MathOverflow is a remarkable recent platform for research level questions and answers in mathematics. Joe O’Rourke have asked over MO wonderful questions. (Here is a link to the questions) Many of those questions can be the starting point of a research project usually in discrete and computational geometry and sometimes in other areas. Many of the questions remained open, quite a few have led to definite quick solutions, and for many others substantial answers were offered. Usually Joe’s questions (and also his MO answers) contain beautiful and illuminating pictures. Amog the highlights: Joe’s question on Billiard knots; a poetic question about “light reflecting off christman-tree balls“; rolling a random walk on a sphere – with a definite answer by S. Carnahan; Pach animals of high genus; Fair irregular dice (with a nice answer by Bill Thurston); Parabolic envalope of fireworks; Coiling rope in a box; A convex polyhedral analog of the pentagram map ; Random-polycube-shapes ; Which convex bodies roll along closed geodesics and many more. The 100th question is The rain hull and the rain ridge.
Here is an excellent question asked by Liza on “Mathoverflow“.
What is the explanation of the apparent randomness of high-level phenomena in nature? For example the distribution of females vs. males in a population (I am referring to randomness in terms of the unpredictability and not in the sense of it necessarily having to be evenly distributed).
1. Is it accepted that these phenomena are not really random, meaning that given enough information one could predict it? If so isn’t that the case for all random phenomena?
2. If there is true randomness and the outcome cannot be predicted – what is the origin of that randomness? (is it a result of the randomness in the micro world – quantum phenomena etc…)
Where can I find resources about the subject?
Some answers and links can be found below the question in MO. (The question was closed after a few hours.) More answers and further discussion are welcome here.
And here is a related post on probability by Peter Cameron relating to the question “what is probability”.