QM 1

Before completing this post, I need to acknowledge that my goal in writing about modern physics was to create a milieu for more talking about Western Zen. However, as I’ve proceeded, the goal has somewhat changed. I want you, as a reader, to become, if you aren’t already, a physics buff, much in the way I became a history buff after finding history incredibly boring and hateful throughout high school and college. The apotheosis of my history disenchantment came at Stanford in a course taught by a highly regarded historian. The course was entitled “The High Middle Ages” and I actually took it as an elective thinking that it was likely to be fascinating. It was only gradually over the years that I realized that history at its best although based on factual evidence, consists of stories full of meaning, significance and human interest. Turning back to physics, I note that even after more than a hundred years of revolution, physics still suffers a hangover from 300 years of its classical period in which it was characterized by a supposedly passionless objectivity and a mundane view of reality. In fact, modern physics can be imagined as a scientific fantasy, a far-flung poetic construction from which equations can be deduced and the fantasy brought back to earth in experiments and in the devices of our age. When I use the word “fantasy” I do not mean to suggest any lack of rigorous or critical thinking in science. I do want to imply a new expansion of what science is about, a new awareness, hinting at a “reality” deeper than what we have ever imagined in the past. However, to me even more significant than a new reality is the fact that the Quantum Revolution showed that physics can never be considered absolute. The latest and greatest theories are always subject to a revolution which undermines the metaphysics underlying the theory. Who knows what the next revolution will bring? Judging from our understanding of the physics of our age, a new revolution will not change the feeling that we are living in a universe which is an unimaginable miracle.

In what follows I’ve included formulas and mathematics whose significance can be easily be talked about without going into the gory details. The hope is that these will be helpful in clarifying the excitement of physics and the metaphysical ideas lying behind. Of course, the condensed treatment here can be further explicated in the books I mention and in Wikipedia.

My last post, about the massive revolution in physics of the early 20th century, ended by describing the situation in early 1925 when it became abundantly clear in the words of Max Jammer (Jammer, p 196) that physics of the atom was “a lamentable hodgepodge of hypotheses, principles, theorems, and computational recipes rather than a logical consistent theory.” Metaphysically, physicists clung to classical ideas such as particles whose motion consisted of trajectories governed by differential equations and waves as material substances spread out in space and governed by partial differential equations. Clearly these ideas were logically inconsistent with experimental results, but the deep classical metaphysics, refined over 300 years could not be abandoned until there was a consistent theory which allowed something new and different.

Werner Heisenberg, born Dec 5, 1901 was 23 years old in the summer of 1925. He had been a brilliant student at Munich studying with Arnold Sommerfeld, had recently moved to Göttingen, a citadel of math and physics, and had made the acquaintance of Bohr in Copenhagen where he became totally enthralled with doing something about the quantum mess. He noted that the electron orbits of the current theory were purely theoretical constructs and could not be directly observed. Experiments could measure the wavelengths and intensity of the light atoms gave off, so following the Zeitgeist of the times as expounded by Mach and Einstein, Heisenberg decided to try make a direct theory of atomic radiation. One of the ideas of the old quantum theory that Heisenberg used was Bohr’s “Correspondence” principle which notes that as electron orbits become large along with their quantum numbers, quantum results should merge with the classical. Classical physics failed only when things became small enough that Planck’s constant h became significant. Bohr had used this idea in obtaining his formula for the hydrogen atom’s energy levels. In various “old quantum” results the Correspondence Principle was always used, but in different, creative ways for each situation. Heisenberg managed to incorporate it into his ultimate vector-matrix construction once and for all. Heisenberg’s first paper in the Fall of 1925 was jumped on by him and many others and developed into a coherent theory. The new results eliminated many slight discrepancies between theory and experiment, but more important, showed great promise during the last half of 1925 of becoming an actual logical theory.

In January, 1926, Erwin Schrödinger published his first great paper on wave mechanics. Schrödinger, working from classical mechanics, but following de Broglie’s idea of “matter waves”, and using the Correspondence Principle, came up with a wave theory of particle motion, a partial differential equation which could be solved for many systems such as the hydrogen atom, and which soon duplicated Heisenberg’s new results. Within a couple of months Schrödinger closed down a developing controversy by showing that his and Heisenberg’s approaches, though based on seemingly radically opposed ideas, were, in fact, mathematically isomorphic. Meanwhile starting in early 1926, PAM Dirac introduced an abstract algebraic operator approach that went deeper than either Heisenberg or Schrödinger. A significant aspect of Dirac’s genius was his ability to cut through mathematical clutter to a simpler expression of things. I will dare here to be specific about what I’ll call THE fundamental quantum result, hoping that the simplicity of Dirac’s notation will enable those of you without a background in advanced undergraduate mathematics to get some of the feel and flavor of QM.

In ordinary algebra a new level of mathematical abstraction is reached by using letters such as x,y,z or a,b,c to stand for specific numbers, numbers such as 1,2,3 or 3.1416. Numbers, if you think about it, are already somewhat abstract entities. If one has two apples and one orange, one has 3 objects and the “3” doesn’t care that you’re mixing apples and oranges. With algebra, If I use x to stand for a number, the “x” doesn’t care that I don’t know the number it stands for. In Dirac’s abstract scheme what he calls c-numbers are simply symbols of the ordinary algebra that one studies in high school. Along with the c-numbers (classic numbers) Dirac introduces q-numbers (quantum numbers) which are algebraic symbols that behave somewhat differently than those of ordinary algebra. Two of the most important q-numbers are p and s, where p stands for the momentum of a moving particle, mv, mass times velocity in classical physics, and s stands for the position of the particle in space. (I’ve used s instead of the usual q for position to try avoid a confusion with the q of q-number.) Taken as q-numbers, p and s satisfy

ps – sp = h/2πi

which I’ll call the Fundamental Quantum Result in which h is Planck’s constant and i the square root of -1. Actually, Dirac, observing that in most formulas or equations involving h, it occurs as h/2π, defined what is now called h bar or h slash using the symbol ħ = h/2π for the “reduced” Planck constant. If one reads about QM elsewhere (perhaps in Wikipedia) one will see ħ almost universally used. Rather than the way I’ve written the FQR above, it will appear as something like

pqqp = ħ/i

where I’ve restored the usual q for position. What this expression is saying is that in the new QM if one multiplies something first by position q and then by momentum p, the result is different from the multiplications done in the opposite order. We say these q-numbers are non-commutative, the order of multiplication matters. Boldface type is used because position and momentum are vectors and the equation actually applies to each of their 3 components. Furthermore, the FQR tells us exact size of the non-commute. In usual human sized physical units ħ is .00…001054… where there are 33 zeros before the 1054. If we can ignore the size of ħ and set it to zero, p and q, then commute, can be considered c-numbers and we’re back to classical physics. Incidentally, Heisenberg, Born and Jordan obtained the FQR using p and q as infinite matrices and it can be derived also using Schrödinger’s differential operators. It is interesting to note that by using his new abstract algebra, Dirac not only obtained the FQR but could calculate the energy levels of the hydrogen atom. Only later did physicists obtain that result using Heisenberg’s matrices. Sometimes the deep abstract leads to surprisingly concrete results.

For most physicists in 1926, the big excitement was Schrödinger’s equation. Partial differential equations were a familiar tool, while matrices were at that time known mainly to mathematicians. The “old quantum theory” had made a few forays into one or another area leaving the fundamentals of atomic physics and chemistry pretty much in the dark. With Schrödinger’s equation, light was thrown everywhere. One could calculate how two hydrogen atoms were bound in the hydrogen molecule. Then using that binding as a model one could understand various bindings of different molecules. All of chemistry became open to theoretic treatment. The helium atom with its two electrons couldn’t be dealt with at all by the old quantum theory. Using various approximation methods, the new theory could understand in detail the helium atom and other multielectron atoms. Electrons in metals could be modeled with the Schrödinger’s equation, and soon the discovery of the neutron opened up the study of the atomic nucleus. The old quantum theory was helpless in dealing with particle scattering where there were no closed orbits. Such scattering was easily accommodated by the Schrödinger equation though the detailed calculations were far from trivial. Over the years quantum theory revealed more and more practical knowledge and most physicists concentrated on experiments and theoretic calculations that led to such knowledge with little concern about what the new theory meant in terms of physical reality.

However, back in the first few years after 1925 there was a great deal of concern about what the theory meant and the question of how it should be interpreted. For example, under Schrödinger’s theory an electron was represented by a “cloud” of numbers which could travel through space or surround an atom’s nucleus. These numbers, called the wave function and typically named ψ, were complex, of the form a + ib, where i is the square root of -1. By multiplying such a number by its conjugate a – ib, one gets a positive (strictly speaking, non-negative) number which can perhaps be physically interpreted. Schrödinger himself tried to interpret this “real” cloud as a negative electric change density, a blob of negative charge. For a free electron, outside an atom, Schrödinger imagined that the electron wave could form what is called a “wave packet”, a combination of different frequencies that would appear as a small moving blob which could be interpreted as a particle. This idea definitely did not fly. There were too many situations where the waves were spread out in space, before an electron suddenly made its appearance as a particle. The question of what ψ meant was resolved by Max Born (see Wikipedia), starting with a paper in June, 1926. Born interpreted the non-negative numbers ψ*ψ (ψ* being the complex conjugate of the ψ numbers) as a probability distribution for where the electron might appear under suitable physical circumstances. What these physical circumstances are and the physical process of the appearance are still not completely resolved. Later in this or another blog post I will go into this matter in some detail. In 1926 Born’s idea made sense of experiment and resolved the wave-particle duality of the old quantum theory, but at the cost of destroying classical concepts of what a particle or wave really was. Let me try to explain.

A simple example of a classical probability distribution is that of tossing a coin and seeing if it lands heads or tails. The probability distribution in this case is the two numbers, ½ and ½, the first being the probability of heads, the second the probability of tails. The two probabilities add up to 1 which represents certainty, in probability theory. (Unlike the college students who are trying to decide whether to go drinking, go to the movies or to study, I ignore the possibility that the coin lands on its edge without falling over.) With the wave function product ψ*ψ, calculus gives us a way of adding up all the probabilities, and if they don’t add up to 1, we simply define a new ψ by dividing by the sum we obtained. (This is called “normalizing” the wave function.) Besides the complexity of the math, however, there is a profound difference between the coin and the electron. With the coin, classical mechanics tells us in theory, and perhaps in practice, precisely what the position and orientation of the coin is during every instant of its flight; and knowing about the surface the coin lands on, allows us to predict the result of the toss in advance. The classical analogy for the electron would be to imagine it is like a bb moving around inside the non-zero area of the wave function, ready to show up when conditions are propitious. With QM this analogy is false. There is no trajectory for the electron, there is no concept of it having a position, before it shows up. Actually, it is only fairly recently that the “bb in a tin can model” has been shown definitively to be false. I will discuss this matter later talking briefly about Bell’s theorem and “hidden” variable ideas. However, whether or not an electron’s position exists prior to its materialization, it was simply the concept of probability that Einstein and Schrödinger, among others, found unacceptable. As Einstein famously put it, “I can’t believe God plays dice with the universe.”

Max Born, who introduced probability into fundamental physics, was a distinguished physics professor in Göttingen and Heisenberg’s mentor after the latter first came to Göttingen from Munich in 1922. Heisenberg got the breakthrough for his theory while escaping from hay fever in the spring of 1925 walking the beaches of the bleak island of Helgoland in the North Sea off Germany. Returning to Göttingen, Heisenberg showed his work to Born who recognized the calculations as being matrix multiplication and who saw to it that Heisenberg’s first paper was immediately published. Born then recruited Pascual Jordan from the math department at Göttingen and the three wrote a famous follow-up paper, Zur Quantenmechanik II, Nov, 1925, which gave a complete treatment of the new theory from a matrix mechanics point of view. Thus, Born was well posed to come up with his idea of the nature of the wave function.

Quantum Mechanics came into being during the amazingly short interval between mid-1925 and the end of 1926. As far as the theory went, only “mopping” up operations were left. As far as the applications were concerned there was a plethora of “low hanging fruit” that could be gathered over the years with Schrödinger’s equation and Born’s interpretation. However, as 1927 dawned, Heisenberg and many others were concerned with what the theory meant, with fears that it was so revolutionary that it might render ambiguous the meaning of all the fundamental quantities on which both the new QM and old classical physics depended. In 1925 Heisenberg began his work on what became the matrix mechanics because he was skeptical about the existence of Bohr orbits in atoms, but his skepticism did not include the very concept of “space” itself. As QM developed, however, Heisenberg realized that it depended on classical variables such as position and momentum which appeared not only in the pq commutation relation but as basic variables of the Schrödinger equation. Had the meaning of “position” itself changed? Heisenberg realized that earlier with Einstein’s Special Relativity that the meaning of both position and time had indeed changed. (Newton assumed that coordinates in space and the value of time were absolutes, forming an invariable lattice in space and an absolute time which marched at an unvarying pace. Einstein’s theory was called Relativity because space and time were no longer absolutes. Space and time lost their “ideal” nature and became simply what one measured in carefully done experiments. (Curiously enough, though Einstein showed that results of measuring space and time depended on the relative motion of different observers, these quantities changed in such an odd way that measurements of the speed c of light in vacuum came out precisely the same for all observers. There was a new absolute. A simple exposition of special relativity is N. David Mermin’s Space and Time in Special Relativity.)

The result of Heisenberg’s concern and the thinking about it is called the “Uncertainty Principle”. The statement of the principle is the equation ΔqΔp = ħ. The variables q and p are the same q and p of the Fundamental Quantum Relation and, indeed, it is not difficult to derive the uncertainty principle from the FQR. The symbol delta, Δ, when placed in front of a variable means a difference, that is an interval or range of the variable. Experimentally, a measurement of a variable quantity like position q is never exact. The amount of the uncertainty is Δq. The uncertainty equation above thus says that the uncertainty of a particle’s position times the uncertainty of the same particle’s momentum is ħ. In QM what is different from an ordinary error of measurement is that the uncertainty is intrinsic to QM itself. In a way, this result is not all that surprising. We’ve seen that the wave function ψ for a particle is a cloud of numbers. Similarly, a transformed wave function for the same particle’s momentum is a similar cloud of numbers. The Δ’s are simply a measure of the size of these two clouds and the principle says that as one becomes smaller, the other gets larger in such a way that their product is h bar, whose numerical value I’ve given above.

