Home » Intelligent Design » “there is a strangeness in the air”, a quasi ID-friendly essay in Dennett and Hofstadter’s 1981 book on intelligence

“there is a strangeness in the air”, a quasi ID-friendly essay in Dennett and Hofstadter’s 1981 book on intelligence

In 1981 Dennett and Hofstadter edited a compilation of essays entitled The Mind’s I: Fantasies and Reflections on Self & Soul . The book is a compilation of essays by Dawkins, Morowitz, Searle, Alan Turing, and several other big names on the nature of mind and intelligence. Since ID implies a mind of some sort, it is appropriate to ponder what a mind really is, and this is a surprisingly good book on the topic.

Dennett’s co-author, Hofstadter, makes an interesting remark about the ultimate mind:

one way to think of the universal wave function [of quantum physics] is as the mind– or brain, if you prefer–of the great novelist in the sky, God.

[For the reader's benefit, the science of the universal wave function and God are described here: Peer-Reviewed Stealth ID Classic : The Anthropic Cosmological Principle (1987).]

I found it curious Dennett would put his name to a book where such statements were asserted by his co-author, Hofstadter. Even more curious was a somewhat ID-friendly essay in the book by renowned origin-of-life researcher, Harold Morowitz. It was that essay that inspired Hofstadter’s words quoted above.
Harold Morowitz

Morowitz’s essay is available online here: Rediscovery the Mind. Morowitz offered the following:

Something peculiar has been going on in science for the past 100 years or so. Many researchers are unaware of it, and others won’t admit it even to their own colleagues. But there is a strangeness in the air.

What has happened is that biologists, who once postulated a privileged role for the human mind in nature’s hierarchy, have been moving relentlessly toward the hard-core materialism that characterized nineteenth-century physics. At the same time, physicists, faced with compelling experimental evidence, have been moving away from strictly mechanical models of the universe to a view that sees that mind as playing an integral role in all physical events. It is as if the two disciplines were on fast-moving trains, going in opposite directions and not noticing what is happening across the tracks.
….
During the period in which psychologists and biologists were steadily moving toward reducing their disciplines to the physical sciences, they were largely unaware of perspectives emerging from physics that cast an entirely new light on their understanding. Toward the close of the last century [the 1800s], physics presented a very ordered picture of the world, in which events unfolded in characteristic, regular ways, following Newton’s equations in mechanics and Maxwell’s in electricity. These processes moved inexorably, independent of the scientist, who was simply a spectator. Many physicists considered their subject as essentially complete.

Starting with the introduction of the theory of relativity by Albert Einstein in 1905, this neat picture was unceremoniously upset. The new theory postulated that observers in different systems moving with respect to each other would perceive the world differently. The observer thus became involved in establishing physical reality. The Scientist was losing the spectator’s role and becoming an active participant in the system under study.

With the development of quantum mechanics, the role of the observer became an even more central part of physical theory, an essential component in defining an event. The mind of the observer emerged as a necessary element in the structure of the theory. The implications of the developing paradigm greatly surprised early quantum physicists and led them to study epistemology and the philosophy of science. Never before in scientific history, to my knowledge, had all of the leading contributors produced books and papers expounding the philosophical and humanistic meaning of their results.

Werner Heisenberg, one of the founders of the new physics, became deeply involved in the issues of philosophy and humanism. In Philosophical Problems of Quantum Physics, he wrote of physicists having to renounce thoughts of an objective time scale common to all observers, and of events in time and space that are independent of our ability to observe them. Heisenberg stressed that the laws of nature no longer dealt with elementary particles, but with our knowledge of these particles – that is, with the contents of our minds. Erwin Schrodinger, the man who formulated the fundamental equation of quantum mechanics, wrote an extraordinary little book in 1958 called Mind and Matter. In this series of essays, he moved from the results of the new physics to a rather mystical view of the universe that he identified with the “perennial philosophy” of Aldous Huxley. Schrodinger was the first of the quantum theoreticians to express sympathy with the Upanishads and Eastern philosophical thought. A growing body of literature now embodies this perspective, including two popular works, The Tao of Physics by Fritjof Capra and The Dancing Wu Li Masters by Gary Zukav.

