No bugs, no us

 kw: book reviews, nonfiction, science, ecology, insects, polemics

I've been reading a lot of natural history lately. It is one of my great loves. Having read Silent Spring by Rachel Carson when it appeared in 1962 (I was 14), when I saw Silent Earth: Averting the Insect Apocalypse by Dave Goulson, I just had to read it. Goulson's message is as timely and urgent for our generation as Carson's was for its time. Perhaps it is more urgent.

I think to most people, all the little creepy-crawlies—insects, spiders, centipedes, and so forth—are "bugs", to be squashed or sprayed with something immediately upon detection. The primary impetus and funding for research about insects and related animals is aimed at killing them, mainly supported by the pesticide industry.

Dr. Goulson wants to reset our understanding of insects (et cetera). Perhaps some large number of people realize that bees and other pollinating insects are "good". Their understanding of insect benefits stops there. I wonder, though, how many stop to think what we would miss if the bees vanished.

I got this image from a page at Izismile.com titled Imagine Our World Without Insects. They have short pieces about 8 kinds of insects, including cockroaches (most roach species speed up the recycling of nitrogen in forests) and ants (although many ants eat seeds, many of the seeds they carry are dispersed, spreading plants faster).

Fun fact: According to Dr. E.O. Wilson, the world famous "ant man", ants are the only major group of insects that don't carry any diseases. They are so beneficial, he claims it is OK to let them invade your kitchen; they will kill and eat many other kinds of small insects that DO carry disease, making your house a healthier place to live.

At the end of the Izismile page, they picture mosquitos, saying they can't think of anything good about them. I can: Food for bats and fireflies and many, many species of small bird. Some species of hummingbird eat mostly mosquitoes and gnats. They are not all nectar-sippers.

Much of Silent Earth records what we have been doing with insects. Mostly, killing them. As a matter of fact, the number of insects on Earth today is about 1/10th what it was when I was a child. And the use of DDT had already reduced them, as Ms Carson outlined in Silent Spring. Have you heard of the "windshield indicator"? In the 1960's and before, taking a road trip required a stop every 50-100 miles to wash the dead insects off the windshield, and sometimes out of the grille. Not any more.

The core conclusion of both books is the same: There is no "focused" insecticide. Every insecticide kills every kind of insect. DDT was intended to kill flies. It also killed bees, and even birds, indirectly. Modern pesticides may be less lethal to birds and mammals, but they have already gone a long way towards making many beneficial insects extinct. Sadly, flies and other "more pesky pests" seem to develop resistance to pesticides more rapidly than wholly beneficial insects. If we manage to make all insects extinct, the last ones to go will be flies.

Further, if we manage to make all insects extinct, we are next on the list. Their "ecosystem services" are not well known, but they are worth tens of trillions. Maybe much, much more. We truly cannot exist without insects.

Can this juggernaut be turned? Possibly. In time? possibly. There are no guarantees.

Trees on the move

 kw: book reviews, nonfiction, forestry, biology, trees, climate change

The lighter green area in this figure shows the Canadian range of the Great Horned Owl, Bubo virginianus, an iconic North American owl.

The northern boundary of the owls' range is close to the northern tree line, for these birds need trees. It illustrates the American range of the subject of The Treeline: The Last Forest and the Future of Life on Earth by Ben Rawlence.

The tree line (or sometimes treeline) in the north circles the Arctic, passing through nearly every circumpolar country, although Greenland is nearly all to its north, and Iceland is wholly south of it, being warmed by the ocean currents that produce an equable climate in the British Isles and southern Norway. The tree line is the northern boundary of the boreal forests of Canada, Alaska, Siberia and northern Europe. To its north we find tundra, which is consumed where the trees advance, and itself advances anywhere the trees might retreat (just about nowhere, in living memory). This forest, primarily its northern portions, is the subject of the book.

The six primary sections of the book weave their stories around six species of hardy tree, each being the primary tree species in one or another section of the northern boreal forest. From the Scots Pine in Scotland (in America it is called Scotch Pine, which is probably a solecism), around the circumference of the Arctic to the Greenland Mountain Ash of southern Greenland and eastern Canada, these trees respond quickly (in tree terms) to climatic trends. Their varied methods of seed dispersal either facilitate or limit the rapidity with which they can spread northward as the land warms over years and decades. But all are on the move to the North.

