Beyond solipsism

 kw: book reviews, nonfiction, science, cosmology, theories, biocentrism

Near the end of the book I reviewed last week (here), the possibility that the observer creates the universe was discussed. The next book I read, The Grand Biocentric Design: How Life Creates Reality, by Robert Lanza, MD and Matej Pavšič, PhD, with Bob Berman, presents the theory in detail.

Quite a number of physicists have said things like, "We are the opening through which the universe examines itself." While this is typically uttered as a self-referential metaphor, some, including Drs Lanza and Pavšič, take it more literally, and in this case in particular, attempt to offer proof.

The authors take their time building up to the real meaning of Biocentrism. Things seem to proceed by easy stages, then in mid-book, they get more explicit. On page 145 I find this: "There remains a certain fluidity—a certain degree of uncertainty—to anything that is not actually observed." They go on to explain that whatever has not been observed, such as most of the Earth beneath our feet, exists in "a range of possible states, and it's not until observed that they take on real properties."

At that point, I thought, "As a kid I hunted fossils in a limestone stream bank near our house. Were those fossils 'not there' until I went looking for them?" Later on the authors write of "the consensus world we're aware of during the day" (p 183), discussing the seeming unreality of many dreams, supposedly not constrained by that "consensus world." So now, the world is whatever we all agree it is? Wow! Soon (p 186) I read, "By observing your world, you keep collapsing probability waves, and thus you effortlessly create an ever-more detailed world that includes reinforcing memories," and a few sentences later, with no irony at all: "It is amazing how far we've come by following the implications of quantum mechanics in an unbiased way." At this point, it is clear that their view is so biased there is no meeting of minds with realists like me. They go on in the following chapter to posit this (my paraphrase): All the past, all 14 billion years of it, is brought into existence by observations in the present and near-present.

They have the gall to claim that this is not solipsism. By a strict definition ("The view or theory that the self is all that is known to exist"), they are right. But they turn it on its head, making the universe not just "in our head", but created ex nihilo because of our observations. All of this supposition (and that is all it is) is based on a few experiments that seem to prove that an observation taken now can affect something that happened in the past. Here I must dwell a little.

The starting point for all this is the Copenhagen Interpretation, propounded and promoted by Neils Bohr. Werner Heisenberg had determined the limits of accuracy of measurement, particularly as applied to quanta (elementary particles such as electrons and force-carrier particles such as the photons of light). Thousands, perhaps millions, of versions of the two-slit experiment have made this clear. If one allows a beam of light or of low-energy electrons (electrons with an energy more than about 10 eV have a wavelength too short to be useful here) to pass through a pair of narrow slits, separated by a small distance, ideally between 10x and 100x the wavelength, a suitable detector or screen will show an interference pattern. This experiment shows that not just light but also electrons (and more recently buckyballs and even larger molecules) express a wave nature. Much is made of "collapsing the wave" to get the particle that is finally detected when it strikes the detector.

(An aside: photons act as waves as they enter your eye, being diffracted by the pupil and refracted by the lens, something particles can't do, then within 18-19 millimeters, express particle behavior when they deposit their energy onto the opsin proteins in the retina so they can be "seen".)

The fun comes when we get to Bohr's expression, "Each particle must pass through both slits and interfere with itself." We don't know that. No experiment yet done has shown that, because any attempt to discern where a photon or electron or whatever "is going" between the emitter and the detector, messes up the pattern and there is no interference. Many physicists, including me, would say that the measurement cannot discern where or how fast the particle is moving without disturbing it so much that the measurement's accuracy is limited. In this case, it is limited such that the uncertainty of position is large compared to the separation between the slits.  Bohr claimed that the particle was really "fuzzed out" to be bigger than that, and "really goes through both slits". Baldly put, that is the Copenhagen Interpretation. For photons, maybe; for electrons, I am not so sure. For buckyballs, the idea is ludicrous. I think Bohr was wrong.

