COMMENT’S ON SHA XIN WEI’S “WHITEHEAD’S POETICAL MATHEMATICS”

Sha Proposes to: “yield a way out of the static and atomistic aspects of Whitehead’s metaphysics”, “enrich a plenist and process-oriented concept of unbifurcated nature.” Replace Whitehead’s topological methods with more modern tools.

My Comments Will: Defend Whitehead’s atomism on the basis of its concordance with, and utility for, contemporary basic physical theory. Suggest a different way to improve Whitehead’s topological method.

Whitehead’s Core Idea: “CONTINUITY CONCERNS WHAT IS POTENTIAL, WHEREAS ACTUALITY IS INCURABLY ATOMIC”

Whitehead’s ontology is built out of atomic (indivisible) actual entities! “The final facts are, all alike, actual entities, and these actual entities are drops of experience” p.18 “an actual entity is an act of experience” p.68 “ ‘Actual entities’---also termed ‘actual occasions’, are the final real things of which the world is made.” p.18

Wm. James’ “drops of perception” “Either your experience is of no content, of no change, or it is of a perceptible amount of content or change. Your acquaintance with reality grows literally by buds or drops of perception. Intellectually and on reflection you can divide them into components, but as immediately given they come totally or not at all.” (p. 68)

Atomism “The actual entities atomize the extensive continuum. This continuum is in itself merely potentiality for division.” p.67 “The contemporary world is in fact divided and atomic, being a multiplicity of definite actual entities. These contemporary actual entities are divided from each other, and are not themselves divisible into other actual contemporary actual entities” p. 62

Atomism “in the actual world there are definite atomic actualities determining one coherent system of real divisions throughout the region of actuality. Every actual entity …is…somewhere in the continuum…” (p.67)

Atomism “every actual entity in the temporal world is to be credited with a spatial volume for its perspective standpoint.. These conclusions are required by the consideration of Zeno’s arguments in connection with the presumption that every actual entity is an act of experience.” (p.68)

Atoms of Action:Decisions “Actual entities atomize it [the extensive continuum] and thereby make real what was antecedently merely potential.” (p.72) “every decision is referred to one or more actual entities…Actuality is decision amid potentiality.” (p. 43). “Actual entities are the only reasons.[causes]. ” (p.24)

Continuity, Causation, and Discreteness in Physics Newton/Classical physics. Continuous process satisfying “causal closure of the physical”: mind/consciousness is left out of the causal structure! Quantum theory has discrete events: the Geiger counter clicks or does not click. Bohr: “The element of wholeness symbolized by the action, and completely foreign to classical physical principles.

Quantum theory has causal gaps and discrete decisions. Two kinds of discrete decisions needed to make quantum theory work! Process 1 “free choice” by experimenter. Nature’s choice of outcome. Like “Twenty Questions” Each discrete decision is associated with a particular region in space Each drop of experience seems to balance an active input from consciousness with a passive or coercive input from the physical world.

Actual and Knowledge in Quantum Mechanics Heisenberg: “The observation itself changes the probability function discontinuously; it selects of all possible events the actual one that has taken place. Since through the observation our knowledge of the system has changed discontinuously, its mathematical representation has also undergone the discontinuous change”

Transition from Possible to Actual in Quantum Mechanics Heisenberg: “the transition from the ‘possible’ to the ‘actual’ takes place during the act of observation.”

Tomonaga-Schwinger and Whitehead Ψ(t)  Ψ(σ) t~A continuous three-dimensional surface in the four-dimensional space-time continuum, with all spatial point lying at the same time t σ~A continuous three-dimensional surface in the four-dimensional space-time continuum, with no pair of points light-like separated.

Compatible with relativity Predictions are independent of ordering of space-like separated events. Newton’s “receptacle” space and time: exists even if nothing is in it, versus Leibniz’s relational view. Space-time pertains to relations among existing things: Empty space is a nonsensical idea.

Whiteheadian Quantum Ontology World Process consists of a sequence of psychophysical events, each of which is associated with a “standpoint”, which is a space-time region that separates space- like surface σ(n-1) from its successor σ(n). Prior events atomize the space-time region prior to the space-like surface “now”, and they combine to create potentialities for future events.

Each Event Makes A Decision Each decision “n” is based in part on physical input described by the part of the quantum state σ(n-1) lying at the start of the standpoint, and in part by psychological input coming from the psychological content of the events that atomize the space-time region prior to σ(n-1).

Completing Quantum Theory. QT gives no theory about how we decide what we will do: What determines the Process 1 “Free Choice”? QT gives no theory about how nature chooses the outcome: What determines outcomes? The Whitehead Quantum ontology provides a rational conceptual framework for approaching issues that contemporary quantum theory leaves unaddressed: How are the key decisions made? How does mind enter into these decisions?

Whitehead’s Straight-Line Problem Question: How does the event of perceiving the scene before you get created from the information coming, via neuronal impulses, from the sense organs? The information seemingly gets projected out from the standpoint of the experiencing actual occasion via “straight lines”. How do these “straight lines” emerge from an ontology the has only open regions?

Whitehead’s Topological Method Whitehead adopts an awkward topological method to solve his straight-line problem. I think it fails, because it (admittedly) provides no unique solution. The key concept is “ovate sets”, which are supposed to be like sets of ovals. But, as Sha correctly points out, their properties are like those of sets of convex sets, and that comes close to begging the question.

Sha’s more modern methods Sha suggests that replacing Whitehead’s topological methods by more exotic modern method, such as point-free topologies,and noncountable sets involving the transfinite axiom of choice might help, and also evade the atomism of Whitehead’s approach. That would disrupt the connection to orthodox quantum theory.

A different approach How do visual scenes get created from sense data and past experiences. Problem in computational/theoretical neuroscience. Baysian methods are promising, and mesh nicely with the Whiteheadian quantum ontology.