The core story of Treeline is that in the North, the warming trend of recent decades is in no way subtle. Most of us live in areas of temperate weather. For us, a difference of a degree or two F (half to one degree C) is hardly noticeable. Year-to-year variations swamp the signal. But in Alaska, for instance, the people have noticed dramatic changes for at least 30-40 years, in the kinds of plants that have been spreading across the landscape, sightings of birds not seen before but that are becoming common, and the instability of the landscape itself wherever permafrost is melting and in some places washing away entirely.

Throughout, the author describes the dependence upon trees seen in all the life around them. This is not just species that feed on their substance, nor birds that nest in them, but such things as the many beneficial substances emitted by pine trees as their leaves and cones grow: the "fresh pine smell" is actually medicinal, which may be what is behind the practice in Japan of "forest bathing". A walk in the forest is healthier than a walk in the absence of trees, for both physiological and psychological reasons. Trees' roots host fungi that help them extract water and minerals from the soil, and the fungi in turn are fed by the trees in one of the oldest synergistic relationships. Materials shed by the trees and their fungi make their way into nearby waters, where—in ways we have not yet determined—they greatly increase the fertility of the waters. Forest pools and streams are very rich in species of fish and other vertebrates and in insects and other small invertebrates, as compared to bodies of water in meadows and other areas far from forests (though those can be rather prolific in their own right).

The author sums up the matter in this marvelous sentence: 

"If how the treeline made our world habitable in the first place, if how forests create rain, drive winds, manage water, seed the oceans, provide the foundations of much modern medicine, cleanse the air of man-made pollution and disinfect the atmosphere were more widely taught and understood, it would be much harder to cut them down." (p 266)

Clearing forested areas does more harm than we ever imagined. If somehow everyone on Earth could be made to know the true value of the forests, everyone would nurture them as priceless treasures, rather than exploit them for a dollar today and leanness of soul tomorrow.

I thoroughly enjoyed this book, as bittersweet as it is. I am glad to live near a forested area that is intended to remain so. When our son was growing up, he and I sometimes "rock hopped" our way down a little stream, sometimes for as much as a mile. Just breathing feels different in a forest, even a little one.

I have a nit or two to pick, so if you don't care to see the errata, feel free to stop reading here.

• On page 93 the Russian Bios-3 experiment was described. It was stated as having an internal volume of 1,111 cubic feet. That is slightly bigger than a 10-foot cube. I looked it up. The volume is 1,700 cubic meters, which comes to a bit over 60,000 cubic feet.
• On page 185 it is stated, "Sunlight activates their [plants'] chloroplastic structures, and they use the photons from the sun's gamma rays to split carbon from the oxygen in carbon dioxide." Solar gamma rays do not make it through the atmosphere; if they did, we would soon be consumed with cancers, if we did not first die of radiation poisoning. Leaves are green because chlorophyll uses the red and blue photons to do the splitting. They have sufficient energy, while a gamma ray typically has a million times as much energy as a visible photon.
• On page 222 beluga whales are called baleen whales. They are not. They are toothed whales, as are all dolphins.
• In the same paragraph but on page 223, plus in the last paragraph on the page, the whales are described as attracted to oxygenated water. They breathe air from the atmosphere, as do all mammals, and the oxygen content of the water is irrelevant to them. They are not fish!
• This is more of an anomaly. Each place the author visited is prefaced with a name and a latitude, but the latitude is expressed thus: 64° 50' 37' N. In only one place did I find the correct notation, for Huslia, Koyukuk, Alaska: 65° 42' 7" N (p 160). The subtle difference between using " and using ' for seconds of latitude is easy for a reader to compensate for, but it is a bit jarring on first sight.

Sociality – a winning combination

 kw: book reviews, nonfiction, animals, biology, social behavior, sociality

Some animals socialize only within their own "nuclear family", and live solitary lives when not raising their young. Some animal parents work together to raise young (such as red foxes like the cubs shown here); for others only the female raises them alone (think tigers).

Over the full spectrum of animal types, some are primarily solitary, some are a little social, some are very social (such as wolves or starlings), and a small number are eusocial (bees and termites are the prototypes).

With thousands of mammal species, more than 10,000 species of bird and 30,000 species of fish, and on to the millions of species of insect, there is a lot of room for evolution to have produced more patterns of sociality than we can imagine. In The Social Lives of Animals, Ashley Ward reveals the breadth of social life and social patterns among animals.

If an animal is the apex predator in an ecosystem, such as the tiger throughout the East (historically, anyway), being a solitary hunter that meets a mate for perhaps an hour, and then raises her cub or cubs alone, can make sense. Other apex predators, such as wolves, live in packs. Prey animals are more likely to live in herds: there is safety in numbers, and a swirling flock can confuse a predator.