The problem faced by quantum theorists can best be seen in the famous paradox, “Who killed Schrodinger’s cat?” In a hypothetical formulation, a kitten is put in a closed box with a jar of poison and a triphammer poised to smash the jar. The hammer is activated by a counter that records random events, such as radioactive decay. The experiment lasts just long enough for there to be a probability of one-half that the hammer will be released. Quantum mechanics represents the system mathematically by the sum of a live-cat and a dead-cat function, each with a probability of one-half. The question is whether the act of looking (the measurement) kills or saves the cat, since before the experimenter looks in the box both solutions are equally likely.

This lighthearted example reflects a deep conceptual difficulty. In more formal terms, a complex system can only be described by using a probability distribution that relates the possible outcomes of and experiment. In order to decide among the various alternatives, a measurement is required. This measurement is what constitutes and event, as distinguished from the probability, which is a mathematical abstraction. However, the only simple and consistent description physicists were able to assign to a measurement involved an observer’s becoming aware of the result. Thus the physical event and the content of the human mind were inseparable. This linkage forced many researchers to seriously consider consciousness as an integral part of the structure of physics. Such interpretations moved science toward the idealist as contrasted with the realist conception of philosophy.

The views of a large number of contemporary physical scientists are summed up in the essay “Remarks on the Mind-Body Question” written by Nobel laureate Eugene Wigner. Wigner begins by pointing out that most physical scientists have returned to the recognition that thought – meaning the mind – is primary. He goes on to state: “It was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness.” And he concludes by noting how remarkable it is that the scientific study of the world led to the content of consciousness as an ultimate reality.

A further development in yet another field of physics reinforces Wigner’s viewpoint. The introduction of information theory and its application to thermodynamics has led to the conclusion that entropy, a basic concept of that science, is a measure of the observer’s ignorance of the atomic details of the system. When we measure the pressure, volume, and temperature of an object, we have a residual lack of knowledge of the exact position and velocity of the component atoms and molecules. The numerical value of the amount of information we are missing is proportional to the entropy. In earlier thermodynamics, entropy had represented, in an engineering sense, the energy of the system unavailable to perform external work. In the modern view, the human mind enters once again, and entropy relates not just to the state of the system but to our knowledge of that state.

The founders of modern atomic theory did not start out to impose a “mentalist” picture on the world. Rather, they began with the opposite point of view and were forced to the present-day position in order to explain experimental results.

We are now in a position to integrate the perspectives of three large fields: psychology, biology, and physics. By combining the positions of Sagan, Crick, and Wigner as spokenmen for various outlooks, we get a picture of the whole that is quite unexpected.

First, the human mind, including consciousness and reflective thought, can be explained by activities of the central nervous system, which, in turn, can be reduced to the biological structure and function of that physiological system. Second, biological phenomena at all levels can be totally understood in terms of atomic physics, that is through the action and interaction of the component atoms of carbon, nitrogen, oxygen, and so forth. Third and last, atomic physics, which is now understood most fully by means of quantum mechanics, must be formulated with the mind as a primitive component of the system.

In addition to being an origin-of-life researcher, Morowitz was the director of the Krasnow Institute of Advanced Studies which does pioneering work in studies of the mind, brain, and intelligence. He has also accepted grants from the Templeton Foundation for some of his empirical research. He said in another book, Emergence of Everything

We study God’s immanence through science…Deep within the laws of physics and chemistry the universe is fit for life. This fitness we identify with God’s immanence….The present study of this fitness take place under the rubric of ‘design’ “.

