# Can we consider the field of futures probabilities as a chaotic system ?

We illustrate the field of futures probabilities using the concept of the ?cone of plausibility?:
https://studentsatthecenterhub.org/resource/tool-exploring-plausible-probable-possible-preferred-futures/

Suppose that for any time value tn in this projected cone we had a value y1 and a value y2 to define the upper and the lower limits of plausibility ? or extremum of the bidimensional cone slice for the time value tn ? see the graph: https://www.aam-us.org/2011/09/16/futurist-friday-exploring-the-cone-of-plausibility/

Also, we can define a mean for each value of time tn:
M = (y1+y2)/2
Which would expressed on the graphs by the default vector of time.

1. Having defined a bounded space, could we consider  the field of future probabilities ? included between y1 and y2 in the cone of plausibility at tn and observable from t0 ? as a chaotic system ?
2. If it can be considered as so, would it be a linear or a nonlinear system ?
3. If it can be considered as so, could we call M for the time value tn an attractor ? A global attractor ? Something else ?
4. Finally, if it can be considered as so and if you had to express your mathematician's point of view, would such a system have any interest, be practical, or useful ?

• 0. y_1 and y_2 are not really well defined. The cone is a didactic representation to explain a concept, but there is no way to define a boundary for the possibilities or the 'extremum' of all possibilities. 1. Barring my previous comment, you could choose to model it as such. Modeling is always a choice, I'm afraid. 2. You choose. 3. Depends on the equations we end up positing. 4. I fear there are too many things undefined. The cone works conceptually but not mathematically.

• Please consider that y1 and y2 are defined as working extremums through a non classical logical system but it cannot be disclosed here. Would it change something ? If i understand correctly, modeling this would produce a totally abstract system. Exploring this part of mathematic for a potential application was necessary before continuing my work. Is there a mathematical working consensus to represent "the futur field of possibilities" ? If yes, is it linear or nonlinear ?

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