It's funny: Having read the book, and enjoyed it greatly, I don't find a series of stories I want to repeat, which is my frequent pattern. I find myself musing on a philosophical point. I'll set it up this way. There is a range of social patterns found within any particular social species. For example, the stereotypical wolf pack has an alpha pair that does all the breeding, and the other wolves help raise their cubs. This view is outdated; some packs do seem to work that way, but it is much more common for only certain pack members, such as the omega male and omega female, to be prevented from mating, while some or many of the middle-ranking animals can mate. Another pattern is seen in most prides of lions, which includes only one fully adult male who mates with all the females, and drives away any young fellow who tries to cuckold him. Now, what about humans?

I find a greater range of patterns of sociality among humans than among any particular animal species. However, the extreme of eusociality is apparently not seen in human societies (although the Chinese Communist Party is trying to mold the Chinese people into a hive society…but they don't seem to be working toward having one "Queen bee"). A few cases:

• It has been my misfortune to be acquainted with a few psychopaths. Not all psychopaths are criminally-minded, but they all are devoid of empathy, and use sociality only for the purpose of gaining advantage. Anyone who trusts one of them can expect to be betrayed at any time. Some are happiest with little to no human contact. Some are so self-focused they cannot even bear to raise their own child. This isn't just living like a tiger; it is beyond that.
• Near the other end of the spectrum, long ago I subscribed to Utne Reader. In an editorial, Eric Utne self-servingly described his "quasi-commune" and wrote that he and his wife were the "designated breeders", while the others helped them raise their children. This sounds like the stereotypical wolf pack.
• My brothers and I grew up in a nuclear family, raised by two parents who remained married for life, nearly 60 years. It is reflected in the lives of geese, which usually mate for life. While this was the norm in America in the 1950's and '60's, things are changing. 
• Our parents both grew up in extended-family environments, with aunts, uncles, siblings, cousins and second cousins all around. There was little need for "friends" because family provided so many built-in friends. This is similar to the way Orcas and some other cetaceans live.
• Churches that become close-knit become like tribes. Many members find they are closer to fellow believers than to their own nuclear family members. I am not sure what animal model this may resemble.

In some directions, human associations go beyond anything found in the animal realm. The TV show "Modern Family" explored a few such relationships, and there have been reports of groups practicing polyamory: polygamy plus polyandry with multiple partners of both sexes, and probably both gay and straight "activities". Presumably, whatever children are produced are raised by everybody.

That's a few of the ideas that ran through my head as I read the book, and then contemplated its messages.

A shortcut is not cutting corners

 kw: book reviews, nonfiction, mathematics, science, sociology, efficiency

"Work smarter and not harder," was a proverb of a good friend. He supervised a group of 21 superprogrammers, myself included, in a skunk works inside Conoco's research department. Contrary to a stereotype that hyper-fast coders are less creative, the group produced an incredibly creative array of tools for the oil exploration community. One of our secrets was access to a huge library of well-written subroutines and functions, including one called IMSL ("SL" means "software library"; I don't know what "IM" means). Our group motto was, "Don't write what you can appropriate." That last could be the motto of the mathematical establishment, beginning at least with Isaac Newton, who claimed that the source of his productivity was "standing on the shoulders of giants."

I was delighted to see the title: Thinking Better: The Art of the Shortcut in Math and in Life, by Marcus du Sautoy. I was even more delighted as I read his accounts of shortcuts, mathematical and otherwise, that have simplified processes of all kinds. Finding a way to do something better can often be arduous and time-consuming, but it makes things ever so much better in the long run. Dr. du Sautoy likens it to making a tunnel through a ridge or mountain; for example, the Gotthard Base Tunnel that traverses 57 km beneath the Alps took 17 years to dig, but now trains traverse it in 17 minutes. There is a road over an Alpen pass which takes you from one end of the tunnel to the other, if you want to drive about an hour on frequently scary mountain roads.

The development of numbers—from notches cut in a stick, to systems such as the Mayan (1-2-3-4 dots, then a bar), and onward to the positional notation we call "Arabic numerals"—is a series of shortcuts in the technology of counting. The Romans took a side step, similar to the Mayan system, but less flexible in their handling of numbers greater than 10. Anyone care to use the Roman system to convert my height in inches (LXXII) to centimeters (CLXXXIII), with the conversion "factor" being to multiply first by 254 (CCLIV) and then divide by 100 (C)? And while we're at it, look at the Babylonian numbers shown at the right. They counted to 60, not 10, and they used positional notation (extra big spaces between symbols) for counting beyond 59.