And in his book Cosmic Joy, Morowitz commenting on Quantum Physics, wrote,

What emerges from all this is the return of “mind” to all areas of scientific thought. This is good news from the point of view of all varieties of natural theology. For a universe where mind is a fundamental part of reality more easily makes contact with the mind of god than does a mindless world.”

These words are all the more surprising given that Morowitz testified against the creationists in the landmark 1982 case, McLean vs. Arkansas, and has vigorously criticized intelligent design.

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44 Responses to “there is a strangeness in the air”, a quasi ID-friendly essay in Dennett and Hofstadter’s 1981 book on intelligence

  1. AP wrote:

    Yes, the failure of the tevatron to find the higgs within the recently discovered “bump” at the recalculated energy scale, increases the confidence level that there is something fundamentally misunderstood, and if the large hadron collider further confirms this, then there is a good chance that there will be some serious rethinking of the most fundamental interpretations and assumptions of particle theory.

    Thank you for your informative discussion. For the reader’s benefit, the Higgs Boson has been dubbed the “God Particle”. When Weinberg was before congress answering questions ast to why US Taxpayers should fund an 8 Billion Dollar Super Collider, one of the congressmen asked, “Will we find God?”

    To which Weinberg replied, “No.”

    Tipler in his book, contested that saying the Super Collider found the Higgs Boson we would have evidence of God. Although I don’t personally accept the Higgs Boson as proof of God.

    Before the discussion gets to involved, it should be apparent that ultimate explanations are on the minds of serious physcists.

    The fundamental principles discussed echo the Kalaam Cosmological argument, whether there is some ulitimate uncaused cause. This idea is simply being debated in the language of modern physics.

    Sal

  2. geoffrobinson, the described mechanism is commonly used in inflationary models that use the “Bunch-Davies” vacuum solution, as well as Paul Davies studies of matter generation from quantum field theory in curved space-time. The effect is different in a finite vacuum, is all.

    Michaels7, the physics is strictly deterministic, but the least action principle as applied to our imperfect universe doesn’t only derive straight lines. However, our best models of “normal” turbulance driven structuring don’t even come close to the extremely low entropy that is observed, and this is the reason that the anthropic principle, (and then inflationary theory, and then the multiverse), was formalized in the first place, since the otherwise unexpected structuring includes a bunch of balance points in nature that are intricately related to both the structure of the universe and the existence of carbon based life.

    If the universe is finite, (which, FYI, has yet to be determined, regardless of popularized notion to the contrary), then the AP also derives an energy conservation law, since work is maximized in a “near-flat”, yet expanding universe, by comparison to a wide-open universe that wastes a lot of energy that becomes inert before it can do any work. In this context you can understand how the economy of the universe relates the AP to the least “ultimate” action, since energy cannot be conserved if it gets wasted.

    The near-”flat” structuring acts as a natural damping mechanism for a quantum oscillator, and this prevents a finite universe from expanding inhomogeneously. The special form of the Lindblad Equation is the only current means that quantum theory has for addressing this as it relates to far from equilibrium dissipative structuring.

  3. Just let me know if I run-on too much as I could have left it at…

    There is a logically indicated prediction that falls from the strong interpretation, which notes that there is *necessarily* an inherent reciprocal connection to the human evolutionary process, and that means that physicists **should** be ACTIVELY looking for a mechanism that enables the universe to “leap” to higher orders of the same basic structure… but they don’t.

    This all of course assumes that we allow that the basic tenants of evolutionary theory are, for the most part, correct, that is… and yes, I realize that this topic is more debatable around here, than it might be among the “mainstream”… who doesn’t like strong interpretations of the AP!… ;)

  4. Saw the derivation of the equation, but had no idea how a nonmaterial entity could come from that – okay, I’ll admit it just have no idea what the math was saying.

    Is it possible for someone to explain the derivation and how it shows God?

    Jpark,

    Sorry for my delay in responding.

