The importance of brain teasers A noumenal world A note on telepathy In the name of ScienceFootnotes
https://manyworlds784.blogspot.com/p/footnotes.html
The importance of brain teasers
The Monty Hall problem
The scenario's opener: The contestant is shown three curtains and told that behind one is a new car and behind each of the others an old boot and she is told to choose one of the three curtains, which we will label from left to right as ABC.
She chooses B.
Monty opens curtain A and reveals a boot. He then surprises her with the question: "Do you want to stick with your choice of A, or do you want to switch to curtain C?"
The problem is: Should she switch?
The counterintuitive answer, according to numerous probabilists, is yes. When the problem, and its answer, first appeared in the press there were howls of protest, including from mathematicians and statisticians.
Here is the reasoning: When she chose B she had a 1/3 chance of winning a car. Hence her choice of B had a 2/3 chance of being wrong. Once Monty opened curtain A, her choice still carried a 2/3 probability of error. Hence a switch to C gives her a 2/3 probability of being right!
Various experiments were done and it was found that a decision to switch tended to "win a car" in two out of three trials.
A few points:
The contestant starts out with complete observer ignorance. She has no idea whether a "common" permutation is in effect and so she might as well assume a randomization process has established the permutation.
Once Monty opens curtain A, the information available to her increases and this affects the probabilities in an unanticipated way. The typical reaction is to say that whether one switches or not is immaterial because the odds are now 50/50. It seems quite bothersome that her mental state can affect the probabilities. After all, when she chose B, she wasn't in the standard view actually making anything happen. So why should the disclosure of the boot at A make any difference as to what actually happens? Hence the thought that we have a new trial which ought to be independent from the previous, making a probability of 1/2.
However, the new information creates conditions for application of conditional probability. This experiment then tends to underscore that Bayesian reasoning has "real world" applications. (There exist Monty Hall proofs that use the Bayesian formula, by the way.)
The initial possible permutations, in terms of car or boot, are:
bcb
bbc
cbb
where bcb means, for example, boot behind curtain A, car behind curtain B, boot behind curtain C.
By raising curtain A, the contestant has the information that two orderings remain, bcb and bbc, leading to the thought that the probability of guessing correctly is 1/2. But before Monty asks her if she wishes to switch, she has made an estimate based upon the initial information. In that case, her probability of guessing wrong is 2/3. If she switches, her probability of winning the car becomes 2/3.
Part of the perplexity stems from the types of randomness and probability at hand. A modern American tends to relate probabilities to assumed random forces in the external world, rather than only to mental state (the principle of insufficient reason).
And yet, if we grant that the six permutations entail six superposed histories, we then must consider a negative feedback control process that might affect the probabilities, as suggested above and described in Toward. The brain's method of "selecting" and "constructing" reality may help explain why a few people are consistently well above or well below the mean in such low-skill games of chance.
This point of course raises a serious difficulty: solipsism. I have addressed that issue, however inadequately, in Toward.
There are a number of other probability brain teasers, with attendant controversy over proper methods and quantifications. A significant issue in these controversies is the usefulness of the probabilistic process in making decisions. As Paul Samuelson observed, the St. Petersburg paradox is a poser that would never happen in actuality because no sane person would make such an offer.
Samuelson on paradoxes
http://www.jstor.org/stable/2722712
Keynes argued similarly that simple expectation value is not always valid, as when the risk is unacceptable no matter how great the payoff.
In the case of the Sleeping Beauty problem, we could notionally run a series of trials to find the limiting relative frequency. But such an experiment is likely to encounter ethics barriers and, even more likely, to be seen as too frivolous for the time and expense.
These and other posers are legitimate questions for those inclined to logical analysis. But note that such scenarios all assume a "linear" background randomness. Such an assumption may serve in many instances, but what of potential exceptions? For example, Sleeping Beauty, from her orientation, may have several superposed "histories" upon awakening. Which history "happens" is, from the experimenter's orientation, partly guided by quantum probabilities. So to ask for the "linear" probability solution to the Sleeping Beauty problem is to ignore the "reality wave" probabilities that affect any solution.
The St. Petersburg paradox
https://en.wikipedia.org/wiki/St._Petersburg_paradox
http://books.google.com/books?id=vNvXkFUbfM8C&pg=PA267&lpg=PA267&dq=robert+martin+st+petersburg+paradox+dictionary&source=bl&ots=x5NVz53Ggc&sig=JrlvGjnw5tcX9SEbgaA1CbKGW9U&hl=en&sa=X&ei=OdzmUdWXItK24AOxqoHQAQ&ved=0CDYQ6AEwAQ#v=onepage&q=robert%20martin%20st%20petersburg%20paradox%20dictionary&f=false
The Sleeping Beauty problem
https://en.wikipedia.org/wiki/Sleeping_Beauty_problem
http://www.u.arizona.edu/~thorgan/papers/other/Beauty.htm
A noumenal world
Ludwig Wittgenstein's Tractatus does something very similar to what Goedel proved rigorously, and reflects the paradoxes of Bertrand Russell and Georg Cantor. That is, philosophy is described by statements, or propositions, but cannot get at "the problems of life." I.e., philosophy uses a mechanistic structure which cannot apprehend directly what others have called the noumenal world. Hence, the propositions used in Tractatus are themselves nonsense. Again, the self-referencing dilemma.
Interestingly, later on Wittgenstein was unable to follow Goedel and dropped work on the philosophy of mathematics.
The phenomenal versus the noumenal is reflected in experiments in which participants at a console are urged to inflict pain on a subject allegedly connected to an electroshock device, but who is in fact an actor simulating pain responses. Here we see Hannah Arendt's "banality of evil" among those who obey the experimenter's commands to inflict greater and greater pain. Those who passively obey criminal orders are responding to the social clues suggested by the situation, and are rather easily persuaded when they see others carrying out obnoxious deeds under "legal" circumstances. They accept rationalizations because, essentially, they see their immediate interest in conforming to settings controlled by some authority. In some cases, they may also have a psychological need to express the primitive predator within (which for most people is expressed during sporting events or entertainment of other sorts). These persons are close to the phenomenal world accepted by Darwinists.
Yet there are those who resist criminal orders or cajoling, whatever the setting. Is this only the Freudian superego that has been programed to bar such behavior (the internalization of parental strictures)? If so, one would suspect that such inhibitions would be weakened over time by consistent exposure to the actions of the herd. Yet, there are those who do not respond well to the blandishments that come from herd leaders and who strenuously resist being pushed into criminal (even if "legalized") behavior. Very often such persons cite religious convictions. Still, as shown by the horrific history of religious warfare, it is possible for a person to have a set of religious ideas that do not work against the stampede effect.
So such peculiar individuals point to an interior moral compass not found in others, or if some others do possess that quality, it has been greatly repressed. The idea that such a moral compass is a consequence of random physical forces is, by today's standards, plausible. But another possibility is connection with a noumenal world, which holds the source of the resistance of banal evil.
Types of intuition
Consider Type 1 intuition:
Let us consider mathematical intuition, in which we have what is really an informed guess as to a particular mathematical truth.
Such intuition is wrong often enough that the word "counterintuitive" is common among mathematicians. Such informed guesswork is based on one's experience with similar sets of relations. So such intuition can improve with experience, thus the respect given to experts.
There is also intuition based on subtle clues, which may tip one off to imminent danger.
Then we have someone who is vexed by a scientific (or other) problem and, no matter how much he spins his mental wheels, is unable to solve it. But while asleep or in a reverie, he suddenly grasps an answer.
The following scenario is plausible:
He has the intuition, based on experience, that the problem is solvable (though he may be wrong about this). In many cases he has quieted the left-brain analytic function in order to permit the right brain to make associations at a more "primitive" level. It is noteworthy that the left brain will call to consciousness the precise left-right, or time sequence, order of a telephone number. When fatigue dims the analytic function, the right brain will call to consciousness the digits, but generally not in left-right order. So one can see how some set of ideas might similarly be placed in an unexpected arrangement by the right brain, leading possibly to a new insight recognized by the integrated mind.
The analytic functions are in some people "closer to consciousness," being centered in the frontal lobes which represent the most recent major adaptation of the human species. The more basic associative functions are often regarded as an expression of an earlier, in an evolution sense, segment of the brain, and so further into the unconscious. This is the region expressed by artists of all sorts.
Mental relaxation means curtailing the analytic function so as to let the associative region express itself. When one is dreaming, it may be said that one's analytic function and executive control is almost shut down -- though the dream censorship shows that the mental monitor is still active.
So we might say that, at times, what is meant by intuition is that the brain's executive function is refereeing the analytic and associative processes and integrating them into an insight that may prove fruitful.
We regard this form of intuition as belonging to the phenomenal, and not the noumenal world -- though the noumenal world's influence is felt, I daresay, at all times.
[Another view of intuition is that of Henri Bergson.
Discussion of Bergson's ideas
http://plato.stanford.edu/entries/bergson/ ]
But Type 2 intuition is the direct knowledge of something without recourse to the phenomenal world associated with the senses (of which there are many, and not five). This form of communication (though who's to say what is doing the communicating) bypasses or transcends the phenomenal world, as when an individual turns about upon being gazed at from a distance. I realize that such a phenomenon doesn't get much support in the available literature; however, I have on many occasions looked at people from behind from a distance -- say while on public transport -- and noticed them turning about and scanning the middle distance, often with a quizzical look on their faces. Of course such an effect can be "explained," but it seems quite apparent that the person -- more often a woman than a man -- is not turning around for identifiable reasons.
The person who turns about may not even be conscious of what prompted her. Part of her brain has "intuitive" or direct knowledge of another's presence. One can view this effect in terms of a Darwinistic survival advantage. That is, one may say that conscious life forms interact with an unknown world, which, by its nature is immaterial and apparently not subject to the laws of physics as they apply in the phenomenal world.
Sometimes, and perhaps always, Type 1 intuition would seem to have at its core Type 2 intuition.
This is to say there is something other than digital and analog reasoning, whether unconscious or not. Hence, one would not expect an artificial intelligence program, no matter how advanced, to have Type 2 intuition (77).
Of course, it is to be expected that some will disparage such ideas as constituting a "revival of vitalism." However, the anti-vitalist must do more than wave hands against "paranormal" events; he must make serious attempts to exclude the likelihood of what I term noumenal effects.
