Pothos & Busemeyer's (P&B's) answer to the question posed by the title of their article, “Can quantum probability provide a new direction for cognitive modeling?” addresses almost all the relevant issues. In particular, from an empirical viewpoint, the authors offer substantial evidence that quantum probability, explicated through its most transparent mathematical representation in generalized phase space, fits a great mass of cognitive data more closely than does classical Bayesian probability. P&B show through numerous examples that this superior fit applies with respect to quantum probability's superpositional characteristics, unitarily time-evolved interfererence effects, entangled composition, and mutual incompatibility of precision in measurements entailing ordered context for certain pairs of observables enlisted as operators.
However, the word “certain” in the last sentence points toward one residual hole in the authors' agenda. That defect is their professed “agnosticism” regarding possibilities for physical embodiment of quantum probability in the thinking brain. Such agnosticism opens up an anarchical lack of limitation in choosing those particular pairs of observables that must be treated as mutually incompatible in cognitive applications of quantum probability.
Physicists as a rule take incompatibility between operator pairs to be a concept whose applicability is restricted only to “certain” – that is, canonically conjugate physical – coordinates. Examples of canonically conjugate coordinate pairs include energy yoked to time and momentum yoked to distance. Each such pair yields a quantitative product with the qualitative dimensionality of action applicable to Planck's constant at the foundation of quantum mechanics and to the path-integrated functionals of quantum field theory.
If P&B were to follow the restrictive practices of physicists by limiting their choices of operator pairs to canonically conjugate observables, then physical embodiment of mental cognition in corporeal brain processes would be easy to infer. However, the authors also propose to consider for quantum probability theory qualitatively mentalistic observables, for example “happiness” or “feminism,” entirely abstracted from the material brain, and non-corporeally applied to mind. Some such observables might conceivably be posited as mutually incompatible, non-commutatively order-sensitive sets of operators, even if they have been arbitrarily untethered from the physical anchor of canonical conjugation and the dimensionality of action, but that kind of rash detachment from the canonically conjugate constraints of physics could condemn cognitive science to a new form of Cartesian dualism. There would issue mentalistic forms of superposable probability amplitudes pertaining to properties and extended in “spaces” whose unitary “evolutions,” mutual interference “effects,” entangled “non-locality,” and Fourier-dual “measurement” uncertainties lack any necessary connections to established physical observables and space times (or, alternatively, to their spin-networked foundations per loop quantum gravity) in which brains exist.
These caveats are especially germane if one stipulates that cognition, beyond the empirical question of its conformity to quantum probability, is formally quantum computational. The latter possibility remains an open biophysical question, insofar as classically engineered hardware can only imperfectly simulate but not fully support a quantum mode of abstract computation. As P&B mention at the end of their article, nobody really knows yet whether the brain's biophysics are compatible with the coherence of putative quantum wetware processes. Some, such as Tegmark (Reference Tegmark2000), have championed principled thermodynamic objections to any such brain capabilities. Rebuttals by Hameroff and others (Hagan et al. Reference Hagan, Hameroff and Tuszynski2002) to Tegmark's concerns about thermal decoherence have centered on two classes of argument. First, recent experimental evidence that quantum physics plays a role in photosynthesis (Engel et al. Reference Engel, Calhoun, Read, Ahn, Mancal, Cheng, Blankenship and Fleming2007) has been invoked against the idea that temperatures far colder than those found in living biological systems are needed to sustain quantum-coherent states. Second, proposals for thermal insulators that might protect physical quantum processes in the brain have been advanced. These include, for example, ordered water and pumped phonons, but to date none have been proven experimentally to operate in the relevant biological contexts.
Let us suppose that Tegmark's opponents turn out to be wrong, and quantum wetware substrates are nowhere to be found in neural tissue. If it transpires that the brain cannot sustain a quantum-biophysical “wetware” for cognition, then it will be hard to see how quantum-probabilistic “software” can offer a compelling perspective on cognitive phenomena within the framework of known metaphysical monisms. Thereafter those cognitive phenomena whose statistics conform more closely to abstract quantum probability than to classical Bayesian probability will be stuck between a rock and a hard place. Either quantum probability's disembodied elegance will have to be given up, or a new kind of dualism will be needed for cognitive science.
Making unified sense of that dualism will perhaps require some kind of trans-physical, post-Cartesian gauge, mimicking the generators of standard physical forces through coordination among “certain” local symmetries, but bridging quantitative intervals in “spacetimes” that, unlike the standard gauge fields of today's physics, are in a qualitative sense not purely physical. The new “gauge” would be required both to contact and to transcend corporeal physics while either obeying accepted physical laws or compensating against its own violations of those laws. A crucial underlying supposition in constructing such a psychophysical gauge might be the “local” character of canonically conjugate Fourier-duality as a kind of symmetry embedded within the “metrical” contexts of qualitatively neurocognitive “spaces” and “times.” The specifics of that psychophysical gauge's design, which will have to confront head on Chalmers' “hard problem” of generally relating perceptual qualia and physical quantitation (Chalmers Reference Chalmers1995), could well prove to be the most daunting neuroscientific challenge for any quantum probabilistic cognitive paradigm.
