23-02-2000 03:54									#61
	Lose 30 kilos (of popups)

Richard:

Engineering...
uses a lot of diverse things, but there are also many approaches, and a "mindset" that all the engineering fields Do have in common. Anyway, my recommendation is to use engineering as a basic "technology". Doing it this way just feels better to me than the way you have it. That said, do it whichever way you want, and I'll work with it.

Agriculture/Farming...
you are right, these are redundant. The reason I put them in that way is my personal picture that all the things that have real quantifiable "area" effects for the player should show up on level 3. Perhaps we should just lose Agriculture as a level 2 Tech. The problem with splitting it into more specific skills, is that if we have five things for agriculture on level 3,then I would need 50 to do the whole economic model, which is way too many. That's also why I made Improved Crops an application, because otherwise we will quickly overload the space in level 3 IMO. You guys are in charge, but I am with Axi, if there is too much stuff the player needs to deal with than the game will become a nightmare. Anyway, one of the reasons I took this on is so I could use the economic area as a guinea pig for how the technology model structure actually works.

Every level 3 needs an application...
you are right , I somehow got into that bad habit! You are right that Herding and other level 3 things do not need further elaboration in level 4.

The main message I get from your post, is that you picture an awful lot of things being in level 3. Obviously we have a different perspective on the game function of level 3, or at least the gameplay consequences of having 200 + things in level 3. I think something like 100 is the Absolute Maximum of things that we can have the player be expected to deal with. It's probably already too many... I'm just trying to picture an interface that allows you to deal with more than 100 discrete things, and having real trouble seeing how it can work without having multiple layers of stuff for the player to burrow through. A number like 100,already requires at least a too-level menu system, with the first level containing to attend major areas, and the second level allowing these ten major areas to split down the into 10 subdivisions. I think we need to reserve level 3, or Some subset of the model, to allow the player reasonably fine control over the general areas that are important. And like Axi said, these should be things that have a substantial effect on the models, or they are pointless clutter.

So, for instance, the reason I just want a single Farming technology at level 3 is so that when the player wants more food from the land they can just dump money and resources into it. The player shouldn't need to worry as to whether what is needed is better irrigation techniques, improved crop species, or better farm implements. Right now we already have three level 3 things pertaining to food production: Farming, Fishing, and Herding. I think that is his much detail as we can spare out of a potential maximum of 100 technologies. I would be significantly happier if we could get it down to 50!

If you and LGJ could please respond on this vitally important issue (to me anyway) as soon as possible I would appreciate it. If you have an alternative view of the interface, and how the player is actually supposed to wade through the enormous amount of detail you want to throw at them, then I would like to hear it stated explicitly. I agree that for the people that are really into the details, there is the level 4 stuff that they can romp around in. They are by definition willing to wade through some more menus to get the ultimate in fine control. I'm talking about what the average player who just wants some broad management of technology, with an occasional specific tweak, should do.

	23-02-2000 04:46									#62
	Support Apolyton buy from Amazon

Axi: That is one reason we are asking the model leaders what they want. Also playtesting is really the only way to fine tune this to the extent ur looking for, but if u have any current ideas let me know.

Mark: I posted above that 100 is a reasonable goal to shoot for, however we shouldn't be constrained by a maximum number if we need more, nor should we reach that number if we don't.

Also we shouldn't have something like farming if we have agriculture, only more specific aspects. Also something like "improved crops" i'm not really for unless that's simply a coding name because i don't want any arbitrary names for anything because "improved" is very subjective.
[This message has been edited by Lord God Jinnai (edited February 22, 2000).]

	23-02-2000 05:12									#63
	Support Apolyton, buy Call to Power 2

Axi: That is what I have been saying all along. Level 3 belongs to the model leaders; they tell us what is needed and we put it in. We will probably have to trim their lists a bit, but they will probably have a use in mind for everything they will give us.

Mark:

The Construction basic tech could be expanded to Construction and Engineering. Would that work?

