The following equations are the result of my attempts to find a way to quantify controversiality. However, I instead found a way to measure "member impact" and "the probability of topic metamorphosis".

P= member's posts that were positive with respect to the factor under examination
N= member's posts that were negative with respect to the factor under examination
T= total posts by member
I = impact

[(P/T)-(1/N)] - [(N/T)-(1/P)] = I

This is not just random letters on a page. The basis of this equation is not the number of posts you have - it's the RATIO of the posts. Positive to negative. P/T is the absolute positivity of a member. N/T is the absolute negativity of a member. However, because he/she will likely have some posts of the other type, this value must be corrected by (1/N) or (1/P), respectively. I call this the Webboard Inertia Coefficient, or W. (A member can't have unlimited influence, because there are so many of us and not all of us know him/her. That's why it's 1 over the number, instead of the number itself.) If I is positive, the member's post has a net positivity. If I is negative, the post has a net negativity. The "factor under examination" may be attitude (flame or help), intelligence, (stupid or smart) or sanity (crazy or not).

Why is this important? See the next equation:

M=I(s)

where

M = the probability of a topic metamorphosing

I(s) = the sum of the impacts of all the posts in the topic.

As the impacts are added, positive and negative, M may approach + or - 1. As a topic approaches these values, xtal's Trigger (xtal's Zeroth Law) may leap into action. This Law (The most benign comment has the capability to spontaneously invert an intelligent topic into an asinine one, or vice versa) should actually be rephrased as "positive" or "negative" instead of "intelligent" or "asinine". The Law is still valid - it's just broader than xtal himself first realized. If a member's topic pushes the value of I(s) past a critical point (Guapo's Impact Maximum), the topic will metamorphose.

However, we must remember that Webboard Mechanics deals with probabilities. A given post may well change a topic. But it may not. Similarly, it may metamorphose a topic at a low or a high probability.

Ergo, "controversiality" is not the factor we seek. Rather, it is ONE of the factors we seek. "Impact" or "influence" is a better term for quantification.

Probability is a good science when the sample size is sufficiently large. However, if a member has a very small number of posts, it isn't always easy to predict the effects of his/her posts. However, Guapo's Impact Equation can be applied to posts in a topic.

P= topic's posts that were positive with respect to the factor under examination
N= topic's posts that were negative with respect to the factor under examination
T= total posts in topic
Q= Metamorphosis Probability

[(P/T)-(1/N)] - [(N/T)-(1/P)] = Q

Again, as Q approaches + or - 1 and passes Guapo's Impact Maximum, the Zeroth Law Trigger may act, metamorphosing the topic.

Notes on the Impact Equations

If a topic, when started, is already positive or crazy or whatever, it cannot metamorphose to be more positive or more crazy or more whatever. It can only go in another direction. Down or left or right.

U = number of neutral posts
J = Topic Insulation
T = Number of posts in topic

J = (1/U)*T

Divide 1 by the number of posts in the topic that are insulating (neither positive or negative) and multiply that by the total posts in the topic. This insulates the topic from radical changes. When used with the Impact Equations, any change in the net positivity or negativity must first subtract from the topic insulation. Then and only then can the topic begin to add or subtract negativity. This is why the topics featured in this law do not radically change, degenerate, or metamorphose.

A Note on Guapo's Impact Equation With Respect to Captain Scurvy's Law

P= member's posts that were positive with respect to the factor under examination
N= member's posts that were negative with respect to the factor under examination
T= total posts by member
I = impact

[(P/T)-(1/N)] - [(N/T)-(1/P)] = I

The "factors" tested in this equation can be extended to include "likability". Ergo, posts that make you like a member/moderator will be positive, and posts that make you hate a member/moderator are negative. Substituting these values in the Impact Equation will give you a value for the member/moderator's influence: V. (ergo, how much you are likely to listen to him). If you like a member a lot, you will likely listen to his opinion. If you don't like a member a lot or at all, his influence will be minimal/nonexistent. Influence (V) can be less than zero - after all, if you hate someone enough, you might go and do the opposite of what he/she says just to spite him/her. xtal's Zeroth Law may be applicable here - however, because the actions of single individuals are hard to predict using probability, it tends to be somewhat unreliable in this case.

"Controversiality" as tested for in the Impact Equations is an absolute probability, not a relative thing. There is a certain probability that something is considered to be "controversial" or not.

A webboard can "decide" whether a topic is "controversial" or not (based on the xtal Trigger and the topics I value) - but the end result is: if they do not consider a topic controversial, then they will either:

a) not reply to it

or

b) post Neutral (U) posts. They do not approve or disapprove of it.

This is why effects may seem to be "diluted" - these "insulating" posts keep a topic stable. Therefore OctoberFost's First Law is subject to the Topic Insulation Equation, and Webboard Mechanics has a effect on all webboards.