    The arguments are actually simpler than the math suggests. There are two issues:

    1. Is there an ultimate uncaused cause? (hence the question who designed the designer)

    2. What is the nature of the uncaused cause?

    In general the answer to #1 is a qualified “yes”. If one is a materialist, the ultimate uncaused cuase is matter and energy or some other “material”. If one is a theist the answer is God.

    Since #1 is for the most part true for every world view that admits causation, what is the answer to #2? The way the materialist answer can be demolished is to use a proof by contradiction, whereby one assumes materialism is true, and then demonstrate that this assumption leads to a contradiction (for the readers benefit, see a classic example of this in mathemtics Reductio ad absurdum.)

    That’s the general gist of Wigner’s invocation of non-material causes for the material universe. That part of argument is solid. Whether the non-material entity is intelligent is a matter of reasonable inference. For example, you can’t formally prove there are other conscious beings in the universe aside from yourself, you have to make a certain degree of assumption. By way of extension, we infer the non-material cause of the universe is probably intelligent based on the fact that intelligent beings have been shown to be a trigger in laboratory quantum experiments like the double slit delayed choice experiment.

    Let me suggest the two following essays:

    God in the Equations

    and

    Quantum Philosophy

    Look at the part referring to Wigner:

    Wigner tried to flesh out von Neumann’s idea by suggesting that there were two fundamentally different types of physical system:

    i. Purely physical systems — i.e. systems which do not contain observers — that always evolve
    in accordance with the Schr¨odinger equation. (At least, as long as they remain isolated from
    observers.)

    ii. Conscious systems — i.e. systems which do contain observers — that evolve in accordance
    with the collapse postulate.

    To motivate his suggestion, consider what happens when we have a type (ii) system, i.e. when we
    have a system which contains an observer:

    ² Suppose that the system in question is an electron, e, and we have some apparatus, a, for
    measuring its spin in the x-direction. We shall label the corresponding spin-up and spin-down
    states of the electron by j “xie and j #xie, and the corresponding final states of the apparatus
    as j “xia and j #xia depending on whether the result it gives is ‘the electron is spin-up in the
    x-direction’ or ‘the electron is spin-down in the x-direction’ respectively.

    ² If we can discover that after the interaction between the electron (i.e. the physical system) and
    the measuring apparatus, the apparatus was in a state j “xia, then it would be known that the
    final state of the electron is j “xie.

    ² But, how do we discover that the apparatus is in the state j “ia? By using another apparatus to measure the state of the first apparatus. That is, we use another apparatus, a0, to measure the state of the first apparatus.3

    ² But, this leads to an infinite regress since then we need to know the state of the second apparatus
    which, in turn, requires a third apparatus etc.

    So, simply put, Wigner’s point is that: If we are ever to know the outcome of a measurement, then
    this regress has to stop somewhere. That is,

    ² A measurement must be a finite operation, completed by an act of observation. (For example:
    seeing a flash.)

    ² The process leading to the result of the measurement can’t involve a type (i) system since it
    has to be completed by an act which is discontinuous and non-causal.

    That is, observation
    must be an act that involves a type (ii) system. This may prompt us to ask two questions: How and why does this act occur? To which, Wigner gives two answers:

    ² The act occurs as a result of the collapse of the superposition. Why?

    Because:

    Immediately after the measurement of the electron’s x-component of spin, the observation gives the result ‘spin-up in the x-direction’, the state of the apparatus is j “xia and the state of the system is j “xie. Such determinate outcomes can occur
    via the collapse postulate, i.e. the superposition state (predicted by the Schr¨odinger equation) is ‘projected’ into the eigenstate corresponding to the result obtained in the measurement. (That is, due to the measurement, the type (I) dynamics ceases
    to apply and the type (II) dynamics takes over. Note that, after the measurement,
    the type (I) dynamics takes over again.)

    ² The act of observation occurs due to the mind of the conscious observer. Why? Because:
    Given that QM applies to all purely physical systems (whether macro or micro — see later), the collapse cannot occur due to an interaction with a purely physical system.4
    Thus, the collapse must occur via an interaction with a non-physical system, i.e. the mind of a conscious observer.

