eccentric probability

[AntonioLao]

For 3 of the 4 conics, the eccentricity is less than or equal to unity. In the theory of probability, unity represents absolute certainty while less than unity represents certain probability and zero represents impossibility.

Therefore, the parabolas represent certainty of classical Newtonian mechanics. Ellipses represent uncertainty of quantum mechanics. Circles represent the impossibility of detecting the true vacuum even though its existence is a theoretical certainty.

[Guille]

Continuing the analysis, what to hyperbolas represent?

Also, what is the probability of the eccentricities? What I mean by this question is that if, for example, it is more probable (there are more possibilities) to get a parabola or an elipsis than a perfect circle?

[Mohan.C]

Antonio,
But Ellipses have a probability to be a circle. As I have studied it is said Circle is a special case of an Ellipse. But then if one of the probability of an Ellipse is to be a circle then how can the circle be impossible.

[AntonioLao]

Continuing the analysis, what to hyperbolas represent?

I don't know. According to probability theory, no probability is greater than unity. Maybe, it's related to the probable existence of hyperspacetime, for example, from general relativity.

what is the probability of the eccentricities?

I have no idea.

But Ellipses have a probability to be a circle.

That's not my argument.

[Guille]

I don't know. According to probability theory, no probability is greater than unity. Maybe, it's related to the probable existence of hyperspacetime, for example, from general relativity.

In your starter you say 'in 3 of the 4 conics the eccentricity is equal or less than 1'. So, do you think that there is a necessary incoerence between geometry and probability, or that they can live together (I still think their union, as I said months ago, shoul dbe the main task of mathematicians and mathematical physicists).

[AntonioLao]

that there is a necessary incoerence between geometry and probability

Geometry deals with static deterministic variables (points, lines, curves, and surfaces in topology). On the other hand, probability deals with dynamic random variables.