A confusion here is the claim that "because" vitalism can't be tested or falsified in a Popperian sense, the idea is hence unscientific and must be ignored by scientifically minded people. True, there has been an ongoing battle of statistics between the yay sayers and the nay sayers. But I wonder about attempts to use repeated trials, because it seems unlikely that the independence criterion will work. Here is a case where Bayesian methods might be more appropriate.
In the Newtonian-Laplacian era, prior to the quantum mechanics watershed, the concept of randomness was tied to the belief in a fully deterministic cosmos, in which humans are players on a cosmic stage. The Laplacian clockwork model of the cosmos forbids intrinsic randomness among the cogs, wheels and pulleys. The only thing that might, from a human viewpoint, be construed as random would have been the actions of the elan vitale. Of course the devout did not consider the vital spirit to be random at all, but rather saw it as stemming from a direct influence of God.
Curiously, in the minds of some, a clockwork cosmos seemed to imply a need for God. Otherwise, there would be no free will. Humans would be reduced to delusional automatons.
So uncertainty, in the clockwork model, was viewed as simply a lack of sufficient knowledge for making a prediction. In the famous conceit of Laplace, it was thought that a grand robot would be able to calculate every trajectory in the entire universe to any extent forward or backward in time. It was lack of computing power, not inherent randomness that was thought to be behind the uncertainty in gambling systems.
In the early 20th century, R.A. Fisher introduced random selection as a means of minimizing bias. Or, a better way to express this is that he sought ways to screen out unwanted extraneous biases. The methods chosen for filtering out bias were then seen as means of ensuring randomness, and this perspective is still in common use. So one might then define randomness as a consequence of low (in the ideal case zero) bias in sampling. In the 1930s, however, some prominent probabilists and statisticians, influenced by the new quantum theory, accepted the notion of intrinsic background randomness, leading them to dispense with the idea that probability measures a degree of belief. They thought there was an objective discipline of probability that did not require "subjectivism." To them, quantum mechanics justified the idea that a properly calculated probability result yields a "concrete" truth that is true regardless of the observer.
However, physicists do not tend to see quantum logic as an easy way to dispose of subjectivism. In fact, a number take quite the opposite tack, acknowledging a strong logical case for a "spooky" interface between subject and object. Such a noumenal world -- where space and time are "transcended" -- should indeed interact with the phenomenal world in "weird" ways, reminiscent of the incident in the science fiction film The Matrix when the hero observes a cat move oddly, as in a quick film rewind and replay. The example may be silly, but the concept is not.
Now, as a great many reports of "paranormal" events are subjective first-person accounts, it is easy to dismiss them all under the rubric "anecdotal." Clearly, many scientists want nothing to do with the paranormal because it attracts so many starry eyed "true believers" who have very little scientific background. Such notoriety can be a career destroyer for a young academic.
Bruce Hood, who sits on the board of The Skeptic magazine, is a psychologist who take's a neuroscience view of cognition. To Hood, the fact that the "self" is an integrated composite of physical functions implies that consciousness is an epiphenomenon. Hence, religion, faith and assorted superstitions are delusions; there is no self in need of being saved and no evidence of a soul, which is viewed as paranormal nonsense (78).
Hood on 'the self illusion'
http://www.psychologytoday.com/blog/the-self-illusion/201205/what-is-the-self-illusion
While I agree that phenomenal reality, including in part the reality of self, is interwoven with the perception-cognition apparatus, my point is that if we look closely enough, we apprehend something beyond our usual set of conceits and conceptions. The observer has much to do with forming phenomenal reality, and to me this of itself points to a component of cognition which is non-phenomenal or, as we say, noumenal.
Hence, it is not unreasonable after all to think in terms of a noumenal world in which transactions occur that are beyond our immediate ken. It is safe to say that for quite some time a great many men of high caliber knew as self-evident that the world was flat. And yet there were clues, such as sailing ship masts sinking below the horizon, that suggested a revolutionary way of conceiving of the world, one that at first makes no sense: if the world is round, why don't people fall off on the underside?; if this round world is spinning, why isn't everyone hurled off?
So I would say that for the flat-earthers, the reality of a round world was hidden, part of an "implicate order" in need of unfolding.
Writing prior to the development of thermonuclear bombs, J.D. Stranathan gives this account of the discovery of deuterium (79) :
G.H. Aston in 1927 had obtained a value 1.00778 +- 0.00015 for the atomic weight of hydrogen, which differed from the accepted chemical value of 1.00777 +- 0.00002. The figures were so close that no isotope seemed necessary.
But, the discovery of the two heavier isotopes of oxygen forced a reconsideration because their existence meant that the physically derived and chemically derived scales of atomic weight were slightly, but importantly, different. This meant that Aston's value, when converted to the chemical scale, was 1.00750, and this was appreciably smaller than the chemically determined atomic weight. The alleged close agreement was adjudged to be false.
That discrepancy spurred Harold C. Urey, Ferdinand G. Brickwedde and George M. Murphy to hunt for deuterium, which they found and which became a key component in the development of the atomic bomb.
But, this discrepancy turned out to have been the result of a small experimental error. It was shown that the 1927 mass spectrograph value was slightly low, in spite of having been carefully confirmed by Kenneth T. Bainbridge. When the new spectrograph value of 1.0081 was converted to the chemical scale, there was no longer a substantive disagreement. Hence, there was no implication of the existence of deuterium.
Though the chemical and physical scales were revealed to have been slightly different, that revelation, without the 1927 error, would have yielded no reason to expend a great deal of effort searching for heavy hydrogen.
Had heavy water been unknown, would allied scientists have been fearful of German development of atomic fission weapons (British commandos wrecked Germany's heavy water production in occupied Norway) and have spurred the British and American governments into action?
Even had the Manhattan Project been inevitable, it is conceivable that, at the outset of World War II, the existence of heavy water would have remained unknown and might have remained unknown for years to come, thus obviating postwar fulfillment of Edward Teller's dream of a fusion bomb. By the time of deuterium's inevitable (?) discovery, the pressure for development of thermonuclear weapons might well have subsided.
That is, looking back, the alleged probability of the discovery of heavy water was miniscule, and one is tempted to wonder about some noumenal influence that fated humanity with this almost apocalyptic power.
At the least, we have the butterfly effect on steroids.
At any rate, the idea here is not to idolize paranormal phenomena, but rather to urge that there is no sound epistemological reason to justify the "Darwinistic" (or, perhaps, Dawkinsistic) edict of ruling out any noumenal world (or worlds) and the related prohibition of consideration of any interaction between phenomenal and noumenal worlds.
In fact, our attempt to get a feel for the noumenal world is somewhat analogous to the work of Sigmund Freud and others in examining the unconscious world of the mind in order to find better explanations of superficially cognized behaviors. (Yet I hasten to add that, though Carl Jung's brilliance and his concern with what I term the noumenal world cannot be gainsaid, I find that he has often wandered too far from the beaten path even for my tastes.)
A note on telepathy
There is a great deal of material that might be explored on "paranormal" phenomena and their relation to a noumenal world. But, we will simply give one psychologist's thoughts on one "noumenal" subject. Freud was quite open-minded about the possibility of extra-normal thought transference.
In New Introductory Lectures on Psycho-Analysis, he writes: "One is led to the suspicion that this is the original, archaic method of communication between individuals and in the course of phylogenetic evolution it has been replaced with the better method of giving information via signals which are picked up by the sense organs."
He relates a report of Dorothy Burlingham, a psychoanalyst and "trustworthy witness." (She and colleague Anna Freud did pioneering work in child psychology.)
A mother and child were in analysis together. One day the mother spoke during analysis of a gold coin that had played a particular part in one of her childhood experiences. On her return home, the woman's son, who was about 10, came to her room and gave her a gold coin which he asked her to keep for him. Astonished, she asked him where he had got it. It turned out that it had been given him as a birthday present a few months previously, but there was no obvious reason why he had chosen that time to bring her the coin.
Freud sees this report as potential evidence of telepathy. One might also suspect it as an instance of Jungian "synchronicity" or of the reality construction process as discussed in Toward.
At any rate, a few weeks later the woman, on her analyst's instructions, sat down to write an account of the gold coin incident. Just then her child approached her and asked for his coin back, as he wanted to show it during his analysis session.
Freud argues that there is no need for science to fear telepathy (though his collaborator, Ernest Jones, certainly seems to have feared the ridicule the subject might bring); Freud, who never renounced his atheism, remained open-minded not only about telepathy, but about the possibility of other extra-normal phenomena.
From our perspective, we argue that reports of "paranormal" communication and other such phenomena tip us off to an interaction with a noumenal world that is the reality behind appearances -- appearances being phenomena generally accepted as ordinary, whether or not unusual.
See Appendix C:
Freud and telepathy
https://manyworlds784.blogspot.com/p/appendix-c-freud-on-telepathy.html
Freud, of course, was no mathematician and could only give what seemed to him a reasonable assessment of what was going on. Keynes's view was similar to Freud's. He was willing to accept the possibility of telepathy but rejected the "logical limbo" of explaining that and other "psychic phenomena" with other-worldly spirits.
Many scientists, of course, are implacably opposed to the possibility of telepathy in any form, and there has been considerable controversy over the validity of statistical studies for and against such an effect.
On the other hand, Nobelist Josephson has taken on the "scientific system" and upheld the existence of telepathy, seeing it as a consequence of quantum effects.
Josephson's page of psychic phenomena links
http://www.tcm.phy.cam.ac.uk/~bdj10/psi.html
In the name of Science
The tension between Bayesian reasoning and the intrinsic background randomness imputed to quantum physics perforce implies Wheeler's "participatory universe" in which perception and "background reality" (the stage on which we act, with the props) merge to an extent far greater than has previously been suspected in the halls of academia -- despite herculean efforts to exorcise this demon from the Realm of Science. In other words, we find that determinism and indeterminism are inextricably entangled at the point where consciousness meets "reality."
Nevertheless, one cannot avoid the self-referencing issue. In fact, if we suspend the continuity assumptions of space and time, which quantum theory tells us we should, we arrive at infinite regress. But even with continuity assumptions, one can see infinite regress in say an asymmetric three-sink vector field. Where is the zero point at time Tx? In a two-sink field, the symmetry guarantees that the null point can be exactly determined. But in a three-sink field that is not symmetric, one always faces something analogous to quantum uncertainty -- and which also points to problems of infinite regress.