    Now, in recent times, John Cramer created a quantum interpretation (one I’m partial to) that compartmentalizes out all these ultimate questions, and from an operational standpoint it works by avoiding questions of ultimate causation (by way of comparison, one can believe an automobile works with knowing all the ultimate reasons as to why).

    Nevertheless, the question remains regarding the ultimate causation of what drives the quantum world. As Morowitz pointed out, MIND is now as much a part of physics as are matter and energy, if not more so!

    PS
    Regarding Wigner’s original essay on the mind-body problem, it’s in a collection of his works. Amazon sells it for $100-$400. I haven’t had time to get a hold of the original paper in the library, and much as like Wigner, $100-$400 isn’t cheap.

  5. Ah!

    Thanks so much Sal. I think the distinction btwn pure physical systems and conscious systems was the thing I needed to know! Never really thought about it that way.

    Thanks a lot – Fight on.

    -John

  6. “There is a strangeness
    in the air”

    (Sung to the tune of “Strangers in the Night”.)

    Ahem. Sorry, but that’s as much as I can muster in the few minutes between my attempts to battle my Soloflex machine, and my bedtime.

  7. J Parker,

    Thank you for the article. There is a feeling (by people like Penrose) that the human brain has quantum computing capability and exploits physics in ways we do not yet appreciate. I think that is true of biology.

    Nobel Lareate Laughlin may have ushered a new era of solid state physics (the brain is a solid state device) when he pioneered work on the fractional quantum Hall effect. ARN has an excellent article on developments in solid state physics here: Challenging Particle Physics as a Path to Truth

    The new physics suggest Irreducible Complexity in physics and the role of an intelligent observer!!!

    “The stakes here are very high,” said Dr. Robert B. Laughlin, a Stanford University theorist who shared a Nobel Prize in 1998 for discoveries in solid-state physics. “At issue is a deep epistemological matter having to do with what physics is.”

    Last year Dr. Laughlin and Dr. David Pines, a theorist at the University of Illinois and Los Alamos National Laboratory, published a manifesto declaring that the “science of the past,” which seeks to distill the richness of reality into a few simple equations governing subatomic particles, was coming to an impasse.

    Many complex systems — the very ones the solid-staters study — appear to be irreducible. Made of many interlocking parts, they display a kind of synergy, obeying “higher organizing principles” that cannot be further simplified no matter how hard you try.

    Carrying the idea even further, some solid-state physicists are trying to show that the laws of relativity, long considered part of the very bedrock of the physical world, are not platonic truths that have existed since time began.


    When systems become very complex, completely new and independent laws emerge. “More is different,” as the Nobel laureate Philip W. Anderson put it in a landmark paper in 1972. To the solid-staters, it would take something the size of a circus tent to hold all the equations capturing the unruliness of the physical world.
    ….
    In the world of solid-state physics, quasi particles abound. In some substances, like the semiconductors used to make computer chips, the displacement of an electron leaves behind a “hole” that behaves like a positively charged particle. An electron and a hole can sometimes stick together to form a chargeless quasi particle called an exciton. Other such ephemera include magnons and polarons.

    Evanescent though they are, quasi particles act every bit like elementary particles, obeying the laws of quantum mechanics. This has led some mavericks to wonder whether there is really any difference at all. Maybe elementary particles are just quasi particles — an effervescence in the vacuum.

    Particularly intriguing is a phenomenon, occurring at extremely low temperatures, called the fractional quantum Hall effect. In certain substances, quasi particles appear that act curiously like electrons but with one-third the normal charge. (Dr. Laughlin won his Nobel Prize for a theory explaining this.)

    By way of extension, this will affect our understanding of the brain.

  8. AP, thanks and Sal for a good discussion. Please, do run on. We can only learn.

    AP, perhaps in more lay terms if you have time for my benefit and others lurking?