The first shortcut, the one that begins the book, is finding patterns. Agricultural seasons are a pattern that repeats yearly. Other patterns overlie it; El Niño and its opposite La Niña comprise a multiyear climate pattern that was recognized by the Incas, centuries before we had satellite sensing to discern the ocean-wide pattern that drives it.

Each chapter has appended to it a "Pit Stop"; the first, is Music. Music appeals to us not only because of the pleasing sounds of tones and chords, but also the patterns. We can often recognize a song just from the drum beat. Poetry of the traditional type, with rhyme and rhythm, is music without the harmony. The patterns in the lyrics or poems help our memories retain songs and poems. Song must have preceded language, because aphasics (those with a damaged left temporal lobe who cannot speak) can still sing. As infants we are comforted by the rhythm of our mother's heartbeat.

Jumping to Chapter 5 (because I want to keep this review shorter than the book) we find Diagrams. We all know, "A picture is worth a thousand words," and a well-designed diagram or chart or graph is frequently worth 10,000 words. For example, this chart of the Federal Reserve's M2 Money Supply over the past decade shows how the recent jump in inflation, which began in early 2020, is directly a consequence of the various "stimulus" packages and other Federal spending programs; thus the historical truism, "Increased inflation derives from too much money chasing too few goods." The gradual slope prior to 2020 shows total inflation of about 6% yearly (one must subtract out the population increase of about 2% yearly, leaving the 4% increase that the Consumer Price Index reports). For the past two years, divide 21,800 by 15,500 to get 1.406, and take the square root to get an average of 1.186, or 18.6% for each of the past two years. Then subtract population growth (2% each year), for 16.6%, which is the real figure (a closer look shows it was worse in 2020 and a little better in 2021).

I picked an economic example because the Pit Stop for this chapter is Economics. There the author discusses the "doughnut economic diagram" that Kate Raworth discovered (and wrote about in Doughnut Economics, a book I think I'll track down). Outside the doughnut (du Sautoy is British; here we spell it "donut") we find nine external influences on the economy, such as pollution and groundwater withdrawal, and in the donut hole we find twelve internal influences, such as housing, networks and food. An increase in the external matters can overstretch an economy and put it in danger; a shortfall in the internal matters puts it in danger from the opposite direction. The donut is the "safe economic space". It's a powerful image.

One other I'll mention, Chapter 8, Probability. Here we find a great discussion of the way statistical tools can be used to take the measure of something large, such as the net worth of 150 million households, by sampling in an appropriate way. In the statistics courses I took, the "appropriate way" was a huge subject, because there are so many ways to get it wrong, whether from malice or incompetence. Sampling biases are the basis of the statement, "Figures don't lie, but liars figure." Polls from Pew Trust or Gallup are based on sampling, hopefully appropriately, to get the mood of the population on something. Some polls are renowned, others reviled. 

The chapter also touches on the Bayesian method. This is a way of making an estimate based on what we know, and updating that estimate as we learn more. Numerically, Bayesian Statistics are a little bit tricky to learn, but the principle is actually something we all do. For example, from our upbringing (and perhaps some genetics) we have a default level of trust that we confer on others. When we meet someone new, we may trust that person to a certain extent. Over time, we observe how that person performs, and if that one is very trustworthy all the time, our trust will grow; otherwise, we will withhold trust more and more.

Interestingly, the Pit Stop for this chapter is Finance. I am not sure how that morphed into a discussion of ways to profit from the stock market, based on the work of Ed Thorp (who wrote both Beat the Dealer about blackjack and Beat the Markets about stocks and warrant hedging). But the discussion morphs again to the value of having multiple viewpoints, such as that of the historian he interviewed about her success as an investor! It reminds me of the bibliography of my Thesis, in which are found references to an article by Leonhard Euler 250 years ago and a work on civil engineering by Werner Romberg in 1955: I was simulating heat flow and fluid flow under the primeval Black Hills… It took my committee members a while to get used to the very diverse viewpoints I drew together.

The last chapter draws attention to some things for which no shortcut exists. In mathematics, and life in general, operations that are easy when there are a few things to deal with get harder when more things are added. Some tasks get harder so rapidly that dealing with more than a handful of items is practically impossible. An example is the Traveling Salesman problem. Given a list of a dozen stops, and the need to return to the starting point (the sales office, perhaps), how should the salesperson order the stops? Even with just twelve stops, the number of possible routes is called "twelve factorial", with 12! as the symbol. 12! equals almost half a billion. Of course, we can quickly shorten the list "by eye", but there may be ten or more possible routes that all look similar. Then we just have to try them all, perhaps by adding up the miles for each. 