You assume that the interface will simply be a list of all the Level 3 techs. I agree that if we choose to do this, then the interface will be a mess. But I thought that the techs would be organized like the folders on a hard drive, with Level 1 and 2 techs serving as the big folders that organize things.

The first layer of the interface is a list of the Level 1 techs. If you choose to do so, you can allocate RP to that overall tech and it will be split among all of the sub-techs. Or, you can choose to be more specific. You can expand the tech 'folder' and look at its contents, which are Level 2 techs. Here you have the same option. You can allocate RP to an entire Level 2 tech, which means that all Level 3 techs under that tech are supported. So if you simply wanted to make farms better, you put a lot into the Level 2 tech of Agriculture. If you wanted to be more specific, you can expend this tech 'folder', look at the Level 3 techs, and deal with them individually.

Note that when you allocate RP to a broad group you are not improving the Level 1 and 2 techs. You are telling the RP's to be split among all of the Level 3 techs that the the Level 1 and 2 techs are vital techs for. Whenever you get the option to support the Level 1 and 2 techs, the research is split among those as well.

There are some Level 2 techs that are not under a specific Level 1 tech. If supported by multiple Level 1 techs, they are placed in each 'folder.' If they are not supported by any Level 1 tech, they would be placed with the Level 1 techs, in the first organization window.

This isn't a definite proposal; it is just an idea to show how the techs could be organized to ease the player interface. An alternate organization scheme would be to organize them based on the things they are useful for, like Food or Production or Happiness.

Anyway, as I see it the player will easily be able to play an entire game without messing with the tech tree more than a couple times. Most RP's are assigned automatically; the player will not be making tech decisions every few turns.

For a while now I have been working on Tech System 5.2. I have been looking at basic dynamics of the system and crunching a lot of numbers and formulas. Issues regarding the interface and RP generation are also in there. As I haven't yet done any work on the actual tech chart, I will post 5.2 in two parts. The first will have the system analysis and the second will have the chart with (hopefully) everyone's techs included. The first post should be done in a couple days. The second will have to wait on more input from model leaders.

	23-02-2000 06:17									#64
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

Richard
The chart being developed by you is going to be level 1,2,3, Yes? We can then debate that list and get it sorted.

The list of applications (lv 4) can be developed over more time. The full application list will have numerous applications and will take quite a while to beat into shape. Also most customisation of the system by users, would involve the application level.

I am looking forward to both parts of the model.

Paul Krenske.

	23-02-2000 06:40									#65
	Support Apolyton, buy Alpha Centauri

We are going to make a chart with three tech levels and applciations, but that is on the back burner for now as I concentrate on the actual system dynamics. I need techs from model leaders before I can compile the actual chart for review. And this draft will have many Level 4 techs, at least the ones that will ba used in ancient times.

	23-02-2000 08:05									#66
	Increase Your PM Length

LGJ:

I know 100 is an arbitrary goal. But my point is if we don't keep a lid on things and it gets to 250, I don't think it will be any fun. What I'm trying to do is stop things from blowing up to a ridiculous level before we invest a lot of time in figuring out which level 4 applications hookup to which other technologies.

On the "Improved Crops" it's not arbitrary, but there is a continual advancement in food crops, and to not have it in there simply because we don't want to name every single strain doesn't seem to be the right approach to me.

Richard:

Well, construction and engineering is better than nothing... and a decent compromise.

Personally, I strongly feel that the interface needs to be done at the function level. Nobody will want to drill down through chemistry to get to firearms. That will very quickly drive people crazy IMO. Your folder should be "military", "economics" etc. IMO.

quote: Note that when you allocate RP to a broad group you are not improving the Level 1 and 2 techs. You are telling the RP's to be split among all of the Level 3 techs that the the Level 1 and 2 techs are vital techs for. Whenever you get the option to support the Level 1 and 2 techs, the research is split among those as well.

sorry, you lost me... the player Has to be able to invest in Physics in the modern age. Modern governments actually do that. And it's very important. In the pre-modern world I don't think you should be able to invest in level one or two techs at all in a realistic system. But for gameplay purposes we may have to break from realism. If investing in level 1 in 2 turns out to be impossible to do well I don't have any problem with ditching reality, but if it's easy to do Clash should support what happens in the real world. Maybe I misunderstood you here.

quote: Anyway, as I see it the player will easily be able to play an entire game without messing with the tech tree more than a couple times. Most RP's are assigned automatically; the player will not be making tech decisions every few turns.