    First, can you answer directly my thought question of the mind overriding the simple principle of going straight from A to B in favor or a roundabout pleasure tour?

    How does AP and determinency figure in the Observer-Conscience-Mind that willingly “determines” different and longer routes in preference over the short routes?

    Another observation can be made indirectly from the longer route regarding efficient use of energy.

    1) Energy is in fact wasted, albeit from a utilization standpoint. For my example, the length of the drive uses more energy, lets say twice as much. Although energy is “conserved” due to Laws of Thermodynamics within our known system. What law do we apply to the inefficiency of the routes taken on the journey? That also takes into consideration determinate outcomes of the longer routes taken at will by the Mind?

    Just to play. I could set out on a journey from A to B, but halfway to B, willfully turn around for no obvious determinate reason and return to B. The entire trip can be one long runabout with no purpose other than my choice to be whimsical in nature. Now, I guess the argument could be that this was determined by the thought of “observation” that impacts such a display on the will of the participant.

    But this in turn also means the Observer of the particpant driving between A and B is intimately intwined with the observant. We are somewhat back to the infinite regress, are we not?

    And is a mind a wasteful engine? :)

  9. Grrr, had preview and did not use it.

    correction:

    “Just to play. I could set out on a journey from A to B, but halfway to B, willfully turn around for no obvious determinate reason and return to A.”

    return to A not B.

    And my thought question(or experiment) was not answered by the following:

    “Michaels7, the physics is strictly deterministic, but the least action principle as applied to our imperfect universe doesn’t only derive straight lines.”

    Not that I disagree with regards to “straight lines” regarding physics, relativity, etc., but what I am not understanding is the simple derivatives that can connect between the observer who see’s a comet and does notthin – compared – to an observer who alters the course of the comet willfully for any number of reasons.

    The intentions are related to the physical actions only by active will of a Mind.

  10. 40

    Hi Salvador.

    Reverend John Polkinghorne writes that “the nearest analogy in the physical world to God would be … the Quantum Vacuum.”

    When you wrote “the ultimate Source of design and bounding is not part of the physical universe, but rather non-physical, non-material and not subject to the laws of physics.”

    Do you hold a similar view?

  11. I was browsing the website of a John Hopkins physicist professor, and he mentioned that discoveries in quantum physics made him make the leap from atheist to deist.

    Even though I’m just a passive reader of such things, I can’t help but sympathize. I’m surprised more serious philosophers and theologians don’t discuss the subject nowadays.

  12. nullasalus wrote:
    Even though I’m just a passive reader of such things, I can’t help but sympathize. I’m surprised more serious philosophers and theologians don’t discuss the subject nowadays.

    Welcome, nullasulus. Of all people, anti-IDist Ken Miller has this to say.

    Many people has rejected scientific values because they regard materialism as a sterile and bleak philosophy, which reduces human beings to automatons and leaves no room for free will and creativity. These people can take heart: materialism is dead.

    Quantum physics undermines materialism because it reveals that matter has far less ’substance’ than we might believe….

    physicists Paul Davies and John Gribbin,
    Matter Myth

    This [quantum uncertainty] is something biologists, almost universally, have not yet come to grips with. And its consequences are enormous. It certainly means that we should wonder more than we currently do about the saying that life is made of “mere” matter….
    ….
    This means that absolute materialism, a view that control and predictability and ultimate explanation are possible, breaks down in a way that is biologically significant.
    ….
    The core assumptions supporting the “scientific” disbelief [atheism] of the absolute materialist are wrong, even by the terms of science itself…
    ….
    What matters is the straightforward, factual, strictly scientific recognition that matter in the universe behaves in such a way that we can never achieve complete knowledge of any fragment of it…breaks in causality at the atomic level make it fundamentally impossible to exclude the idea that what we have really caught a glimpse of might indeed reflect the mind of God.
    …
    In the final analysis, absolute materialsm does not triumph because it cannot fully explain the nature of reality.
    …..
    few theologians appreciate the degree to which physics has rescued religion from the dangers of Newtonian predictability. I suspect that they do not know (at least not yet) who their true friends are!

