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.

As the universe darkens

 kw: book reviews, nonfiction, cosmology, dark energy, dark matter

I had one expectation when I saw the title: Fear of a Black Universe: An Outsider's Guide to the Future of Physics by Stephon Alexander. I surmised that it was literal, though metaphor is always possible. As it happens, Dr. Alexander means it both ways. He is black, and in the physics community, that makes him an outsider. Sad to say, institutional racism is more entrenched in academia than it is in most of suburbia, where I dwell.

I will not dwell on the author's reports of prejudice. Being white (or, having no more than about 1/16th African ancestry), I've seen such things from a different perspective than he has. Some aspects of what he is, he has been forced to become. Whether in spite of such handicaps or because of them, he is an excellent scientist (Neil deGrasse Tyson, another black scientist I admire, freely admits he "over-achieved" in reaction to being discriminated against). Suffice it to say, it was clear that the colleagues who denigrated him did so out of fear, thus the book's title. His significant achievements indicate that their fear was well-based, though ill-conceived.

This illustration explains why the universe is becoming darker, tending toward a future of infinite, unending blackness.

According to the cosmology accepted by a great many, something, dubbed "dark energy", is causing the expansion of the universe to accelerate. Some conjecture that at a time between one and 10 billion years in the future, the acceleration will increase rapidly, leading to a "big rip", eventually even dragging atoms apart, leaving nothing material remaining. Others expect something more sedate, but still leading to the "nearest" galaxies being too far away to see, and resulting in the dissolution of galaxies. If living beings remain on any planets in such a universe, there won't be a starry sky. The "sun" will be the only star visible.

Much of the book describes in laymans' terms the observations and hypotheses behind the understanding of "dark matter" (stuff that gravitates but doesn't shine) and "dark energy" (something about space that pushes it apart, ever more rapidly).

Cosmology is a difficult science. If you were to study chemistry, you could do experiments that take place in minutes or hours or days, typically…although I do recall a reaction that required about a month's exposure to the UV light in sunlight. The second term of my Organic Chemistry course, we performed a synthesis that began with the usual "measure carefully, mix thoroughly" stuff, and then we stoppered our flasks and set them on a windowsill until halfway through the term.

There's no such alacrity possible if your subject is the history of the universe. Tons of interesting stuff happened billions of years ago, that doesn't happen now, so astrophysicists have to infer what it was by looking for subtle signals in the light (loosely construed: wavelengths from gamma rays to radio waves) arriving from space. No "experiments" are possible. How can you repeat something that took 12 billion years to happen?

Modern supercomputers can simulate really huge systems at incredibly high speed. That's not enough (yet?) to permit a useful model of the whole universe to be built and run in a useful amount of time. So a lot of theorizing goes on. A LOT!

Dr. Alexander likes string theory. After reading his explanations, however, I was no closer to understanding string theories than before. "Theories": there are a lot of them; the most recent estimate is upwards of 10⁵⁰⁰ of them (that's a number with at least 500 digits. The number of atoms in the universe can be counted with 80-85 digits).

In the last chapter or two the author writes of the theory that, based on the Copenhagen Interpretation of Quantum Physics, nothing exists until it is observed. The Copenhagen Interpretation was the brainchild of Niels Bohr. Quite frankly, I disagree, but I'll get into that when I review another book on that subject in particular, which I've just begun to read.

I am also skeptical of the existence of dark energy, or the cosmological constant, or whatever it is currently called. I have read a number of journal articles challenging the premises on which it is based. It posits a kind of "vacuum energy" that, if it exists, should be 10¹²⁰ times as large as it is claimed to be. To me, that's the largest error so far to be found in any theory I know of. Dr. Alexander has a humorous possible solution to that dilemma: Aliens, great multitudes of them, who can harness dark energy for their own uses, using a "gravitonic computer". The amount of dark energy we observe is the trickle that is left over, leakage from their technology. If that were so, there's a lot of waste heat that has to go somewhere, enough to boil every planet and star in the known universe trillions of times. Second-biggest error? Maybe!

So, the book was enjoyable to read, but I am afraid I didn't gain much enlightenment. Dr. Alexander is a brilliant physicist. I'll have to read more, multiple times, to grasp where he is going.

If you don't like errata, you can stop here. I noticed a couple of things that slipped past the proofreader or copy editor:

• On page 184, discussing the gravitonic computer, two numbers are presented, shown as 10,120 and 10,100. These should have been represented as 10¹²⁰ and 10¹⁰⁰. These are just typos.
• On page 197, two theories of gravitational wave spectra are discussed. One is said to be more "red", the other more "blue": "In inflation the power spectrum is said to be red. This simply means that the longer wavelength perturbations have slightly less power than the shorter wavelength ones." No, "red" means longer wavelengths are stronger, while "blue" means shorter wavelengths are stronger.
• On page 205, John von Neumann is said to have "proved that when a quantum system exists in a superposition of states, a chain of measurements ultimately leading to the consciousness of an observer is what collapses the wave function into one definite state." This is based on the Copenhagen Interpretation, and it is a claim, that so far has not been proved. It cannot be proved. All experiments that purport to prove it, and I have read about many of them, ultimately depend on circular reasoning.
• Two things on page 206: Firstly, Erwin Schrödinger is said to have predicted the basic helical structure of DNA. He actually predicted a regular, aperiodic structure, akin to a crystal but with variable items at each node, so it could carry information. Language is a useful analogy. The helix was posited later, by others. 
• Secondly, Schrödinger "argued that living things fight against entropy, otherwise known as negentropy." He did indeed, but better reasoning has overtaken that theory: living things take advantage of the flow of energy in non-equilibrium environments, and thus they take advantage of the flow of entropy as well, producing small, local reductions in entropy at the expense of larger increases in entropy in their surroundings. That's not "negentropy", it is redirected entropy.

