A brief problem I've been working on.

[Kaos]

So yes, I am a nerd. I am working on a role playing engine, where some of the key structure of my system is to work with the hardness of known elements.
Unfortunately, the only system I know to be widely accepted by this practice is Moh's hardness scale.
The problem with Moh's scale is that it isn't linear. 10 is four times as hard as 9, where 2 isn't even close to twice as hard as 1.
I found some hinting at an absolute formula for mineral hardness, and found values for moh's scale. The problem I have, is that there is no conversion formula listed.
Could anyone help me with this?

Conversion theorum = A(M)
where M = the Moh's hardness and A(M) is the absolute hardness value.
A(1) = 1
A(2) = 3
A(3) = 9
A(4) = 21
A(5) = 48
A(6) = 72
A(7) = 100
A(8) = 200
A(9) = 400
A(10) = 1600

I thought that I might end up having to use a nonic or decic equation to solve this, but if other people have simpler ways I am more than open to hearing them.

[MinionJoe]

I dropped the data into Excel and did a quick and dirty exponential trendline and here's what it came up with:



An equation of y=0.767e^(0.7348*x) where x is Moh's hardness factor is pretty close.

For something a little more accurate, you'll probably have to buy some curve fitting software.

http://www.uniphiz.com/best-fit.htm

[Kaos]

I was wondering about that. I ran it through my graphing calculator several times and wound up with something much closer, but still not perfect.
Ah well, I guess I just keep plugging away until I find something that works.

[ThrowSomething]

I doubt polynomials have "formulas" above the fourth degree. Although, you could probably run linearly with a known ratio. Perhaps A(m+m/1-F) where F is say maybe Fibonacci or some other Golden rule to brute force linearity by parallel means. I'm guessing your scale is 2d? If not, looks like you left out some values in your post citing a need to work at such levels to achieve linearity. Getting linear can include exponential rates...by I've seen most scales top out as a constant,(or bottom out if negative) like apparent flat lining, unless there's that missing data to jump to the 3rd degree. You mentioned the ninth and tenth like 'holy-sh*t!... is this dude constructing the most diabolical algorythm in role playing or what! lol...

What language is this 'engine' written in...? If your heart is set at using the moh scale, perhaps have the script sort with regex, noticing the values of every set of 3 numbers' first and second digits blah blah....

Need more info....

Sounds interesting...

[Kaos]

Actually, it's simply a pen and paper game. I was developing it so that, essentially, anything from real life could be seamlessly integrated into the game. Using formulas for acceleration, gravitational velocity, hardness, malleability and others, my ultimate goal is to create a game which could be modified by almost anyone, and easily.
If I have a formula for hardness that can transfer any element measured in Moh's hardness (say about a few thousand - I've seen some of the data tables), I can, essentially, make it so that it never gets outdated. Until Moh's hardness is antiquated, the game can continue to evolve.

I'm not expecting to finish this overnight, but I want to work on it for years and see what I come up with. I've made role playing games in the past, and I want to seriously test my mettle.

As far as the ninth and tenth degree, well I was thinking to start from the top and work my way down. If there is absolutely no way to make a perfectly linear graph (that I can see), by putting in changes at 9 or 10 vertexes, I can essentially mimic the graph perfectly (Because for every quadratic formula, you have changes at two points, nonic formulas would be at 9.)

Also, a quick note.
Apparently there are conflicting views on what is truly the absolute value of these. Some scales use what I listed above, but others use this scale.

Conversion theorum = A(M)
where M = the Moh's hardness and A(M) is the absolute hardness value.
A(1) = 1
A(2) = 2
A(3) = 9
A(4) = 21
A(5) = 48
A(6) = 72
A(7) = 100
A(8) = 200
A(9) = 400
A(10) = 1500

Because of this, I'm simply looking for a scale that works somewhere between these two ranges

[arnie532]

Although this does not neccisarily relate to your problem although I can try and do what I can I just wanted to know you said you made RPGs before is there any way we could see some or even try some

[Davo]

I'd like to try them too, no matter how bad you thought they were.

[Kaos]

Okay, well as I said they are, in fact, pen and paper games. If you want to start messing around in some of them, I could start up a topic here and begin a casual game

[Davo]

i say give it a shot. thats what this forum is for.

[Kaos]

All right, I'll try to get a topic up over the weekend.

[ThrowSomething]

""Don't overlook the obvious!""


dammit...

[Kaos]

Life has been busy. I'll set up a topic for the game tonight or tomorrow.