    Ken Miller, Finding Darwin’s God

  13. a5 asked:

    Do you hold a similar view [about God being like quantum vacuum]?

    Although I like Polkinghorne, I don’t view God that way. An analogy to God in the physical universe? I don’t think there isn’t any parallel in terms of power and majesty. When one watches the bonus feature of the Privileged Planet video, “Journey”, one will get an idea of power and majesty.

    Without all the power, and majesty, but simply in terms of personality, a flawed approximation or image of God is the human person. That is a philosophical view, not a scientific one, however.

    The one quality that is inferred scientifically where there are parellels is the idea that human observers are like God in their ability to choose and therefore bring quantum systems out of their indeterminacy through observation.

    Come to think of it, here is an illustration of the power of observational choice in mathematics. This is non-rigorous (I can seem my comrades cringing now), but you will get the gist of the power of observational choice to create something out of nothing. In fact, nobel laureate Abdul Salaam suggested this idea for creation out of nothing.

    consider the infinte series

    S_zero = 0 + 0 + 0 + …..

    but what if I intelligently choose to perceive this infinite series like this:

    S_zero = [1 + -1] + [1 + -1] ….

    But what if through my power of intelligent choice, I choose to perceive the above series in yet another way. In fact, let me label this new perception as S1, where I simply take S_zero and simply rearrange the brackets.

    Rearranging terms I will transform S_zero into S_1

    S_1 = 1 + [-1 + 1] + [-1 + 1] ….

    S_1 = 1 + 0 + 0 + 0…..

    S_1 = 1

    Therefore via manipulation of infinite series I can make something out of nothing. Hehe!

    God being infinite can make these sort of tricks possible since I presume adding up infinite series is doable for Him. Hehe! Curiously, the great mathematician Cantor (who pioneered investiagations into the mathematical notion of infinity), thought of God as the Absolute Infinity. That is my thought as well….

    Here is another cute paradox that relates the capacity to choose, and the capacity to create something out of nothing: Banach–Tarski paradox.

    First stated by Stefan Banach and Alfred Tarski in 1924, the Banach-Tarski paradox or Hausdorff-Banach-Tarski paradox is the famous “doubling the ball” paradox, which states that by using the axiom of choice it is possible to take a solid ball in 3-dimensional space, cut it up into finitely many (non-measurable) pieces and, moving them using only rotations and translations, reassemble the pieces into two balls of the same radius as the original. Banach and Tarski intended this proof to be evidence in favor of rejecting the axiom of choice, but the nature of the proof is such that most mathematicians take it to mean that the axiom of choice merely results in bizarre and unintuitive consequences.

    Choice is fundamental to the characterization of intelligence. Intelligence may also be rooted deeply in mathematics in ways we don’t yet appreciate. It’s a rather shocking thought, but Paul Davies suggests free-will is rooted in mathematics through Godel’s incompleteness.

    The examples above shows that an intelligent being’s power to choose how he wishes to perceive things affects a mathematical outcome!!! This ought to be very disturbing but liberating as well.

    The way God chooses to perceive us is deeply influential on what we are or eventually become. This would be a mere curiosity from a theological standpoint, but now it seems to be a disturbing and exciting possiblity since we see echoes of it in physics (double slit delayed choice) and math.

    Sal

  14. For those of you with appropriate Adobe Acrobat capability here is a superb explanation of the Double Slit Delayed Choice Experiment which I have frequently referred.

    WARNING: Strong theological content at the end.

    But the physics are superb. The reader is invited to edit-out the end of the essay if pondering the final conclusions do not fit the reader’s fancy. Despite the theology, this is THE best explanation of Wheeler’s Double-Slit Delayed Choice Experiment on the net.

    Predestination: An Analogy in Quantum Mechanics

    Salvador

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