We first examine the process of using logic to establish conclusions, noting that each step is in actuality an approximation treated as absolute truth; and then we compare that picture to the phenomenology of the collapsed and uncollapsed wave functions of quantum mechanics. Finally we suggest the existence of a "quantum logic" and a medium in which it might exist.

Any system of logic starts with a list of axioms or definitions. Normally, these postulates correspond to some physical or mathematical reality, and as such are seemingly self-evident. If we postulate that there is a reality; that there is something that is absolute and true (and that this postulate itself may be more or less true); then we have to admit that any definition, axiom or postulate is at most an approximation of that reality. Some postulates may be highly probable, just as some measurements in physics can have an accuracy of ten or more decimal places, and others may approximate the truth very poorly. So there are degrees of better and worse approximations.

As such, it appears that all statements are fundamentally approximate. The previous sentence itself is therefore approximate. It is not untrue (false). Nor is it true (i.e., absolutely true). All statements are in between true and false, which is called approximate, rather than being one or the other as demanded by logical thinking. Our conclusions are self-consistent with their statement: we can approximately say that all statements are approximate. In fact, if all statements including axioms and conclusions are approximate to some degree, then the most we can hope for is consistency with itself and perhaps with external constraints like measurements.

On the other hand the process of logic proceeds as if each of the axioms, intermediate conclusions and final conclusions is absolutely true. Each postulate and succeeding statement is taken to be either completely true or completely false. The inherent fundamental often unspoken pretense of logic is that "Logic is Rigorous", when in reality every postulate, every step along the way, in fact every word in every statement, has some degree of approximation. Logic claims to be able to prove things rigorously. Logic claims to prove that conclusions of logical arguments are true if the axioms are true. But actually Logic can at most claim a level of confidence: such as, we are 90% sure, and then we have to define what that level of confidence means, approximately , of course.

Quantum mechanics is similar to the approximate aspect of logic. In the use of quantum mechanics, for example by solving Schroedinger’s equation for (uncollapsed) wave functions, we obtain at most a probabilistic description of physical reality. We can say that particles such as electrons or photons, etc., are located at given points with given energies, only as a matter of probability. So what we can actually solve for using quantum mechanics is inherently probabilistic and approximate.

Ironically, what we cannot solve for in quantum mechanic are the so-called "collapsed" wave functions. They are like the rigorous statements of logic. Apparently, and we are less certain about this statement than most others in physics and mathematics, when we make a measurement, for example to determine the location and energy of a photon, we "collapse" the wave functions to the size of the photon detector or smaller and measure an energy with an accuracy consistent with Pauli’s Uncertainty Relationship. If we get a detection, we know for sure that the photon hit the detector. But according to quantum mechanics, before detection we can have only approximate knowledge of where the photon is.

Take a beam of light that is so weak that it transmits very few photons per second. A single small photon detector located in the beam might get a detection every minute or so. This suggests that photons are actually point particles flying through space. But actually more sophisticated experiments involving wave interference indicate that the (uncollapsed) wave functions are continuous electromagnetic fields that pervade the entire beam of light. It’s interesting that quantum mechanics, a logical system, solves for a Probability distribution dependent on fields that are seemingly real even though we cannot measure them directly. We can only measure their probability distribution from a collection of a great many photon detections, each one being independent and probably point-like.

Logic is just like that. Each set of conclusions from a set of axioms is like the detection of a single photon. It could be a gross approximation of the actual truth. Only by exercising logic over the range of possible axioms are we likely to approach the truth, and then we only obtain a range of possible conclusions with different degrees of probability. Nature always gives us similar probability distributions under similar conditions. It’s self-limiting and entirely self-consistent. Human logic normally fails to exercise an appropriate number of sets of axioms or to weigh their importance correctly (if indeed we bother to look at even more than one set).

