(After reading A.K. Dewdney’s “Computer Recreations”, Scientific American, December 1989.)

Computers follow algorithms, even when engaged in “Artificial Intelligence”. But there are limits to computability. Some are time limits; since the time to execute some algorithms increases exponentially as the value of the parameter increases. Some are fundamental limits; Goedel’s theorem shows that some mathematical truths cannot be proved to be true, although they are true; they are beyond the reach of algorithms.

Dewdney speculates that human brains (“natural intelligence”) may be able to use “the infinite computer”, a thought-experiment invention of Dewdney’s. This also occurs in Hofstadter’s book “Goedel Escher Bach” in the form of the story about the Djinns. This involves an infinite regress of sub-routines (visualized as ever smaller computers-within-computers); the reason why this infinite sequence of computations can be executed in finite time is that, as the subroutines grow smaller, the time to execute them also grows smaller, and the series of computations down the scale of sizes and back up again converges to a finite limit. This would then constitute an important difference between the mode of thinking of a computer and a human mind.

The way I felt urged to express it, after reading it, was that human minds are REAL right down to the bottom level, while computers skim the surface, even though a fairly thick slice of the surface. It is a bit like statues representing the surface of the human body with great fidelity (in realistic sculpture), but lacking any of the interior structures which make the living body REAL. Again, by REAL I mean right to the bottom, to the smallest material structures conceivable. I seem to be alluding to some concept of degrees of reality.

Could it be (now comes a flight of fancy) that at the bottom of the infinite regress, human minds are attached, like the stem of a flower is attached to its root system, to another realm of reality? Just like the plot of tan x vs. x or of a hyperbola jumps from plus infinity to minus infinity, exhibiting to us finite observers a discontinuous curve, but perhaps being truly connected in some nether realm, so possibly the bodily realm of the brain is truly connected to a mental or spiritual realm quite beyond the body. The point of infinite regress could be like the juncture between universes sometimes encountered in science fiction. Descartes tried to solve the mind-body problem through parallelism, not very convincingly. This might be a better way to bridge the dualism, if there is any validity to it. Right now it’s just a bunch of metaphors.

Maybe the mystics can cross the bridge of infinite regress, and find that Atman is Brahman; they come from different universes, but meet at the junction like images merging into a hologram.

Through the bridge junction, we have access to the “collective unconscious” of all of humanity, past as well as present, as Jung has postulated. To return to the metaphor of the plant: our leaves and branches are in the material natural world, where we share the air, water and their nutrients with the rest of the creatures (THEIR leaves and branches, so to speak); and our roots are in the spiritual world, which we share as a common substrate with at least our fellow-humans, perhaps all living beings. We are thus doubly connected. We live in two spheres. In the material we exchange substances, both beneficial and noxious. (Many nitrogen molecules that passed through the lungs of Socrates and Jesus pass through our lungs.) In the spiritual sphere we share ideas, images, myths, archetypes. Why else would some images arouse such rich reverberations? Only because they resonate with the experience of thousands of human generations.

If we call the material sphere our exteriority and the spiritual sphere our interiority, we can postulate that other living beings (but not computers and other machines) possess these two aspects. How far down in the world of living creatures? All the way down, to diminishing and perhaps qualitative!)-different degrees. Even farther down (another flight of fancy) to stones and minerals and non-living things. (Machines may have interiority of the mineral kind, but not of the organismic kind. ) Yet we have no right to assume that human interiority is superior to that of a whale or a honeybee. Only different.

If even atoms, even electrons and quarks, have interiority (another flight of fancy), then mind is coextensive with matter throughout the universe. If higher forms (atoms from quarks and electrons. molecules from atoms, macromolecules from small molecules, cells from macromolecules, complex cells from simple cells, plants and animals from complex cells) come together through the synergy or cooperation of lower forms, then synergy or Love is a basic universal force which drives evolution, all the way down to the smallest units. Sometimes it acts physically through forces of attraction (any of the four fundamental forces which physicists recognize. i.e. gravitation, electro-magnetic, weak and strong). sometimes through the negentropic tendencies which Prigoginian open far-from-equilibrium systems have. One would think that consciousness is always present – all the way down – but becomes brighter and brighter in ascending the scale. The brighter levels would so obscure the less bright levels that the latter would seem to disappear when the former are present. as the rising sun seems to extinguish the stars at dawn, or as the waking consciousness erases dreams into gossamer shreds scarcely remembered. Synergy or love can be pursued deliberately (by purpose-oriented will) only at the higher levels; but the inchoate desire to cooperate, to come together. to love, is present throughout the universe, diffuse like the background radiation from the Big Bang.

REAL right down to the bottom, and suffused with the essence of love. How could it be otherwise. with a God of Love as its creator?