We can think of this in terms of a nonlinear feedback control system. Some such systems maintain an easily understood homeostasis. The thermostat is a case in point. But others need not follow such a simple path to homeostasis. A particular input value may yield a highly unpredictable output within the constraint of homeostasis. In such systems, we tend to find thresholds and properties to be the best we can do in the way of useful information. Probabilities may help us in estimating properties, as we find in the behavior of idealized gas systems.
However, these probabilities cannot really be frequency based, except in the classical sense based on the binomial distribution. Trials can't be done. E.T. Jaynes thought that the Shannon approach of simply expropriating what I call the classical approach sufficed for molecular physics. However, I add that when Einstein used probabilities to establish that Brownian motion conformed to the behavior of jostling atoms, he was not only implicitly using the classical approach, but also what we might call a propensity approach in which the presumed probabilities were assigned in accordance with system start-up information, which in this case was given by Newtonian and Maxwellian mechanics.
The above considerations suggest that it is a mistake to assume that human affairs are correctly portrayed in terms of intrinsic randomness played out in some background framework that is disentangled from the observer's consciousness.
In fact, we may see some kind of malleable interconnectedness that transcends the phenomenal world.
This also suggests that linear probability reckoning works well enough within limits. We use the word linear to mean that the influences among events are small enough so as to be negligible, permitting us the criterion of independence. (Even conditional probabilities rest on an assumption of independence at some point.) The limits are not so easily defined, as we have no system of nonlinear differential equations to represent the sharing of "reality" among minds or the balance between the brain's reality construction versus "external" reality.
Certainly in the extremes, probability assessments do not seem terribly satisfactory within a well-wrought metaphysical system, and should not be so used, even though "linear" phenomenal randomness is viewed as a component of the Creed of Science, being a basic assumption of many a latter day atheist, whether or not scientifically trained.
"Everyone knows" that some phenomena are considered to be phantasms of the mind, whether they be optical or auditory illusions or delusions caused by temporary or permanent brain impairment, and that, otherwise, these phenomena are objective, meaning that there is wide agreement that such phenomena exist independently of any observer, especially if such phenomena have been tested and verified by an accepted scientific process. However, the underlying assumptions are much fuzzier than the philosophical advocates of "hard science" would have us believe.
So this suggests there exists some holistic "uber force," or organizing principle. Certainly we would not expect an atheist to believe this uber force is conscious, though he or she might, like Einstein, accept the existence of such an entity in Spinoza's pan-natural sense. On the other hand, neither Einstein, nor other disciples of Spinoza, had a logical basis for rejecting the possibility that this uber force is conscious (and willing to intervene in human affairs). This uber force must transcend the laws of physics of this universe (and any clonelike cosmoses "out there"). Here is deep mystery; "dark energy" is a term that comes to mind.
I have not formalized the claim for such an uber force. However we do have Goedel's ontological proof of God's existence, though I am unsure I agree that such a method is valid. An immediate thought is that the concept of "positive" requires a subjective interpretation. On the other hand, we have shown that the human brain/mind is a major player in the construction of so-called "concrete" phenomenal reality.
Goedel's ontological proof of God's existence
http://math.stackexchange.com/questions/248548/godels-ontological-proof-how-does-it-work
Background of god theorem
https://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof
Formalization, mechanization and automation of Gödel's proof of god's existence
http://arxiv.org/abs/1308.4526
In a private communication, a mathematician friend responded thus:
"For example, BMW is a good car. BMW produces nitrous oxide pollution. Therefore nitrous oxide pollution is good."
My friend later added: "But maybe the point of the ontological proof is not 'good' but 'perfect.' God is supposed to be perfect. A perfect car would not pollute."
Again, the property of goodness requires more attention; though dubious, I am not fully unpersuaded of Goedel's offering.
In this respect, we may ponder Tegmark's mathematical universe hypothesis, which he takes to imply that all computable mathematical structures exist.
Tegmark's mathematical universe paper
http://arxiv.org/pdf/gr-qc/9704009v2.pdf
Tegmark's mathematical universe hypothesis has been stated thus: Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense. So in worlds "complex enough to contain self-aware substructures," these entities "will subjectively perceive themselves as existing in a physically 'real' world." The hypothesis suggests that worlds corresponding to different sets of initial conditions, physical constants, or altogether different equations may be considered equally real. Tegmark elaborates his conjecture into the computable universe hypothesis, which posits that all computable mathematical structures exist.
Here I note my paper:
On Hilbert's sixth problem
http://kryptograff.blogspot.com/2007/06/on-hilberts-sixth-problem.html
which argues against the notion that the entire cosmos can be modeled as a Boolean circuit or Turing machine.
An amusing aside:
Go to Chapter 2 HERE.
The Monty Hall problem
The scenario's opener: The contestant is shown three curtains and told that behind one is a new car and behind each of the others an old boot and she is told to choose one of the three curtains, which we will label from left to right as ABC.
She chooses B.
Monty opens curtain A and reveals a boot. He then surprises her with the question: "Do you want to stick with your choice of A, or do you want to switch to curtain C?"
The problem is: Should she switch?
The counterintuitive answer, according to numerous probabilists, is yes. When the problem, and its answer, first appeared in the press there were howls of protest, including from mathematicians and statisticians.
Here is the reasoning: When she chose B she had a 1/3 chance of winning a car. Hence her choice of B had a 2/3 chance of being wrong. Once Monty opened curtain A, her choice still carried a 2/3 probability of error. Hence a switch to C gives her a 2/3 probability of being right!
Various experiments were done and it was found that a decision to switch tended to "win a car" in two out of three trials.
A few points:
The contestant starts out with complete observer ignorance. She has no idea whether a "common" permutation is in effect and so she might as well assume a randomization process has established the permutation.
Once Monty opens curtain A, the information available to her increases and this affects the probabilities in an unanticipated way. The typical reaction is to say that whether one switches or not is immaterial because the odds are now 50/50. It seems quite bothersome that her mental state can affect the probabilities. After all, when she chose B, she wasn't in the standard view actually making anything happen. So why should the disclosure of the boot at A make any difference as to what actually happens? Hence the thought that we have a new trial which ought to be independent from the previous, making a probability of 1/2.
However, the new information creates conditions for application of conditional probability. This experiment then tends to underscore that Bayesian reasoning has "real world" applications. (There exist Monty Hall proofs that use the Bayesian formula, by the way.)
The initial possible permutations, in terms of car or boot, are:
bcb
bbc
cbb
where bcb means, for example, boot behind curtain A, car behind curtain B, boot behind curtain C.
By raising curtain A, the contestant has the information that two orderings remain, bcb and bbc, leading to the thought that the probability of guessing correctly is 1/2. But before Monty asks her if she wishes to switch, she has made an estimate based upon the initial information. In that case, her probability of guessing wrong is 2/3. If she switches, her probability of winning the car becomes 2/3.
Part of the perplexity stems from the types of randomness and probability at hand. A modern American tends to relate probabilities to assumed random forces in the external world, rather than only to mental state (the principle of insufficient reason).
And yet, if we grant that the six permutations entail six superposed histories, we then must consider a negative feedback control process that might affect the probabilities, as suggested above and described in Toward. The brain's method of "selecting" and "constructing" reality may help explain why a few people are consistently well above or well below the mean in such low-skill games of chance.
This point of course raises a serious difficulty: solipsism. I have addressed that issue, however inadequately, in Toward.
There are a number of other probability brain teasers, with attendant controversy over proper methods and quantifications. A significant issue in these controversies is the usefulness of the probabilistic process in making decisions. As Paul Samuelson observed, the St. Petersburg paradox is a poser that would never happen in actuality because no sane person would make such an offer.
Samuelson on paradoxes
http://www.jstor.org/stable/2722712
Keynes argued similarly that simple expectation value is not always valid, as when the risk is unacceptable no matter how great the payoff.
In the case of the Sleeping Beauty problem, we could notionally run a series of trials to find the limiting relative frequency. But such an experiment is likely to encounter ethics barriers and, even more likely, to be seen as too frivolous for the time and expense.
These and other posers are legitimate questions for those inclined to logical analysis. But note that such scenarios all assume a "linear" background randomness. Such an assumption may serve in many instances, but what of potential exceptions? For example, Sleeping Beauty, from her orientation, may have several superposed "histories" upon awakening. Which history "happens" is, from the experimenter's orientation, partly guided by quantum probabilities. So to ask for the "linear" probability solution to the Sleeping Beauty problem is to ignore the "reality wave" probabilities that affect any solution.
The St. Petersburg paradox
https://en.wikipedia.org/wiki/St._Petersburg_paradox
http://books.google.com/books?id=vNvXkFUbfM8C&pg=PA267&lpg=PA267&dq=robert+martin+st+petersburg+paradox+dictionary&source=bl&ots=x5NVz53Ggc&sig=JrlvGjnw5tcX9SEbgaA1CbKGW9U&hl=en&sa=X&ei=OdzmUdWXItK24AOxqoHQAQ&ved=0CDYQ6AEwAQ#v=onepage&q=robert%20martin%20st%20petersburg%20paradox%20dictionary&f=false
The Sleeping Beauty problem
https://en.wikipedia.org/wiki/Sleeping_Beauty_problem
http://www.u.arizona.edu/~thorgan/papers/other/Beauty.htm
A noumenal world
Ludwig Wittgenstein's Tractatus does something very similar to what Goedel proved rigorously, and reflects the paradoxes of Bertrand Russell and Georg Cantor. That is, philosophy is described by statements, or propositions, but cannot get at "the problems of life." I.e., philosophy uses a mechanistic structure which cannot apprehend directly what others have called the noumenal world. Hence, the propositions used in Tractatus are themselves nonsense. Again, the self-referencing dilemma.
Interestingly, later on Wittgenstein was unable to follow Goedel and dropped work on the philosophy of mathematics.
The phenomenal versus the noumenal is reflected in experiments in which participants at a console are urged to inflict pain on a subject allegedly connected to an electroshock device, but who is in fact an actor simulating pain responses. Here we see Hannah Arendt's "banality of evil" among those who obey the experimenter's commands to inflict greater and greater pain. Those who passively obey criminal orders are responding to the social clues suggested by the situation, and are rather easily persuaded when they see others carrying out obnoxious deeds under "legal" circumstances. They accept rationalizations because, essentially, they see their immediate interest in conforming to settings controlled by some authority. In some cases, they may also have a psychological need to express the primitive predator within (which for most people is expressed during sporting events or entertainment of other sorts). These persons are close to the phenomenal world accepted by Darwinists.