Well I think a player Could play a game without messing with the tech tree more than a few times, but most will want more than that. Being in control of the technological progression of one's civilization is one of the big attractions of a civ-type game! At least for me. And if someone who is interested in technology can't do much of anything, we are going to lose Huge Numbers of players. This is one place where I think we really need to break with realism. Unless the player selects, through a realism slider, that they want to be prevented from doing unhistorical things with the technology, I think we Need to let them. I am firmly convinced that the interface needs to be able to support tweaking on a "once every ten turns" basis or so without it being a huge pain. For instance every time a war comes along I can see generally pacifistic governments really sinking money into military research in the modern world. Those transitions will happen fairly frequently.


Is your next version close enough that I should wait before going further on the economic model? Please let me know.

	23-02-2000 12:25									#67
	Tired of ads?

What do u mean by historically accuracte?

Also esp in modern times most civ governments didn't develope much in the way of technology, except for perhaps military purposes, but only then if they were at war/thought they might be at war. If not they didn't. And a pacificst type people wouldn't sink money into military, although it will increase. Even so most would be in defenive technology, not offensive (FE walls). I really think that allowing the player to have a lot of control in this time period is wrong. I'm not saying none, just not too much. (IE the free RPs which can be placed anywhere will be much more scarce than modern times). If they player wants to invest more in another area he'd have to find other ways to subtly change this. Remember even in this time period, even the God-Kings didn't have as much influence as some of the governemnts of today, such as communism, which pretty much controls every aspect of everyones life. No one could do that back then and without that power one cannot control exactly how techs advance.

BTW mark if we use a system like what Rich says for the tech levels, so long as we don't have 1000 level 3 techs the number shouldn't be a problem, reguardless of how they are organised. I also like his method with a few changes:

Lvl 2 techs w/o prereq could be listed under a Misc category and one couldn't assign RP to that lvl 1 category, but only its lvl 2 sections and beyond.

A player can have a special quick referances to certain level 3 techs they might use the most these would be with the lvl 1 techs, but kinda with a devider so the player knew it wasn't lvl 1 techs. Or i could be under a "Most used" category

	23-02-2000 19:56									#68
	Suffering from ads?

LGJ:

On the player being able to influence tech, I didn't mean they should get control of the RPs produced by the people. I very poorly stated my position. What I mean is that the player should be able to invest state resources (basically cash) much more than is historically accurate.

In terms of folders based on Level 1 techs...
That is more like a 9th-grade project than a game! A Game has an interface that allows the player quickly and intuitively to change what they want. I'd have no problem with an Alternative that allows starting with the Biology folder, etc. But we Must have the main tech interface be based on game function IMO.

	23-02-2000 21:31									#69
	Help yourself to an AD-FREE life

---
Mark Everson:

sorry, you lost me... the player Has to be able to invest in Physics in the modern age. Modern governments actually do that. And it's very important. In the pre-modern world I don't think you should be able to invest in level one or two techs at all in a realistic system.
---
That is exactly what I said. In pre-medern times, giving cash to Agriculture does not improve the Level 2 tech, it simply supports all of the Level 3 techs under Agriculture. In modern times, it would also raise the Level 2 tech level.
---
Being in control of the technological progression of one's civilization is one of the big attractions of a civ-type game! At least for me.
---
Most players I know don't care how they get advancements; they simply want to get everything. Things will all advance at about the same rate, so they will get the tech they want by concentrating on expanding the empire and improving infrastructure. The ability to chage things is still there, but my point is that a player will never be forced to go into the guts of the tree. They can, but they don't have to.