Consider this: all matter has an electronic nature, and is always accompanied by electromagnetic (EM) fields. The slits are holes in a material. They disturb the symmetry of the EM field of the otherwise smooth material membrane or plate (frequently a metallic foil or thin ceramic sheet). The moving particle is affected by the EM field. The disturbed EM field in the vicinity of two slits is different from that near a single slit. I haven't seen any attempting to calculate what effect that EM field may have on the moving particle, all by itself.

Do you know what is the Airy disc of a star image in a telescope's focal plane? It is the expression of the diffraction of the telescope's diameter. The wider the mirror or lens, the smaller the Airy disc. That is why one needs a really wide telescope to see small or distant things. Resolution (angular accuracy) is inversely proportional to the diameter of the aperture. That's why the new Webb telescope's mirror is 21 feet (6.5m) in diameter. Big area to gather a lot of light, but even more importantly, big diameter so see tiny things far away. The Airy disc seems to indicate that the incoming photons can sense how big the mirror is. Taken to an extreme, the phenomenon of diffraction indicates that the path a photon takes is affected by the presence of everything in the universe. If you don't mind doing the calculations to a few thousand decimals, you could probably calculate how the shape of the Airy disc of any particular telescope would be modified by the presence of the Moon or any of the other planets, in the general direction the telescope is pointed. That's probably true.

Some physicists get around the Copenhagen view by considering "observer" to be anything that is "close enough" to affect a particular particle. Bohr claimed the observer had to be "intelligent". So what? (Neils, Baby, sayin' it don't make it so.) It is a claim, and a claim only. A huge superstructure of physics calculations has been built upon it, including the nonsense in this book.

I took the trouble to closely read the two articles at the end of the book, in its Appendices. They contain a ton of calculations. It was hard because it's been fifty years since I last worked with Hamiltonians (a type of obtuse mathematical expression, needed to do anything useful with Schrödinger's equation). The articles are intended to prove that an intelligent observer is needed to bring the universe into being. The authors truly believe that, before there was a living mind to think about it, the entire universe, and all its billions of years of history, existed as a great lot of potentiality, a universal wave function (a really complex version of Schrödinger's Equation, with a trillion trillion trillion trillion trillion trillion trillion—I think that's enough trillions—partial differential equations). The first eye with a brain behind it "collapsed the wave function" so that at least a few trillion trillions of particles, making up that animal or person, and its surroundings, could exist in a more concrete form. (By the way, one gram of matter consists of about 1.2 trillion trillion particles).

I eventually saw a pattern in all the math. A few equations would be presented, then there would be a statement such as, "Equation 12a is similar to the Jim-Dandy formula, when expressed thus", and a rather similar equation would follow, numbered 13. Then a little later, a reference to "the formalization of Glock and Winchester", turning Equation 24 into Equation 25. And so forth and so on. There were several such shifts of perspective. I consider each to be a potential disconnect in the logic. I didn't dig deeply enough to discern which ones are true disconnects…but I am sure there are several!

Here is my analogy: A friend asked her neighbor for the recipe for her wonderful German chocolate cake. It required many ingredients, and numerous steps. Later she invited the friend over to taste it. The new cake tasted very good, but the neighbor said, "It's not quite the same, is it?" "Oh, no!" my friend said, "Of course, I substituted <brand D> chocolate for <brand A>, and I boiled some milk and added a little brown sugar in place of the evaporated milk, but it's really the same cake." The neighbor was diplomatic and didn't complain further. We all could tell, it wasn't the same. When you get down to it, with enough substitutions, you can start with the recipe for cherry pie and wind up with pineapple upside-down cake.

What we have in this book and the carefully crafted documents it contains is upside-down physics.

Sadly, the godlike powers that lie behind the authors' supposition are useless without volition. If the universe has to be created by us, why did we have to create one so full of frustration? If I create the universe by observing it, why is my wife always late? If you want to be a god, be prepared for theodicy: "if God is good, why is there pain?"

