Cookie cutter paradigm

Cookie cutter paradigm (CCP) refers to the following set of notions:

# The parts of a material object are defined by the parts of the space it occupies.
# The parts of space are defined by delimiting surfaces (boundaries).

Divisibility of matter

Is matter infinitely divisible or is it made of ultimate, not further divisible parts? A new twist was given to this ancient conundrum by the discovery of quantum mechanics. Until then, no distinction was made between "dividing" a piece of matter and "cutting" it into smaller pieces; hence the common translation of the Greek word "átomos" ("ἄτομος"), which literally means "unable to be cut", as "indivisible". Whereas the modern atom is indeed divisible, it is in fact uncuttable: there is no partition of space such that its parts correspond to parts of the atom. In other words, the quantum-mechanical description of matter no longer conforms to the CCP. The importance of this paradigm, like that of Bell's inequality, lies in the fact that the quantum world — the physical world as described by quantum mechanics — is inconsistent with it.

Psychological and neurobiological underpinnings

The reasons why the CCP seems virtually self-evident — and has been so treated for most of the history of occidental metaphysics — are psychological and neurobiological in nature.

Studies during the 1980s and 1990s have put it beyond reasonable doubt that the visually perceived world is a creation by the mind and/or the brain that is guided by a surprisingly sparse stream of clues from "outside". [M. Velmans (2000), "Understanding Consciousness" (London: Routledge).] [D. Ballard (2002), "Our perception of the world has to be an illusion", "Journal of Consciousness Studies" 9 (5-6), 54-71.] [T. Davies, D. Hoffman, and A.M. Rodriguez (2002), "Visual worlds: construction or reconstruction?", "Journal of Consciousness Studies" 9 (5-6), 72-87.] [F. Durgin (2002), "The tinkerbell effect: motion perception and illusion", "Journal of Consciousness Studies" 9 (5-6), 88-101.] The bulk of the data received and processed by the visual cortex concern "discontinuities" in the field of view — the locations and states of motion of boundaries (across which changes in color and/or brightness occur) and the changes occurring across boundaries. Uniformly colored and evenly lit regions are "filled in" (much like coloring books) as determined by these changes. (For an illustration see blind spot (vision).) The well-known experiments by David H. Hubel and Torsten Wiesel in particular have revealed that line segments and outlines play a major part in the construction of the visual world. [D. H. Hubel, "Eye, Brain, and Vision" (Scientific American Library, New York, 1995).] [D. H. Hubel and T. N. Wiesel, "Brain mechanisms of vision", "Scientific American", March 1979, 150-62.] These and related findings strongly suggest that the construction of the visual world involves a three-step synthesis:

# first line segments are integrated into two-dimensional contours,
# then contours are integrated into 3-D outlines,
# and finally the outlines are covered with colored and textured surfaces much like the wire frames of 3D computer graphics and CAD software.

A striking illustration of the first step is Kanizsa's triangle: it is all but impossible "not" to see a complete white triangle. Well-known illustrations of the second step in this synthesis are the Necker cube, which causes a multistable 3D perception rather than the perception of a 2D diagram, the Penrose triangle, and the impossible cube.

In a world model conforming to the CCP, the parts of a material object are defined by bounding or delimiting surfaces. In such a world, spatial extension exists in advance of multiplicity, for only what has spatial extent can be cut up by 3-dimensional equivalents of cookie cutters. And if the parts of a material object are defined by the parts of the space it "occupies", then the parts of space exist in advance of the parts of material objects. But if one thinks of physical space as an intrinsically divided expanse, then it is hard to see why it should not be by itself divided at all conceivable scales. (Exceptions are found in the literature on quantum gravity, where it is has been observed that an indeterminate metric conflicts with the description of space as a set of points that are sharply localized relative to each other.)

Thus it is largely due to its psychological and neurobiological underpinnings that the set-theoretic description of physical space (or spacetime) is all but universally accepted.

Conflict with quantum mechanics

Because the visual world is constructed in conformity with the CCP, we tend to construct our theoretical models of the physical world along lines laid down by the CCP. The enormous difficulty of the task of making sense of the quantum world is to a considerable extent due to our projecting into the quantum world features that are (i) implied by the CCP and (ii) hard (if not impossible) to reconcile with the quantum-mechanical description of matter. [U. Mohrhoff, "The Quantum World, the Mind, and the Cookie Cutter Paradigm," [http://cogprints.org/4480/ Cogprints] ] [ U. Mohrhoff, "Is the end in sight for theoretical pseudophysics?", in V. Krasnoholovets and F. Columbus (Eds.), "New Topics in Quantum Physics Research" (Nova Science, New York, 2006).] Some of these features are discussed below.

The above images are accurate depictions of the indeterminate position of the electron relative to the proton in three stationary states of atomic hydrogen — as accurate as a depiction of a quantum state can be. In the first three images, lightness corresponds to the line-of-sight integral of the probability density of the depicted orbitals. The fourth image depicts an arbitrary surface of constant probability density, emphasizing the orbital's invariance under rotations about the vertical axis. The volume integral of the probability density over the interior R of a closed surface yields the probability of finding the electron in R, rather than the amount of "stuff" (of any kind) located in R. This illustrates the fact that the parts of a material object, quantum-mechanically described, are not congruent to parts of space. What gets divided by a geometric surface is neither the electron nor the proton nor the atom as a whole nor the atom's internal relative position — for a relative position is not something that can be divided — but merely the probability of finding the electron (relative to the proton) on either side of that surface (if an appropriate measurement is made).

What kind of reality does such a surface have, then? And if it has none, what kind of reality does an intrinsically and infinitely divided space or spacetime continuum have? It has been argued by U. Mohrhoff, author of the Pondicherry interpretation of quantum mechanics, that quantum indeterminacy is irreconcilable with the set-theoretic description of space. It requires that we conceive of space, instead, as the totality of (more or less indeterminate) spatial relations existing between material objects. The parts of a material object can then be simply and adequately defined as the relata of its (more or less indeterminate) internal spatial relations.

References

External links

* [http://thisquantumworld.com/ht/content/view/67/45/ The cookie cutter paradigm]