You are right about going through Level 1 techs. That would be an unnecessary layer. But currently, all of the Level 2 techs correspond to some game function like Agriculture, Architecture, Combat Engineering, Explosives, or Navigation. I think that an interface designed around the Level 2 techs would be intuitive and reasonable.

There are about 50 Level 2 techs. We could just list them, or we could put them in groups based on broader game function. Each Level 2 tech could have up to 10 Level 3 tech under it, but the average will be about two or three.

For example, the Level 2 tech Agriculture would have Level 3 techs of Animal Husbandry, Crop Plants, Farm Landscaping, and Farm Machines and Tools. The Animal Husbandry tech would determine the food producing ability of your nomad provinces, and to a lesser extent your normal farms. The Crop Plants tech would have Crop Rotation as an application and it would have a direct effect on farm productivity. The Farm Landscaping would have Irrigation, Drainage, Terraces, and Contour Plowing as applications. The Farm Machines would have the various plows and advanced machines like the reaper.

If you are a tech oriented person you can have fun with this detail, but if you are in a hurry you can simply put cash into the big category of Architecture and the money will be spread among the Level 3 techs based on some algorithm.

For another example, if you don't want to worry about the details of Navigation, then you simply stuff cash into that category, like Prince Henry of Portugal did. The RP will be split among all Level 3 techs that have Navigation as a vital tech. If you are a tech oriented person then you can expand the category and tweak the Level 3 techs under Navigation.

The next version of the tech system is 100% compatible with the current tech lists. The only difference is the equations that make the computer crunch the numbers for tech growth, helper techs, and the application factors. LGJ wanted to review it first, so I'll get his comments and then post it.
[This message has been edited by Richard Bruns (edited February 23, 2000).]

	24-02-2000 10:27									#70
	Browse Apolyton AD-FREE

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.

	24-02-2000 02:26									#71
	Support Apolyton buy from Amazon

Mark:
---
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.
---
I must have missed something. Where did you propose an interface plan? I didn't know there was any plan; I had been simply been tossing out ideas. I never meant to make a seroius proposal, and I said as much. I just saw that everyone was assuming that the interface would be a list of all the level 3 techs, and I wanted to consider other options.

What I was describing was only meant for Level 3 techs that fit into a larger category. I think I was also unconsciously using Axi's tree, where everything fits into nice categories.

Also, I assumed that we would have the tech chart in the reference materials and people would be somewhat familiar with that, so an organization system based on the chart would be the most natural thing. If a person wanted to figure out how to acquire something, then they would look in the chart and see what techs they would have to build so that they would get that thing. Once they did that, they would be familiar with the requirements and would know where to go to deal with the thing after they were created.

You are right about the path for some construction processes being convoluted. These would have to be put in seperate categories. But for most areas of skill, the Level 2 techs are the same as the thing that needs to be helped.

	24-02-2000 02:40									#72
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

Mark:

Airplanes--- Fluid Dynamics 35%, Engines 50%
------
In mine example Airplanes would be linked under aircraft or air transportation for level 2 (airplanes being level 3), and level one would be transportation in general. Military section may also have some related level 3 and 4 stuff that is appropraite to it, but prob not since Military developement isn't a type of research/tech, its the application of those techs.

I think we should go by the easiest to do interface right now and see where it needs tweeking from there.

	24-02-2000 03:45									#73
	Increase Your PM Length

Richard:

My interface plan, as far as it got...

quote: posted February 03, 2000 21:35 I picture the interface as being run at the Specific tech (3) level. The player IMO, generally doesn't really give a damn about Physics or Economics, they want the stuff that will allow them to get applications. In fact I really hated the new idea from both a player, and AI perspective, until it occurred to me that the management should really be done at the Specific Tech level. After that, it seemed just fine! I do like the educational aspect of knowing what the foundations are for a specific application. But making the player drill down endlessly through menus to exert some fine control on the technology process seems like a losing idea to me. The picture I have is that the player can be presented with many Specific Techs at the same time coded in "traffic light" fashion. The green ones are ones that could give you immediate benefit in terms of applications. When you put resources into one of these the research points would (Player option) go up levels to push along the higher techs that are needed, and also trickle-down into specific applications that are attainable. This is basically a pretty straight adaptation of the idea I presented in my post around 1300 today. When the specific tech is coded yellow, you are close to being able to use some applications in, but not quite there yet. In this case research points that you put into it would go mainly up levels to further the basic technologies that this Specific Tech relies upon. When it gets practical to actually get applications out of it, it would turn green. Finally, the red ones (which might or might not be shown) would be very far from practicality. If you decided to put resources into these the resources would be directed completely "upwards" to build the foundations that will eventually result in this Specific Tech coming to fruition.