Yet there are those who resist criminal orders or cajoling, whatever the setting. Is this only the Freudian superego that has been programed to bar such behavior (the internalization of parental strictures)? If so, one would suspect that such inhibitions would be weakened over time by consistent exposure to the actions of the herd. Yet, there are those who do not respond well to the blandishments that come from herd leaders and who strenuously resist being pushed into criminal (even if "legalized") behavior. Very often such persons cite religious convictions. Still, as shown by the horrific history of religious warfare, it is possible for a person to have a set of religious ideas that do not work against the stampede effect.
So such peculiar individuals point to an interior moral compass not found in others, or if some others do possess that quality, it has been greatly repressed. The idea that such a moral compass is a consequence of random physical forces is, by today's standards, plausible. But another possibility is connection with a noumenal world, which holds the source of the resistance of banal evil.
Types of intuition
Consider Type 1 intuition:
Let us consider mathematical intuition, in which we have what is really an informed guess as to a particular mathematical truth.
Such intuition is wrong often enough that the word "counterintuitive" is common among mathematicians. Such informed guesswork is based on one's experience with similar sets of relations. So such intuition can improve with experience, thus the respect given to experts.
There is also intuition based on subtle clues, which may tip one off to imminent danger.
Then we have someone who is vexed by a scientific (or other) problem and, no matter how much he spins his mental wheels, is unable to solve it. But while asleep or in a reverie, he suddenly grasps an answer.
The following scenario is plausible:
He has the intuition, based on experience, that the problem is solvable (though he may be wrong about this). In many cases he has quieted the left-brain analytic function in order to permit the right brain to make associations at a more "primitive" level. It is noteworthy that the left brain will call to consciousness the precise left-right, or time sequence, order of a telephone number. When fatigue dims the analytic function, the right brain will call to consciousness the digits, but generally not in left-right order. So one can see how some set of ideas might similarly be placed in an unexpected arrangement by the right brain, leading possibly to a new insight recognized by the integrated mind.
The analytic functions are in some people "closer to consciousness," being centered in the frontal lobes which represent the most recent major adaptation of the human species. The more basic associative functions are often regarded as an expression of an earlier, in an evolution sense, segment of the brain, and so further into the unconscious. This is the region expressed by artists of all sorts.
Mental relaxation means curtailing the analytic function so as to let the associative region express itself. When one is dreaming, it may be said that one's analytic function and executive control is almost shut down -- though the dream censorship shows that the mental monitor is still active.
So we might say that, at times, what is meant by intuition is that the brain's executive function is refereeing the analytic and associative processes and integrating them into an insight that may prove fruitful.
We regard this form of intuition as belonging to the phenomenal, and not the noumenal world -- though the noumenal world's influence is felt, I daresay, at all times.
[Another view of intuition is that of Henri Bergson.
Discussion of Bergson's ideas
http://plato.stanford.edu/entries/bergson/ ]
But Type 2 intuition is the direct knowledge of something without recourse to the phenomenal world associated with the senses (of which there are many, and not five). This form of communication (though who's to say what is doing the communicating) bypasses or transcends the phenomenal world, as when an individual turns about upon being gazed at from a distance. I realize that such a phenomenon doesn't get much support in the available literature; however, I have on many occasions looked at people from behind from a distance -- say while on public transport -- and noticed them turning about and scanning the middle distance, often with a quizzical look on their faces. Of course such an effect can be "explained," but it seems quite apparent that the person -- more often a woman than a man -- is not turning around for identifiable reasons.
The person who turns about may not even be conscious of what prompted her. Part of her brain has "intuitive" or direct knowledge of another's presence. One can view this effect in terms of a Darwinistic survival advantage. That is, one may say that conscious life forms interact with an unknown world, which, by its nature is immaterial and apparently not subject to the laws of physics as they apply in the phenomenal world.
Sometimes, and perhaps always, Type 1 intuition would seem to have at its core Type 2 intuition.
This is to say there is something other than digital and analog reasoning, whether unconscious or not. Hence, one would not expect an artificial intelligence program, no matter how advanced, to have Type 2 intuition (77).
Of course, it is to be expected that some will disparage such ideas as constituting a "revival of vitalism." However, the anti-vitalist must do more than wave hands against "paranormal" events; he must make serious attempts to exclude the likelihood of what I term noumenal effects.
A confusion here is the claim that "because" vitalism can't be tested or falsified in a Popperian sense, the idea is hence unscientific and must be ignored by scientifically minded people. True, there has been an ongoing battle of statistics between the yay sayers and the nay sayers. But I wonder about attempts to use repeated trials, because it seems unlikely that the independence criterion will work. Here is a case where Bayesian methods might be more appropriate.
In the Newtonian-Laplacian era, prior to the quantum mechanics watershed, the concept of randomness was tied to the belief in a fully deterministic cosmos, in which humans are players on a cosmic stage. The Laplacian clockwork model of the cosmos forbids intrinsic randomness among the cogs, wheels and pulleys. The only thing that might, from a human viewpoint, be construed as random would have been the actions of the elan vitale. Of course the devout did not consider the vital spirit to be random at all, but rather saw it as stemming from a direct influence of God.
Curiously, in the minds of some, a clockwork cosmos seemed to imply a need for God. Otherwise, there would be no free will. Humans would be reduced to delusional automatons.
So uncertainty, in the clockwork model, was viewed as simply a lack of sufficient knowledge for making a prediction. In the famous conceit of Laplace, it was thought that a grand robot would be able to calculate every trajectory in the entire universe to any extent forward or backward in time. It was lack of computing power, not inherent randomness that was thought to be behind the uncertainty in gambling systems.
In the early 20th century, R.A. Fisher introduced random selection as a means of minimizing bias. Or, a better way to express this is that he sought ways to screen out unwanted extraneous biases. The methods chosen for filtering out bias were then seen as means of ensuring randomness, and this perspective is still in common use. So one might then define randomness as a consequence of low (in the ideal case zero) bias in sampling. In the 1930s, however, some prominent probabilists and statisticians, influenced by the new quantum theory, accepted the notion of intrinsic background randomness, leading them to dispense with the idea that probability measures a degree of belief. They thought there was an objective discipline of probability that did not require "subjectivism." To them, quantum mechanics justified the idea that a properly calculated probability result yields a "concrete" truth that is true regardless of the observer.
However, physicists do not tend to see quantum logic as an easy way to dispose of subjectivism. In fact, a number take quite the opposite tack, acknowledging a strong logical case for a "spooky" interface between subject and object. Such a noumenal world -- where space and time are "transcended" -- should indeed interact with the phenomenal world in "weird" ways, reminiscent of the incident in the science fiction film The Matrix when the hero observes a cat move oddly, as in a quick film rewind and replay. The example may be silly, but the concept is not.
Now, as a great many reports of "paranormal" events are subjective first-person accounts, it is easy to dismiss them all under the rubric "anecdotal." Clearly, many scientists want nothing to do with the paranormal because it attracts so many starry eyed "true believers" who have very little scientific background. Such notoriety can be a career destroyer for a young academic.
Bruce Hood, who sits on the board of The Skeptic magazine, is a psychologist who take's a neuroscience view of cognition. To Hood, the fact that the "self" is an integrated composite of physical functions implies that consciousness is an epiphenomenon. Hence, religion, faith and assorted superstitions are delusions; there is no self in need of being saved and no evidence of a soul, which is viewed as paranormal nonsense (78).
Hood on 'the self illusion'
http://www.psychologytoday.com/blog/the-self-illusion/201205/what-is-the-self-illusion
While I agree that phenomenal reality, including in part the reality of self, is interwoven with the perception-cognition apparatus, my point is that if we look closely enough, we apprehend something beyond our usual set of conceits and conceptions. The observer has much to do with forming phenomenal reality, and to me this of itself points to a component of cognition which is non-phenomenal or, as we say, noumenal.
Hence, it is not unreasonable after all to think in terms of a noumenal world in which transactions occur that are beyond our immediate ken. It is safe to say that for quite some time a great many men of high caliber knew as self-evident that the world was flat. And yet there were clues, such as sailing ship masts sinking below the horizon, that suggested a revolutionary way of conceiving of the world, one that at first makes no sense: if the world is round, why don't people fall off on the underside?; if this round world is spinning, why isn't everyone hurled off?
So I would say that for the flat-earthers, the reality of a round world was hidden, part of an "implicate order" in need of unfolding.
Writing prior to the development of thermonuclear bombs, J.D. Stranathan gives this account of the discovery of deuterium (79) :
G.H. Aston in 1927 had obtained a value 1.00778 +- 0.00015 for the atomic weight of hydrogen, which differed from the accepted chemical value of 1.00777 +- 0.00002. The figures were so close that no isotope seemed necessary.
But, the discovery of the two heavier isotopes of oxygen forced a reconsideration because their existence meant that the physically derived and chemically derived scales of atomic weight were slightly, but importantly, different. This meant that Aston's value, when converted to the chemical scale, was 1.00750, and this was appreciably smaller than the chemically determined atomic weight. The alleged close agreement was adjudged to be false.
That discrepancy spurred Harold C. Urey, Ferdinand G. Brickwedde and George M. Murphy to hunt for deuterium, which they found and which became a key component in the development of the atomic bomb.
But, this discrepancy turned out to have been the result of a small experimental error. It was shown that the 1927 mass spectrograph value was slightly low, in spite of having been carefully confirmed by Kenneth T. Bainbridge. When the new spectrograph value of 1.0081 was converted to the chemical scale, there was no longer a substantive disagreement. Hence, there was no implication of the existence of deuterium.
Though the chemical and physical scales were revealed to have been slightly different, that revelation, without the 1927 error, would have yielded no reason to expend a great deal of effort searching for heavy hydrogen.
Had heavy water been unknown, would allied scientists have been fearful of German development of atomic fission weapons (British commandos wrecked Germany's heavy water production in occupied Norway) and have spurred the British and American governments into action?
Even had the Manhattan Project been inevitable, it is conceivable that, at the outset of World War II, the existence of heavy water would have remained unknown and might have remained unknown for years to come, thus obviating postwar fulfillment of Edward Teller's dream of a fusion bomb. By the time of deuterium's inevitable (?) discovery, the pressure for development of thermonuclear weapons might well have subsided.
That is, looking back, the alleged probability of the discovery of heavy water was miniscule, and one is tempted to wonder about some noumenal influence that fated humanity with this almost apocalyptic power.
At the least, we have the butterfly effect on steroids.