I'll be careful not to use the term "believe" here, because of its religious overtones. Here is my view of the universe. The fossils I found as a child were there millions of years before I was. Could a Trilobite be an "observer" in terms satisfactory to Bohr, or to these authors? Could a coral, or a sponge? The universe existed for at least nine billion years before the Sun and Earth and the rest of the Solar system came into being. They were as real then as they are now. Their existence was not affected, either then or since, by the "observing" animals that arose on Earth about one billion years ago, or by the "observing" humans that arose perhaps a million years ago, or at the very latest, 200,000 years ago. Nor were they affected by supposed aliens that may have arisen five or ten billion years ago.

Every article I have read that describes an experiment on a photon or electron or whatever, being "entangled" with another, and somehow "deciding" to point its spin axis "up" because a scientist forced its entangled partner to point "down", is flawed by circular reasoning. From their creation (emission), the pair of particles had opposed spins, which may have been detected at different times and places, but were there already. Period. Oh, and speaking of time: the authors claim that time is a construct of our perception, and doesn't otherwise exist. It's interesting that so many of the equations in their articles are time-dependent!

I've exhausted my interest in pursuing this matter. I'll read about real stuff in the future.

Errata: 

• On page 39, in a footnote, we read of the size of an atom, "It's 0.0529 nanometer, or about 1/200th of an angstrom in width." There are three errors in this statement:
• A nanometer is 10 angstroms, so the fraction should be 1/2.
• The Bohr radius of neutral Hydrogen is 0.0529 nm; the Bohr radius is the mean distance of the electron from the proton. This isn't just "any atom".
• The word "width" implies diameter, not radius.
• Bonus error (because this should have been specified): every neutral atom has a different radius, and hydrogen is one of the smallest; only atomic oxygen, fluorine and neon are smaller. The radius of a neutral, isolated carbon atom (this rarely occurs!) is 0.067 nm, and that of gold is 0.174 nm. Gold atoms are by no means the largest.
• On page 50 it is stated, "Longitudinal (vertical) waves can pass through liquids and gasses while transverse (sideways) waves require the material to be solid." Remove the parentheses, and this is a correct statement. However, "longitudinal" is not "vertical"; it is a compression-rarefaction wave that varies in the direction of travel, while "vertical" is just transverse on the vertical axis as compared to the horizontal axis.
• On page 128 we read, "…unlike all the other major moons in the solar system—our moon doesn't orbit around its planet's equator." (The point of the paragraph is that the moon's off-equator orbit helps stabilize Earth's axis of rotation.) A more accurate way to state this is that most (not all) other natural satellites orbit nearer their planet's equator, as compared to the Moon. Most of the major satellites' orbits are inclined within a degree of the host planet's equator. However, Triton and Nereid, satellites of Neptune, are inclined 130° (or -50° retrograde) and 27.6°. The inclination of the Moon's orbit is 5.1°. The real issue here is the Moon's large size relative to Earth; 1/80th of the Earth's mass. A tiny satellite, whatever its orbital inclination, would have little effect on the axial direction of Earth.

Seven edges of knowledge

kw: book reviews, nonfiction, science, theories, knowledge

Can we (collectively) know everything, or will some things remain forever beyond our ken? The answer depends on how much there is to know. If knowledge is, quite literally, infinite, then given the universe as we understand it, there is no possibility that everything can be known. But there is another way to look at the question, one taken by Professor Marcus du Sautoy in The Great Unknown: Seven Journeys to the Frontiers of Science: are some things forever unknowable by their very nature? His "Seven Journeys" are studies of the cutting edge of seven scientific and socio-scientific disciplines; they are explorations into what can be known accordingly.

