However in attempting to more clearly define the shades of pink that lie betweem True and False some interesting mathematics has been proposed which can be used for a lot of lighthearted mathematical fun. It attempts to evaluate how truthful a statement might be on a scale that lies between 1 (completely truthful) and 0 (utterly false).
For example a statement could be mathematically determined to have a truth value 0.15 ie be 15% true. (Or may be it is 85% false?)
If you want to understand more about fuzzy logic it would be better to read the article (a partly true story) or look
elsewhere since this page is oriented, in the main, to the mathematics involved rather than the underlying philosophy. It suffices to say that the formulæ at play in what is refered to as the Chaotic Dualist can be used to produce the beautiful "Escape-Time" diagrams which appear on the fuzzy-logic pages of this website.
The fundamental logic is enshrined in these two statements:
X : X is as true as Y is true
Y : Y is as true as X is false
The dynamics are formularized as follows:
x <= 1 - |x - y|
y <= 1 - |y - (1 - x)|
The escape-time diagrams are generated from these two equations.
Here quoted is an excerpt from the original article:-
"...To see what it does, you chose an initial pair of values, say, (x,y) = (0.2,0.9), and calculate successive pairs of values. Think of them as coordinates and plot them in the plane. You get a geometric shape called the 'attractor of the the dynamic system'. In this case, you get a triangle densly filled with points,[illustration included in original but not here]. This representation can be transformed into a beautiful and intricate image known as an escape-time diagram. To create it, temporarily relax the conditions that x and y lie between 0 and 1.
The idea is to watch how far (x,y) moves from the origin (0,0) and to count how many calculation steps are needed before it goes beyond some threshold value. Then the point (x,y) is plotted in a color that depends on the number of steps required.
To start, you should try a threshold value just larger than 1 ( comment: one will do nicely)..."(end of quote)
However the content of the article, (partly) true to its premise, only delivers a percentage of the truth and fails to give all the information neccessary to reproduce the diagram displayed. The programmer is left to figure much out for him/her self. For example the center of the escape-time diagram plots at (0.5,0.5)