In fact, back in 1958 when I was in Eikenberry’s QM course and we derived the uncertainty relation from the FQR, I wondered what the big deal was. I was aware that the uncertainty principle was considered rather earthshaking but didn’t see why it should be. What I missed is what Heisenberg’s paper really did. The equation I’ve written above is pure theory. Heisenberg considered the question, “What if we try to do experiments that actually measure the position and momentum. How does this theory work? What is the physics? Could experiments actually disprove the theory?” Among other experimental set-ups Heisenberg imagined a microscope that used electromagnetic rays of increasingly short wavelengths. It was well known classically by the mid-nineteenth century that the resolution of a microscope depends on the wavelength of the light it uses. Light is an electromagnetic (em) wave so one can imagine em radiation of such a short wavelength that it could view with a microscope a particle, regardless of how small, reducing Δq to as small a value as one wished. However, by 1927 it was also well known because of the Compton effect that I talked about in the last post, that such em radiation, called x-rays or gamma rays, consisted of high energy photons which would collide with the electron giving it a recoil momentum whose uncertainty, Δp, turns out to satisfy ΔqΔp = ħ. Heisenberg thus considered known physical processes which failed to overturn the theory. The sort of reasoning Heisenberg used is called a “thought” experiment because he didn’t actually try to construct an apparatus or carry out a “real” experiment. Before dismissing thought experiments as being hopelessly hypothetical, one must realize that any real experiment in physics or in any science for that matter, begins as a thought experiment. One imagines the experiment and then figures out how to build an apparatus (if appropriate) and collect data. In fact, as a science progresses, many experiments formerly expressed only in thought, turn real as the state of the art improves.

Although the uncertainty principle is earthshaking enough that it helped confirm the skepticism of two of the main architects of QM, namely, Einstein and Schrödinger, one should note that, in practice, because of the small size of ħ, the garden variety uncertainties which arise from the “apparatus” measuring position or momentum are much larger than the intrinsic quantum uncertainties. Furthermore, the principle does not apply to c-numbers such as e, the fundamental electron or proton charge, c, the speed of light in vacuum, h, Planck’s constant. There is an interesting story here about a recent (Fall, 2018) redefinition of physical units which one can read about on line. Perhaps I’ll have more to say about this subject in a later post. For now, I’ll just note that starting on May 20, 2019, Planck’s constant will be (or has been) defined as having an exact value of 6.626070150×10−34 Joule seconds. There is zero uncertainty in this new definition which may be used to define and measure the mass of the kilogram to higher accuracy and precision than possible in the past using the old standard, a platinum-iridium cylinder, kept closely guarded near Paris. In fact, there is nothing muddy or imprecise about the value of many quantities whose measurement intimately involves QM.

During the years after 1925 there was at least one more area which in QM was puzzling to say the least; namely, what has been called “the collapse of the wave function.” Involved in the intense discussions over this phenomenon and how to deal with it was another genius I’ve scarcely mentioned so far; namely Wolfgang Pauli. Pauli, a year older than Heisenberg, was a year ahead of him in Munich studying under Sommerfeld, then moved to Göttingen, leaving just before Heisenberg arrived. Pauli was responsible for the Pauli Exclusion Principle based on the concept of particle spin which he also explicated. (see Wikipedia) He was in the thick of things during the 1925 – 1927 time period. Pauli ended up as a professor in Zurich, but spent time in Copenhagen with Bohr and Heisenberg (and many others) formulating what became known as the Copenhagen interpretation of QM. Pauli was a bon vivant and had a witty sarcastic tongue, accusing Heisenberg at one point of “treason” for an idea that he (Pauli) disliked. In another anecdote Pauli was at a physics meeting during the reading of a muddy paper by another physicist. He stormed to his feet and loudly said, “This paper is outrageous. It is not even wrong!” Whether the meeting occurred at a late enough date for Pauli to have read Popper, he obviously understood that being wrong could be productive, while being meaningless could not.

Over the next few years after 1927 Bohr, Heisenberg, and Pauli explicated what came to be called “the Copenhagen interpretation of Quantum Mechanics”. It is well worth reading the superb article in Wikipedia about “The Copenhagen Interpretation.” One point the article makes is that there is no definitive statement of this interpretation. Bohr, Heisenberg, and Pauli each had slightly different ideas about exactly what the interpretation was or how it worked. However, in my opinion, things are clear enough in practice. The problem QM seems to have has been called the “collapse of the wave function.” It is most clearly seen in a double slit interference experiment with electrons or other quantum particles such as photons or even entire atoms. The experiment consists of a plate with two slits, closely enough spaced that the wave function of an approaching particle covers both slits. The spacing is also close enough that the wavelength of the particle as determined by its energy or momentum, is such that the waves passing through the slit will visibly interfere on the far side of the slit. This interference is in the form of a pattern consisting of stripes on a screen or photographic plate. These stripes show up, zebra like, on a screen or as dark, light areas on a developed photographic plate. On a photographic plate there is a black dot where a particle has shown up. The striped pattern consists of all the dots made by the individual particles when a large number of particles have passed through the apparatus. What has happened is that the wave function has “collapsed” from an area encompassing all of the stripes, to a tiny area of a single dot. One might ask at this point, “So what?” After all, for the idea of a probability distribution to have any meaning, the event for which there is a probability distribution has to actually occur. The wave function must “collapse” or the probability interpretation itself is meaningless. The problem is that QM has no theory whatever for the collapse.

One can easily try to make a quantum theory of what happens in the collapse because QM can deal with multi-particle systems such as molecules. One obtains a many particle version of QM simply by adding the coordinates of the new particles, which are to be considered, to a multi-particle version of the Schrödinger equation. In particular, one can add to the description of a particle which approaches a photographic plate, all the molecules in the first few relevant molecular layers of the plate. When one does this however, one does not get a collapse. Instead the new multi-particle wave function simply includes the molecules of the plate which are as spread out as much as the original wave function of the approaching particle. In fact, the structure of QM guarantees that as one adds new particles, these new particles themselves continue to make an increasingly spread out multi-particle wave function. This result was shown in great detail in 1929 by John von Neumann. However, the idea of von Neumann’s result was already generally realized and accepted during the years of the late 1920’s when our three heroes and many others were grappling with finding a mechanism to explain the experimental collapse. Bohr’s version of the interpretation is simplicity itself. Bohr posits two separate realms, a realm of classical physics governing large scale phenomena, and a realm of quantum physics. In a double slit experiment the photographic plate is classical; the approaching particle is quantum. When the quantum encounters the classical, the collapse occurs.

The Copenhagen interpretation explains the results of a double slit experiment and many others, and is sufficient for the practical development of atomic, molecular, solid state, nuclear and particle physics, which has occurred since the late 1920’s. However, there has been an enormous history of objections, refinements, rejections and alternate interpretations of the Copenhagen interpretation as one might well imagine. My own first reaction could be expressed as the statement, “I thought that ‘magic’ had been banned from science back in the 17th century. Now it seems to have crept back in.” (At present I take a less intemperate view.) However, one can make many obvious objections to the Copenhagen interpretation as I’ve baldly stated it above. Where, exactly, does the quantum realm become the classic realm? Is this division sharp or is there an interval of increasing complexity that slowly changes from quantum to classical? Surely, QM, like the theory of relativity, actually applies to the classical realm. Or does it?

During the 1930’s Schrödinger used the difficulties with the Copenhagen interpretation to make up the now famous thought experiment called “Schrödinger’s Cat.” Back in the early 1970’s when I became interested in the puzzle of “collapse” and first heard the phrase “Schrödinger’s Cat”, it was far from famous so, curious, I looked it up and read the original short article, puzzling out the German. In his thought experiment Schrödinger uses the theory of alpha decay. An alpha particle confined in a radioactive nucleus is forever trapped according to classical physics. QM allows the escape because the alpha particle’s wave function can actually penetrate the barrier which classically keeps it confined. Schrödinger imagines a cat imprisoned in a cage containing an infernal apparatus (hollenmaschine) which will kill the cat if triggered by an alpha decay. Applying a multi-particle Schrödinger’s equation to the alpha’s creeping wave function as it encounters the trigger of the “maschine”, its internals, and the cat, the multi-particle wave function then contains a “superposition” (i.e. a linear combination) of a dead and a live cat. Schrödinger makes no further comment leaving it to the reader to realize how ridiculous this all is. Actually, it is even worse. According to QM theory, when a person looks in the cage, the superposition spreads to the person leaving two versions, one looking at a dead cat and one looking at a live cat. But a person is connected to an environment which also splits and keeps splitting until the entire universe is involved.

What I’ve presented here is an actual alternative to the Copenhagen Interpretation called “the Many-worlds interpretation”. To quote from Wikipedia “The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternate histories and futures are real, each representing an actual ‘world’ (or ‘universe’).” The many-worlds interpretation arose in 1957 in the Princeton University Ph.D. dissertation of Hugh Everett working under the direction of the late John Archibald Wheeler, who I mentioned in the last post. Although I am a tremendous admirer of Wheeler, I am skeptical of the many-worlds interpretation. It seems unnecessarily complicated, especially in light of ideas that have developed since I noticed them in 1972. There is no experimental evidence for the interpretation. Such evidence might involve interference effects between the two versions of the universe as the splitting occurs. Finally, if I exist in a superposition, how come I’m only conscious of the one side? Bringing in “consciousness” however, leads to all kinds of muddy nonsense about consciousness effects in wave function splitting or collapse. I’m all for consciousness studies and possibly such will be relevant for physics after another revolution in neurology or physics. At present we can understand quantum mechanics without explicitly bringing in consciousness.

In the next post I’ll go into what I noticed in 1971-72 and how this idea subsequently became developed in the greater physics community. The next post will necessarily be somewhat more mathematically specific than so far, possibly including a few gory details. I hope that the math won’t obscure the story. In subsequent posts I’ll revert to talking about physics theory without actually doing any math.

Physics, Etc.

In telling a story about physics and some of its significance for a life of awareness I’ll start with an idea of the philosopher Immanuel Kant (1724 – 1804). Kant, in my mind, is associated with impenetrable German which translates into impenetrable English. To find some clarity about Kant’s ideas one turns to Wikipedia, where the opening paragraph of the Kant entry explains his main ideas in an uncharacteristically comprehensible way. One of these ideas is that we are born into this world with our minds prepared to understand space, time, and causality. And with this kind of mental conditioning we can make sense of simple phenomena, and, indeed, pursue science. This insight predates Darwin’s theory of evolution which offers a plausible explanation for it, by some sixty-odd years, and was thus a remarkable insight on the part of Kant. Another Kant idea that is relevant to our story is his distinction between what he calls phenomena and noumena. Quoting from Wikipedia, “… our experience of things is always of the phenomenal world as conveyed by our senses: we do not have direct access to things in themselves, the so-called noumenal world.” Of course, this is only one aspect of Kant’s thought, but the aspect that seems to me most relevant to what might be meant by physical reality. Kant was a philosopher’s philosopher, totally dedicated to deepening our understanding of what we may comprehend about the world and morality by purely rational thought. He was born in Königsberg, East-Prussia, at the time a principality on the Baltic coast east of Denmark and north of Poland-Lithuania; and died there 80 years later. Legend has it that during his entire life he never traveled more than 10 miles from his home. The Wikipedia article refutes this slander: Kant actually traveled on occasion some 90.1 miles from Königsberg.

The massive extent of Kant’s philosophy leaves me somewhat appalled, particularly since I understand little of it and because what I perhaps do understand seems dubious at best and meaningless at worst. What Kant may not have realized is the idea that the extent and nature of the noumenal world is relative to the times in which one lives. Kant was born 3 years before Isaac Newton died, so by the date of his birth the stage was well set for the age of classical physics. During his life classical mechanics was developed largely by two great mathematicians, Joseph-Louis Lagrange (1736 – 1813) and Pierre-Simon Laplace (1747 – 1849). Looking back from Kant’s time to the ancient world one sees an incredible growth of the phenomenal world, with the Copernican revolution, a deepening understanding of planetary motion, and Newton’s Laws of mechanics. In the time since Kant lived laws of electricity and magnetism, statistical mechanics, quantum mechanics, and most of present-day science were developed. This advance raises a question. Does the growth of the phenomenal world entail a corresponding decrease in the noumenal world or are phenomena and noumena entirely independent of one another? Of course, I’d like to have it both ways, and can do so by imagining two senses of noumena. To get an idea of the first original idea, I will tell a brief story. In the early 1970’s we were visited at Auburn University by the great physicist, John Archibald Wheeler, who led a discussion in our faculty meeting room. I was very impressed by Dr. Wheeler. To me he seemed a “tiger”, totally dedicated to physics, his students, and to an awareness of what lay beyond our comprehension. At one point he pointed to the tiles on the floor and said to us physicists, something like, “Let each one of you write your favorite physics laws on one of these tiles. And after you’ve all done that, ask the tiles with their equations to get up and fly. They will just lie there; but the universe flies.” Wheeler had doubtless used this example on many prior occasions, but it was new to me and seems to get at the meaning of noumena as a realm independent of anything science can ever discover. On the other hand, as the realm of phenomena that we do understand has grown, we can regard noumena simply as a “blank” in our knowledge, a blank which can be filled in as science, so to speak, peels back the layers of an “onion” revealing the understanding of a larger world, and at the same time, exposing a new layer of ignorance to attack. This second sense of the word in no way diminishes the ultimate mystery of the universe. In fact, it appears to me that the quest for ultimate understanding in the face of the great mystery is what gives physics (and science) a compulsive, even addictive, fascination for its practitioners. Like compulsive gamblers experimental physicists work far into the night and theorists endlessly torture thought. Certainly, the idea that we could conceivably uncover ever more specifics into the mystery of ultimate being is what drew me to the area. That, as well as the idea that if one wants to understand “everything”, physics is a good place to start.