At any rate, the idea here is not to idolize paranormal phenomena, but rather to urge that there is no sound epistemological reason to justify the "Darwinistic" (or, perhaps, Dawkinsistic) edict of ruling out any noumenal world (or worlds) and the related prohibition of consideration of any interaction between phenomenal and noumenal worlds.
In fact, our attempt to get a feel for the noumenal world is somewhat analogous to the work of Sigmund Freud and others in examining the unconscious world of the mind in order to find better explanations of superficially cognized behaviors. (Yet I hasten to add that, though Carl Jung's brilliance and his concern with what I term the noumenal world cannot be gainsaid, I find that he has often wandered too far from the beaten path even for my tastes.)
A note on telepathy
There is a great deal of material that might be explored on "paranormal" phenomena and their relation to a noumenal world. But, we will simply give one psychologist's thoughts on one "noumenal" subject. Freud was quite open-minded about the possibility of extra-normal thought transference.
In New Introductory Lectures on Psycho-Analysis, he writes: "One is led to the suspicion that this is the original, archaic method of communication between individuals and in the course of phylogenetic evolution it has been replaced with the better method of giving information via signals which are picked up by the sense organs."
He relates a report of Dorothy Burlingham, a psychoanalyst and "trustworthy witness." (She and colleague Anna Freud did pioneering work in child psychology.)
A mother and child were in analysis together. One day the mother spoke during analysis of a gold coin that had played a particular part in one of her childhood experiences. On her return home, the woman's son, who was about 10, came to her room and gave her a gold coin which he asked her to keep for him. Astonished, she asked him where he had got it. It turned out that it had been given him as a birthday present a few months previously, but there was no obvious reason why he had chosen that time to bring her the coin.
Freud sees this report as potential evidence of telepathy. One might also suspect it as an instance of Jungian "synchronicity" or of the reality construction process as discussed in Toward.
At any rate, a few weeks later the woman, on her analyst's instructions, sat down to write an account of the gold coin incident. Just then her child approached her and asked for his coin back, as he wanted to show it during his analysis session.
Freud argues that there is no need for science to fear telepathy (though his collaborator, Ernest Jones, certainly seems to have feared the ridicule the subject might bring); Freud, who never renounced his atheism, remained open-minded not only about telepathy, but about the possibility of other extra-normal phenomena.
From our perspective, we argue that reports of "paranormal" communication and other such phenomena tip us off to an interaction with a noumenal world that is the reality behind appearances -- appearances being phenomena generally accepted as ordinary, whether or not unusual.
See Appendix C:
Freud and telepathy
https://manyworlds784.blogspot.com/p/appendix-c-freud-on-telepathy.html
Freud, of course, was no mathematician and could only give what seemed to him a reasonable assessment of what was going on. Keynes's view was similar to Freud's. He was willing to accept the possibility of telepathy but rejected the "logical limbo" of explaining that and other "psychic phenomena" with other-worldly spirits.
Many scientists, of course, are implacably opposed to the possibility of telepathy in any form, and there has been considerable controversy over the validity of statistical studies for and against such an effect.
On the other hand, Nobelist Josephson has taken on the "scientific system" and upheld the existence of telepathy, seeing it as a consequence of quantum effects.
Josephson's page of psychic phenomena links
http://www.tcm.phy.cam.ac.uk/~bdj10/psi.html
In the name of Science
The tension between Bayesian reasoning and the intrinsic background randomness imputed to quantum physics perforce implies Wheeler's "participatory universe" in which perception and "background reality" (the stage on which we act, with the props) merge to an extent far greater than has previously been suspected in the halls of academia -- despite herculean efforts to exorcise this demon from the Realm of Science. In other words, we find that determinism and indeterminism are inextricably entangled at the point where consciousness meets "reality."
Nevertheless, one cannot avoid the self-referencing issue. In fact, if we suspend the continuity assumptions of space and time, which quantum theory tells us we should, we arrive at infinite regress. But even with continuity assumptions, one can see infinite regress in say an asymmetric three-sink vector field. Where is the zero point at time Tx? In a two-sink field, the symmetry guarantees that the null point can be exactly determined. But in a three-sink field that is not symmetric, one always faces something analogous to quantum uncertainty -- and which also points to problems of infinite regress.
We can think of this in terms of a nonlinear feedback control system. Some such systems maintain an easily understood homeostasis. The thermostat is a case in point. But others need not follow such a simple path to homeostasis. A particular input value may yield a highly unpredictable output within the constraint of homeostasis. In such systems, we tend to find thresholds and properties to be the best we can do in the way of useful information. Probabilities may help us in estimating properties, as we find in the behavior of idealized gas systems.
However, these probabilities cannot really be frequency based, except in the classical sense based on the binomial distribution. Trials can't be done. E.T. Jaynes thought that the Shannon approach of simply expropriating what I call the classical approach sufficed for molecular physics. However, I add that when Einstein used probabilities to establish that Brownian motion conformed to the behavior of jostling atoms, he was not only implicitly using the classical approach, but also what we might call a propensity approach in which the presumed probabilities were assigned in accordance with system start-up information, which in this case was given by Newtonian and Maxwellian mechanics.
The above considerations suggest that it is a mistake to assume that human affairs are correctly portrayed in terms of intrinsic randomness played out in some background framework that is disentangled from the observer's consciousness.
In fact, we may see some kind of malleable interconnectedness that transcends the phenomenal world.
This also suggests that linear probability reckoning works well enough within limits. We use the word linear to mean that the influences among events are small enough so as to be negligible, permitting us the criterion of independence. (Even conditional probabilities rest on an assumption of independence at some point.) The limits are not so easily defined, as we have no system of nonlinear differential equations to represent the sharing of "reality" among minds or the balance between the brain's reality construction versus "external" reality.
Certainly in the extremes, probability assessments do not seem terribly satisfactory within a well-wrought metaphysical system, and should not be so used, even though "linear" phenomenal randomness is viewed as a component of the Creed of Science, being a basic assumption of many a latter day atheist, whether or not scientifically trained.
"Everyone knows" that some phenomena are considered to be phantasms of the mind, whether they be optical or auditory illusions or delusions caused by temporary or permanent brain impairment, and that, otherwise, these phenomena are objective, meaning that there is wide agreement that such phenomena exist independently of any observer, especially if such phenomena have been tested and verified by an accepted scientific process. However, the underlying assumptions are much fuzzier than the philosophical advocates of "hard science" would have us believe.
So this suggests there exists some holistic "uber force," or organizing principle. Certainly we would not expect an atheist to believe this uber force is conscious, though he or she might, like Einstein, accept the existence of such an entity in Spinoza's pan-natural sense. On the other hand, neither Einstein, nor other disciples of Spinoza, had a logical basis for rejecting the possibility that this uber force is conscious (and willing to intervene in human affairs). This uber force must transcend the laws of physics of this universe (and any clonelike cosmoses "out there"). Here is deep mystery; "dark energy" is a term that comes to mind.
I have not formalized the claim for such an uber force. However we do have Goedel's ontological proof of God's existence, though I am unsure I agree that such a method is valid. An immediate thought is that the concept of "positive" requires a subjective interpretation. On the other hand, we have shown that the human brain/mind is a major player in the construction of so-called "concrete" phenomenal reality.
Goedel's ontological proof of God's existence
http://math.stackexchange.com/questions/248548/godels-ontological-proof-how-does-it-work
Background of god theorem
https://en.wikipedia.org/wiki/G%C3%B6del's_ontological_proof
Formalization, mechanization and automation of Gödel's proof of god's existence
http://arxiv.org/abs/1308.4526
In a private communication, a mathematician friend responded thus:
"For example, BMW is a good car. BMW produces nitrous oxide pollution. Therefore nitrous oxide pollution is good."
My friend later added: "But maybe the point of the ontological proof is not 'good' but 'perfect.' God is supposed to be perfect. A perfect car would not pollute."
Again, the property of goodness requires more attention; though dubious, I am not fully unpersuaded of Goedel's offering.
In this respect, we may ponder Tegmark's mathematical universe hypothesis, which he takes to imply that all computable mathematical structures exist.
Tegmark's mathematical universe paper
http://arxiv.org/pdf/gr-qc/9704009v2.pdf
Tegmark's mathematical universe hypothesis has been stated thus: Our external physical reality is a mathematical structure. That is, the physical universe is mathematics in a well-defined sense. So in worlds "complex enough to contain self-aware substructures," these entities "will subjectively perceive themselves as existing in a physically 'real' world." The hypothesis suggests that worlds corresponding to different sets of initial conditions, physical constants, or altogether different equations may be considered equally real. Tegmark elaborates his conjecture into the computable universe hypothesis, which posits that all computable mathematical structures exist.
Here I note my paper:
On Hilbert's sixth problem
http://kryptograff.blogspot.com/2007/06/on-hilberts-sixth-problem.html
which argues against the notion that the entire cosmos can be modeled as a Boolean circuit or Turing machine.
An amusing aside:
1. Assuming the energy resources of the universe are finite, there is a greatest expressible integer.
2. (The greatest expressible number) + 1.
3. Therefore God exists.
Arthur Eddington once observed that biologists were more likely to be in the camp of strict materialists than physicists. Noteworthy examples are Sigmund Freud, who considered himself a biologist, and J.B.S. Haldane, a pioneer in population genetics. Both came of age during the first wave of the Darwinian revolution of the 19th century, a paradigm that captured many minds as a model that successfully screened out God just as, as it was thought, the clockwork cosmos of Laplace had disposed of the need for the God hypothesis. Freud and Haldane were convinced atheists, and it is safe to say that Freud's view of extraordinary communication was thoroughly materialist. Haldane's severe materialism can be seen in the context of his long-term involvement in communism.
Though physicists often remained reticent about their views on God, those who understood the issues of quantum theory were inclined toward some underlying transcendency. This situation remains as true today as it did in the 1930s, as we see with the effectively phenomenalist/materialist world view of the biologist Richard Dawkins, who is conducting a Lennonist crusade against belief in God.
A previous generation witnessed Bertrand Russell, the logician, in the role of atheist crusader. Russell with his colleague Alfred North Whitehead, in their Principia Mathematica had tried to assure that formal knowledge could be described completely and consistently. One can see that such an achievement would have bolstered the cause of atheism. If, at least in principle, the universe can be "tamed" by human knowledge, then one can explain every step of every process without worry about God, or some transcendental entity. God, like the ether, would have been consigned to the rubbish heap of history.