Interestingly, there is a shortcut that is not mathematical (the book doesn't mention this). It's not hard to determine that certain ways to go don't make sense, by looking at a hand drawn map where the roads that exist are shown by scaled lines between the points. For the roads you want to use, cut pieces of string that match the length of the roads, and attach them, possibly by gluing to colored beads. Now, hold the mass of string by the bead for the home office, and observe which bead is at the bottom. The strings that are straight show you the shortest route to the farthest point. Note these roads down on the map you started with. Then cut all those strings. Now, hang the remaining mass of string by that farthest point. There may be a single "tightest" route back to the home office, or there may be another "next farthest" point. If the latter, repeat the above process. Otherwise, if all the beads are attached to a tight string, you have your return route. There may be one or two that are off to the side. Just add the road to and from them as needed. This may sound a bit tedious, but it is much faster than having your computer run half a billion tests. Wayfinding is similar, without the need to return home. In this case, you have a single destination in mind. Make the string model for all the routes that possibly make sense (there will usually be just a few). Hold "home" up and see which set of strings is straight. That's your shortest route. In a GPS navigator, the wayfinding program factors in speed limits, and makes estimates of how many seconds or minutes delay one may encounter on a street with stop signs or stop lights, and uses travel time on each street instead of pure length. 

In the concluding chapter the author gets a bit philosophical. Sometimes, taking the fastest way (a helicopter ride to a mountaintop, for example) is not the way you really want. The experience of the climb is more important than taking the shortest amount of time. Sometimes it is good to take the "scenic route" (I do this a lot). And I like his concluding paragraph:

"A shortcut is not a fast way to finish your journey, but rather a stepping-stone to beginning a new one. It is a pathway cleared, a tunnel dug, a bridge constructed to allow others to quickly reach the frontiers of knowledge so they can make their own journey into the darkness. Equipped with the tools that Gauss and his fellow mathematicians [pick your own heroes of efficiency!] through the ages have honed, stretch out your arms for the next great conquest." [the bracketed sentence is not part of the quote, it's my suggestion]

I hate it when a book I like so much has an error. On page 52, in an explanation of the Mayan number system, based on 20 rather than 10, we read, "111 in Mayan represents 1x20² + 20 + 1 = 4041." Oops! 20² = 400, so the result should be 421, and for clarity the expression should be 1x20² + 1x20 + 1 = 421. 

Today's buzzword: nonrenormalizable

 kw: science, philosophy of science, explanations

In a post last week I reviewed The Grand Biocentric Design: How Life Creates Reality, by Robert Lanza, MD and Matej Pavšič, PhD, with Bob Berman. Much of the post expressed my objections to the theory that "life creates reality", a theory based on a dramatic over-extension of the Copenhagen Interpretation of quantum theory (I disagree also with Neils Bohr, who concocted CI). 

I decided now to add a brief discussion of a point made several times in the book, that the version of quantum gravity theory these authors espouse is "non-renormalizable". The word is never explained. Perhaps I can at least give the public some understanding of "normalization" and "renormalization".

A problem arose in the early 1900's when scientists began to solidify the mathematics of quantum electrodynamics (i.e., the dynamics of charged particles in the quantum realm). If equations for the behavior of an electron (for example) were to be solved, partway through the solution one had to contend with expressions that divided by zero, leading to "infinities". Eventually, mathematical methods were developed that "renormalized" these equations, so that the term(s) leading to division by zero could be removed before one actually had to calculate the result.

To understand renormalization, it helps to first understand normalization, which is used to derive the basic equations of differential calculus. The term "derivative" means a function, derived from another function, that expresses the slope at any point. It is the basis for a large family of functions that are needed to optimize functions and, used "in reverse", to calculate areas and volumes (among many other useful summation operations). 

I will illustrate by deriving the "first derivative" of two functions. The first is a basic parabolic function, y = 5x². This states that, in an x-y coordinate system, the value of y is found by squaring x and multiplying by 5. Thus, for x = 3, y = 5*3*3 = 45. The second is a simple quartic, y = x⁴. For this one, when x = 3, y = 3*3*3*3 = 81. Both functions are very useful in mechanics: the position of an object falling in a uniform gravitational field is expressed by a parabolic function, and the energy radiated by a heated body is related to the temperature by a quartic function.