In my understanding, the story of physics during my lifetime and the 30 years preceding my birth is the story of a massive, earthshaking revolution. Thomas Kuhn’s The Structure of Scientific Revolutions, mentioned in earlier posts is a story of many shifts in scientific perception which he calls revolutions. In his terms what I’m talking about here is a “super-duper-revolution”, a massive shift in understanding whose import is still not fully realized in our society at large at the present time. Most of the ”revolutions” that Kuhn uses as examples affect only scientists in a particular field. For example, the fall of the phlogiston theory and the rise of Oxygen in understanding fire and burning was a major revolution for chemistry, but had little effect on the culture of society at large. Similarly, in ancient times the rise of Ptolemaic astronomy mostly concerned philosophers and intellectuals. The larger society was content with the idea that gods or God controlled what went on in the heavens as well as on earth. The Copernican revolution, on the other hand, was earth shaking (super-duper) for the entire society, mainly because it called into question theories of how God ran the universe and because it became the underpinning of an entirely new idea of what was “real”. Likewise, the scientific revolution of the 16th and 17th centuries was earthshaking to the entire society, which, however, as time wore on into the 18th and 19th centuries became accustomed to it and assumed that the classical, Newtonian “clockworks” universe was here to stay forever however uncomfortable it might be to artists and writers, who hoped to live in a different, more meaningful world of their own experience, rejecting scientific “reality” as something which mattered little in a spiritual sense. Who could have believed that in the mid 1890’s after 300 years (1590 – 1890, say) of continued, mostly harmonious development the entire underpinning of scientific reality was about to be overturned by what might be called the quantum revolution. Yet that is what happened in the next forty years (1895 – 1935) with continuing advances and consolidation up to the present day. (From now on I’ll use the abbreviation QM for Quantum Mechanics, the centerpiece of this revolution.) Of course, as with any great revolution, all has not been smooth. Many of the greatest scientists of our times, most notably Albert Einstein and Erwin Schrödinger, found the tenets of the new physics totally unacceptable and fought them tooth and nail. In fact, there is at least one remaining QM puzzle epitomized by “Schrödinger’s Cat” about which I hope to have my say at some point.

It is my hope that readers of this blog will find excitement in the open possibilities that an understanding of the revolutionary physical “reality” we currently live in suggests. In talking about it I certainly don’t want to try “reinvent the wheel” since many able and brilliant writers have told portions of the story. What I can do is give references to various books and URL’s that are with few exceptions (which I’ll note) great reading. I’ll have comments to make about many of these and hope that with their underpinning, I can tell this story and illuminate its relevance for what I’ve called Western Zen.

The first book to delve into is The Quantum Moment: How Planck, Bohr, Einstein, and Heisenberg Taught us to Love Uncertainty by Robert P. Crease and Alfred Scharff Goldhaber. Robert Crease is a philosopher specializing in science and Alfred Goldhaber is a physicist. The book, which I’ll abbreviate as TQM, tells the history of Quantum Mechanics from its very beginning in December, 1900, to very near the present day. Copyrighted by W.W. Norton in 2014 it is quite recent, today as I write being early November, 2018. The story this book tells goes beyond an exposition of QM itself to give many examples of the effects that this new reality has had so far in our society. It is very entertaining and well written though, on occasion it does get slightly mathematical in a well-judged way in making quantum mechanics clearer. A welcome aspect of the book for me was the many references to another book, The Conceptual Development of Quantum Mechanics by Max Jammer. Jammer’s book (1966) is out of print and is definitely not light reading with its exhaustive references to the original literature and its full deployment of advanced math. Auburn University had Jammer in its library and I studied it extensively while there. I was glad to see the many footnotes to it in TQM, showing that Jammer is still considered authoritative and that there is no more recent book detailing this history. Recently, I felt that I would like to own a copy of Jammer so found one, falling to pieces, on Amazon for fifty odd dollars. If you are a hotshot mathematician and fascinated by the history of QM, you will doubtless find Jammer in any university library.

The quantum revolution occurred in two great waves. The first wave, called the “old quantum theory” started with Planck’s December, 1900, paper on black body radiation and ended in 1925 with Heisenberg’s paper on Quantum Mechanics proper. From 1925 through about 1932, QM was developed by about 8 or so geniuses bringing the subject to a point equivalent to Newton’s Principia for classical mechanics development. Besides the four physicists of the Quantum Moment title, I’ll mention Louis de Broglie, Wolfgang Pauli, PAM Dirac, Max Born, Erwin Schrödinger. And there were many others.

A point worth mentioning is that The Quantum Moment concentrates on what might be called the quantum weirdness of both the old quantum theory and the new QM. This concentration is appropriate because it is this weirdness that has most affected our cultural awareness, the main subject of the book. However, to the physicists of the period 1895 – 1932, the weirdness, annoying and troubling as it was, was in a way a distraction from the most exciting physics going on at the time; namely, the discovery that atoms really exist and have a substructure which can be understood, an understanding that led to a massive increase in practical applications as well as theoretical knowledge. Without this incredible success in understanding the material world the “weirdness” might have well have doomed QM. As we will mention below most physicists ignore the weirdness and concentrate on the “physics” that leads to practical advances. Two examples of these “advances” are the atomic bomb and the smart phone in your pocket. In the next few paragraphs I will fill in some of this history of atomic physics with its intimate connection to QM.

The discovery of the atom and its properties began in 1897 as J.J. Thomson made a definitive breakthrough in identifying the first sub-atomic particle, the lightweight, negatively charged electron (see Wikipedia). Until 1905, however, many scientists disbelieved in the “reality” of atoms in spite of their usefulness as a conceptual tool in understanding chemistry. In the “miracle year” 1905 Albert Einstein published four papers, each one totally revolutionary in a different field. The paper of interest here is about Brownian motion, a jiggling of small particles, as seen through a microscope. As a child I had a very nice full laboratory Bausch and Lomb microscope, given by my parents when I was about 7 years old. In the 9th grade I happened to put a drop of tincture of Benzoin in water and looked at it through the microscope, seeing hundreds of dancing particles that just didn’t behave like anything alive. I asked my biology teacher about it and after consulting her husband, a professor at the university, she told me it was Brownian motion, discovered by Robert Brown in 1827. I learned later that the motion was caused because the tiny moving particles are small enough that molecules striking them are unbalanced by others, causing a random motion. I had no idea at time how crucial for atomic theory this phenomenon was. It turns out that the motion had been characterized by careful observation and that Einstein showed in his paper how molecules striking the small particles could account for the motion. Also, by this time studies of radioactivity had shown emitted alpha and beta particles were clearly sub-atomic, beta particles being identical with the newly discovered electrons and the charged alpha particles turning into electrically neutral helium as they slowed and captured stray electrons.

Einstein’s other 1905 papers were two on special relativity and one on the photoelectric effect. As strange as special relativity seems with its contraction of moving measuring sticks, slowing of moving clocks, simultaneity dependent upon the observer to say nothing of E = mc², this theory ended up fitting comfortably with classical Newtonian physics. Not so with the photoelectric effect.

In December, 1900, Max Planck started the quantum revolution by finding a physical basis for a formula he had guessed earlier relating the radiated energy of a glowing “black body” to its temperature and the frequencies of its radiation. A “black body” is made of an ideal substance that is totally efficient in radiating electro-magnetic waves. Such a body could be simulated experimentally with high accuracy by measuring what came out of a small hole in the side of an enclosed oven. To find the “physics” behind his formula Planck had turned to statistical mechanics, which involves counting numbers of discrete states to find the probability distribution of the states. In order to do the counting Planck had artificially (he thought) broken up the continuous energy of electromagnetic waves into chunks of energy, hν, ν being the frequency of the wave, denoted historically by the Greek letter nu. (Remember: the frequency is associated with light’s color, and thus the color of the glow when a heated body gives off radiation) Planck’s plan was to let the “artificial” fudge-factor h go to zero in the final formula so that the waves would regain their continuity. Planck found his formula, but when he set h = 0, he got the classical Raleigh-Jeans formula for the radiation with its “ultra-violet catastrophe”. The latter term refers to the Raleigh-Jeans formula’s infinite energy radiated as the frequency goes higher. Another formula, guessed by Wien, gave the correct experimental results at high frequencies but was off at lower frequencies where the Raleigh-Jeans formula worked just fine. To his dismay what Planck found was that if he set h equal to a very small finite value, his formula worked perfectly for both low and high frequencies. This was a triumph but at the same time, a disaster. Neither Planck nor anyone else believed that these hν bundles could “really” be real. Maybe the packets came off in bundles which quickly merged to form the electromagnetic wave. True, Newton had thought light consisted of a stream of tiny particles, but over the years since his time numerous experiments showed that light really was a wave phenomenon, with all kinds of wave interference effects. Also, in the 19th century physicists, notably Fraunhofer, invented the diffraction grating and with it the ability to measure the actual wave length of the waves. The Quantum Moment (TQM) has a wonderfully complete detailed story of Planck’s momentous breakthrough in its chapter “Interlude: Max Planck Introduces the Quantum”. TQM is structured with clear general expositions followed by more detailed “Interludes” which can be skipped without interrupting the story.

Einstein’s 1905 photoelectric effect paper assumed that the hν quanta were real and light actually acted like little bullets, slamming into a metal surface, penetrating, colliding with an atomic electron and bouncing it out of the metal where it could be detected. It takes a certain energy to bounce an electron out of its atom and then past the surface of the metal. What was experimentally found (after some tribulations) was that energy of the emerging electrons depended only on the frequency of the light hitting the surface. If the light frequency was too low, no matter how intense the light, nothing much happened. At higher frequencies, increasing the intensity of the light resulted in more electrons coming out but did not increase their energy. As the light frequency increased the emitted electrons were more energetic. It was primarily for this paper that Einstein received his Nobel Prize in 1921.

A huge breakthrough in atomic theory was Ernest Rutherford’s discovery of the atomic nucleus in the early years of the 20th century. Rather than a diffuse cloud of electrically positive matter with the negatively charged electrons distributed in it like raisins (the “plum pudding” model of the atom) Rutherford found by scattering alpha particles off gold foil that the positive charge of the atom was in a tiny nucleus with the electrons circling at a great distance (the “fly in the cathedral model”). There was a little problem however. The “plum pudding” model might possibly be stable under Newtonian classical physics, while the “fly in the cathedral” model was utterly unstable. (Note: Rutherford’s experiment, though designed by him, was actually carried out between 1908 and 1913 by Hans Geiger and Ernest Marsden at Rutherford’s Manchester lab.) Ignoring the impossibility of the Rutherford atom physics plowed ahead. In 1913 the young Dane Niels Bohr made a huge breakthrough by assuming quantum packets were real and could be applied to understanding the hydrogen atom, the simplest of all atoms with its single electron circling its nucleus. Bohr’s model with its discrete electron orbits and energy levels explained the spectral lines of glowing hydrogen which had earlier been discovered and measured with a Fraunhofer diffraction grating. At Rutherford’s lab it was quickly realized that energy levels were a feature of all atoms, and the young genius physicist, Henry Moseley, using a self-built X-ray tube to excite different atoms refined the idea of the atomic number, removing several anomalies in the periodic table of the time, while predicting 4 new chemical elements in the process. At this point World War I intervened and Moseley volunteered for the Royal Engineers. One among the innumerable tragedies of the Great War was the death of Moseley August 10, 1915, aged 27, in Gallipoli, killed by a sniper.

Brief Interlude: It is enlightening to understand the milieu in which the quantum revolution and the Great War occurred. A good read is The Fall of the Dynasties – The Collapse of the Old Order: 1905 – 1922 by Edmond Taylor. Originally published in 1963, the book was reissued in 2015. The book begins with the story of the immediate cause of the war, an assassination in Sarajevo, Bosnia, part of the dual monarchy Austria-Hungary empire; then fills in the history of the various dynasties, countries and empires involved. One imagines what it would be like to live in those times and becomes appalled by the nationalistic passions of the day. While explicating the seemingly mainstream experience of living in the late 19th and early 20th century, and the incredible political changes entailed by the fall of the monarchies and the Great War, the aspects of the times, which we think of, these days, as equally revolutionary are barely mentioned. These were modern art with its demonstration that aesthetic depth lay in realms beyond pure representation, the modern novel and poetry, the philosophy of Wittgenstein which I’ve discussed above and perhaps most revolutionary of all, the fall of classic physics and rise of the new “reality” of modern physics which we are talking about in this post. (With his deep command of the relevant historical detail for his story the author does, however, get one thing wrong when he briefly mentions science. He chooses Einstein’s relativity of 1905 but calls it “General Relativity” putting in an adjective which makes it sound possibly more exciting than plain “relativity”. The correct phrase is “Special Relativity” which indeed was quite exciting enough. General Relativity didn’t happen until 1915.)

Unlike the second world war the first was not a total war and research in fundament physics went on. The mathematician turned physicist Arnold Sommerfeld in Munich generalized Bohr’s quantum rules by imagining the discrete electron orbits as elliptical rather than circular and taking their tilt into account, giving rise to new labels (called quantum numbers) for these orbits. The light spectra given off by atoms verified these new numbers with a few discrepancies which were later removed by QM. During this time and after the war ended, physicists became concerned about the contradiction between the wave and particle theories of light. This subject is well covered in TQM. (See the chapter “Sharks and Tigers: Schizophrenia”. It is easy to see the problem. If one has surfed or even just looked at the ocean, one feels or sees that a wave carries energy along a wide front, this energy being released as the wave breaks. This kind of energy distribution is characteristic of all waves, not just ocean waves. On the other hand, a bullet or billiard ball carries its energy and momentum in a compact volume. Waves can interfere with each other, reinforcing or canceling out their amplitudes. So, what is one to make of light which makes interference patterns when shined through a single or double slit but acts like a particle in the photoelectric effect or, even more clearly, like a billiard ball collision when a light quantum, called a photon, collides with an electron, an effect discovered by Arthur Compton in 1923. To muddy the waters still further, in 1922 the French physicist Louis de Broglie reasoned that if light can act like either a particle or wave depending on circumstances, by analogy, an electron, regarded hitherto as strictly a particle, could perhaps under the right conditions act like a wave. Although there was no direct evidence for electron waves at the time, there was suggestive evidence. For example, with the Bohr model of the hydrogen atom if one assumed the lowest, “ground state” orbit was a single electron wave length, one could deduce the entire Bohr theory in a new, simple way. By 1924 it was clear to physicists that the “old” quantum mechanics just wouldn’t do. This theory kept classical mechanics and classical wave theory and restricted their generality by imposing “quantum” rules. With both light and electrons being both wave and particle, physics contained an apparent logical contradiction. Furthermore, though the “old” theory had successes with its concept of energy levels in atoms and molecules, it couldn’t theoretically deal at all with such seemingly simple entities as the hydrogen molecule or the helium atom which experimentally had well defined energy levels. The theory was a total mess. It was in 1925 that the beginnings of a completely new, fundamental theory made its appearance leading shortly to much more weirdness than had already appeared in the “old quantum” theory. In the next post I’ll delve into some of the story of the new QM.

Reality

Reality is what we all know about as long as we don’t think. It’s not meant to be thought about but reacted to; as threats, awareness of danger; bred into our bones by countless years of evolution. But now, after those countless years, we have a brain and a different kind of awareness that can wonder about such things. Is such wonder worthless? Who knows. Worthless or not, I’m stuck with it because I enjoy ruminations and trying to understand what we take for granted, finding as I think harder, nothing but mystery. In this post I will begin to talk about “reality” and try to clarify the idea somewhat, bringing in Zen, which may or may not be relevant.