Of course, in 1931 Goedel proved this goal an illusion, using Principia Mathematica to demonstrate his proof. Goedel's incompleteness theorem caught the inrushing tide of the quantum revolution, which brought the question of traditional scientific external reality into question. The revolution had in part been touched off by experimental confirmation of Louis de Broglie's proposed matter waves, an idea that made use of Einstein's energy/matter relation to posit matter waves, So the doctrine of materialism was not only technically in question, but, because material waves obeyed probability amplitudes, the very existence of matter had become a very strange puzzle, a situation that continues today.
Even before this second quantum revolution, the astrophysicist Arthur Eddington had used poetic imagery to put into perspective Einstein's spacetime weirdness (77aa).
Perhaps to move His laughter at their quaint opinions wide Hereafter, when they come to model Heaven And calculate the stars, how they will wield The mighty frame, how build, unbuild, contrive To save appearances. -- John Milton, Paradise Lost
Quantum weirdness only strengthened Eddington's belief in a noumenal realm (77a).
"A defence of the mystic might run something like this: We have acknowledged that the entities of physics can from their very nature form only a partial aspect of the reality. How are we to deal with the other part?" Not with the view that "the whole of consciousness is reflected in the dance of electrons in the brain" and that "quasi-metrical aspects" suffice.
Eddington, in countering Russell on what Eddingon said was Russell's charge of an attempt to "prove" distinctive beliefs of religion, takes aim at loose usage of the word "reality," warning that it is possible to employ that word as a talisman providing "magic comfort." And, we add that cognitive dissonance with internal assumptions and rationalizations usually provokes defensive reactions.
"We all know that there are regions of the human spirit untrammeled by the world of physics" and that are associated with an "Inner Light proceeding from a greater power than ours."
Another English astrophysicist, James Jeans, also inclined toward some noumenal presence (77a).
Jeans writes that the surprising results of the theories of relativistic and quantum physics leads to "the general recognition that we are not yet in contact with ultimate reality." We are only able to see the shadows of that reality. Adopting John Locke's assertion that "the real essence of substances is unknowable," Jeans argues that scientific inquiry can only study the laws of the changes of substances, which "produce the phenomena of the external world."
In a chapter entitled, "In the Mind of Some Eternal Spirit," Jeans writes: "The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures." Or, I would say, the typical human brain/mind's empirically derived expectations of physical reality are inapplicable. In a word, the pictures we use for our existence are physically false, delusional, though that is not to say the delusional thinking imparted via the cultic group mind and by the essentials of the brain/mind system (whatever they are) are easily dispensed with, or even safe to dispense with absent something reliably superior.
In a play on the old epigram that the cosmos had been designed by a "Great Architect," Jeans writes of the cosmos "appearing to have been designed by a pure mathematician."
He adds: "Our remote ancestors tried to interpret nature in terms of anthropomorphic concepts and failed. The efforts of our nearer ancestors to interpret nature on engineering lines proved equally inadequate. Nature refused to accommodate herself to either of these man-made moulds. On the other hand, our efforts to interpret nature in terms of the concepts of pure mathematics have, so far, proved brilliantly successful."
Further, "To my mind the laws which nature obeys are less suggestive of those which a machine obeys in its motion than those which a musician obeys in writing a fugue, or a poet in composing a sonnet."
Remarks:
Materialism, writes Heisenberg, is a concept that at root is found wanting. "For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or -- in Plato's sense -- Ideas, which can be unambiguously spoken of in the language of mathematics."
Heisenberg relates the paradox of Parmenides: "Only being is; non-being is not. But if only being is, there cannot be anything outside this being that articulates it or could bring about changes. Hence being will have to be conceived of as eternal, uniform, and unlimited in space and time. The changes we experience can thus be only an illusion."
Though initially unnerved that his wave mechanics could not resolve the "quantum jump" problem, Erwin Schroedinger's concept of reality evolved.
Schroedinger did not care for the idea he attributes to another quantum pioneer, Pascual Jordan, that quantum indeterminacy is at the basis of free will, an idea echoed in some ways by Penrose. If free will steps in to "fill the gap of indeterminacy," writes Schroedinger, the quantum statistics will change, thus disrupting the laws of nature.
In the same article, Schroedinger talks about how scientific inquiry can't cope very well, if at all, with what we have called noumena:
"The scientific picture of the real world around me is very deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously."
Further, "The scientific world-picture vouchsafes a very complete understanding of all that happens -- it makes it just a little too understandable. It allows you to imagine the total display as that of a mechanical clockwork which, for all that science knows, could go on just the same as it does, without there being consciousness, will, endeavour, pain and delight and responsibility connected with it -- though they actually are."
Hence, "this is the reason why the scientific worldview contains of itself no ethical values, no aesthetical values, not a word about our own ultimate scope or destination, and no God, if you please" (77a).
Elsewhere, he argues that Science is repeatedly buffeted by the unjust reproach of atheism. When we use the clockwork model of the cosmos, "we have used the greatly simplifying device of cutting our own personality out, removing it; hence it is gone, it has evaporated, it is ostensibly not needed” (77a).
My thought is that such a method of depersonalization has strong advantages, if the scope of inquiry is limited, as in Shannon's depersonalized information. Depersonalization of information for specific purposes does not imply, of course, that information requires that no persons are needed to justify existence of information.
"No personal god," says Schroedinger, "can form part of a world model that has only become accessible at the cost of removing everything personal from it. We know, when God is experienced, this is an event as real as an immediate sense perception or as one’s own personality. Like them he must be missing in the space-time picture."
Though Schroedinger does not think that physics is a good vehicle for religion, that fact does not make him irreligious, even if he incurs blame from those who believe that "God is spirit.”
And yet Schroedinger favored Eastern philosophy: “Looking and thinking in that manner you may suddenly come to see, in a flash, the profound rightness of the basic conviction in Vedanta: it is not possible that this unity of knowledge, feeling and choice which you call your own should have sprung into being from nothingness at a given moment not so long ago; rather this knowledge, feeling, and choice are essentially eternal and unchangeable and numerically one in all men, nay in all sensitive beings.”
Schroedinger upheld "the doctrine of the Upanishads" of the "unfication of minds or consciousnesses" despite an illusion of multiplicity.
In a similar vein, Wolfgang Pauli, another quantum pioneer, relates quantum weirdness to the human means of perception:
"For I suspect that the alchemistical attempt at a unitary psychophysical language miscarried only because it was related to a visible concrete reality. But in physics today we have an invisible reality (of atomic objects) in which the observer intervenes with a certain freedom (and is thereby confronted with the alternatives of "choice" or "sacrifice"); in the psychology of the unconscious we have processes which cannot always be unambiguously ascribed to a particular subject. The attempt at a psychophysical monism seems to me now essentially more promising, given the relevant unitary language (unknown as yet, and neutral in regard to the psychophysical antithesis) would relate to a deeper invisible reality. We should then have found a mode of expression for the unity of all being, transcending the causality of classical physics as a form of correspondence (Bohr); a unity of which the psychophysical interrelation, and the coincidence of a priori instinctive forms of ideation with external perceptions, are special cases. On such a view, traditional ontology and metaphysics become the sacrifice, but the choice falls on the unity of being" (77a).
Pauli appears here to be sympathetic with the notion of Jungian archetype, along with possibly something like the Jungian collective unconscious. Though he relates quantum weirdness to the human means of perception, one cannot be sure of any strong support of Jung's synchronicity theory.
Pauli, says his friend Heisenberg, was very fussy about clear thinking in physics and arrived at the idea of a psychophysical interrelation only after painstaking reflection. Even so, it should be noted that Pauli had been a patient of Jung and remained on good terms with Jung for many years.
Einstein made strict physical causality an article of faith, an outlook that underlies his Spinoza-style atheism. That view, however, did not make him irreligious, he argues. Despite church-state persecution of innovative thinkers, "I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research" (77a).
Yet he makes plain his belief in strict causality, which meant there is no need for a personal God to interfere in what is already a done deal. Consider the "phenomenological complex" of a weather system, he says. The complex is so large so that in most cases of prediction "scientific method fails us." Yet "no one doubts that we are confronted with a causal connection whose causal components are in the main known to us."
Leon Brillouin, on the other hand, says bluntly that because exact predictibility is virtually impossible, a statement such as Einstein's was an assertion of faith that was not the proper province of science (77xa). Curious that Brillouin uses the logical positivist viewpoint to banish full causality from the province of science, just as Einstein used the same philosophical viewpoint to cast the luminiferous ether into outer darkness.
Einstein, of course, was swept up in the Darwinisitic paradigm of his time, which I believe, is reflected in his point that early Jewish religion was a means of dealing with fear, but that it evolved into something evincing a sense of morality as civilization advanced. He believed that spiritual savants through the ages tended to have a Buddhist-style outlook, in which a personal, anthropomorphic God is not operative. Einstein did on occasion however refer to a "central order" in the cosmos, though he plainly did not have in mind Bohm's implicate order, which accepts quantum bilocalism.
Einstein: “I see on the one hand the totality of sense-experiences, and, on the other, the totality of the concepts and propositions which are laid down in books. The relations between concepts and propositions among themselves and each other are of a logical nature, and the business of logical thinking is strictly limited to the achievement of the connection between concepts and propositions among each other according to firmly laid down rules, which are the concern of logic. The concepts and propositions get 'meaning,' viz., 'content,' only through their connection with sense-experiences. The connection of the latter with the former is purely intuitive, not itself of a logical nature. The degree of certainty with which this relation, viz., intuitive connection, can be undertaken, and nothing else, differentiates empty fantasy from scientific 'truth'" (77bb).
The idea that abstract concepts draw meaning from the content and context of sense experiences is a core belief of many. But is it true? It certainly is an unprovable, heuristic allegation. What about the possibility that meaning is imparted via and from a noumenal realm? If you say, this is a non-falsifiable, non-scientific speculation, you must concede the same holds for Einstein's belief that meaning arises via the sensory apparatus. We note further that "meaning" and "consciousness" are intertwined concepts. Whence consciousness? There can never be a scientific answer to that question in the Einsteinian philosophy. At least, the concept of a noumenal world, or Bohmian implicate order, leaves room for an answer.
In buttressing his defense of strict causality, Einstein lamented the "harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori" (77b). Logic be damned, is my take on this remark.
Louis de Broglie, another pioneer of quantum physics, at first accepted matter-wave duality, but later was excited by David Bohm's idea of what might be termed "saving most appearances" by conceding quantum bilocalism.