The seven disciplines are simply stated: Chaos (in the mathematical sense), Matter, Quantum Physics, The Universe, Time, Consciousness, and Infinity (again, in the mathematical sense). Six of these are related to the "hard" sciences, while Consciousness is considered a "soft" problem by many, but in reality, it may be the hardest of all!

I knew beforehand of the three great theoretical limits to the hard sciences that were gradually elucidated in the past century or so: Heisenberg Uncertainty, Schrödinger Undecidability, and Gödel Incompleteness. Each can be considered from two angles:

1. Heisenberg Uncertainty (H.U.) is the principle that the combination of momentum and position can be known to a certain level of precision, but no further. It primarily shows up in the realm of particle physics. Thus, if you know with very great accuracy where a particle is or has been (for example, by letting it pass through a very small hole), you cannot be very certain of its momentum, in a vector sense. In the realm of things on a human scale, diffraction of light expresses this. If you pass a beam of light through a very small hole, it fans out into a beam with a width that is wider the smaller the hole is. This has practical applications for astronomers: the large "hole" represented by the 94-inch (2.4 meter) aperture of the Hubble Space Telescope prevents the "Airy circle" of the image for a distant star from being smaller than about 0.04 arc seconds in visible light, and about 0.1 arc seconds in near-infrared light. The mirror for the James Webb Space Telescope will be 2.7 times larger, and the images will therefore be 2.7 times sharper. But no telescope can be big enough to produce images of "infinite" sharpness, for the aperture would need to be infinite. All that aside, the two interpretations of H.U. are 
1. The presence of the aperture "disturbs" the path of the particle (in the case of astronomy, each photon), which can somehow "feel" it and thus gets a random sideways "kick".
2. The Copenhagen Interpretation, that the particle is described by a wave equation devised by Schrödinger that has some value everywhere in space, but the particle's actual location is not determined until it is "observed". The definition of "observer" has never been satisfactorily stated.
2. Schrödinger Undecidability, proposed originally as a joke about a cat that might be both dead and alive at the same moment, is the principle that the outcome of any single quantum process cannot be known until its effect has been observed. The "cat" story places a cat in a box with some poison gas in a flask which has a 50% chance of being broken open in the next hour according to some quantum event such as the radioactive decay of a radium nucleus. Near the end of the hour, you are asked, "Is the cat dead or alive?" You cannot decide. Again that pesky "observer" shows up. But nowhere have I read that the cat is also an observer! Nonetheless, the principle illustrates that, while we can know with a certain accuracy the average number of quantum events of a certain kind that might occur, we have no way to know if "that nucleus over there" will be the next to go. Two ways of interpreting this situation are given, similar to the above, firstly that the event sort of "decides itself", and the other, also part of the Copenhagen Interpretation, that only when an outcome has been observed can you know anything about the system and what it has done.
3. Gödel Incompleteness is described in two theorems that together proved mathematically that in any given algorithmic system, questions can be asked, and even their truth can be described, but those questions' veracity cannot be proven within that algorithmic system. Most examples you'll find in the literature are self-referential things such as a card that reads on one side, "The statement on the other side of this card is true" and on the other, "The statement on the other side of this card is false." Such bogeys are models of ways of thinking about the Incompleteness theorems, without really getting to their kernel. A great many of them were discussed in gory detail by Doug Hofstadter in his book Gödel, Escher, Bach: The Eternal Golden Braid, without getting to the crux of the matter: Is our own consciousness an algorithmic system? because it seems we can always (given time) develop a larger system in which previously uncrackable conundrums are solvable. But then of course, we find there are "new and improved" conundrums that the tools of the new system cannot handle. An example given in The Great Unknown is the physics of Newton being superseded and subsumed into the two theories of Relativity developed by Einstein. Again, there are two ways this principle is thought of. Firstly, that given time and ingenuity we will always be able to develop another level of "meta system" and solve the old problems. But secondly, we get into the realm of the "hard-soft" problem of consciousness: Is consciousness algorithmic? for if it is, we will one day run out of meta systems and can go no further.