This illustration shows both functions graphed in the domain x = [-1,2].

NOTE: There are several notations used in calculus, because of the complicated history of its discovery three-plus centuries ago. Here I use notation based on that of Gottfried Liebniz (d. 1716).

The mathematical slope of either of these curves is dy/dx, and one can approximate it by calculating the functions at x and x+dx, for very small dx. But the exact value can only be found when dx = 0!

Below is the derivation for the parabolic equation as I learned it in high school.

"Lim" means the limit of the expression in brackets, as the term in parentheses is satisfied. We do the derivation using dx and dy as algebraic variables.

The three lines in the middle expand the function. The following line is the "normalization": dividing by dx removes dx from one of the terms in the equation.

Then, as shown in the last line, when we set dx to zero, the term that contains it vanishes, leaving us with a function in x only. This function is the first derivative of function y1.

Let's drive the point home by performing the same operation on the quartic function:

This time, multiplying out the function results in a larger number of terms. As before, the calculations are shown in the three-line cluster in the middle. The next step, normalization, divides by dx to yield one term that doesn't include dx, and three others that include it. Setting dx to zero yields the first derivative of function y2.

To summarize: Normalization is a mathematical process of deriving expressions that would contain a division by zero if carried out with numbers, but then dividing out the term that will become zero, so that a perfectly calculable function remains.

We can do a simple verification to see how these derivatives perform. Here is a table of the two functions, calculated from the values of x as given. The graph above was produced from these numbers.

In the graph above the green lines are anchored to x = 1.5. Let's start with dx = 0.1 and calculate y1 and y2 at x = 1.6, subtracting values found in this table at 1.5:

y1(1.6) = 5*1.6*1.6 = 12.8; dy1 = 12.8 - 11.25 = 1.55; dy1/dx = 15.5.

y2(1.6) = (1.6)⁴ = 6.5536; dy2 = 6.5536 - 5.0625 = 1.4911; dy2/dx = 14.911.

We can shrink dx to 0.01, so we calculate at 1.51. The results are then 

dy1 = 11.4005 - 11.25 = 0.1505; dy1/dx = 15.05.

dy2 = 5.19885601 - 5.0625 = 0.13635601; dy2/dx = 13.635601.

These numbers seem to be closing in on 15 and something more than 13.

Now let's find exact slopes using the two derivatives:

Slope #1 = 10*1.5 = 15.0

Slope #2 = 4*(1.5)³ = 13.5

It's possible to use smaller and smaller values of dx to get a converging series, from which we can get pretty accurate results. However, the mathematics of the derivative ensure that the values calculated by them are exact.

Based on all that, what is Renormalization? Here I must get conceptual because the functional expressions are enormous, and people got Nobel prizes for figuring them out. Calculus, which is already based on Normalization, was used to determine the functions needed by quantum electrodynamics. The equations were labored over until a version of each derivation could be performed that "divided out" the expressions (analogous to dx but much more elaborate) that caused trouble. This second dividing-out process is renormalization.

In one of his books, Richard Feynman tells of being asked, at the Nobel Prize ceremony, "What did you do?" He answered, "Buddy, if I could tell you that in one minute, it wouldn't be worth a Nobel Prize." Renormalization was part of it.

So what is Non-renormalizable? The authors of The Grand Biocentric Design make much of their contention that a quantum theory of gravity cannot be renormalized. No such theory has yet been fully developed, as the authors admit. Since we don't know what form such a theory will take, we (and they) don't have a way to determine if their contention is anywhere close to being correct.

On a plane ride several years ago I sat with a young man who, it developed, is a cosmologist. I said, "I have a question I've been hoping to ask a cosmologist, if you're willing to give it a crack." He agreed. I asked, "If gravity is a quantum phenomenon, that means there is a gravitational quantum, a 'graviton'. The most powerful sources of these gravitons are black holes. What is it, for a black hole or for any other massive body, that emits the gravitons? If they start 'inside', where the mass is, how do they get out?" He said, "That's two questions, but it's worth some thought." After a half hour of silence he said, "By analogy to photons, which are emitted when charged particles such as electrons are accelerated or make a quantum jump from one orbital to another: The motion of an electron may cover at most a nanometer or two, particularly in an orbital transition. The photon that is emitted has a wavelength of a few hundred nanometers or more. We don't yet know what is the wavelength of a typical graviton. But I think gravitons are emitted over an area larger than the typical black hole, not from inside it. That's the best I can say on short notice." That was pretty good! I reckon it will be a while before a better answer is in the offing.