The last item may not be a copy error, but a conceptual error on the part of the author. He goes on to discuss the "observation creates reality" theory, based on the assertion by von Neumann, which has been developed by many others. This isn't physics any more, it is metaphysics, and ought to stand on its own two feet and proclaim so. That's enough at the moment.

Swedish spiders?

 kw: blogs, blogging, spider scanning

Well, that's a hoot! I checked blog stats to see that about 800 hits came yesterday (a normal day is about 50). Guess where they were from this time? Not Russia:

Sweden! And that was all yesterday. The 14 from Russia (in a week) are a bit more than usual when Russian spiders are inactive, but not excessive. But...Sweden!!

The dance of climate and biology

 kw: book reviews, nonfiction, biology, bioclimatology, climate change

The title of the book caught my eye: Hurricane Lizards and Plastic Squid: The Fraught and Fascinating Biology of Climate Change, by Thor Hanson. Midway through the book I found the stories behind the title. This illustrates the first. The three overlaid images show an anole lizard clinging to a branch in artificial winds of 35, 55, and 85 mph.

Anole lizards on Caribbean islands are frequently caught in gales or hurricanes. In the article that is the source of this image, "Lizards, toepads, and the ghost of hurricanes past", by Raymond P. Huey and Peter R. Grant, the authors report mapping the frequency of past hurricanes and comparing the forelimb strength and toepad size of anole lizards with each island's "hurricane index". They used the simple expedient of bringing a high-powered leaf blower to island after island, and measuring how much wind it took to blow a lizard off a branch it chose to cling to when the "wind" began blowing. Islands with more frequent hurricanes harbored stronger lizards with bigger toepads.

I'll leave it to you to check out the story of the lifestyle plasticity of certain species of squid. Such plasticity is one characteristic that helps some species thrive in spite of change, compared to less plastic species, which are more likely to go extinct. Perhaps bears and roaches really will outlive all of us.

Dr. Hanson spends little time discussing climate change as such; leaving that to others, he begins with the fact that climate warming is happening, and chronicles the various ways animals and plants are changing along with it. 

Some change by moving, either poleward or uphill. Census surveys of mountaintop species over many years reveal just how rapidly such changes can occur. The species that "liked" the crest of a mountain in cooler times find themselves with nowhere to go (unless they are birds), and die out, even as species that had been living at lower elevations move upward. I was quite interested by the description of just how rapidly some tree species can "move" by sending fruits and seeds on their way. Some can move many miles per generation, if they produce a fruit that is eaten by a mobile creature. Others are restricted to the distance a nut might be blown during its fall from the treetop. But the love some birds such as jays have for acorns means that oaks can be dispersed quite a distance, by acorns that birds hide but forget about (the trees are hoping for imperfect memories!).

Evolution is generally considered too slow to help creatures survive a warming as rapid as the one currently going on. That is probably true in many cases, but not all. The anoles shown above are actually evolving fast enough that some will survive a doubling or tripling of the number of category 5 hurricanes across their island. Initially, adaptation keeps some anoles alive through a season, but there is also the weeding-out of weaker-limbed individuals, so the next generation includes a larger proportion of stronger lizards. Random genetic drift ensures that a few will be extra-strong, as the occasional helpful mutations accumulate. This can go pretty fast in animals with a generation time of a year or two.

How far will climate change go? Dr. Hanson describes a "kitchen experiment" with carbon dioxide and a heat lamp, originally done a couple centuries ago in a brewery (where huge amounts of CO₂ are produced), that illustrates the heat-blanketing effect of the gas. It roughly confirms a calculation that I learned to do before I was in high school (I had smart parents and a couple of good mentors): it shows that greatly increasing CO₂ seems to top out the heating at 4°C. That may not end civilization, but it won't be pretty. It certainly won't "destroy the earth" or the biosphere, but it will make some big changes. So of course the author asks us, "What can we do?", answering, "As much as we can, in as many ways as we can." For me, that includes convincing Limousine Liberals to drop out of the jet set. A single cross-country or cross-ocean flight produces, for each person aboard, as much CO₂ as a few months of driving an SUV.

Meantime, I'm a homebody, married to a homebody. Out total miles driven for two cars is less than 12,000 miles yearly, while the average distance driven by most cars in the US tops 14,000 miles. It doesn't mean we are particularly virtuous, just boring. This book is anything but boring. It's a fun read, with many interesting stories. 

