Imposssible II

 

Impossible

Impossible! But the world is full of zanies and fools
Who don't believe in sensible rules
And won't believe what sensible people say
And because these daft and dewy eyed dopes
Keep building up impossible hopes
Impossible things are happening every day!

I think the song means imPROBABLE.

If the odds are a million to one, not NO chance, that is the very definition of improbable but not impossible. This is because of how zero is treated and that relates to dominance and certainty. There are two types of zero, an absolute zero and a relative zero. An absolute zero is the absence of an absolute. A relative zero is the midpoint between two absolutes. They may look the same, but just as a human may not see any difference, while a computer makes a distinction between 0 and “0”, it is because of the absolute that there is a difference between dominance and certainty, although they may look the same.

Certainty is the probability of an outcome subtracted from 1. Dominance is when one party of an outcome is greater than any other party. Thus a zero as an absolute is different than a zero as a relative. If there are a positive integer number members of a group,  it can  only reflect certainty if the number of outcomes is also zero. The probability before any outcome is zero and the certainty is 100%. However the moment that there are any outcomes, the certainty by definition is always less than 100%, while the dominance is assured as long as one outcome for one party of the contest is greater than an other party of the same contest.

For example let’s assume that there are 9 members of a group, say the number of justices on the current supreme court. A 9-0 decision may appear certain but the moment the justices have made a decision it is no longer certain. That 9-0 decision is only one of 2⁹, 512, possible outcomes. The dominance of that 9-0 outcome is 100%, but the certainty is only 1-1/512=99.8%. An 8-1 decision also has a 100% dominance, but there are 9 possible outcomes that could give that 8-1 decision, so its certainty is 1-9/512, 98.24%. A 7-2 decision is still 100% dominant, but there are 36 possible outcomes that could be 7-2 making its certainty only 1-36/512, 92.97% even if it is 100% dominant. There are 84 possible outcomes, a certainty of 83.59% for a 6-3 decision, while it is still 100% dominant. There are 126 possible outcomes, a certainty of 75.39% for a 5-4 decision, while it is still 100% dominant. There are 256 possible outcomes for every remaining decision, a certainty of 50.0% while every one of those decisions is 0% dominant.

In any contest between two parties, where neither party is an absolute,  one of those parties may be dominant, but by definition that party can not be 100% certain. Dominance can be 100%, but that is NOT certainty. Lack of dominance does not determine that its is impossible, only that it is improbable.