Thus the two questions that really need answering are, "What is Consciousness?" and, "Is Space Quantized?"

The only way we know to study consciousness is to study our own and that of a small number of animals that seem to be self-aware. Some would posit that we can create conscious artificial intelligence (AI), but this is questionable because all known methods in the sphere of AI studies are algorithmic, even if the algorithm is "hidden" inside a neural network. Since we do not yet know if natural intelligence (NI) is algorithmic, we cannot compare AI to NI in any meaningful sense!

One consequence of a possibly infinite universe is that everything we see around us might be duplicated an endless number of times, right down to the atomic and subatomic level. Thus there could be infinite numbers of the Polymath at Large typing this sentence, right now, in an infinite number of places, though very widely separated, to be sure (say, by a few trillions or quadrillions of light years, or perhaps much, much more). But, if I understand the proposition correctly, that is only possible if space is quantized. Quantization of space is based on the discovery of the Planck length and the Planck time about a century ago. They are the smallest meaningful units of length and time known. The Planck length is about 1.62x10^-35 m, or about 10^-20 the size of a proton. If space is quantized, it is most likely quantized on this scale. The Planck time is the time it takes a photon to travel a Planck length, or about 5.4x10^-44 sec.

If space is quantized with the space quantum being a Planck length, that means that positions can be represented by very large integers, and that those positions will be not just very precise, but exact. How large an integer? If we consider only the visible universe, which has a proper radius of about 75 billion light years, or 7.1x10²⁶ m, you'd need a decimal integer of 44+26+1 = 71 digits, or a binary word (for the computer) containing 236 bits or 29.5 → 30 bytes.

The trouble comes when you want to learn positions to this kind of precision/exactitude. To learn a dimension to an accuracy of one micron you need to use light (or another sort of particle such as an electron) with a wavelength of a micron, or smaller, to see it. To see the position of a silicon atom in a crystal, you need x-ray wavelengths smaller than 0.2nm (or 200 pm), which comes to 6,200 eV per photon. X-rays of that energy are a little on the mild side. But to "see" a proton, you are getting in the sub-femtometer range, which requires gamma ray photons with several million eV each. Twenty orders of magnitude smaller yet, to be able to distinguish a Planck length, would require such energetic gamma rays (about an octillion eV each) that two of them colliding would probably trigger a new Big Bang.

By the way, photon energies of billions to trillions of eV would be needed to pin down the locations of the quarks inside nucleons, which is what would actually be needed to get a "Star Trek Transporter" to work, at both the scanning and receiving end. Each such photon has the energy of a rifle bullet. You would need several per quark of your sample to transport. Maybe that's why the transporter hasn't been invented yet, and probably never could be…even if Dilithium and Rubindium get discovered one day.

Also, just by the bye, in a quantized universe there would be no irrational numbers, not truly. I am not sure how lengths "off axis" could be calculated, but they would somehow have to be jiggered to the next quantum of space. There goes Cantor's Aleph-1 infinity!

OK, I got so wrapped up in all of this that I hardly reviewed the book. It's a great read, so get it and read it and go do your own rant about the limits of knowledge!

If we are light, why aren't we shining?

kw: book reviews, nonfiction, physics, theories

If you had a fast enough camera, with sharp enough "vision", a snapshot of a proton (the hydrogen nucleus) might bear some resemblance to this artistic depiction. How fast and how sharp? A full cycle (not a rotation but something roughly similar) takes about 10^-24 seconds, so the shutter speed needs to be 10^-26 seconds or faster, and the size of the whitish enveloping sphere is about 10^-13 cm, so the "camera" needs to resolve details in the 10^-15 cm range. Strangely enough, that kind of camera would not be really, really tiny; it would be huge. A particle accelerator, which Dr. Frank Wilczek calls a "superstroboscopic ultramicroscope", with a size of twenty kilometers or so, is expected to do the trick: the Large Hadron Collider, which is soon to come on-line. Its detector is not a postage-stamp-size chip like the one in your digital camera, but a complex the size of a five-story building (or several thereof).