In thinking about “reality” I will take it as a primitive, attempting no definition. One may try to get at reality by considering “fiction”, perhaps a polar opposite. In this consideration one notes that Aristotelean logic doesn’t apply. There is a middle one can’t exclude, because, in this case, the middle is larger and more important than the ends of the spectrum.

One can begin to work into this middle by considering the use of the word “fiction” in Yuval Harari’s Sapiens: A Brief History of Humankind, where “fiction” is applied to societal conventions and laws. Sapiens is a fascinating book, but Harari’s use of the word “fiction” for “convention” rubbed me the wrong way. Although laws and conventions are, strictly speaking, fictions, they have one property popularly attributed to “reality”. A common saying is: “One doesn’t have to believe in reality. It will up and bite you whether you believe in it or not.” The same applies to laws and convention. If one is about to be executed for “treason”, it doesn’t matter that the law is really a “fiction”, compared perhaps with physical reality. In fact, most “realities” whether physical or societal possess a large social component. This area of social agreement comes up when one judges whether another human is sane or crazy. The sine qua non of insanity is its defiance of reality as it is conceived by we “sane ones.” Unfortunately, it is all too easy to forget that conventions are a product of society and take them as absolutes. Teenagers are notorious for wanting to be “in” with their crowd even when the fashions of the crowd are highly dubious. But many so-called grown-ups are equally taken in by the conventions of society. Most of the time it is easy and harmless to go along with the conventions, but one should always realize that they are, in fact, made up and vary from society to society. Presumably that is what Harari was trying to emphasize.

Then there are questions of the depth of realities. In many cultures there is a claim for “levels of reality” beyond everyday physical realities like streets, tile floors, buildings, weather, and the world around us. Hindu mystics consider the “real” world Maya, an illusion. Modern physics grants the reality of the everyday world, but has found a world of possibly deeper reality behind it. There are atoms, molecules, elementary particles, all governed by the “reality” of quantum mechanics which lies behind what one might be tempted to call the “fiction” of classical mechanics. No physicist “really” considers classical mechanics a fiction, though perhaps many would claim there is a wider and possibly deeper reality behind it. Most physicists would leave such questions to philosophers and would consider serious thought about them, a waste of time. Physics first imagined the reality of molecules in the nineteenth century, explaining concepts and measurements of heat related phenomena. For example, temperature is the mean kinetic energy of molecular motion related to what we measure with a thermometer by Boltzmann’s constant. In the early 20th century there were very reputable scientists skeptical of the existence of atoms and molecules. Most of them were convinced of the atom’s reality by Einstein’s theory of Brownian motion (1905). As the 20th century wore on the entire basis of chemistry was established in great detail by quantum theories of electron states in atoms and molecules. In the twenties and thirties cosmology came into being. Besides explaining the genesis of atomic elements, cosmology, using astronomical observations and theory, finds a universe consisting of 10’s of billions of galaxies, each consisting on average of 10’s of billions of stars, all of which originated in a “big bang” some 13.6 billion years ago. In a later post I’ll consider the current situation physics finds itself in, with dark matter, dark energy, string theory, and ideas of a multi-verse. If one considers these as realities, one should not hold such a belief too firmly. History teaches us that physics is subject to revolutions which alter the very “facts” of physical reality. Besides the lurking revolutions of the future one notes that the “realities” of physics and chemistry lie in their theories which have proved essential for the “reality” of our modern technologies. One might claim however, that these are theories of reality, rather than a more immediate impingement of reality in our lives. I hope to say more about “physical reality” in the next post.

Leaving the physical world, one asks, “What about myth, an admitted fiction?” If a myth has a deep meaning and lesson for our lives, doesn’t that entail a certain kind of reality of more importance than a trivial sort of physical reality? Consider “myth” vs. “history”. Reality for history depends on “primary sources”, written records. The “written” record might be that of an oral interview when recent history is concerned; but the idea is that there is a concrete record of some kind that relates directly to the happenings that history is reporting. Consider the stories about Pythagoras I wrote about in the last post. These stories were based on “secondary sources”, accounts written hundreds of years after Pythagoras’s death, relying on hearsay or vanished primary sources with no way of telling which was which. They form the basis for the shallow kind of myth that gives “myth” its common pejorative connotation. We dismiss the myths about Pythagoras’s golden thigh, his flying from place to place, where he may appear simultaneously, not simply because these claims conflict with our present scientific world view, but because they have no relevance to facts about Pythagoras which matter to us in considering his contributions to the history of mathematics. The myths about Pythagoras can be considered “trivial” myths which discredit the very idea of myth. But what about deeper myths? Most religions tell stories about their founders and contributors which have a high mythic content. I ask in this context, “Does distinguishing between myth and historical reality in matters of religious history, really matter, or matter at all?” Buddhists are notorious for being unfazed when various historical stories are proven fictional by historians. I would baldly state their attitude as: “The religious importance of the story is what matters; not the factual truth of every so-called fact in the canon.” Getting closer to home, I might ask, “Suppose the facts about Jesus’s physical existence were convincingly proved to be completely fictional. Would it matter to Christianity?” I would guess that it WOULD be devastating to believers, but that, in fact, it SHOULDN’T be. What matters in Christianity is the insight that feelings of love are deeply embedded in the universe and that Jesus, whether a fictional person or not, is responsible for bringing this “fact” to life, to showing that in the deep mystery one might call “God”, there is a forgiveness of the animal brutishness of humans. If through an active nurture of love in ourselves we experience this deep truth and express it in the way we act towards others, we redeem ourselves, and potentially, all of humanity. The stories, “myths” if you will, help us towards this experiential realization, a realization that is utterly unrelated to “belief”, a realization which could be called “Christian Satori”. The uniqueness of Christianity, as far as I can tell, is this emphasis on “love”. Unfortunately, the methodology of Christianity, with its historical emphasis on grasping ever harder at “belief”, is deeply flawed, leading backwards to the brutishness, rather than forward to love. Certain Christian thinkers, Thomas Merton for example, seem to have realized that Zen practice can be helpful in reaching a deeper understanding of their religion. One aspect of a Western Zen would be its applicability to a Western religious practice of a more deeply realized Christianity. Actually, whether or not “love” is embedded in the universe, we, as humans are susceptible to it, and can choose to base our lives on realizing its full depths in our beings.

Getting back to “reality”, I’ll consider possible insights from traditional Eastern Zen. So far in talking about Zen I’ve emphasized the Soto school of Japanese Zen and have tried to show how various Western ideas are susceptible to a deeper understanding by means of what might be called Western Zen. Actually, I claim that the insights of Zen lie below any cultural trappings; and that for a complete understanding, particularly as such might relate to “reality”, one should consider Zen in all its manifestations. The Rinzai Japanese school is the one we typically find written about in the US. It is the school which perhaps (I’m pretty ignorant about such matters) has deeper roots in China where Zen originated and the discipline of concentrating on Koans came into being. An excellent introduction to this school is the book Zen Comments on the Mumonkan, by Zenkei Shibayama, Harper and Row, 1974. The Chinese master Wu-men, 1183-1260, collected together 48 existing Koans and published them in the book, Wu-wen kuan. In Japan Wu-wen is called “Mumon” and his book is called the Mumonkan.

During the late 1960’s and early 1970’s I attended an annual conference of what was then called the Society for Religion in Higher Education. Barbara, my wife at the time, as a former Fulbright scholar, was an automatic member of this Society. As her husband I could also attend the conference. The meetings of the Society were always very interesting with deeply insightful discussions going on, day and night. These discussions never much concerned belief in anything, but concentrated on questions of meaning and values. In fact, the name of the Society was later changed to the Society for Values in Higher Education. During one of the last meetings I attended, possibly in 1972, there was much discussion about a new Zen book that Kenneth Morgan, a member of the Society was instrumental in bringing into being. Professor Morgan had arranged for the Japanese Master Zenkei Shibayama to give Zen presentations of the Mumonkan at Colgate University. The entire Mumonkan had been translated into English by Sumiko Kudo, a long-time acolyte at Master Shibayama’s monastery and was soon to be published. Having committed to understanding Zen, I was very interested in all of this and looked forward to seeing the book. After moving to Oregon in 1974 I kept my eyes open for it and immediately bought it when it first appeared at the University of Oregon bookstore. Later, I developed a daily routine of doing some Yoga after breakfast and then reading one of the Koans.

The insights that the Koans are to help one realize are totally beyond language. The Koans may be considered to be a kind of verbal Jiujitsu, which when followed rationally will throw one momentarily out of language thinking into an intuitive realization of some sort. I had encountered various Koans before working through the Mumonkan and had found little insight, but, as a student of physics and mathematics, thought of them as fascinating problems to be enjoyed and solved. I realized that in working on a difficult problem in math or physics, the crucial break-through often comes via intuition. One has a sudden insight, and even before trying to apply it to the problem, one realizes that one has found a solution. In a technical area one’s insight can be attached to mathematical or scientific language and the solution is a concrete expression which solves a concrete problem. I realized that with Zen, one might have a similar kind of intuitive insight even if it could not be expressed in ordinary language, but, perhaps, could be stated as an answering Koan to the one posed. Another metaphor besides the Jiujitsu one, is the focusing of an optical instrument, such as a microscope, telescope or binoculars. Especially when trying to focus a microscope one can be too enthusiastic in turning the focusing wheel and turn right past the focus, seeing that for an instant one had it, but that it was now gone. With a microscope one can recover the focus. With a Zen Koan the momentary insight is usually lost and efforts at recovery hopeless.

A somewhat better example of this focusing metaphor occurred when I was a professor at Auburn University. One quarter I taught a lab for an undergraduate course in electricity and magnetism. This was slightly intimidating as I was a theoretical physicist with little background in dealing with experimental apparatus. One afternoon the experiment consisted of working with an ac (alternating current) bridge similar to a Wheatstone bridge for direct current, but with a complication arising from the ac. Electrical bridges were developed in the nineteenth century to measure certain electrical quantities which are these days more easily measured by other means. Nowadays the bridges mainly have pedagogical value. With a Wheatstone bridge one achieves a balance in the bridge by adjusting a variable resistor until the current across the bridge, measured by a delicate ammeter, vanishes. One can then deduce the value of an unknown resistor in the circuit. With ac there is not only resistance but also a quantity called reactance, which arises because a magnetic coil or capacitor will pass an ac current. To adjust an ac bridge, one twiddles not only a variable resistance but a variable magnetic coil (inductor) which changes the reactance. In the lab there were about 5 or 6 bridges to be set up, each tended by a pair of students. The students put their bridges together with no difficulties; but then, after about 10 minutes, it became clear that none of the student teams had been able to balance their bridge. The idea was to adjust one of the two adjustable pieces until there was a dip in the current through the ammeter. Then adjust the other until the dip increased, continuing in this back and forth manner until the current vanished or became very small. It turned out that no matter what the students did, the current though the ammeter never dipped at all. Of course, the students turned to their instructor for help in solving their problem and I was on the spot. The experience the students had is quite similar to dealing with a Koan. No matter what one does, how much one concentrates, or how long one works at it, the Koan never comes clear. With the ac bridge the students could actually have balanced it by a systematic process, but this would have taken a while. I should have suggested this, but didn’t think of it. Instead I had a pretty good idea of some of the quantities involved in the circuit, whipped out my slide rule (no calculators in those days), and suggested a setting for the inductor. This setting was close enough that there was a current dip when the resistor was adjusted and all was well. The reason that balancing an ac bridge is so difficult is that the two quantities concerned, the resistance R and the reactance X, are in a sense, at right angles to each other, even though they are both quantities measured by an electrical resistance unit, ohms, which is not spatial at all. Nevertheless, even though non-spatial, they satisfy a Pythagorean kind of equation

R² + X² = Z²

where Z is called the Impedance in an ac circuit. The quantities R and X can be plotted at right angles to each other and a triangle made with Z as the hypotenuse. If one adjusts either R or X separately, one is reducing the contribution towards the impedance of one leg of the triangle which does not greatly affect the impedance, at least not enough to noticeably change the current through the ammeter of an ac bridge. Incidentally, what I’ve just explained is a trivial example of a tremendously important idea in theoretical physics and mathematics called isomorphism, in which quantities in wildly different contexts share the same mathematical structure.

I hope that the analogies of verbal Jiujitsu and getting things into focus make somewhat clearer the problem of dealing with Koans. One might well ask if such dealing is worth the trouble and, on a personal note, what kind of luck I’ve had with them, especially as they might throw some light on the nature of “reality”. First, I must say that I have found that engaging the Koans of the Mumonkan is very worthwhile even though most of them remain completely mysterious to me. Moreover, even though I have had epiphanies when reading some of the Koans or the comments about them, there is no way for me to tell whether or not I have really understood what, if anything, they are driving at. Nevertheless, after spending some years with them, off and on, in a very desultory, undisciplined manner, I feel that they have helped indirectly to make my thinking clearer. My approach when I first spent a year going through Zen Comments was to do a few minutes of Yoga exercises, with Yoga breathing and meditation, attempting to clear my mind. Then I would carefully read the Koan and the comments, not trying to understand at all, while continuing meditation. Typically, at that point, I would have a peaceful feeling from the meditation but no epiphany or understanding. I would then put the book aside and go about the business of the day until I repeated this exercise with the next Koan the next day. Sometimes I would skip a day and sometimes I would go back and look at an earlier Koan. This reading was very pleasant as an exercise. I tried to develop the attitude of indifference towards whether I understood anything or not and avoided getting wrought up in trying to break through. My feeling about this kind of exercise is that it does lead to some kind of spiritual growth whether or not the Koans make any sense. As for “enlightenment”, I think it is a loaded word and best ignored. A Western substitute might be “clarity of thought”. Whether or not meditation, studying Koans or just thinking has anything to do with it, I have, on occasion, been unexpectedly thrown into a state of unusual clarity, in which puzzles which once seemed baffling seemed to come clear. As for the Zen Comments I might make a few suggestions especially as they relate to “reality”. Consider, for example, Koan 19, “Ordinary Mind is Tao”, towards which the metaphor above, of finding a focus, might be relevant. If you haven’t heard about the concept of Tao, pick up and read the Tao Te Ching, Lao Tzu’s fundamental Chinese classic. Tao may be loosely translated as “Deep Truth Path”. Koan 19, as translated by Ms. Kudo reads as follows:

“Joshu once asked Nansen, ‘What is Tao?’ Nansen answered, ‘Ordinary mind is Tao.’ ‘Then should we direct ourselves towards it or not?’ asked Joshu. ‘If you try to direct yourself toward it, you go away from it,’ answered Nansen. Joshu continued, ‘If we do not try, how can we know that it is Tao?’ Nansen replied, ‘Tao does not belong to knowing or not knowing. Knowing is illusion; not knowing is blankness. If you really attain to Tao of no-doubt, it is like the great void, so vast and boundless. How then can there be right or wrong in the Tao?’ At these words Joshu was suddenly enlightened.”

