Yes Cavediver knows hyperincursive mathematics, he should be able to explain a bit. Hyperincursive math is the kind of math able to deal with choosing. In this kind of math the formula is itself an actor. So the formula is not so much for describing a thing, it is saying that a formula is an informationprocessor and that things (like rocks or anything) are too information processors. Information about past, present and future states, and then by the formula this information is processed, and the formula also processes the formula itself.
(from Review of Incursive, Hyperincursive and Anticipatory Systems - Foundation of Anticipation in Electromagnetism, Daniel M Dubois)
"6.1 Free Will as Unpredictable Hyperincursive Anticipation
Karl Pribram asked me (by email, after the CASYS'99 conference):
"How can an anticipatory hyperincursive system be modeled without a
future defined goal?".
My answer was: an hyperincursive anticipatory system generates
multiple potential states at each time step and corresponds to one-to-
many relations. A selection parameter must be defined to select a
particular state amongst these multiple potential states. These
multiple potential states collapse to one state (amongst these
states,) which becomes the actual state.
This reminds me the following comment an auditor made after a
conference on anticipatory hyperincursion I made:
"You have found the basic theory of free will".Indeed, the brain may
be considered as an anticipatory hyperincursive neural net which
generates multiple potential future states which collapse to actual
states by learning: the selection process of states to be actualized
amongst the multiple potential states is independent of
the fundamental dynamics of the brain, independent of initial
conditions and so completely unpredictable (and computable). The
selection by learning deals with inputs from the brain itself (via the
genetic code and self-reflection) and from environment. These inputs
are final causes at each time step. This creates a memory and at the
same time a program, which give rise to the mind, what I called a
computing memory. Each mind is unique in the sense that this is the
subjective experience of each brain that actualized potential states.
The free will means that we can choose a state amongst the multiple
potential states emerging from the preceding already actualized
states. The free will depends strongly on the history of all the past
memorized events and is not identical for each mind. The free will
does not means that the mind can make what he wants but that he can
choose amongst multiple possible choices. For a human being, this is
not possible to fly by itself, like a bird, but man invented airplanes
to actualize that."