Such a "camera" puts the energy of a small stick of dynamite into two clumps of protons (a few million per clump) by zipping them around in a huge circle in opposite directions, and letting them collide head-on inside a building-size detector. The resulting "picture" is not a 10-Megapixel or so image, but a clump of data thousands of times that voluminous, perhaps a terabyte, with which one may determine where the quarks and gluons (see next paragraph) are situated (or were, before everything went Wham). In the realm of subatomic physics, you have to destroy a proton to figure out how it was put together. To get reliable results, you have to do it many times. Luckily, there are lots of protons on hand.

In the image, the three colored globes represent quarks, and the smaller two-colored items represent the appropriate gluons that bind the quarks together into a proton, in this case. Other configurations result in other kinds of particles. The quarks are said to exchange the gluons and thus remain bound together as a proton.

A similar image that showed the particle physics explanation of the binding of an electron to the proton to make a hydrogen atom would show two small spheres of different sizes exchanging a pale wisp that represented a photon, in such a way that they were kept together at a distance about 100,000 times greater than the scale of the image above.

There are two more kinds of binding that we have some idea about. One has its components in pairs rather than triplets, and describes the weak interaction that can change a proton to or from a neutron. The other has, perhaps, a single binding particle, that interacts with both "matter" particles and their energy content, and literally binds the universe together. It is called the graviton. "It" may consist of more than one "thing"…nobody knows yet.

In Dr. Wilczek's book The Lightness of Being: Mass, Ether and the Unification of Forces, he describes the theories behind the understanding of these forces. This popularization of the deepest concerns and strongest theories of physics is written for the educated amateur. I have to confess, I got lost time and again; perhaps I am not a sufficiently "educated" amateur. But I am not totally bereft of understanding. My opening paragraphs outline major elements of the theory of forces, most of which I learned from this book. And the way of thinking and explaining the author uses helped me work out a partial understanding of something I've asked a few scientists about, though none has answered my e-mail.

As simply as possible, I've asked this:

Black holes permit the escape of nothing, not even light (photons), because the gravitation potential below the event horizon of a black hole exceeds the speed of light. If gravity is quantized, and is carried by a particle (which we've chosen to dub the graviton), will not the intense field trap such particles also? If so, how does any gravity escape from the black hole to mediate its attraction for the objects that continue to fall into it, and thus make black holes such as Cygnus X-1 detectable?

I expected an answer that invoked the general theory of relativity, in which gravity is considered a distortion of space-time by concentrations of matter and energy, such that the inertial paths of objects are curved in the way we would calculate for a centrally-directed "force". However, general relativity conflicts with any quantum theory of gravity in which its effect are attributed to particles.

I see that both sides, relativity and my concept of quantum gravity, are incomplete. Regardless of what the relativistic explanation might be, and regardless of how gravitational quanta might be reconciled to it, such a graviton , which I will call the G particle, must have these characteristics:

• G is a boson, like the photon, the gluon, and the W and Z bosons that ferry the Weak force about.
• G is massless, like the photon, so it propagates at the speed of light, c.
• Because both masses and energy are subject to gravitational attraction, the G particle carries no energy, and is thus not subject to gravitational attraction—else it could not escape a black hole.
• G probably has spin zero, like the photon.
• Whereas the photon can mediate both attraction and repulsion, because it is subject to (or carries) electrical charge, G is "blind" to electromagnetic forces and to the "color" charges of both gluons (dubbed either r, g, b or r, w, b) and W/Z bosons (with colors g and p, to make them distinct from gluon colors). Thus G can mediate only attraction—unless it is somehow also "visible" to the "dark energy" that is accelerating the universe, and mediates repulsion for whatever it is that the term "dark energy" refers to!