Mumon Commented. This comment is very relevant.

“Questioned by Joshu, Nansen immediately shows that the tile is disintegrating, the ice is dissolving, and no communication whatsoever is possible. Even though Joshu may be enlightened, he can truly get it only after studying for thirty more years.”

I picked this particular Koan because it is one of the few that I feel I actually understand (although I may need another thirty years to really get it). Of course, I can in no way prove this. You must NOT be naïve and think that I understand anything. Furthermore, there is no real explanation of the Koan I can give. I can make a few remarks which should be considered as random twiddles of dials that may chance to zero the impedance in your mind.

First, the whole thing is a logical mess. On the one hand there is nothing special or esoteric about “deep truth path”. It is just the ordinary world (reality) that we sense. On the other hand, when we get “it”, the ordinary world dissolves and we feel an overwhelming sense of the infinite ignorance and non-being which surrounds the small island of knowledge we have attained in our human history so far. In fact, both the ordinary and the transcendent are simultaneously present to our awareness and one cannot be considered more significant than the other.

Note that this Koan is superstition free. There are no claims of esoteric knowledge. There are no contradictions of any scientific or historical claims to knowledge. There are no contradictions of anything we might consider superstitions. There is no contradiction of the doctrines of any religion. One might say that the Koan is empty of content. Of verbal content that is.

There is an implicit criticism of Aristotelean logic with its excluded middle. As I’ve already pointed out more than once in this blog, logic has a limited applicability. Part of the “game” of science is to accept only statements to which logic DOES apply. I may later go into stories from the history of physics of the difficulties of playing this exciting game of science, keeping logic intact, when experimental evidence seems to deny it. However, the “game” of physics or any other science is not all of life; and, in fact, Aristotelian logic has been, as I’ve called it in earlier blogs, “the curse of Western Philosophy” and an impediment to a deeper understanding of realities outside of science.

There is more to say about the Mumonkan, but I will leave such to a later blog post. As to differences between Soto and Rinzai Zen I wonder how serious these really are. Koan 19 seems to embody the Rinzai idea of instantaneous enlightenment until one sees Mumon’s comment about another 30 years being required for Joshu to really get it. The Soto doctrine is of gradual enlightenment and a questioning of the very “reality” of the enlightenment concept. A metaphor for either view is the experience of trying to get above a foggy day in a place like Eugene, Oregon, where, when the winter rain finally stops, the clear weather is obscured by a pea-soup fog. One climbs to a height such as Mt. Pisgah or Spencer’s Butte and often finds that though the fog is thinner with hints of blue sky, it is still present. But then there is perhaps a partial break and one sees through a deep hole towards a clear area beyond the fog. This vision may be likened to an epiphany or even to the “Satori” of Rinzai Zen. If we imagine we could wait on our summit for years until, after many breaks, the fog completely clears away, that would be full enlightenment.

Leaving any further consideration of Koan 19, I will end this post on a personal note. If indeed I’ve had a deep enough epiphany to consider it as Satori, this breakthrough has helped reveal that I have a healthy ego, lots of “ego strength”, a concept that Dr. Carr, head of the physics department at Auburn came up with. Experimental physicists, such as Dr. Carr, like to measure things. “Having a lot of ego strength” was his amusing term for people who are overly wrapped up in themselves. My possible Zen insights have not diminished my ego at all. Rather, they have helped to reveal it. I’ve learned not to be too exuberant about insights which as a saying goes, “leave one feeling just as before about the ordinary world except for being two inches off the ground.” If I get too exuberant, I wake up the next day, feeling “worthless”, in the grip of depression. This is a reaction to an unconscious childhood ego build-up in the face of very poor self-esteem. Part of spiritual growth is perhaps not losing one’s ego, but lessening the grip it has on one. I hope that further practice helps me in this regard. Perhaps, some psychological considerations can be the subject of a later post. I will now, however, work on the foundations for such a post by attempting to clarify the “reality” status of scientific theories.

Funny Numbers

During the century between about 600 BCE to 500 BCE, the first school of Greek philosophy flourished in Ionia. This, arguably, is the first historical record of philosophy as a reasoned attempt to explain things without recourse to the gods or out-and-out magic. But where on earth was Ionia? Wherever it was it’s now long gone. Wikipedia, of course, supplies an answer. If one sails east from the body of Greece for around 150 miles, passing many islands in the Aegean Sea, one reaches the mainland of what is now Turkey. Along this coast at about the same latitude as the north coast of the Peloponnesus (37.7 degrees N) one finds the island of Samos, a mile or so from the mainland; and just to the north is a long peninsula poking west which in ancient times held the city-state of Ionia. Wikipedia tells us that this city-state, along with many others along the coast nearby formed the Ionian League, which in those days, was an influential part of ancient Greece, allying with Athens and contributing heavily, later on, to the defeat of the Persians when they tried to conquer Greece. One can look at Google Earth and zoom in on these islands and in particular on Samos, seeing what is now likely a tourist destination with beaches and an interesting, rocky, green interior. On the coast to the east and somewhat south of Samos was the large city of Miletus, home to Thales, Anaximander, Heraclitus and the rest of the Ionian philosophers. At around 570 BCE on the Island of Samos Pythagoras was born. Nothing Pythagoras possibly might have written has survived, but his life and influence became the stuff of conflicting myths interspersed with more plausible history. His father was supposedly a merchant and sailed around the Mediterranean. Legend has it that Pythagoras traveled to Egypt, was captured in a war with Babylonia and while imprisoned there picked up much of the mathematical lore of Babylon, especially in its more mystical aspects. Later freed, he came home to Samos, but after a few years had some kind of falling out with its rulers and left, sailing past Greece to Croton on the foot of Italy which in those days was part of a greater Greek hegemony. There he founded a cult whose secret mystic knowledge included some genuine mathematics such as how musical harmony depended on the length of a plucked string and the proof of the Pythagorean theorem, a result apparently known to the Babylonians for a thousand years previously, but possibly never before proved. Pythagoras was said to have magic powers, could be at two places simultaneously, and had a thigh of pure gold. This latter “fact” is mentioned in passing by Aristotle who lived 150 years later and is celebrated in lines from the Yeats poem, Among School Children:

Plato thought nature but a spume that plays

Upon a ghostly paradigm of things;

Solider Aristotle played the taws

Upon the bottom of a king of kings;

World-famous golden-thighed Pythagoras

Fingered upon a fiddle-stick or strings

What a star sang and careless Muses heard:

 

Yeats finishes the stanza with one more line summing up the significance of these great thinkers: “Old clothes upon old sticks to scare a bird.” Although one may doubt the golden thigh, quite possibly Pythagoras did have a birthmark on his leg.

I became interested in Ionia and then curious about its history and significance because I recently wondered what kind of notation the Greeks had for numbers. Was their notation like Roman numerals or something else? I found an internet link, http://www.math.tamu.edu/~dallen/history/gr_count/gr_count.html which explained that the “Ionian” system displaced an earlier “Attic” notation throughout Greece, and then went on to explain the Ionian system. In the old days when a classic education was part of every educated person’s knowledge, this would be completely clear as an explanation. Although I am old enough to have had inflicted upon me three years of Latin in high school, since then I had been exposed to no systematic knowledge of the classical world so was entirely ignorant of Ionia, or at least of its location. I had heard of the Ionian philosophers and had dismissed their philosophy as being of no importance as indeed is the case, EXCEPT for their invention of the whole idea of philosophy itself. And, of course, without the rationalism of philosophy, it is indeed arguable that there would never have been the scientific revolution of the seventeenth century in the West. (Perhaps that revolution was premature without similar advances in human governance and will yet lead to disaster beyond imagining in our remaining lifetimes. Yet we are now stuck with it and might as well celebrate.)

The Ionian numbering system uses Greek letters for numerals from 1 to 9, then uses further letters for 10, 20, 30 through 90, and more letters yet for 100, 200, 300, etc. The total number of symbols is 27, quite a brain full. The important point about this notation along with that of the Egyptian, Attic, Roman and other ancient Western systems is that position within a string of numerals has no significance except for that of relative position with Roman numerals. This relative positioning helps by reducing the number of symbols needed in a numeric notation, but is a dead end compared to an absolute meaning for position which we will go into below. The lack of meaning for position in a string of digits is similar to written words where the pattern of letters within a word has significance but not the place of a letter within the word, except for things like capitalizing the first letter or putting a punctuation mark after the last. As an example of the Ionian system, consider the number 304 which would be τδ, τ being the symbol for 300 and δ being 4. There is no need for zero, and, in fact, these could be written in reverse order δτ and carry the same meaning. In thinking about this fact and the significance of rational numbers in the Greek system I came to understand some of the long history with the sparks of genius that led in India to OUR numbers. In comparison with the old systems ours is incredibly powerful but with some complexity to it. I can see how with unenlightened methods of teaching, trying to learn it by rote can lead to early math revulsion and anxiety rather than to an appreciation of its remarkable beauty, economy and power.

In the ancient Western systems there is no decimal point and nothing corresponding to the way we write decimal fractions to the right of the decimal point. What we call rational numbers (fractions) were to Pythagoras and the Greeks all there was. They were “numbers”, period, and “obviously” any quantity whatever could be expressed using them. Pythagoras died around 495 BCE, but his cult lived on. Sometime during the next hundred years, one of his followers disproved the “obvious”, showing that no “number” could express the square root of 2. This quantity, √2, by the Pythagorean theorem, is the hypotenuse of a right triangle whose legs are of length 1, so it certainly has a definite length, and is thus a quantity but to the Greeks was not a “number”. Apparently, this shocking fact about root 2 was kept secret by the Pythagoreans, but was supposedly betrayed by Hippasus, one of them. Or perhaps it was Hippasus who discovered the irrationality. Myth has it that he was drowned (either by accident or deliberately) for his impiety towards the gods. The proof of the irrationality of root 2 is quite simple, nowadays, using easy algebra and Aristotelian logic. If a and b are integers, assume a/b = √2. We may further assume that a and b have no common factor, because we may remove them all, if any. Squaring and rearranging, we get a²/2 = b². Since b is an integer, a²/2 must also be an integer, and thus “a” itself is divisible by 2. Substituting 2c for a in the last equation and then rearranging, we find that b is also divisible by 2. This contradicts our assumption that a and b shared no common factor. Now we apply Aristotelian logic, whose key property is the “law of the excluded middle”: if a proposition is false, its contrary is necessarily true, there is no “weaseling” out. In this case where √2 is either a fraction or isn’t, Aristotelian logic applies, which proves that a/b can’t be √2. The kind of proof we have used here is called “proof by contradiction”. Assume something and prove it false. Then by the law of the excluded middle, the contrary of what we assumed must be true. In the early twentieth century, a small coterie of mathematicians, called “intuitionists”, arose who distrusted proof by contradiction. Mathematics had become so complex during the nineteenth century that these folks suspected that there might, after all, be a way of “weaseling” out of the excluded middle. In that case only direct proofs could be trusted. The intuitionist idea did not sit well with most mathematicians who were quite happy with one of their favorite weapons.

Getting back to the Greeks and the fifth century BCE one realizes that after discovering the puzzling character of √2, the Pythagoreans were relatively helpless, in part because of inadequacies in their number notation. I haven’t tried to research when and how progress was made in resolving their conundrum during the 25 centuries since Hippasus lived and died, but WE are not helpless and with the help of our marvelous number system and a spreadsheet such as Excel, we can show how the Greeks could have possibly found some relief from their dilemma. The answer comes by way of what are called Pythagorean Triplets, three integers like 3,4,5 which satisfy the Pythagorean Law. With 3,4,5 one has 3² + 4² = 5². Other triplets are 8,15,17 and 5,12,13. There is a simple way of finding these triplets. Consider two integers p and q where q is larger than p, where if p is even, q is odd (or vice-versa) and where p and q have no common factor. Then let f = q² + p², d = q² – p², and e = 2pq. One finds that d² + e² = f². Some examples: p = 1, q = 2 leads to 3,4,5; p = 2, q = 3 leads to 5,12,13. These triplets have a geometrical meaning in that there exist right triangles who sides have lengths whose ratios are Pythagorean triplets. Now consider p = 2, q = 5 which leads to the triplet 20,21,29. If we consider a right triangle with these lengths, we notice that the sides 20 and 21 are pretty close to each other in length, so that the shape of the triangle is almost the same as one with sides 1,1 and hypotenuse √2. We can infer that 29/21 should be less than √2 and 29/20 should be greater than √2. Furthermore, if we double the triangle to 40,42,58, and note that 41 lies halfway between 42 and 40, the ratio 58/41 should be pretty darn close to √2. We can check our suspicion about 58/41 by using a spreadsheet and find that the 58/41 is 1.41463 to 5 places, while √2 to 5 places is 1.41421. The difference is 0.00042. The approximation 58/41 is off by 42 parts in 100,000 or 0.042%. The ancient Greeks had no way of doing what we have just done; but they could have squared 58 and 41 to see if the square of 58 was about twice the square of 41. What they would have found is that 58² is 3364 while 2 X 41² is 3362, so the fraction 58/41 is indeed a darn good approximation. Would the Greeks have been satisfied? Almost certainly not. In those days Idealism reigned, as it still does in modern mathematics. What is demanded is an exact answer, not an approximation.

While there is no exact fraction equal to √2, we can find fractions that get closer, closer and forever closer. Start by noticing that a 3,4,5 triangle has legs 3,4 which though not as close in length as 20, 21, are only 1 apart. Double the 3,4,5 triangle to 6,8,10 and consider an “average” leg of 7 relative to the hypotenuse of 10. The fraction 10/7 = 1.428 to 3 places while √2 = 1.414. So, 10/7 is off by only 1.4%, remarkably close. Furthermore, squaring 10 and 7, one obtains 100, 49 while 2 = 100/50. The Pythagoreans could easily have found this approximation and might have been impressed though certainly not satisfied.

I discovered these results about a month or so ago when I began to play with an Excel spread sheet. Playing with numbers for me is relaxing and fun; and is a pure game whether or not I find anything of interest. I suspect that this kind of “playing” is how “real” mathematicians do find genuinely interesting results, and if lucky, may come up with something worthy of a Fields prize, equivalent in mathematics to a Nobel prize in other fields. While my playing is pretty much innocent of any significance, it is still fun, throws some light on the ancient Greek dilemma, and for those of you still reading, shows how a sophisticated idea from modern mathematics is simple enough to be easily understood.