Thus we note that logic proceeds step by step assuming the absolute truth of each step-- a very descrete process-- just like our notion of descrete quantum particles; whereas our recognition that each step involves approximation is closer to field theory where quantum entities are continuous (or uncollapsed) waves. Quantum field theory has been fully developed, but descrete measurements theory is incomplete. Asymmetrically, descrete theories of logic abound, but we lack a quantum logic

The similarity between logic and descrete particle measurement theory motivates us to consider what we call "quantum logic" which is more like a full-wave quantum theory. Such a logic is difficult to define but fairly easy to imagine. Take Euclidean geometry with its nine axioms. A quantum logic description of this system of thought might assign a probability distribution to every word in its axioms. The distribution would range over the variety of meanings of each word in each sentence expressing an axiom and assign a probability to each meaning. The distribution could be both descrete for disjoint meanings and/or be continuous for shades of meanings. The axiom probability distribution, the sum of all the word distributions, would be as well multi-dimensional in meanings.

Take the simple case of approximately straight lines, say one with a Gaussian distribution of curvatures, from which we derive approximate theorems such as the probability of the number of degrees in a triangle. A probability distribution for the number of degrees in a triangle would be a Gaussian distribution with a peak at 180 degrees.

It’s easy to imagine such a logic but very difficult to program a computer to perform complex calculations with such complicated distributions. The methods of Operations Research have established confidence levels (of the truth of some outcome), but usually with a single-dimensional distribution of how true or accurate each axiom and/or step of the logic is. A multi-dimensional distribution over a range of possible axioms each with a truth probability is much more complex.

But some progress has been made in a field called "fuzzy logic". The proponents of fuzzy logic recognize that thinking is fundamentally "fuzzy", or approximate, and have designed a logic to approximate the thinking process. Our contention, rather, is that thinking is fundamentally quantum mechanical. Although not proven on an experimental basis, Frolich’s Hypothesis postulates that the membranes of the brain, and the entire human body for that matter, contain dipoles that can act with quantum coherence under the right condition; which is that there is sufficient metabolic drive. Or in simpler terms, you are awake. Take away the metabolic drive and you fall asleep, and lose consciousness. All that aside, what is important for this discussion is that from Frolich’s Hypothesis the membranes of the brain are capable of supporting uncollapsed quantum waves; and therefore the brain is (within approximation) capable of "fuzzy" thinking, or equivalently, quantum logic.

It is our belief, and this is consistent with the tenets of quantum mechanics, that the "uncollapsed" quantum wave functions in the brain, such as would be derived from Schroedinger’s equation, are actually invisible to us. In a sense they are part and parcel of our "unconscious" thinking. By "unconscious" thinking we do not mean sleeping or dreaming, although invisible thinking may occur in those states as well. What we mean is that for example, we can solve problems "unconsciously"—without conscious thinking—while being awake. It may also be possible while asleep, but that goes beyond Frolich’s Hypothesis and beyond the scope of this discussion.

The process of seeing or hearing involves the detection and therefore the collapse of wave functions. Our visual field obviously involves the optical detection of photons reflected from surfaces that we claim to see. The electromagnetic fields that compose the reflected light are collapsed into electrical stimuli in our retinas, if memory serves us correctly, and reprojected on to the screen in our brain, where the brain’s dipole wave functions are again detected and collapsed. Likewise, we hear sound by the detection of phonons in our ear. Although sound waves are not quantum mechanical. That is, they are not collapsed in the ear in the quantum mechanical sense. Our hypothesis is that the resulting electrical stimuli is reprojected into dipole quantum waves in the brain which are "heard" or detected internally by collapse of those quantum waves.

Thus, we hypothesize that the medium of the brain consists of membrane dipoles that can support uncollapsed quantum wave functions and that what we consciously see or hear are the collapsed quantum waves resulting from detection. It follows that collapsed quantum brain waves are visible and uncollapsed ones are invisible(or silent in the case of hearing).

