The Moving Finger writes; and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it
Engraved with the Spirit's pen on the Rubaiyat Spire in the Black Hills . . .
Was hoping @jgill might pop in and enlighten us with a bit of game theory
I'm not familiar with modern game theory, which has been extended to decision analysis and beyond. When Von Neumann and others introduced the subject, it relied heavily on fixed-point theory, specifically Brouwer's Fixed-point Theorem, which states that certain sets, no matter how they are shifted about retain a point that is fixed. If a function shifts the points about, then, provided the function is "continuous", there is a point that remains in the same position.
From Wiki: Take an ordinary map of a country, and suppose that that map is laid out on a table inside that country. There will always be a "You are Here" point on the map which represents that same point in the country.
My own investigations have included extending a similar classical result, the Banach Fixed-point Theorem, which tells one how to actually find this point, to a more general setting.
As for the assertion in the title, you are moving into the territory of the old "What is Mind" thread from ST. How are decisions formed? How much of decision-making originates in the subconscious?
@manmountain When I started visiting the Tetons in the mid 1950s solo climbing was prohibited. It was not a popular activity, but those of us who indulged would sneak out onto the rocks, hoping to avoid climbing rangers. I recall coming off Baxter's Pinnacle after a solo of the north face route and being greeted by a party consisting of two climbing rangers and a couple of guides. There were a few moments of awkward silence, then the conversation shifted and I never heard anything more about my transgression. Years later the restriction vanished from park regulations.
@LynneLeicht Perhaps get in touch with Jim Herrington. I have his book "The Climbers" here beside me and it is beautifully done by the Mountaineers. But I don't know if these kinds of books are popular these days. I suspect Jim hasn't made much money (if any) off this heavy coffee-table work. I've done several books on Blurb.com but never for a profit. Their software was pretty good, however.
Mostly my math art is unworldly and as I mentioned completely unpredictable. The mind of the mathematician meld with the mind of the computer, and something surges up from the combined subconscious. Occasionally an image will appear that resembles a 17th century sketch, with imprecise edges. Here is one that cropped up yesterday as I worked out theory for the elementary dynamics of a generalized Joukowski transform. The coloring and shading were altered slightly in Photoshop. This was a tiny image well away from the origin of the plane and magnified about 200X.
I don't know. For me it's whenever there is an uncertain outcome. . . .
Let's not exclude those adventures that are not primarily physical. The scientist or mathematician exploring new terrain. The artist caught up in expressing an internal experience as an art form. The Zen meditator marveling at empty awareness. The philosopher breaking new ground. On and on.
@L-Aura: My Lady, the screen on your computer is a collection of points (pixels). I select a rectangle and starting on the left side go down a column of points. At each point I apply the same complicated math formula that gives that point (or pixel) a non-negative numerical value. I then paint that pixel a color corresponding to the magnitude of that value. Around 0 the pixel is black, and the color changes as the value increases, from dark red to light red, then to shades of green, then shades of blue, to white if the value is over, say, 10^6. Then I move to the next column and do the same thing, point by point. This frequently paints an interesting image that is unexpected, hence is called an example of "weak emergence". The 3-D effect usually arises from a mathematical process involving the trig functions.
I have created many BASIC programs to do this sort of thing. I never use a commercial program.