With spreadsheet in hand what I wondered was this: p,q = 1,2 and p,q = 2,5 lead to approximations of √2 via Pythagorean triplets. Are there other p,q’s that lead to even better approximations? To find such I adopted the most powerful method in all of mathematics: trial and error. With a spreadsheet it is easy to try many p,q’s and I found that p = 5, q = 12 led to another, even better, approximation, off by 1 part in 100,000. With 3 p,q’s in hand I could refine my guesswork and soon came up with p = 12, q = 29. I noticed that in the sequence 1,2,5,12,29,… successive pairs gave increasingly better p,q’s. This was an “aha” moment and led to a question. Could I find a rule and extend this sequence indefinitely?

In my life there is a long history of trying to find a rule for sequences of numbers. In elementary school at Hanahauoli, a private school in the Makiki area of Honolulu, I learned elementary arithmetic fairly easily, but found it profoundly uninteresting if not quite boring. Seventh grade at Punahou was not much better, but was interrupted part way through the year by the Pearl Harbor attack of December 7, 1941. The Punahou campus was taken over by the Army Corps of Engineers and our class relocated to an open pavilion on the University of Hawaii campus in lower Manoa Valley. I mostly remember enjoying games of everyone trying to tackle whoever could grab and run with a football even if I was one of the smaller children in the class. Desks were brought in and we had classes in groups while the rain poured down outside the pavilion. Probably, it was during this year that we began to learn how fractions could be expressed as decimals. In the eighth grade we moved into an actual building on the main part of the University campus and had Miss Hall as our math teacher. The math was still pretty boring, but Miss Hall was an inspiring teacher, one of those legendary types with a fierce aspect, but a heart of gold. We learned how to extract square roots, a process I could actually enjoy, and Miss Hall told us about the fascinating things we would learn as we progressed in math. There would be two years of algebra, geometry, trigonometry and if we progressed through all of these, the magic of “calculus”. It was the first time I had heard the word and, of course, I had no idea of what it might be about, but I began to find math interesting. In the ninth grade we moved back to the Punahou campus and our algebra teacher was Mr. Slade, the school principal, who had decided to get back to teaching for a year. At first, we were all put off a bit by having the fearsome principal as a teacher, but we all learned quickly that Mr. Slade was actually a gentle person and a gifted teacher. As we learned the manipulations of algebra and how to solve “word problems”, Mr. Slade would, fairly often, write a list of numbers on the board and ask us to find a formula for the sequence. I thoroughly enjoyed this exercise and learned to take differences or even second differences of pairs in a sequence. If the second differences were all the same, the expression would be a quadratic and could easily be found by trial and error. Mr. Slade also tried to make us appreciate the power of algebra by explaining what was meant by the word “abstraction”. I recall that I didn’t have the slightest understanding of what he was driving at, but my intuition could easily deal with an actual abstraction without understanding the general idea: that in place of concrete numbers we were using symbols which could stand for any number. Later when I did move on to calculus which involves another step up in abstraction, I at first had difficulty in the notation f(x), called a “function” of x, an abstract notation for any formula; or indeed a representation of a mapping that could occur without a formula. I soon got this idea straight and had little trouble later with a next step of abstraction to the idea used in quantum mechanics of an abstract “operator” that changes one function into another.

Getting back to the sequence 1,2,5,12,29,… I quickly found that taking differences didn’t work; the differences never seemed to get much smaller because the sequence turns out to have an exponential character. I soon discovered, however, using the spreadsheet that quotients worked: take 2/1, 5/2, 12/5, 29/12, all of which become more and more similar. Then multiplying 29 by the last quotient, I got 70.08. Since 29 was odd, I needed an even number for the next q so 70 looked good and indeed I confirmed that the triplet resulting from 29, 70 was 4059, 4060, 5741 with an estimate for √2 that was off by only 1 part in a 100 million. After 70 I found the next few members of the sequence, 169, 408, 985. The multiplier to try for the next member seemed to be closing in on 2.4142 or 1 + √2. At this point I stopped short of trying for a proof of that possibility, both because I am lazy and because the possible result seemed uninteresting. What is interesting is that the sequence of p,q’s goes on forever and that approximations for √2 by using the resulting triplets will converge on √2 as a limit. The ideas of a sequence converging to a limit was only rigorously defined in the 19th century. Possibly it might have provided satisfaction to the ancient Greeks. Instead, the idea of irrational numbers that were beyond fractions became clear only with the invention by the Hindu’s in India of our place based numerical notation and the number 0.

Place based number notation was developed separately in several places, in ancient Babylon, in the Maya civilization of Central America, in China and in India. A place based system with a base of 10 is the one we now use. Somewhere in one’s education one has learned about the 1’s column just to the left of a decimal point, then the 10’s column, the 100’s column and so forth. When the ancient Hindu’s and the other civilizations began to develop the idea of a place based system, there was no concept of zero. Presumably the thought was the idea that symbols should stand for something. Why would one possibly need a symbol that stood for nothing? So, one would begin with symbols 1 through 9 and designate 10 by ”1·”. The dot “·” is called a “place holder”. It has no meaning as a numeral, serving instead as a kind of punctuation mark which shows that one has “10”, not 1. Using the place holder in the example above of Ionian numbers, the τδ would be 3·4, the dot holding the 10’s place open. The story with “place holders” is that the Babylonians and Mayans never went beyond, but the Hindu’s gradually realized the dot could have a numerical meaning within its own right and “0” was discovered (invented?). Recently on September 13 or 14th, 2017, there was a flurry of reports that carbon dating of an ancient Indian document, the Bakhshali manuscript revealed that some of its birch bark pages were 500 years older than previously estimated, dating to a time between 224 – 383 AD. The place holder symbol occurring ubiquitously in the manuscript was called shunya-bindu in the ancient Sanskrit, translated in the Wikipedia article about the manuscript as “the dot of the empty place”. (Note that in Buddhism shunyata refers to the “great emptiness” a mystic concept which we might take as the profound absence of being logically prior to the “big bang”) A readable reference to the recent discovery is https://www.smithsonianmag.com/smart-news/dating-ancient-indian-text-gives-new-timeline-history-zero-180964896/. According to the Wikipedia article the Bakhshali manuscript is full of mathematics including algebraic equations and negative numbers in the form of debts. As a habitual skeptic I wondered when I first heard about the new dating whether Indian mathematicians with their brilliant intuition hadn’t immediately realized the numerical meaning of their place holder. Probably they did not. An easy way to see the necessity of zero as a number is to consider negative numbers as they join to the positives. In thinking and teaching about math I believe that using concrete examples is the best road leading to an abstract understanding. The example of debts is a compelling example of this. At first one might consider one’s debts as a list of positive numbers, amounts owed. One would also have another list of positive numbers, one’s assets, amounts owned. The idea might then occur of putting the two lists together, using “-“ signs in front of the debts. As income comes in one’s worth goes, for example, -3, then -2, -1. Then what? Before going positive, there is a time when one owes nothing and has nothing. The number 0 signifies this time before the next increment of income sends one’s worth to 1. The combined list would then be …, -3, -2, -1, 0, 1, 2, 3, … . Doing arithmetic, using properly extended arithmetic rules, when one wants to combine various sources of debt and income becomes completely consistent, but only because 0 was used.

If the above seems as if I’m belaboring the obvious, let me then ask you why when considering dates, the next year after 1 BCE is not 0, but 1 AD? Our dating system was made up during an early time before we had adopted “0” in the West. Historians have to subtract 1 when calculating intervals in years between BCE and AD and centuries end in hundreds, not 99’s. This example is a good one for showing that if one gets locked in to a convention, it becomes difficult if not impossible to change. I was quietly amused at the outcry as Y2K, the year 2000 came along with many insistent voices pointing out the ignorance of we who considered the 21st century to have begun. The idea of zero is not obvious and I hope I’ve shown in considering the Pythagorean’s and their dilemma with square roots, just how crippled one is trying to get along without it.

WestEastII

My last post was on 8/11/17 shortly before we needed to prepare for a big road trip from Bend, Oregon to the Maritime Provinces of Canada, followed by visits to Sue’s family in Lake George, New York and my daughter’s family in Annapolis, Maryland. Preparations for the trip had to be made early because just before the trip there was the total solar eclipse of 2017 on Monday, the 21st, the shadow passing 25 or so miles north of us. In the days before the eclipse our house filled with family. We had made viewing plans and they worked out well. On Monday before dawn we drove to an open field Northwest of Prineville, saw the sky darken, leaf shadows sharpen, and felt the temperature fall by 12 degrees or so. We then watched as a black shadow fell on Gray’s Butte 10 miles to the West and rushed towards us at 1700 MPH. The last bright spark on the sun’s rim flickered out; and there was the corona and Bailey’s shining diamonds along the rim of the shadowed sun. The entire experience was as stunning as advertised and brought home to us the reality of cosmic events. There really is a moon out there, a sun and an entire cosmos whose very existence is an impenetrable mystery that we can experience during our brief stay in conscious awareness.

After the eclipse we waited a day for the traffic to clear, took my computer to the shop, finding out the mother board was dead, then headed out across the continent after taking Sue’s sister Nancy to the Portland airport. The trip was long and accomplished what travel should. We saw new country and discovered that some Canadians were more concerned with the possible shortcomings of their prime minister than with those of Trump. As a child I’d read about the tides of the Bay of Fundy but had no idea even where it was. Now we saw the 45-foot tide come in (record some 50 odd feet), finally got a good look at a tidal bore and added three provinces to our list. (We’ve traveled in all 50 US states so are now adding Canadian provinces and territories to our travel deeds.) We had been somewhat leisurely going East to the Maritimes. But then, after our family visits, drove across the US in 6 days, seeing some new territory on the way and being moved by a visit to the California Trail Interpretive Center on I80 in Nevada. One reads about the hardships and heartbreaks of the Westward migration and understands intellectually, but seeing the exhibits and dioramas makes for a much deeper emotional understanding. Arriving home on September 30th, we settled in for a week or two before going to the Stanford Alpine Club reunion. Now we’re really back home with a new computer fired up and it’s time to write.

In previous posts I’ve expressed the theme that Western thought would be more satisfying if informed by the spirituality of the East, especially Zen Buddhism. Now I want to turn a somewhat skeptical eye on the foundations of that idea but later move away from the skepticism to try find a clearer and deeper exposition. I begin by considering what seems to be an unbridgeable gap between the Western idea, that in philosophy, science and humanism meaning can only be apprehended in words; and the Eastern idea, in Zen, that the deepest meaning is totally beyond direct expression in language.

Let me first be skeptical about extreme claims for language. I’ve already talked about Plato and Wittgenstein with their thoughts on the limits of what can be said. Some humanists not only ignore possible limits to what language can express, but claim that only with language can there even be thinking. That idea seemed absurd to me the first time I heard it and has so seemed ever since. Perhaps it makes sense if one replaces “thinking” by “intellectualizing”. To me “thinking” is simply conscious mental processing and, at least, for me can occur in an entirely wordless manner. For example, when out hiking one often comes to a stream without a bridge but with rocks that will provide stepping stones if one doesn’t slip and take a fall into the water. When I arrive at such a place, I take in the scene, sketching out possible paths and making a wordless judgement about the slipperiness and stability of the rocks along each possible route. If one path seems feasible and best, I concentrate, get balanced and begin to hop. There has clearly been “thought” here, but none of it has been put into words. Of course, it could have been, and on some occasions, the hiking party might well discuss the matter, analyzing verbally the various possibilities before making a decision about the crossing. Another example, concerns a bear in Yosemite Valley who presumably lacked language, but through experience and awareness learned about canned goods. In one instance, during the night at Camp 4, a less experienced member of our group had left a rucksack full of canned food, out in the open. The next morning, we found the rucksack torn apart and cans scattered about. Some of the cans had been ripped open and the contents eaten. Others were untouched except for a single tooth hole in one end. The bear knew that some cans might have less desirable contents and saved energy by a “puncture and sniff” methodology whose existence to me implied “thought”.

While thought clearly can be nonverbal, it seems to me that Zen seemingly goes further. Let me postulate that for Zen the deepest awareness about life and the emotional reconciliation with our non-existence and loss of awareness in death, is not only wordless, but, unlike the experience of stream crossing, is necessarily completely nonverbal. Further, that attempting to understand this experience through language is not only a distraction, but is counterproductive, a false path, that hinders rather than helps.

Having not had the ultimate Zen experience I am in an excellent position to be skeptical about this postulate. This skepticism can operate on several fronts.

First, though I’m unwilling to doubt the authenticity of the ultimate enlightenment for people who have claimed to have had this experience, I can doubt that it will ever happen to me. The fact of the matter is that other people having the experience is irrelevant to my spiritual understanding. Furthermore, if in the future I claim to have finally achieved satori, that should be irrelevant to you who read this blog.

Second, I do think the Soto Zen insight is true and relevant. One can gradually gain deeper understanding of life and the world. One asks, “What is the alternative?” Just give up? Abandon the struggle to understand? Gradualism has its attractions in that there is at least the experience of “being in the zone” not only athletically, but philosophically and artistically. I definitely HAVE experienced being in the zone so know that it can contribute to almost any life activity. It may not be satori, but may well be a way station on the path and, in any case is well worth experiencing.

Third, if the ultimate experience is totally unreachable through language, why write about it at all? There are countless books about Zen. The standard conclusion is that one must join an Ashram of some sort and devote one’s entire life to practices that will possibly bring about enlightenment. From the beginning I have been skeptical about joining a spiritual community. There are too many frauds about and even sincere gurus have no magic touch for bringing about the desired result. As I’ve said earlier in this blog concerning spiritual matters, “The buck stops here” with you and me. Spiritual support can possibly be of help but quite possibly also contribute to self-delusion.

So why do I write this blog? Simply because I have an irresistible urge to try “get things straight”, to understand as much as possible about everything, to share my ideas, and to become a skillful enough writer to be worth reading. Concerning Zen, I feel that there is a paradox involved. Being as skeptical as possible advances Zen. Smash it. Stomp it. Deny it sincerely.

Such a denial of the basic postulate could be considered a Western approach to Zen. A fundamental trait of Western culture is the idea of “speaking out”, of not holding back. Accompanying this is a certain lack of respect for authority. The Eastern tendency, on the other hand, is to remain quiet and humble in the face of what likely cannot be said or understood. Besides a deep respect for authority, there is the idea that being forward is being egotistical by being “showy” to no end but self-aggrandizement. A Western approach to Zen would be a tradition-denying attempt to actually spell out what “cannot be said”, weaving a magic potion in words. A potion that not only makes perfectly clear but also carries to its reader an emotional acceptance of why one should be content and happy in the thought that the uniqueness that each of us possesses vanishes with our death forever into the emptiness of non-being. To attempt this kind of verbal depth and clarity is not only very Western, but paradoxically very Zen. “Let’s not grasp at the idea that nothing can be said.” At root Zen is neither Eastern nor Western. It is about such a complete letting go, that one mustn’t get hung up even on the idea of letting go.