In other words the brain is a quantum computer as well as a classical computer. It’s actually a mixture of the two. Our visible, unsilent, logical thinking is performed with collapsed wave functions. That much is almost self-evident. We can talk to ourselves, work out problems, imagine geometry’s, all a product of our imagination. So our imagination is composed of collapsed quantum wave functions. It follows that our conscious thinking is subject to the limitations of (descrete, classical) logic as described above. We "have to" in a sense believe in the truth of our reasoning every step of the way, and only when we obtain the logical conclusions, do we step back and check if they make sense. Are they consistent with our previous thinking and expectations? That is a "conscious" critical analysis of the conclusions. But we also judge if the conclusions are "intuitively" correct. Are they desirable, or beautiful? Do they "just feel" good.? These are the "unconscious" means of evaluation. The feelings are evident, but the computations underlying them are not.

The suggestion here is that intuition is a product of "unconscious" thinking involving computations or reasoning using quantum fields. For instance, after much repetitive experience in some endeavor, one develops the feeling that it is known. It just feels comfortable to think about the endeavor. And one can think about it from any angle, just by wishing to do so. Wish to see a triangle and it materializes in your imagination. Our conclusion is that the connection between our conscious and unconscious mind is via feelings and will. We can feel quantum fields (i.e., the uncollapsed wave functions) and we can will them to collapse.

But they can operate independently as well. We have all had the experience of being stymied by some problem, unable to get a solution, particularly if a "mental block" is in effect. Yet later on, when the subject of the problem was completely out-of- mind, the total solution to the problem suddenly flashes into our consciousness. We see the solution all at once, sometimes clearly and sometimes just a glimmer. Often it takes considerable effort to manifest the solution concretely on paper. The point is that the problem never left our mind. It just left our consciousness thereby allowing our invisible quantum mind to work on it. Perhaps truly creative people can allow the quantum mind to work along with the classical or conscious mind. Should such types be called "open-minded"?

Regardless, it seems clear that a powerful form of thinking goes on beyond our notice. This is an approximate conclusion with, we feel, perhaps a 40% level of confidence. It is not immediately amenable to measurement. So the level of confidence could never rise to 90 or more per cent. At this time the conclusions are hypothetical but intuitively satisfying- hence the 40% level. We have used suggestion and inference rather than deductive logic to develop an argument for these conclusions. Those who believe in the rigor of logical or rational thinking might label the above arguments as irrational. But it’s our belief that it’s all a matter of approximation. Perhaps we could say that arguments with greater than 90% confidence are rational in order to keep the terminology, yet make it consistent with our conclusions.

Our primary conclusion, that all statements including all thinking is inherently approximate, is therefore rational. It is almost self-evident. We are very confident that it is true. Yet other conclusions expressed above are more approximate. Our conclusion that the mind has visible and invisible components is also rational and not especially new. The conclusion that we have an invisible quantum mind, as well as a visible classical consciousness, follows from Frohlich’s Hypothesis, and therefore is hypothetical yet amenable to experimental measurement, in principle. The further conclusion, that the invisible quantum mind is calculating is conjecture, but possible, in principle.

• Re: Quantum Logic and Consciousness - Greg_Armel/">Greg Armel - April 14, 1999 - 00:37 UTC
  • Re: Quantum Logic and Consciousness - David/">David - April 14, 1999 - 15:21 UTC
    • Re: Quantum Logic and Consciousness - Greg_Armel/">Greg Armel - April 14, 1999 - 22:05 UTC
      • Re: Quantum Logic and Consciousness - David/">David - April 15, 1999 - 13:11 UTC
        • Re: Quantum Logic and Consciousness - Greg_Armel/">Greg Armel - April 15, 1999 - 21:49 UTC
          • Re: Quantum Logic and Consciousness - David/">David - April 16, 1999 - 13:26 UTC
            • Re: Quantum Logic and Consciousness - Greg Armel - April 17, 1999 - 08:07 UTC
              • Re: Quantum Logic and Consciousness - Tön/">Tön - April 19, 1999 - 15:30 UTC
                • Re: Quantum Logic and Consciousness - Photon - April 20, 1999 - 00:57 UTC
                  • Re: Quantum Logic and Consciousness - nåte - April 20, 1999 - 12:30 UTC
    • A word concerning quantum events and certainty... - nåte/">nåte - April 19, 1999 - 14:28 UTC
• Re: Quantum Logic and Consciousness - yanniru/">yanniru - April 14, 1999 - 17:30 UTC