In the early part of his book, Liber Kaos, Peter Carroll talks about the three formulas that are used in Chaos. For those of you who have the book, it starts at the bottom of page 40 and continues through the remainder of Chapter 1.

When I wrote my last post, I made my example of how little I could affect things if the probability of it happening was too low. Well, I was having a problem with his formula on trying to lower the odds of an event happening in the first place, so I had no prayer of using his ideas on dual casting in some situations. I could work the math by hand, but my spreadsheet would never agree with me, and it wouldn’t graph correctly to Carroll’s versions.

I have spent the last few evenings figuring out where I was having problems within the spreadsheet, and finally hit the solution: It was doing the order of operations wrong. Really? Excel, iWork, and Open Office all agree on the wrong damned number? I found it ridiculous, but I added the proper parentheses to force it into the proper order of operations.

The good news is, if you’re good at casting ‘for’ something to happen and you aren’t as skilled at energy ‘against’ something happening, you’re in luck; you can still help your overall success rate by dual casting on the same target. The same is true for the opposite situation.

The book only made a mention of dual casting:

When conflicting acts of magic are performed to both increase and decrease the probability of an event occurring by chance, the respective M must be subtracted from each other and the remaining part of the largest factor substituted in the appropriate equation. For example M = 0.6 for and M = 0.4 against is assessed by entering M = 0.2 in equation two. M = 0.55 for and M = 0.89 against is evaluated by entering M = 0.34 in equation three.

That’s all we’re really given to work with. So, I figured it out. Based on his first example of M = .02, you put that into equation two, and then you use that answer for the probability in equation three. I know, many of you may have figured it out faster than me, but I’m just like that sometimes. For those of you hoping to wrap your head around it, I hope that was enough of an explanation to get you by. If not, please feel free to leave a comment or email me and I’ll do what I can.

For those of you who don’t care about understanding the math, or would like to dissect the way I do it (I can be wrong once every year or two), I have created a spreadsheet in an Open Office format that will do all the calculations for you. I chose Open Office because you can get it for (almost) every platform, it’s free, and it’s done by Oracle, so you know it’s not virus infected junk.

For those of you who don’t have the book, here are what P.Carroll considers to be the three equations of magic, and these are what my spreadsheet is based on:

The three equations of magic:

M = GL(1-A)(1-R)

P_{M}=P+(1-P)M^{1/P}

P_{M}=P-PM^{1/(1-P)}

Superscript looks terrible on this set/font/whatever. On the last two equations, the parts after the M are superscript.

You will have to use a bunch of parentheses, as I mentioned above, to make it work if you want to create a spreadsheet from scratch, and it makes the formulas kind of hard to read. The letters in the formulas are explained in my last post.

The only thing that I found was ‘wrong’ with something, is that the ‘magic aimed at decreasing’ graph (p. 50) didn’t quite match mine, but I wouldn’t blame him for making it look just like the other one to make a point about the magic being inverted and similar. My graph still has the same flow as his, I just think whomever drew it did it that way just for consistency within the reader’s mind.

The spreadsheet will also be placed under the ‘Resources’ page, so if you lose it, you don’t have to hunt for this specific post.

I hope everyone enjoys a bit of the math, and that it helps you get a more clear picture of how hard/easy it will be to change your reality.

IO CHAOS!