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 ?
Thank you for your time. I’ll ask you kindly to include sources for your references.
Probability
Raoli Raoli
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  • Mathe Mathe
    0

    I got a message saying 'Page not found' from both links.

  • Raoli Raoli
    0

    My bad, I corrected it but the hyperlinks are down now. Thank for the notification

  • Mathe Mathe
    0

    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.

  • Raoli Raoli
    0

    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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