Blueness makes me happy

 kw: book reviews, nonfiction, colors, nature, blue

When I was ten years old my parents bought a set of four drinking cups of different colors to use in the bathroom, and sets of similarly-colored breakfast plates. I was the oldest of four boys; the others were 6, 4 and 2. Mom had prepared for the coming moment by questioning each of us privately, what was our favorite color. The 2-year old didn't understand the question, the 6-year old said, very definitely, "Red!" and while I had also said "Red" at some point, I also liked blue, so when she showed us the four cups, I was quite happy to pick the blue one—it was really a lovely, dark blue—leaving green and yellow to the two youngest boys. The 4-year old was happy enough with green, so the youngest got yellow by default. In later years, I learned that blue is the most common favorite color. It made me wonder, if that is so, why does "feeling blue" mean sadness?

That latter point is scarcely touched in Blue: In Search of Nature's Rarest Color by Kai Kupferschmidt, but the book abounds with lore and learning about Blue: how we see it, use it, and value it. I did wonder, how is it so rare, when the sky is blue? As I soon learned, "blues you can use" are hard to come by. Thus, there are a number of blue minerals, also many blue flowers and fruits, but stable blue pigments made from minerals are historically scarce and thus highly valued, and blue dyes from plant sources even more so.

It's true that though there are a number of blue minerals, only one or two make useful pigments, and the primary one is lapis lazuli (lazurite to a mineralogist). It's scarce and hard to produce because it seldom occurs with much purity, being intergrown with pyrite and other minerals of similar solubility. One must almost pick it apart with tiny tweezers to get the blue mineral grains separated from all the others.

It's also hard to grow, unlike chalcanthite, AKA hydrated copper sulfate. I grew this specimen of copper sulfate in a jar, rather quickly. It is very water soluble, so as a mineral it only occurs in deserts, associated with copper deposits. Good pigments aren't water soluble!

I happen to favor blue minerals, as does Dr. Kupferschmidt. The two pictures below show one natural mineral, light blue fluorite, and a jar-grown phosphate (apatite, chemically).

There is also a chapter on color perception, with quite a discussion of the way some languages have only one word that covers both green and blue hues. Does this mean that some people can't see the difference, or that it just isn't important in some cultures? I do know this: my wife says the phosphate crystals are clear; she doesn't see the aqua color that is so distinct to me. She also tends to see some of my clothing as green, which I see as blue, but the Japanese language has quite distinct words for blue and green colors (she is Japanese).

Another chapter deals with plant dyes, which seem to produce every color except blue, with two exceptions: woad, Isatis tinctoria, and the indigo bean, Indigofera tinctoria. The Latin word tinctoria is from tinctura, meaning "dye". The two plants' extracts are the same chemically, but that from the indigo bean is more concentrated. Denim is dyed either with natural indigo, or a synthetic version. It has the charming characteristic of gradually coming out in the wash, so that older blue jeans and jean jackets (etc.) fade with many washings. If you want blue underwear, wash it with new blue jeans!

I was surprised that mollusk dyes were not mentioned (I happen to work in the mollusk collection of a natural history museum). Of course, "royal purple" is the most famous dye to be made from snails of the genus Murex. It was even more surprising to me because I found this statement, quoting philologist Lazarus Geiger, that "the Bible found 'no opportunity' to mention the color blue." This is blatantly false! viz:

The Hebrew word tekelet occurs 50 times, and nearly every version translates the word as "blue". Historically the word describes the blue dye produced from a secretion of the cerulean mussel; both Mytilus edulis and Mytilus galloprovincialis are found on the Phoenician coast where the purple-yielding Murex species are found. Jewish sources describe the color of "Tyrian purple" from Murex snails as having a range of colors, depending on how much ultraviolet the dye solution is exposed to during processing. The more UV, the bluer the result. Apparently, in the mix of dye chemicals, the red one(s) are bleached by UV. Thus, begin making dye in the late afternoon to get a more magenta, almost reddish color, or begin early in the day to get a sky-blue dye. The dye from the mussels tends more toward blue hues than from the snails. The common name "cerulean mussel" refers to sky blue, which is the color of the fresh shells. And here we mean the darkish blue of a clear winter sky.

The tapestries of the Hebrew tabernacle and later of the temple in Jerusalem, as well as the garments of the priests, were to be of linen embroidered with "blue and purple and scarlet", all colors that can be produced from mollusks. Now, perhaps Lazarus Geiger only had a New Testament available; the word "blue" does not occur in the Greek New Testament, where either kyanos or galazios would have been used. The NT does mention red, scarlet, green and purple.

On a further note, some consider the Hebrew word cappiyr, translated "sapphire", may refer to lapis lazuli, but from the root of the Hebrew word, it refers to the extreme hardness of the stone, and can only refer to corundum; sapphire is blue corundum. The "sapphire pavement" before the throne of God is intended to appear as the blue sky seen from above.

All that aside, It was great fun to read this book. There is much to learn about blue, including why its manufacture was so hard in the past, but is so common now. So I could have a dark blue plastic cup to use when brushing my teeth as a child. P.S. I still have that cup, and still use it!