As I continue in a possibly too-outspoken Western manner, consider that in what I’ve said above is an explicit acceptance of the idea that our awareness does indeed vanish with our death. There is no consciousness after death. Perhaps the mind functions briefly after the heart is stilled, but such functioning is brief and comes to an end. In rejecting the idea of “eternal life” I’m applying the spiritual postulate that there be no acceptance of belief simply because it seems comforting. It certainly would be extremely meaningful and exciting to be reconciled with all one’s family and friends who have passed away. Whether one could be happily conscious for an eternity is another question, but still it seems that any awareness might well be better than none. As a friend of my wife said talking about accidents and sickness, painful medical treatment, and long boring recoveries while incapacitated, “Any kind of living you can live with; it’s the dying you can’t stand.” And I think that is the way most of us instinctively feel. Certainly, although there is no certainty about what happens after death, the weight of the evidence, seems to me, to favor oblivion. Whether or not that is the case, if oblivion is what we really fear, that fear is what we need to grapple with spiritually in order to find understanding and peace.

When I use the word “spiritually”, it brings to mind traditional Western religion; in particular Christianity and the belief in God. What are my thoughts on this matter? Here I’ll deal with them briefly. It seems that there may well be the possibility of a deeper consideration in future posts. So… Am I an atheist? Well, no. Do I believe in God? Well, no. Am I an agnostic? Well, no. Surely either one believes in God or is an Atheist. Well, no. The problem as I’ve said before is Aristotelian logic, the curse of Western Philosophy, and, I might add, Western thought in general. When formalized, logic is tremendously useful in mathematics, theoretical physics, generally in science and in many areas of life. When applied elsewhere, its denial of any possibility beyond true and false, black and white, is untrue to reality. In most areas of life there are “shades of grey” which Aristotelian logic simply can’t deal with. In the distinction between atheism and belief, there is, as well, another problem. The entire distinction, seems to me to be stuck in spiritual shallows. Getting lost in controversy about a dichotomy which may well be meaningless instead of attempting to dive more deeply into spiritual awareness seems to me a waste of time and life. Let us consider belief in “God”. When one uses a word to characterize the deepest experience of spirituality, one inevitably comes to think of God as Something, in particular Something apart from the remainder of existence, having all sorts of contradictory properties. He (certainly not “She” or “It”) is all powerful and all controlling, but tolerates “evil” and the “devil” as a necessary part of existence. And I have mentioned only one muddle. The problem lies in Naming an ultimate which is beyond what we can possibly know. In Judaism and the Old Testament of Christianity, there is a tradition of revulsion in making images of gods or of even speaking God’s name except once a year. The sin involved is called idolatry, a belittling of the ultimate mystery, belief in a false image of God. It seems clear to me, however, that simply in treating the ultimate as a concept and calling it God, one is close to committing idolatry. Whether idolatry is the deep sin claimed by the Old Testament is possibly questionable, but one can well imagine that the ancients had a sound and provocative insight. The idolatry of Naming the ultimate is likely the root cause of religious conflict.

One begins with the Name. From the Name comes the tenets. From the tenets Belief. From Belief comes fanaticism and we all know where fanaticism leads. Of course, this sequence is by no means logically necessary and most thoughtful believers realize that “God” is simply a convenient word for what they apprehend in their deepest religious experience. A word that simply spells out an ultimate mystery whose properties are beyond our understanding. For example, the theologian Paul Tillich is very aware of assigning false attributes to the deity and uses the phase “the ground of being” instead of “God”. Nevertheless, there have been many “believers”, past and present, who HAVE followed the sequence from the concept of God to tenets to a tight grip of belief that can only be labeled as fanaticism. Fanaticism demands the death of all apostates and war against other religions or even other branches of one’s own religion. Every thoughtful person should know about the “Thirty Years War, 1618-1648” to say nothing of the horrors occurring in the name of Christianity before that period and understand the potential for fanaticism which lurks in “belief”.

So where does this leave us? It seems to me that modern, mainstream Western thought, especially in the sciences, but also in philosophy and the humanities, in realizing the trap of belief, has accepted the unspoken idea that any spirituality involves false beliefs about the deity and a lack of critical thinking which leads to an acceptance of SUPERSTITIONS from astrology to witchcraft to evolution by intelligent design; leads in fact to a rejection of the fundamental skepticism which drives science and, above all, to a total abandonment of reason. Any acceptance of spirituality threatens a new dark age.

What I’m pointing out in this blog is not only that there is no necessary link between spirituality and mindless superstition, but that the extreme skepticism of the spirituality which I’m advocating is completely in line with that informing science and modern thinking in general. For lack of a better name and to emphasize its doctrine that ungrasping from all belief leads to depths of meaning and understanding, free from all superstition, I have called it Zen. This label emphasizes and pays respect to the long historical development in the East of the realization that belief is unnecessary for spiritual well-being. Unfortunately, Zen carries the connotation of Eastern thought, of the quietism mentioned earlier in this post. A form of what I’ve called Western Zen would comfortably fit with our Western science, philosophy and humanism. Based on “radical ungrasping” it would take up the idea that our spiritual ignorance can drive a quest for spiritual knowledge and answers, growing out of the deep mysteries that have arisen from our secular science and knowledge. Although we have made remarkable progress in science and in other fields in the past several centuries, our remaining ignorance is not only infinite in extent but concerns the questions most significant to our spiritual well-being.

For the deep questions are not going away. What is the meaning of your life or my life? What is the meaning, if any, of our deaths? What is this universe all about anyway? Can one live in a spiritual vacuum? Is one to suppress the urgency of these questions and lose oneself in the anodynes of work, pleasure, sex, sports and consumerism, resisting of course, the threat of addiction to these as well as to less heathy activities such as drinking, drugs and gambling? Or is one to seek answers in the superstitions mentioned above or in shallow forms of Fundamentalism, stilling any doubts by an ever tighter grasping at unreasonable beliefs? It seems to me that Western thought in ignoring its spiritual vacuum is helping to bring about the very evils it fears.

A final word. What I’m proposing falls short in that it lacks specificity. That fact must be accepted in all humility. Nevertheless, I do think that I’ve made a showing that there is a path towards a Western spirituality which does not violate the integrity of our thought and that such a path is would fill an important gap.

 

 

WestEast

In my last post, “Two Cultures”, I wrote that “…one hopes for a creative amalgam of West and East.” So far this blog has concentrated on Eastern, especially Buddhist ideas, particularly Zen, wondering if Western thought can be helpful in approaching the Zen experience. If I am indeed dedicated to going in the other direction demonstrating that Zen intuition can contribute to Western philosophy, I need now to understand Western philosophy at a deeper level. In fact, it may well be the case that Eastern and Western approaches to ultimate understanding are immiscible like oil and water, so that far from being helpful to one another their intersection becomes nothing more than a contradictory mess. My intuition says otherwise, but in order for me to specifically find and point out ways that each can help the other combine into a single broader and deeper approach to what it’s all about, I need a more thorough appreciation of Western philosophy. That is, I need to understand Plato. I say Plato because I remembered and then found (in the book I’m about to consider) a quote: “The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato” from Process and Reality by Alfred North Whitehead. Besides the Whitehead quote there is a general understanding that Western philosophy only came into full flower with Plato. Plato’s works were the urquell, the Spring from which all flowed.

Of course, over the years, I’ve been casually exposed to Plato. At Stanford, all freshmen at the time I was there, were required to take the year long History of Western Civilization course which consisted of the reading of works deemed significant for Western thought with lectures and discussions in class. The class was largely wasted on me, because, as a freshman, besides being occupied with my interesting roommates, I was on the swimming team, not much interested in History, and bone lazy. I do remember reading Plato’s Phaedo, impressed with the story though far from impressed with Socrates’s reasons for not being afraid of death. Then, over the years, I ran many times into allusions to the story of “the cave.” Then there are Platonic “ideals”. None of this exposure really grabbed me. What did make a difference was running recently into a piece on the internet which discussed a philosophical issue with impressive clarity. Here was someone who could talk philosophy in a way that made sense. The author was a women named Rebecca Goldstein. Googling her on the internet I found that she was a rather unusual philosopher in that she wrote novels as well as philosophy. I won’t get into the interesting biographical details about her because these can easily be found on the internet. After enjoying her novel, 36 Arguments for the Existence of God: A work of Fiction, I looked in Amazon to see what else she had written and saw listed Plato at the Googleplex: Why Philosophy Won’t Go Away. This was available in our library in eBook form so I read it on my Kindle, and then ordered a hard copy from Amazon. Below, in the interests of brevity I will sometimes refer to Ms. Goldstein as RNG (for Rebecca Neuberger Goldstein).

Understanding Plato via the writing of a gifted philosopher who writes with clarity seemed better than trying to find adequate translations of Plato’s work or trying to learn classical Greek so I that I could read him in the original. Of course, there would be the difficulty of really understanding Plato no matter what the approach. So, I will consider Ms. Goldstein’s book not as authoritative, but as a foundation for riffs off of what I conceive her to have said about Plato and Western Philosophy. Of course, I agree with her thesis that philosophy is here to stay and find her criticism of philosophy-jeerers, such as Lawrence Krauss, amusing and telling though that is not what interests me in her book. Incidentally, I have read Krauss’s A Universe from Nothing: Why There is Something Rather than Nothing, and found it fascinating. He is a great physics popularizer and, in my opinion, writes philosophically so his wholesale condemnation of philosophy is not to be taken seriously. Possibly, a critical review of his “Something” book by a philosopher intensified his antagonism toward philosophy to the point that he had to express his outrage. In that state one finds slings and arrows to hurl at philosophy, rather than relaxing one’s ideological grip as suggested in my last post. A wholesale condemnation of philosophy is ridiculous. However, it seems to me that the situation is not “either/or”, for part of the life blood of philosophy is criticism of philosophy. For example, if in getting at what really matters in philosophy, one should consider “differences that make a difference”, (Gregory Bateson’s definition of “information”), I find too often, philosophers seem to haggle over differences that to me make no difference whatsoever. Perhaps I lack a critical component of what it takes to be a philosopher. Whether or not that is so, I find Ms. Goldstein’s writing mostly clear and fascinating.

Before getting into what Ms. Goldstein has to say about Plato I will mention one more thought about philosophy. With most disciplines talking about or discussing the discipline is separate from practicing the discipline. Writing about physics, chemistry or molecular biology, sociology, economics, or engineering, for example, is not doing research in or practicing those disciplines. If one writes about philosophy however, one is actually doing philosophy whether or not one is a professional, card carrying, philosopher. If one writes ignorantly, without sufficient thought or insight, one is doing “bad” philosophy, easily dismissed; but, nevertheless, one is doing philosophy. The only other subject, I can think of offhand, which perhaps possesses this characteristic is literature. A literary critic, writing about a literary work can actually create a piece of literature. I don’t think this claim works for history. A historian can do primary research and write up the story she or he finds (readable history always tells a story), but as soon as she talks in general or makes a judgement, she is doing philosophy of history, not history. Perhaps this last claim is merely a quibble, but certainly one reason philosophy will never go away is that thoughtful people will always continue to practice it, making judgements and seeking insights into whatever is on their mind. Whether university departments of philosophy offering degrees in the subject will wither away in the future is another question. It seems to me intuitively, unlikely.

Turning to Plato whether in classical Greece or in today’s Googleplex, it is clear that as a professional philosopher RNG has read everything Plato wrote or might have written, probably in more than one translation, as well as what other philosophers have had to say about Plato, including inquiries into the meaning of words in classical Greek and into the ethos of the society that gave rise to Plato’s philosophy. A fascinating observation (Googleplex p4) is that it is difficult or impossible to discover what Plato really himself personally thought about any of the far flung positions expounded in his various dialogues. Positions there are aplenty, but no positions that Plato would unambiguously assent to. RNG remarks on the many disagreements that philosophers have had on Plato’s various positions and has compared him to Shakespeare as one, whose personal views are unknowable. Further (on p40), quoting from Plato’s Seventh Letter, RNG concludes that “he never committed his own philosophical views to writing.” And further, “Plato didn’t think the written word could do justice to what philosophy is supposed to do.” This in spite of the fact that he wrote extensively. RNG considers that the form of Plato’s writings as dialogue suggests that Plato’s view of what philosophy is supposed to do is “Nothing less than to render violence to our sense of ourselves and our world, our sense of ourselves in the world.” RNG quotes Plato, talking of philosophy as saying, “… for there is no way of putting it in words like other studies. Acquaintance with it must come rather after a long period of attendance in instruction in the subject itself and of close companionship, when suddenly like a blaze kindled by a leaping spark, it is generated in the soul and at once becomes self-sustaining.” (Googleplex, p40, Seventh Letter quote.)

This last sounds suspiciously like the “enlightenment” that is supposed to come out of Buddhist meditation and training. What is different is the methodology. With Plato’s philosophy one attains the transcendent state by intense thinking about the conundrums of philosophy, trying to gain insight through reason and rationality into deep, questions, compelling but unanswerable, which pursuit ultimately withdraws from one, the “life support” of one’s unquestioned certainties, leaving one “free” in an empty universe. Or am I reading too much into a specious resemblance between Plato and Buddhism? Certainly, besides bringing personal enlightenment, philosophy is attempting to bring about insights which can be expressed in language. It seems, in fact, that over the stretch of time since the days of classical Greece, philosophy has concentrated on trying to bring clarity to its questions using language in a precise way, rather than becoming a means of instilling an awareness beyond language. Western Philosophy, it seems, has given up a quest for transcendence by relinquishing such a pursuit to religions based on faith. It seems to me that Zen has a contribution to make here in that the enlightenment it postulates is beyond language and therefore is irrefutable via language. It is to be approached, according to what I’ve said earlier in this blog via a path which totally rejects superstition, magic or even belief in anything, as far as that is possible. Philosophy, it seems to me, is an excellent Western path for a “seeker” who is attracted in that direction. And if, as I assume, RNG is correct in what she has said about Plato’s philosophy, such seeking would not be new to philosophy, but instead a turn of a spiral back towards Plato’s original conception.