What, de Broglie asks, is the "mysterious attraction acting on certain men that urges them to dedicate their time and labours to works from which they themselves often hardly profiit?" Here we see the dual nature of man, he says. Certain people aim to escape the world of routine by aiming toward the ideal. Yet, this isn't quite enough to explain the spirit of scientific inquiry. Even when scientific discoveries are given a utilitarian value, one can still sense the presence of an "ontological order."
We are nowhere near a theory of everything, de Broglie says. Yet "it is not impossible that the advances of science will bring new data capable" of clarifying "great problems of philosophy." Already, he writes, new ideas about space and time, the various aspects of quantum weirdness and "the profound realities which conceal themselves behind natural appearances" provide plenty of philosophical fodder (77a).
Scientific inquiry yields technology which "enlarges" the body by amplifying the power of brawn and perhaps brain. But, such vast amplification has resulted in massive misery as well as widespread social improvements. "Our enlarged body clamours for an addition to the spirit," says de Broglie, quoting Henri Bergson.
The man who ignited the quantum revolution, Max Planck, warned that because science can never solve the ultimate riddle of nature, science "cannot really take the place of religion" (77a). If one excludes "nihilistic" religion, "there cannot be any real opposition between religion and science," he writes. "The greatest thinkers of all ages were deeply religious" even if quiet about their religious thoughts.
"Anybody who has been seriously engaged in scientific work of any kind realizes that over the entrance to the temple of science are written the words: Ye must have faith."
This last sentiment seems boringly conventional. But how would a person, even a strict determinist, proceed without a strong conviction that the goal is achievable? As Eddington jokes, "Verily it is easier for a camel to pass through the eye of a needle than for a scientific man to pass through a door. And whether the door be barn door or church door it might be wiser that he should consent to be an ordinary man and walk in rather than wait till all the difficulties involved in a really scientific ingress are resolved."
Would, for example, the atheist Alan Turing have achieved so much had he not believed that his initial ideas would bear fruit? Would an AI program that passes the Turing test encounter an idea that provokes it to highly focused effort in anticipation of some reward, such as the satisfaction of solving a problem? Can qualia, or some equivalent, be written into a computer program?
In The Grammar of Science, Pearson has an annoying way of personifying Science, almost as if it is some monolithic God. I realize that Pearson is using a common type of metaphorical shorthand, but nevertheless he gives the impression that he and Science are One, a criticism that is applicable to various thinkers today.
Let us digress for a bit and consider what is meant by the word "science."
At a first approximation, one might say the word encompasses the publications and findings of people who interrogate nature in a "rational" manner.
That is, the scientific methods attempt to establish relations among various phenomena that do not contradict currently accepted major theories. The scientific investigator has much in common with the police detective. He or she often uses a process of elimination, coupled with the sketch of a narrative provided by various leads or "facts." The next step is to fill out the narrative to the degree necessary to establish the "truth" of a particular finding. It is often the case that more than one narrative is possible. The narratives that are crowned with the title "theory" (in the scientific sense of the word) are those which seem to be most internally consistent and which also are not dissonant with the background framework "reality" (and if it is, that theory will encounter strong resistance).
So "science" is a word used to describe the activities of a certain group of people who interrogate nature in accord with certain group norms -- norms concerning process and norms concerning philosophy or metaphysics (denial of such interests nevertheless implies a metaphysical belief set).
One idea of Popper's widely accepted among scientists is that if a statement is not potentially falsifiable via advances in experimental technology, then that statement is not scientific and not a proper focus of scientists (though light-hearted speculations may be tolerated).
Hence, the entire scientific enterprise is not scientific, as its underlying assumptions, which are metaphysical, cannot be falsified by experimental or logical means.
At any rate, many will agree that science as a monolithic entity does not exist. Science does not do anything. Science does not prove anything. The word is really a convenient handle that by itself cannot properly summarize a complex set of human activities. Scientists of course all know that there is no great being named Science. And yet when various thinkers, including scientists, employ this anthropomorphism, they often tend to give this being certain qualities, such as rationality, as distinct from, say, irrational Religion, a straw man which is also an anthropomorphism for a wide range of human activities.
In other words, we should beware scientists propagating their faith in the god Science. They may say they don't mean to do that, but, mean it or not, that is in fact what quite a few of them do.
Though physicists often remained reticent about their views on God, those who understood the issues of quantum theory were inclined toward some underlying transcendency. This situation remains as true today as it did in the 1930s, as we see with the effectively phenomenalist/materialist world view of the biologist Richard Dawkins, who is conducting a Lennonist crusade against belief in God.
A previous generation witnessed Bertrand Russell, the logician, in the role of atheist crusader. Russell with his colleague Alfred North Whitehead, in their Principia Mathematica had tried to assure that formal knowledge could be described completely and consistently. One can see that such an achievement would have bolstered the cause of atheism. If, at least in principle, the universe can be "tamed" by human knowledge, then one can explain every step of every process without worry about God, or some transcendental entity. God, like the ether, would have been consigned to the rubbish heap of history.
Of course, in 1931 Goedel proved this goal an illusion, using Principia Mathematica to demonstrate his proof. Goedel's incompleteness theorem caught the inrushing tide of the quantum revolution, which brought the question of traditional scientific external reality into question. The revolution had in part been touched off by experimental confirmation of Louis de Broglie's proposed matter waves, an idea that made use of Einstein's energy/matter relation to posit matter waves, So the doctrine of materialism was not only technically in question, but, because material waves obeyed probability amplitudes, the very existence of matter had become a very strange puzzle, a situation that continues today.
Even before this second quantum revolution, the astrophysicist Arthur Eddington had used poetic imagery to put into perspective Einstein's spacetime weirdness (77aa).
Perhaps to move His laughter at their quaint opinions wide Hereafter, when they come to model Heaven And calculate the stars, how they will wield The mighty frame, how build, unbuild, contrive To save appearances. -- John Milton, Paradise Lost
Quantum weirdness only strengthened Eddington's belief in a noumenal realm (77a).
"A defence of the mystic might run something like this: We have acknowledged that the entities of physics can from their very nature form only a partial aspect of the reality. How are we to deal with the other part?" Not with the view that "the whole of consciousness is reflected in the dance of electrons in the brain" and that "quasi-metrical aspects" suffice.
Eddington, in countering Russell on what Eddingon said was Russell's charge of an attempt to "prove" distinctive beliefs of religion, takes aim at loose usage of the word "reality," warning that it is possible to employ that word as a talisman providing "magic comfort." And, we add that cognitive dissonance with internal assumptions and rationalizations usually provokes defensive reactions.
"We all know that there are regions of the human spirit untrammeled by the world of physics" and that are associated with an "Inner Light proceeding from a greater power than ours."
Another English astrophysicist, James Jeans, also inclined toward some noumenal presence (77a).
Jeans writes that the surprising results of the theories of relativistic and quantum physics leads to "the general recognition that we are not yet in contact with ultimate reality." We are only able to see the shadows of that reality. Adopting John Locke's assertion that "the real essence of substances is unknowable," Jeans argues that scientific inquiry can only study the laws of the changes of substances, which "produce the phenomena of the external world."
In a chapter entitled, "In the Mind of Some Eternal Spirit," Jeans writes: "The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures." Or, I would say, the typical human brain/mind's empirically derived expectations of physical reality are inapplicable. In a word, the pictures we use for our existence are physically false, delusional, though that is not to say the delusional thinking imparted via the cultic group mind and by the essentials of the brain/mind system (whatever they are) are easily dispensed with, or even safe to dispense with absent something reliably superior.
In a play on the old epigram that the cosmos had been designed by a "Great Architect," Jeans writes of the cosmos "appearing to have been designed by a pure mathematician."
He adds: "Our remote ancestors tried to interpret nature in terms of anthropomorphic concepts and failed. The efforts of our nearer ancestors to interpret nature on engineering lines proved equally inadequate. Nature refused to accommodate herself to either of these man-made moulds. On the other hand, our efforts to interpret nature in terms of the concepts of pure mathematics have, so far, proved brilliantly successful."
Further, "To my mind the laws which nature obeys are less suggestive of those which a machine obeys in its motion than those which a musician obeys in writing a fugue, or a poet in composing a sonnet."
Remarks:
- We are unsure whether Jeans believed in a God who intervenes in human affairs. Often, the denial of "anthropomorphism" includes denial of the basis of Christianity. But what does he mean when he says that, contrary to Kant's idea that the "mathematical universe" was a consequence of wearing mathematical eyeglasses, "the mathematics enters the universe from above instead of from below"? He seems to mean that the mathematics of physics corresponds to an objective reality capable of being discerned by the human mind in terms of mathematics.
- Though he saw the "engineering" paradigm as fundamentally flawed, that message has failed to make much headway in the ranks and files of scientific activity, where full determinism is still accepted as a practical article of faith, based on the incorrect assumption that physical indeterminism is only relevant in very limited areas.
- His enthusiasm about the mathematics is, in another book, tempered when he criticizes Werner Heisenberg for focusing on the lesser problem of the mathematics of quantum relations while ignoring the greater problem of observer influence.
Materialism, writes Heisenberg, is a concept that at root is found wanting. "For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or -- in Plato's sense -- Ideas, which can be unambiguously spoken of in the language of mathematics."
Heisenberg relates the paradox of Parmenides: "Only being is; non-being is not. But if only being is, there cannot be anything outside this being that articulates it or could bring about changes. Hence being will have to be conceived of as eternal, uniform, and unlimited in space and time. The changes we experience can thus be only an illusion."
Though initially unnerved that his wave mechanics could not resolve the "quantum jump" problem, Erwin Schroedinger's concept of reality evolved.
Schroedinger did not care for the idea he attributes to another quantum pioneer, Pascual Jordan, that quantum indeterminacy is at the basis of free will, an idea echoed in some ways by Penrose. If free will steps in to "fill the gap of indeterminacy," writes Schroedinger, the quantum statistics will change, thus disrupting the laws of nature.
In the same article, Schroedinger talks about how scientific inquiry can't cope very well, if at all, with what we have called noumena:
"The scientific picture of the real world around me is very deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously."
Further, "The scientific world-picture vouchsafes a very complete understanding of all that happens -- it makes it just a little too understandable. It allows you to imagine the total display as that of a mechanical clockwork which, for all that science knows, could go on just the same as it does, without there being consciousness, will, endeavour, pain and delight and responsibility connected with it -- though they actually are."
