Re: Latest psychophysics/QM brain article


Igor Khavkine:

bjflanagan wrote:
> (2) it is no accident that we find matrices operating on vectors at
> both the neural and the quantum levels; and

Igor Khavkine:
An extraordinary claim that should be supported by extraordinary proof.
Neural network models that use linear algebra (vectors and matrices)
exist without any reference to quantum mechanics.

Flanagan
Well, no, it's really rather trivial. Consider the following remark
from Dyson, which has about it the genius of simplicity. In his classic
Sci Am article on "Field Theory," he wrote: "There is nothing else
except these [quantum] fields: the whole of the material universe is
built of them."

Given that the brain, being a part of the material universe, just is a
collection of fields, it's not too surprising that we find this kind of
mathematics at work.

Then there is this equally cogent statement from Abdus Salam: "... all
chemical binding is electromagnetic in origin, and so are all phenomena
of nerve impulses."

It seems to follow by a ready consequence that, if conscious processes
are "phenomena of nerve impulses," (which notion seems altogether
plausible, informing the de facto working paradigm of contemporary
neuroscience), it seems to follow that conscious processes are
"electromagnetic in origin."

Curiously, Lockwood and I both arrived at this conclusion independently
of one another (private communication), albeit both of us were
following up Bertrand Russell's thinking.

"Take some range of phenomenal qualities. Assume that these qualities
can be arranged according to some abstract n-dimensional space, in a
way that is faithful to their perceived similarities and degrees of
similarity -- just as, according to Land, it is possible to arrange the
phenomenal colors in his three-dimensional color solid. Then my
Russellian proposal is that there exists, within the brain, some
physical system, the states of which can be arranged in some
n-dimensional state space ... And the two states are to be equated with
each other: the phenomenal qualities are identical with the states of
the corresponding physical system."

Lockwood, Michael. 'Mind, Brain & Quantum' (Oxford)

Now consider the foregoing in relation to the following passage from
Atiyah:

"We shall now recall the data of a classical theory as understood by
physicists and then reinterpret them in geometrical form. Geometrically
or mechanically we can interpret this data as follows. Imagine a
structured particle, that is a particle which has a location at a point
x of R4 and an internal structure, or set of states, labeled by
elements g of G."

Atiyah, MF. Geometry of Yang-Mills Fields. Pisa, Italy: Accademia
Nazionale Dei Lincei Scuola Normale Superiore, 1979.

http://wordassociation1.net/smart2.html

Igor Khavkine:
It is rather likely that the use of linear algebra in both cases is
due to its prevalence in a multitude of areas of mathematics and
physics.

Flanagan
That is only a logical possibility which does not begin to take account
of facts so familiar as to be largely invisible. One could more easily
assert that it is mere coincidence that the tensor mathematics of
gravitation happens to coincide with that of curved space-time. For we
can only induce the presence of gravitation from its operation on
things we directly perceive. Not so with EM, which operates directly on
our senses.

Attend Weyl very carefully:

"To monochromatic light corresponds in the acoustic domain the simple
tone. Out of different kinds of monochromatic light composite light may
be mixed, just as tones combine to a composite sound. This takes place
by superposing simple oscillations of different frequency with definite
intensities."

Now have a look at the superposing wave forms and color disks here:

http://wordassociation1.net/smart1.html

Well, so what? Everyone knows that. Or do they? Here, I would argue, is
a paradigmatic example of the truth of Schrodinger's remark: "Thus, the
task is, not so much to see what no one has yet seen; but to think what
nobody has yet thought, about that which everybody sees."

For on the one side we have superposing "physical" waves (vectors) and
the associated math. On the other side we have what is directly
perceived, the "mental" color (vectors) adding together -- predictably,
reliably, quantifiably, now and forever. Rather like a law of nature.

Finally, on both sides we find vectors respecting our basic ideas about
superposition:

"When a state is formed by the superposition of two other states, it
will have properties that are in some vague way intermediate between
those of the original states and that approach more or less closely to
those of either of them according to the greater or less 'weight'
attached to this state in the superposition process. The new state is
completely defined by the two original states when their relative
weights in the superposition process are known, together with a certain
phase difference, the exact meaning of weights and phases being
provided in the general case by the mathematical theory."

Dirac, PAM. The Principles of Quantum Mechanics. Oxford, 1958.


In closing, I would urge you to pay special attention to what Dirac
said just now about superposed states having "properties that are in
some vague way intermediate between those of the original states" and
"the exact meaning of weights and phases being provided in the general
case by the mathematical theory."

"The aspects of things that are most important for us are hidden
because of their simplicity and familiarity." (Wittgenstein)

.

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