	24-02-2000 05:41									#74
	Lose 30 kilos (of popups)

Mark:
---
Remember Level 3 IMO should Not be the Fine-Control level. That is the specific apps.
---
I don't know what you are thinking of; I have explicitly stated that applications should not be micromanaged. As I imagined the system there is nothing that you can do to control applications, except for changing the Level 3 tech levels. I think that managing all of the applications individually would be a horror; almost as bad as a standard tech tree. The application levels depend solely on the Application Factor equation.

For the reference materials, I envision a hyperlinked help file, not a paper chart. The Level 3 techs would be listed alphabetically, and if you click on one, then you get its description, requirements, effects, and applications. There would also be a diagram showing the connections between the Level 1 and 2 techs.

Another thing that would be great is a right-click for help system. This is an enormous asset. If you need info about something, you right-click to get a little window with help or reference info. If this is possible, it would make the game a lot easier to play.

We should be able to do well with a 2-step tech interface. The first thing is what you want to do, which in most cases will be the Level 2 tech. For things like airplanes we make new categories. The second step is the Level 3 techs. When I compile the tree I will try to include an interface based on player needs. Or, you could do the interface if you think I would foul it up.

Also, why would changing the player interface make the AI harder to program? I assume that for AI purposes, every tech will have a tag, like Hrafnkell proposed. This tag tells the computer what it is most useful for. In normal situations, the computer just builds everything equally. This shouldn't be affected by the thing the player uses to interact with techs.

Speaking of tags, we could make them an option for players. Could there be menu that allows players to spread RP's among all techs with a certain tag?

By the way, what do you think of the Level 3 tech list I had for Agriculture?

	24-02-2000 06:28									#75
	Remove this text

Tags... thats a great idea. It gets around all these problems cause each model lead can pick the most important things. I guess that would remove the level 3 restrictions. Sounds cool, but I need to think about it. Will get back to you on the other stuff.

	24-02-2000 07:23									#76
	Support Apolyton buy from Amazon

It's not my idea; it was in that old tech thread you pointed us to. I had worked them into 5.2 as a suggestion even before this discussion.

	24-02-2000 08:08									#77
	Increase the size of your Attachments

Richard:

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

	25-02-2000 04:12									#78
	Avatar Enlargement: We've got the solution

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).]

	25-02-2000 06:10									#79
	Support Apolyton, buy Alpha Centauri

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

I see the reasoning and it appears quite sound.

	25-02-2000 06:49									#80
	Lose 30 kilos (of popups)

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?

	25-02-2000 07:29									#81
	Help yourself to an AD-FREE life

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?

	25-02-2000 07:43									#82
	Support Apolyton, buy GURPS/ Alpha Centauri

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.

	25-02-2000 09:29									#83
	Support Apolyton, pre-order Civilization IV

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...

	25-02-2000 10:22									#84
	Increase the size of your Attachments

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.

	25-02-2000 17:35									#85
	Avatar Enlargement: We've got the solution

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.

	25-02-2000 17:58									#86
	Support Apolyton buy from Amazon

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).]

	26-02-2000 10:48									#87
	Help yourself to an AD-FREE life

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.

	26-02-2000 04:02									#88
	Lose 30 kilos (of popups)

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).]

	26-02-2000 04:34									#89
	Support Apolyton, pre-order Civilization IV

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.

	27-02-2000 00:09									#90
	Tired of ads?

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).]