So much for this post. Later I would hope to return to RNG, Plato at the Googleplex and further ideas about a joining of East and West. For the immediate future, however I would like to take into account the objection that philosophy as a spiritual path is intellectually elitist, as indeed it might seem if one accepts the idea that “elitism” itself is other than an elitist convention. Be that as may be, now that I’ve brought up the idea of a “seeker”, it would be good to point out that seeking can adopt paths that are physical or artistic in nature though not necessarily anti-intellectual. So, onto the next post…

Two Cultures

In this post I want to take a path that starts with some thoughts about classical Buddhism. These thoughts are far from being based on extensive knowledge or scholarship, but this very lack enables, I hope, a freedom to break free from tradition, and seek a meaningful relevance for our times. Consider the following:

He whose desires have been throttled,
who is independent of root,
whose pasture is emptiness—
signless and free—
his path is as unknowable
as that of birds across the heavens.

I came across this verse in the heading of the first chapter in a sci-fi fantasy book, Lord of Light by Roger Zelasny. The book, incidentally, won both the Hugo and Nebula science fiction awards the year it came out. The hero, a reincarnation of the Buddha, who goes by the name of Sam, is “great souled”, but is also a crafty, scheming fighter for a cause of freedom, which involves defying the Lords of Creation. If there were such a concept as “heresy” in Buddhism, he would perhaps be eligible. But that is somewhat beside the point. I’m concerned here with the verse itself, not the book; though the book is one I love and read repeatedly.

In the book the verse is credited as Dhammapada (93). Consulting Wikipedia one finds that the Dhammapada is part of the Pali Canon, the extensive writings from the early days of Buddhism, forming a tradition called Theravada Buddhism, the Buddhism of South East Asia. A second great Buddhist tradition which developed later is that of Mahayana Buddhism, the Buddhism of Northern India, Tibet, China, Korea and Japan. Zen Buddhism is part of this latter tradition.

It seems to me that the Dhammapada verse summarizes many of the great themes of Buddhism. The first line is echoed in a great poem of Yeats, Sailing to Byzantium whose

3rd stanza reads,

O sages standing in God’s holy fire
As in the gold mosaic of a wall,
Come from the holy fire, perne in a gyre,
And be the singing-masters of my soul.
Consume my heart away; sick with desire
And fastened to a dying animal
It knows not what it is; and gather me
Into the artifice of eternity.

In both of these selections “desire” is a word for all the negative emotions that beset us as human beings: longings, fear, rage, depression, selfishness, egotism; and perhaps too, emotions considered as positive: joy, happiness, complacency, satisfaction. The question arises: Does Buddhist discipline involve trying to “throttle” all of these emotions head on, by leading a disciplined, saintly acetic life, devoid of pleasures? My answer is no, and I have the feeling that an affirmative answer to this question involves a misunderstanding, a putting the cart before the horse so to speak. Certainly discipline is required in following any spiritual path, but discipline, if misdirected is futile and ultimately frustrating. My view is that effective Buddhist discipline lies in an indirect approach to dealing with “desire”; a direction of becoming aware of one’s beliefs and addictions, and of trying to relax ones grasp on them. Ideally one would have no beliefs whatever, and would be totally free in the universe. That is, however, for most of us a distant goal. As unenlightened humans we can’t help having beliefs and addictions. What we can do is to try become aware of them, to relax our grip on our beliefs, holding them lightly, recognize our addictions, and work on bringing them under control.

In our culture a very common attitude is to tighten our grip when one of our beliefs is challenged, to never admit a mistake, and to “double down” if our judgement has proven faulty. If we eye such behavior dispassionately, we see that it is egotistical and basically immoral, a rejection of “truth”; nevertheless, owning up to fault can be very discomforting. If one has ever been a professor, lecturing to a class, one has inevitably been in a position of having a sharp student who is closely following, raise his or her hand and point out a mistake in one’s reasoning. I remember several occasions when this situation happened in a math class taught at Stanford by Professor George Pólya, a distinguished mathematician of the early 20th century (see Wikipedia). Pólya’s lectures were a model of clarity and he always payed close attention to how his students were reacting. When a blunder was pointed out, he would exclaim in his Hungarian accent, “Oh! How stupid of me!”, and then correct his error. I wondered at times if he deliberately made mistakes to keep his students alert, but think it more likely that in concentrating on clarity, he sometimes lost track of a logical connection. Later, when I was a professor, often while teaching elementary physics to future engineers, Pólya’s example stood me in good stead. I would admit to screwing up, congratulate the student who pointed out my blunder, go back over what I had done and correct the error. I did experience some intellectual discomfort in doing this and I’ve noticed that many professors are simply unable to admit their mistakes and try to weasel out of them.

In trying to guard our beliefs when they are challenged, we are obviously hoping to protect our egos and sense of self-worth. However, I think there is more going on than simply ego protection. Our beliefs, especially those which are only partially conscious and which we take for granted, form a foundation for our life, a comfort zone, a cozy nest into which we can relax, the very basis of our being. When these beliefs are questioned, the underlying floor of our security is threatened with break-up. Such beliefs are the psychic equivalent of the safety net which protects a trapeze artist or tight rope walker. Letting go of such beliefs or even relaxing one’s grip on them, is similar to a performer abandoning his or her safety net and moving to the next level where a fall would likely be fatal. The big difference, of course, is that letting go of one’s beliefs is not fatal, but can actually give one a sense of freedom. Such freedom is not a license to act without restraint, but is, instead an openness to see and reason clearly and act with creativity. One does become aware of the difference between social conventions and a deeper fundamental reality. This doesn’t mean that one necessarily defies convention, but simply that one understands that conventions are constructs of the society one lives in, not absolute moral dictates. One role of meditation, besides its calming effects, is to help become aware of our unconscious beliefs and loosen our grip on them. One guide to meditation that I’ve long ago lost track of mentions that as thoughts begin to fade away, a chasm looms in front of us, what Oliver Sacks in Musicophilia calls “an abyss of non-being”. The guide recommends that one mentally hop over it and continue to meditate. Later one hopes to float in this abyss while meditating and lose one’s fear of it in ordinary life by so loosening the grip on one’s beliefs that they no longer act as a support of one’s being above a meaningless void.

If one attains such a free and easy state in one’s life, does that imply a cessation of desire? Or should it? I think that the key to understanding such a question involves the concept of addiction and the relationship between addiction and a tight grip. Surely Buddhism doesn’t forbid joy in life or reveling in pleasure. The problem arises when a pleasure becomes addictive. In dealing with such matters I think that present day psychotherapy has as much to offer as ancient Buddhist ideas, though relaxing one’s grip would seem helpful when undergoing psychotherapy for both the patient and the therapist. See the interesting book Tales from the Couch by Bob Wendorf, a clinical psychologist with 36 years of experience. Trained in behavior modification therapy, Dr. Wendorf discovered that to be successful in practice he needed to relate directly to his patients using whatever theoretical psychological basis seemed appropriate for a particular patient. In other words he was able to see that humans are more complex than any current psychological theory, relaxing his grip on beliefs formed during his training. I’ll have more to say on this subject in a later post. For the moment the point to be made is that while Buddhist ideas may be helpful in this and other areas, they need not, indeed must not, necessarily replace Western ideas. Instead one hopes for a creative amalgam of West and East.

Does a meditative practice help one to loosen one’s grip? Perhaps. What loosening one’s grip really means is allowing a questioning of beliefs that one thinks are correct, a step up from admitting one’s blunders. Such a questioning is the ideal of scientific thought, but seldom actually practiced by scientists when their own beliefs are concerned. Fortunately, in science, one’s colleagues are ready and eager to fill in with doubts and skepticism about one’s latest pet theory. One can claim that this is why science works, to the extent that it actually does. Outside of science, however, we are left to our own awareness and resources.

So where does this leave us? I use the word “us” advisedly, for I assume that you, the reader, have been following along with your own understanding and questions.

Or to put the question another way: What parts of Buddhism in all of its different manifestations can be taken over into our Western culture, helping us to think clearly and ultimately to give us a deep religious understanding which is harmonious with the path our culture has been taking?

Or still another contrary way: Shouldn’t Eastern religion in general and Buddhism in particular be totally rejected as being incompatible with the direction our Western culture should be going?

In considering these questions, in what I’ve written so far in this piece and in the entire blog, it is clear that there is considerable complexity and a danger of getting bogged down in details. There are many directions I could take and enough material for considerable writing.

For now I’ll consider just one area that is amendable to a relaxing of one’s grip. This is the matter of the so-called “two cultures”, the culture of science and of the humanities. There has been a conflict and so much writing over such a long time about these “two cultures” that one would think that there is not much left to say on either side. I became aware that there was supposedly a conflict between humanities and science back around 1960 when I was a graduate student in physics at the University of Virginia while my wife, Barbara, was studying for a degree in English literature. At about the same time the British scientist and novelist C.P. Snow had given his influential 1959 Rede Lecture, “The Two Cultures”, which pointed out this gulf in our scholastic culture. Snow came down hard on the “side” of science. I quote C.P. Snow from the Wikipedia Article, “The Two Cultures.”

“A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is the scientific equivalent of: Have you read a work of Shakespeare’s?

“I now believe that if I had asked an even simpler question — such as, What do you    mean by mass, or acceleration, which is the scientific equivalent of saying, Can you read? — not more than one in ten of the highly educated would have felt that I was speaking the same language. So the great edifice of modern physics goes up, and the majority of the cleverest people in the western world have about as much insight into it as their neolithic ancestors would have had.”

On the other hand many of my lit major friends at the University of Virginia referred me to writers in the humanities who pointed out that as far as they were concerned, beginning with the 17th century scientific revolution, much of the rich meaning of our culture, constructs such as “the great chain of being”, had been destroyed by science and a richness had been reduced to joyless gray empty facts without meaning.
I was shown John Donne’s famous lines from An Anatomy of the World (1611):
……..

And new philosophy calls all in doubt,
The element of fire is quite put out,
The sun is lost, and th’earth, and no man’s wit
Can well direct him where to look for it.

………

John Donne lived from 1573 to 1631. He was a contemporary of Shakespeare (1564-1616) and, more to the point, with Kepler (1571 -1630) and Galileo (1564 – 1642). Galileo was born two months before Shakespeare and died the year that Isaac Newton was born. During his life ideas of the new natural philosophy, later called “the scientific revolution” spread throughout Europe.

At the time rather than getting very upset about any of this, I felt that I understood both cultures and luxuriated in being a “bridge” between them without feeling any compulsion to take sides. Surely, this conflict was simply the aptly called “tempest in a teapot” and would go away with time.

In many ways the conflict has subsided. Awareness of quantum mechanics, though not always very well understood, has spread to humanists who have taken it as deep and fascinating. Many scientists are well read and take great joy in the poetic, in the arts and in music. Nevertheless, in some respects the conflict is worse than ever. From the science side, it is no longer simply annoyance with the ignorance of the educated, an ignorance much reduced, but the growing contempt for science and the emergence in magical thinking among people at large. For the key point of the scientific revolution was the rejection of magic as an explanation of what went on in the physical world. Now people seem to be totally ignorant of the facts which have led to their cell phones, tablets and TV, and take superstitions such as astrology as having serious meaning. Are we at the point of descending into a new dark age?

From the humanities side the concern is “scientism”, the belief that valid knowledge and meaning comes about only through the application of scientific methodology. Ray Monk, Wittgenstein’s biographer, writes

“Scientism takes many forms. In the humanities, it takes the form of pretending that philosophy, literature, history, music and art can be studied as if they were sciences, with “researchers” compelled to spell out their “methodologies”—a pretense which has led to huge quantities of bad academic writing, characterized by bogus theorizing, spurious specialization and the development of pseudo-technical vocabularies. Wittgenstein would have looked upon these developments and wept.” https://www.prospectmagazine.co.uk/magazine/ray-monk-wittgenstein

In my view these quotes, on both “sides”, reveal grasping motivated by two things: fear and laziness. The fear is that our treasured world view is under attack. Not only is defense needed, but also an attack on the “other side”. The laziness comes about because it would take work to relax our grip and grapple with the task of feeling and understanding the meanings of a wider, multi-cultural world including all branches of science, the humanities and arts, history, economics and popular culture. It is easier to relax and allow one’s grip to stroke one’s ego.

The rewards of a more relaxed, aware view would include a flourishing of creativity, a combination of ideas that seem antithetical. Consider the thought of humanizing science, mythologizing about its meaning and mystery. (In future posts I will try to understand the proper place of myth in our culture.) The best science writers are already close to this mythologizing. Does such constitute an attack, a belittling, or even a refutation of the “scientific method”? Certainly not. Actually, “scientific method” itself is far from being a set of cut-and-dried formulaic rules that can be applied blindly in any situation. A beautifully clear exposition of this fact is Richard Feynman’s essay “Cargo Cult Science” in Surely You’re Joking, Mr. Feynman! “Cargo Cults” arose among the natives in certain South Pacific islands as WWII drew to a close. These people had seen giant airplanes land on the newly made runways and disgorge an incredible array of “cargo”: weapons, living quarters, food, bulldozers, and other amazing materials. Then, suddenly, it all stopped; the people left, the islands were deserted and the runways disintegrated. The people wondered, “How could the largess be restored?” And cargo cults resulted. Quoting Feynman:

“So they’ve arranged to make things like runways, to put fires along the sides of the runways, to make a wooden hut for a man to sit in, with two wooden pieces on his head like headphones and bars of bamboo sticking out like antennas – he’s the controller – and they wait for the airplanes to land.”

They’ve recreated the form, but with a naïve theory about the relation of form to “reality”. Lest one feel a smug superiority about these natives, I should point out that this sort of mistaken understanding occurs all the time in science; not only in the pseudo-science noted by Ray Monk, nor in the soft sciences, but in the so-called hard sciences as well. Much of the time one’s ideas are just not right. Even when they are right and experimentally verified, “truth” is not established for all time, but only provisionally and subject to a future scientific revolution. This is not to denigrate science, but rather the opposite. Science is truly difficult and theories usually not obvious when first conceived. When scientific theories do finally become well-established, they really work, and they do bring the miracles and the nightmares of “progress”. Clearly, “scientism” is nonsense, but so is a lack of awareness on humanist’s part for the deep humanistic meanings which may arise from science.

The Buddhist idea that is useful here is that of relaxing one’s grip on all kinds of belief, not simply credulous belief, but skeptical belief as well. One takes in the whole panoply, miracle and craziness of modern life with clear-headedness, joy and awareness, reveling in its diversity, taking action against what seems like mistaken ideas, but without “attachment” to any of it. If one cares to go further on a Buddhist path seeking the “great peace” in the “emptiness” beyond words and beyond the panoply, one should do so in a relaxed manner, with a loosened grip and without attachment or expectations.