Take this as a somewhat chagrined testimony: There isn't really that much math in the book, but most of the author's math left me in the dust. However, he is a great explainer, and is able to transmit the "shape" of a concept even when you don't grasp the math that he finds so beautiful. Much of the material is based on the discoveries in quark-gluon interactions that led to his Nobel Prize five years ago. His colleague Richard Feynman, upon being asked "What did you do to earn the Nobel Prize", answered, "Buddy, if I could explain what I did in one minute, it wouldn't be worth a Nobel." It takes considerably more than one minute to grasp some portion of Dr. Wilczek's explanations (it took me six days), but I learned enough to understand how it is worth the Prize.

What's worse than wrong?

kw: ideas, opinion, theories, testability

In his most recent column in Scientific American, Michael Shermer, publisher of Skeptic, writes about ideas that are "wronger than wrong."

First, an intermediate idea. Wolfgang Pauli said of a proposed theory that made no predictions and couldn't be tested that "it isn't even wrong." He meant, there is no way to determine if it is right or wrong. You can't even call such an idea a theory, for that word is reserved for ideas that can be tested by experiment or observation.

We know, as scientists, that every theory we have is a model, and that it describes some phenomenon, and makes predictions about reproducing that phenomenon; yet that it will be found to "miss" if taken too far. That is because a model is always a simplification; something is of necessity always left out. A theory may be very, very precise (Quantum Electrodynamics makes predictions that have been tested to a numerical accuracy of something like eighteen decimal places). But at some level (maybe the twentieth decimal) its limit will be found. Taken beyond that limit, the theory is "wrong."

To a scientist, "wrong" means testable, provable, and found wanting at some level. Thus, there are degrees of wrongness.

For example, the idea that the earth is flat cannot be sustained once you determine that a vertical plumb line a few miles away isn't parallel to the one next to you (you can see the difference through a telescope). The idea that the earth is a sphere is very ancient, and a rough measurement of the earth's size was made 2,400 years ago. So, most people who know the earth is "round" (a nice, imprecise term) think of it as a sphere. With a little thought, we realize it is a bit lumpy, and so is not really a perfect sphere, but the sphere model is "less wrong" than the flat model.

I was taught when quite young that the earth was an oblate spheroid. That just means the equator is a circle, but the meridians are slightly flattened ellipses. That's a little "less wrong" yet. Later, the term "pear shaped" was used, and so forth.

Now, at some level, every model of the earth's shape is "wrong". However, Shermer makes a great point here: the notion that the "wrongness" of the sphere model is equal to that of the flat model, is "wronger than wrong." With a modicum of thought, we can realize that the sphere model, though a little inaccurate, is much closer to reality than the flat model. It is a lot "less wrong." The kind of thinking that would equate these models in terms of their relative wrongness, is just too wrong to permit discourse.

That is really the problem, here. If someone's thinking is wronger than wrong, you can't talk to them. They can't understand you, and can't even understand why you are bothered.

I remember the very old "black/white versus shades of gray" distinction, impressed on me from way, way back. To a B/W thinker of the pessimistic sort, a single non-white spot makes everything BLACK; an optimist thinks the slightest glimmer means "it's all good." Both are too wrong for reasoned discourse. One must understand, or at least admit, levels of light or dark to get anywhere.

Later, I had a Rorschach test that moved me in a better direction yet. You may know that a few of the blots are multicolored. After my test, the shrink pointed out that, on the black blots, I had lots to say, and tended to pick them apart, like looking for images in clouds; but I had very little to say about the blots with more than one color of ink. I don't know what he said from that point, becuase I began to think furiously, and realized, "There's not just black, white, and gray. There's a rainbow out there."

Let me confess, I was considered almost autistic before that point in my life. Not since. Now, no matter what the issue, I don't only see the "either/or" question, not even the axis between the poles, but I get ideas in all directions perpendicular to that axis. Life may not be "it's all good," but it's better than it once was!