Pothos & Busemeyer's (P&B's) answer to the question posed by the title of their article, “Can quantum probability provide a new direction for cognitive modeling?” addresses almost all the relevant issues. In particular, from an empirical viewpoint, the authors offer substantial evidence that quantum probability, explicated through its most transparent mathematical representation in generalized phase space, fits a great mass of cognitive data more closely than does classical Bayesian probability. P&B show through numerous examples that this superior fit applies with respect to quantum probability's superpositional characteristics, unitarily time-evolved interfererence effects, entangled composition, and mutual incompatibility of precision in measurements entailing ordered context for certain pairs of observables enlisted as operators.
However, the word “certain” in the last sentence points toward one residual hole in the authors' agenda. That defect is their professed “agnosticism” regarding possibilities for physical embodiment of quantum probability in the thinking brain. Such agnosticism opens up an anarchical lack of limitation in choosing those particular pairs of observables that must be treated as mutually incompatible in cognitive applications of quantum probability.
Physicists as a rule take incompatibility between operator pairs to be a concept whose applicability is restricted only to “certain” – that is, canonically conjugate physical – coordinates. Examples of canonically conjugate coordinate pairs include energy yoked to time and momentum yoked to distance. Each such pair yields a quantitative product with the qualitative dimensionality of action applicable to Planck's constant at the foundation of quantum mechanics and to the path-integrated functionals of quantum field theory.
If P&B were to follow the restrictive practices of physicists by limiting their choices of operator pairs to canonically conjugate observables, then physical embodiment of mental cognition in corporeal brain processes would be easy to infer. However, the authors also propose to consider for quantum probability theory qualitatively mentalistic observables, for example “happiness” or “feminism,” entirely abstracted from the material brain, and non-corporeally applied to mind. Some such observables might conceivably be posited as mutually incompatible, non-commutatively order-sensitive sets of operators, even if they have been arbitrarily untethered from the physical anchor of canonical conjugation and the dimensionality of action, but that kind of rash detachment from the canonically conjugate constraints of physics could condemn cognitive science to a new form of Cartesian dualism. There would issue mentalistic forms of superposable probability amplitudes pertaining to properties and extended in “spaces” whose unitary “evolutions,” mutual interference “effects,” entangled “non-locality,” and Fourier-dual “measurement” uncertainties lack any necessary connections to established physical observables and space times (or, alternatively, to their spin-networked foundations per loop quantum gravity) in which brains exist.
These caveats are especially germane if one stipulates that cognition, beyond the empirical question of its conformity to quantum probability, is formally quantum computational. The latter possibility remains an open biophysical question, insofar as classically engineered hardware can only imperfectly simulate but not fully support a quantum mode of abstract computation. As P&B mention at the end of their article, nobody really knows yet whether the brain's biophysics are compatible with the coherence of putative quantum wetware processes. Some, such as Tegmark (Reference Tegmark2000), have championed principled thermodynamic objections to any such brain capabilities. Rebuttals by Hameroff and others (Hagan et al. Reference Hagan, Hameroff and Tuszynski2002) to Tegmark's concerns about thermal decoherence have centered on two classes of argument. First, recent experimental evidence that quantum physics plays a role in photosynthesis (Engel et al. Reference Engel, Calhoun, Read, Ahn, Mancal, Cheng, Blankenship and Fleming2007) has been invoked against the idea that temperatures far colder than those found in living biological systems are needed to sustain quantum-coherent states. Second, proposals for thermal insulators that might protect physical quantum processes in the brain have been advanced. These include, for example, ordered water and pumped phonons, but to date none have been proven experimentally to operate in the relevant biological contexts.
Let us suppose that Tegmark's opponents turn out to be wrong, and quantum wetware substrates are nowhere to be found in neural tissue. If it transpires that the brain cannot sustain a quantum-biophysical “wetware” for cognition, then it will be hard to see how quantum-probabilistic “software” can offer a compelling perspective on cognitive phenomena within the framework of known metaphysical monisms. Thereafter those cognitive phenomena whose statistics conform more closely to abstract quantum probability than to classical Bayesian probability will be stuck between a rock and a hard place. Either quantum probability's disembodied elegance will have to be given up, or a new kind of dualism will be needed for cognitive science.
Making unified sense of that dualism will perhaps require some kind of trans-physical, post-Cartesian gauge, mimicking the generators of standard physical forces through coordination among “certain” local symmetries, but bridging quantitative intervals in “spacetimes” that, unlike the standard gauge fields of today's physics, are in a qualitative sense not purely physical. The new “gauge” would be required both to contact and to transcend corporeal physics while either obeying accepted physical laws or compensating against its own violations of those laws. A crucial underlying supposition in constructing such a psychophysical gauge might be the “local” character of canonically conjugate Fourier-duality as a kind of symmetry embedded within the “metrical” contexts of qualitatively neurocognitive “spaces” and “times.” The specifics of that psychophysical gauge's design, which will have to confront head on Chalmers' “hard problem” of generally relating perceptual qualia and physical quantitation (Chalmers Reference Chalmers1995), could well prove to be the most daunting neuroscientific challenge for any quantum probabilistic cognitive paradigm.