The Math Behind The Chaos

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)

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.


There are times when you can’t do a thing…

So, there is some healing magic I want to do really, really bad. It involves trying to helping an extended family member fight some severe mental illness. He is on a high dose of some “last chance “ medications, and the outlook is pretty grim.

I decided to dowse a bit to see which color I should start with to help give some guidance to my work. I got very strange information from my pendulum, and couldn’t make sense of it. So, being the resourceful fellow that I am, I decided to look into things a bit more with my cards. The outlook from the cards was very grim. I knew it was going to be a bad reading, as the depths of the mental illness he has rarely turns out well, but I didn’t realize that things had gone so far that I really couldn’t do anything about it.

So, I was faced with evaluating the probability of the the final outcome that I desire to the relationship of my magic ability and the natural probability of something happening. I remembered there were some rough guidelines in my Liber Kaos that could give you a good idea of how much influence you could have on any particular situation. It’s a fairly easy process; you just take the number M and use a table that also has the probabilities listed. It’s very similar to what we used in my statistics coursework, but without the annoying finite detail.

Here is the formula to find the value of M:

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

If you haven’t read the book, Liber Kaos, here is a quick rundown of what everything means:

* M = The Magic Factor
* G = Gnosis
* L = Magical Link
* A = Conscious aweareness
* R = Subconscious resistance

I’m not going to go into any more detail about the individual items. This entire portion of the book is quite lengthy and is better to read from the source than it is to get a quick synopsis.

So if we look at three different scenarios, as things can change a LOT if you are too close to the situation and other factors that tend to fluctuate, here is what the odds hypothetically look like.

Great Case Scenario

M = (0.9)(0.9)(1-.1)(1-.1)
So, M = 0.6561
Using a P of 20%:
That only changes the final probability to about 26.2%

Moderate Case Scenario

M = (0.8)(0.8)(1-.2)(1-.2)
In this case M = .4096
Using a P of 20%:
That changes the final probability a lackluster 20.8%

Bad Case Scenario

M = (0.7)(0.7)(1-.3)(1-.3)
In our worst case M = 0.2401
Using a P of 20%:
Our final outcome probability is still right around 20%

So, the odds are terrible, and my estimation of probability may be too high in this case. This means that I would have to be near perfect in my abilities to make any sizable difference. Now I’m quite proud of how far I’ve come with Chaos, but I am still honest with myself. Every time I learn something new, it shows me just how much more I have to learn. I have a couple cheats for Gnosis and Subconscious Resistance, but it still doesn’t make me perfect, and eventually I will have to rely on talent rather than many of the shortcuts that I employ at this time.

My wife is an optimist about these things and gives him a 50/50 shot at it. Although personal experience tells me it’s not that high. The increased odds don’t help my influence very much anyway. The moderate case scenario only raises it by 8%. Honestly, with how much I want him to get better and how close I am to this thing, somewhere around moderate is the best I will be able to realistically achieve. It’s hard to admit such things, but the last thing you want to do in magic is to overestimate your abilities. That’s how people get in serious trouble.

The outlook is grim. The dowsing, the cards, and the math all agree that I can’t do much, if anything, about it. The situation will just have to be what it is going to be, whether I like it or not. Carroll even says in his book that the math can make for a bleak outlook to aspiring magicians, and he was right. It’s not something I can do with my servitors, and it’s not something I can do for someone who is terribly mentally ill and would be resistant to anything that he knew was directed at him.

This situation doesn’t make me lose any faith in Chaos, it just makes me realize how important early action is, and how we can’t control every situation. There are some things I will be able to make a huge difference in, and there will be some situations that will just have to take their course…for now.