Hence, "this is the reason why the scientific worldview contains of itself no ethical values, no aesthetical values, not a word about our own ultimate scope or destination, and no God, if you please" (77a).
Elsewhere, he argues that Science is repeatedly buffeted by the unjust reproach of atheism. When we use the clockwork model of the cosmos, "we have used the greatly simplifying device of cutting our own personality out, removing it; hence it is gone, it has evaporated, it is ostensibly not needed” (77a).
My thought is that such a method of depersonalization has strong advantages, if the scope of inquiry is limited, as in Shannon's depersonalized information. Depersonalization of information for specific purposes does not imply, of course, that information requires that no persons are needed to justify existence of information.
"No personal god," says Schroedinger, "can form part of a world model that has only become accessible at the cost of removing everything personal from it. We know, when God is experienced, this is an event as real as an immediate sense perception or as one’s own personality. Like them he must be missing in the space-time picture."
Though Schroedinger does not think that physics is a good vehicle for religion, that fact does not make him irreligious, even if he incurs blame from those who believe that "God is spirit.”
And yet Schroedinger favored Eastern philosophy: “Looking and thinking in that manner you may suddenly come to see, in a flash, the profound rightness of the basic conviction in Vedanta: it is not possible that this unity of knowledge, feeling and choice which you call your own should have sprung into being from nothingness at a given moment not so long ago; rather this knowledge, feeling, and choice are essentially eternal and unchangeable and numerically one in all men, nay in all sensitive beings.”
Schroedinger upheld "the doctrine of the Upanishads" of the "unfication of minds or consciousnesses" despite an illusion of multiplicity.
In a similar vein, Wolfgang Pauli, another quantum pioneer, relates quantum weirdness to the human means of perception:
"For I suspect that the alchemistical attempt at a unitary psychophysical language miscarried only because it was related to a visible concrete reality. But in physics today we have an invisible reality (of atomic objects) in which the observer intervenes with a certain freedom (and is thereby confronted with the alternatives of "choice" or "sacrifice"); in the psychology of the unconscious we have processes which cannot always be unambiguously ascribed to a particular subject. The attempt at a psychophysical monism seems to me now essentially more promising, given the relevant unitary language (unknown as yet, and neutral in regard to the psychophysical antithesis) would relate to a deeper invisible reality. We should then have found a mode of expression for the unity of all being, transcending the causality of classical physics as a form of correspondence (Bohr); a unity of which the psychophysical interrelation, and the coincidence of a priori instinctive forms of ideation with external perceptions, are special cases. On such a view, traditional ontology and metaphysics become the sacrifice, but the choice falls on the unity of being" (77a).
Pauli appears here to be sympathetic with the notion of Jungian archetype, along with possibly something like the Jungian collective unconscious. Though he relates quantum weirdness to the human means of perception, one cannot be sure of any strong support of Jung's synchronicity theory.
Pauli, says his friend Heisenberg, was very fussy about clear thinking in physics and arrived at the idea of a psychophysical interrelation only after painstaking reflection. Even so, it should be noted that Pauli had been a patient of Jung and remained on good terms with Jung for many years.
Einstein made strict physical causality an article of faith, an outlook that underlies his Spinoza-style atheism. That view, however, did not make him irreligious, he argues. Despite church-state persecution of innovative thinkers, "I maintain that the cosmic religious feeling is the strongest and noblest motive for scientific research" (77a).
Yet he makes plain his belief in strict causality, which meant there is no need for a personal God to interfere in what is already a done deal. Consider the "phenomenological complex" of a weather system, he says. The complex is so large so that in most cases of prediction "scientific method fails us." Yet "no one doubts that we are confronted with a causal connection whose causal components are in the main known to us."
Leon Brillouin, on the other hand, says bluntly that because exact predictibility is virtually impossible, a statement such as Einstein's was an assertion of faith that was not the proper province of science (77xa). Curious that Brillouin uses the logical positivist viewpoint to banish full causality from the province of science, just as Einstein used the same philosophical viewpoint to cast the luminiferous ether into outer darkness.
Einstein, of course, was swept up in the Darwinisitic paradigm of his time, which I believe, is reflected in his point that early Jewish religion was a means of dealing with fear, but that it evolved into something evincing a sense of morality as civilization advanced. He believed that spiritual savants through the ages tended to have a Buddhist-style outlook, in which a personal, anthropomorphic God is not operative. Einstein did on occasion however refer to a "central order" in the cosmos, though he plainly did not have in mind Bohm's implicate order, which accepts quantum bilocalism.
Einstein: “I see on the one hand the totality of sense-experiences, and, on the other, the totality of the concepts and propositions which are laid down in books. The relations between concepts and propositions among themselves and each other are of a logical nature, and the business of logical thinking is strictly limited to the achievement of the connection between concepts and propositions among each other according to firmly laid down rules, which are the concern of logic. The concepts and propositions get 'meaning,' viz., 'content,' only through their connection with sense-experiences. The connection of the latter with the former is purely intuitive, not itself of a logical nature. The degree of certainty with which this relation, viz., intuitive connection, can be undertaken, and nothing else, differentiates empty fantasy from scientific 'truth'" (77bb).
The idea that abstract concepts draw meaning from the content and context of sense experiences is a core belief of many. But is it true? It certainly is an unprovable, heuristic allegation. What about the possibility that meaning is imparted via and from a noumenal realm? If you say, this is a non-falsifiable, non-scientific speculation, you must concede the same holds for Einstein's belief that meaning arises via the sensory apparatus. We note further that "meaning" and "consciousness" are intertwined concepts. Whence consciousness? There can never be a scientific answer to that question in the Einsteinian philosophy. At least, the concept of a noumenal world, or Bohmian implicate order, leaves room for an answer.
In buttressing his defense of strict causality, Einstein lamented the "harmful effect upon the progress of scientific thinking in removing certain fundamental concepts from the domain of empiricism, where they are under our control, to the intangible heights of the a priori" (77b). Logic be damned, is my take on this remark.
Louis de Broglie, another pioneer of quantum physics, at first accepted matter-wave duality, but later was excited by David Bohm's idea of what might be termed "saving most appearances" by conceding quantum bilocalism.
What, de Broglie asks, is the "mysterious attraction acting on certain men that urges them to dedicate their time and labours to works from which they themselves often hardly profiit?" Here we see the dual nature of man, he says. Certain people aim to escape the world of routine by aiming toward the ideal. Yet, this isn't quite enough to explain the spirit of scientific inquiry. Even when scientific discoveries are given a utilitarian value, one can still sense the presence of an "ontological order."
We are nowhere near a theory of everything, de Broglie says. Yet "it is not impossible that the advances of science will bring new data capable" of clarifying "great problems of philosophy." Already, he writes, new ideas about space and time, the various aspects of quantum weirdness and "the profound realities which conceal themselves behind natural appearances" provide plenty of philosophical fodder (77a).
Scientific inquiry yields technology which "enlarges" the body by amplifying the power of brawn and perhaps brain. But, such vast amplification has resulted in massive misery as well as widespread social improvements. "Our enlarged body clamours for an addition to the spirit," says de Broglie, quoting Henri Bergson.
The man who ignited the quantum revolution, Max Planck, warned that because science can never solve the ultimate riddle of nature, science "cannot really take the place of religion" (77a). If one excludes "nihilistic" religion, "there cannot be any real opposition between religion and science," he writes. "The greatest thinkers of all ages were deeply religious" even if quiet about their religious thoughts.
"Anybody who has been seriously engaged in scientific work of any kind realizes that over the entrance to the temple of science are written the words: Ye must have faith."
This last sentiment seems boringly conventional. But how would a person, even a strict determinist, proceed without a strong conviction that the goal is achievable? As Eddington jokes, "Verily it is easier for a camel to pass through the eye of a needle than for a scientific man to pass through a door. And whether the door be barn door or church door it might be wiser that he should consent to be an ordinary man and walk in rather than wait till all the difficulties involved in a really scientific ingress are resolved."
Would, for example, the atheist Alan Turing have achieved so much had he not believed that his initial ideas would bear fruit? Would an AI program that passes the Turing test encounter an idea that provokes it to highly focused effort in anticipation of some reward, such as the satisfaction of solving a problem? Can qualia, or some equivalent, be written into a computer program?
In The Grammar of Science, Pearson has an annoying way of personifying Science, almost as if it is some monolithic God. I realize that Pearson is using a common type of metaphorical shorthand, but nevertheless he gives the impression that he and Science are One, a criticism that is applicable to various thinkers today.
Let us digress for a bit and consider what is meant by the word "science."
At a first approximation, one might say the word encompasses the publications and findings of people who interrogate nature in a "rational" manner.
That is, the scientific methods attempt to establish relations among various phenomena that do not contradict currently accepted major theories. The scientific investigator has much in common with the police detective. He or she often uses a process of elimination, coupled with the sketch of a narrative provided by various leads or "facts." The next step is to fill out the narrative to the degree necessary to establish the "truth" of a particular finding. It is often the case that more than one narrative is possible. The narratives that are crowned with the title "theory" (in the scientific sense of the word) are those which seem to be most internally consistent and which also are not dissonant with the background framework "reality" (and if it is, that theory will encounter strong resistance).
So "science" is a word used to describe the activities of a certain group of people who interrogate nature in accord with certain group norms -- norms concerning process and norms concerning philosophy or metaphysics (denial of such interests nevertheless implies a metaphysical belief set).
One idea of Popper's widely accepted among scientists is that if a statement is not potentially falsifiable via advances in experimental technology, then that statement is not scientific and not a proper focus of scientists (though light-hearted speculations may be tolerated).
Hence, the entire scientific enterprise is not scientific, as its underlying assumptions, which are metaphysical, cannot be falsified by experimental or logical means.
At any rate, many will agree that science as a monolithic entity does not exist. Science does not do anything. Science does not prove anything. The word is really a convenient handle that by itself cannot properly summarize a complex set of human activities. Scientists of course all know that there is no great being named Science. And yet when various thinkers, including scientists, employ this anthropomorphism, they often tend to give this being certain qualities, such as rationality, as distinct from, say, irrational Religion, a straw man which is also an anthropomorphism for a wide range of human activities.
In other words, we should beware scientists propagating their faith in the god Science. They may say they don't mean to do that, but, mean it or not, that is in fact what quite a few of them do.
Go to Chapter 2 HERE.
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