a level of achievement as the technology that is currently being researched.
CD: the Current Difficulty level for a technology.

We will probably need some modifications if we go with this since I haven't thought out in detail all the changes necessary to implement it.

CD = (h1*(T1 +O1-T) + (h2*(T2 +O2-T) +...)/(h1+h2+...) where T is the level of the technology being researched, in this case Economics

So let's make up some values and see what effect this formula has. So in contributing to economics we have:
Math: O1 = + 10; h1 = 2
Social Sciences: O2 = +0; h2 = 5
so in words... social sciences is generally a more important helper technology (strength = 5 vs. 2) for economics. Because of the + 10 in the offset Math can be a positive contributor to social science even if it is behind the current level of social science. It will be a positive contributor until it falls ten points below the relevant Economics level. If it gets even worse than that will start seriously hurting your ability to research Economics. So let's see what the CD looks like for my previous example where math should holdback economics progress.

Current levels
Econ 60%
Math 12%
Social Sciences 60%

If you plug in all the numbers you get CD = - 10 using the parameters above. This level would cause a severe retarding effect on progress in economics. The nominal value of H is zero, and it would default to whatever the minimum value we pick is. So in this case we get the desired result that when mathematics is sufficiently bad, economics can only get so far. You would probably never even get to the illustrated case, because extreme diminishing returns on research invested into Economics would show up around Economics 50% unless the Social Sciences were so good that they compensated for the math being lousy.

If Math were 50%, then CD = 0, the helper technologies neither help nor hinder in the research of Economics (H = 1).

Let me know what you think!

[This message has been edited by Mark_Everson (edited February 26, 2000).]