This is an Extended Abstract of the essay.
This is a toy model of dark energy. The original motivation for building this model was to report to physicists the finding of a new mathematical object I called the Born infomorphism, a transmission of information from the nonstandard future into the nonstandard past involving the Born rule and a nonstandard model of time. Guidelines from the essay contest-- to which this essay is submitted-- have given the model its present form.
New methods introduced by Jon Barwise (e.g. Information and Impossibilities), Samson Abramsky (his paper and his presentation on Big Toy Models) and others (e.g. Jerry Seligman, Information Flow, Lawrence Moss, Vicious Circles) have been applied to the architecture. Specifically, a co-algebra called a stream is built within a Chu space, which is then placed inside the monad (as in nonstandard analysis) that is nonstandard time. Which monad, called clockTime, then becomes the output of another stream, properTime. In previous work, this stream is "zippered" together (a technique for combining streams which are modeled by non-wellfounded sets) with David Bohm's Holomovement. Inside this architecture, the essay presents a new mathematical expression for the collapse of the wave function. This new mathematics for the collapse of the wave function seems, perhaps arguably, like the simplest possible to imagine. Collapse of the wave function seems to look like the diagram which is expressed in the text as a table.
Taking the idea from Bohm and Hiley in The Undivided Universe-- that the two sides of the simplest equation for the Born rule are from two different processes-- the model applies a different algorithm for each side of the equation. These are a pair of algorithms from mathematical game theory-- from the mathematical game called probability learning. In this context, the signature of a learning algorithm becomes evident. What is it learning? The laws of physics. Since it doesn't know the laws of physics, the particle must learn the laws of physics. And so it seems logical that instead of being an object, the particle in this architecture is a process (in fact, a stream). Which in previous work on the model is used to "complete" quantum mechanics, by complementing the Schrödinger equation with a co-algebra that is a stream.
All of which, in this essay, models dark energy as the waste stream from the above mathematical game, now seen as a thermodynamic engine. Forces between particles are in this model entropic.
For context, the mathematics which Feynman used in his famous lectures to talk about the goal of least action is "mindless" insofar as there is no decision process modeled in that mathematics, i.e. in the mathematics Feynman used there is no explicitly modeled process by which a player with intentions selects among possibilities to achieve the goal of least action. Here, the model begins with Abramsky's paper, in which at least the "possibilities" are made explicit. In the new mathematical model for wave function collapse, the mathematical model of such a decision process becomes explicit. So in this architecture, the decision process by which a choice is made among possibilities in order to achieve a goal is universal-- from the Born infomorphism on up.
Which leads to a testable hypothesis-- The Dream Child Hypothesis. In previous work on this model, the non-wellfounded set "self = (self)" was modeled by Petri nets, which are, again, a co-algebra. To make this Petri net model work, a feedback loop is needed. In the case of animals, such a feedback loop may involve either enteroceptors or proprioceptors. The former are involved in the heartbeat and the latter are involved in the breath. The Dream Child Hypothesis holds that "self=(self)" begins, not when the feedback loop is closed by enteroceptors, but when the feedback loop is closed by proprioceptors. Neuro-imaging with laboratory animals should be able to test the hypothesis.
