Oracles

We'll take today's text from a story in the Fifth Galaxy Reader, "Perfect Answer," by L. J. Stecher, Jr., originally published in 1958. I liked it quite a lot when I was young; re-reading it makes its flaws very obvious, but the flaws also illuminate.

The two protagonists are a galactic exploration team, and they have discovered that the galaxy is awash with Homo Sapiens, practically one inhabited world in every viable solar system, and all of them primitives who greet space explorers with either worship or homicidal intent. It's a puzzlement.

Then they come across a civilized world, but one that is oddly decadent. They have such technology as automatic translation machines, but have no idea how they work. When asked, the inhabitants reply, "We asked the Oracle how to make one and it told us."

So, first error in presentation. You don't build things by just being told how to make them. To build a translator (or automobile, or even a stone house) you need pre-existing infrastructure like semiconductor fabs, or foundries, or stone quarries. Knowledge alone isn't enough.

Next, one source of answers simply would not work for an entire world. This is the alien-planet-as-desert-island analogy that I once railed against when critiquing Clarke's Law. A civilized world has billions of people on it, far too many to crowd into a room.

But the Oracle does indeed reside in a room, and our explorers are given an audience. It reveals that it was created by an extra-galactic race (from the Magellenic Cloud) as a weapon that worked by answering all questions truthfully. This destroys the institution of science in those who possess it (no need to pursue answers when they are handed to you an a plate), and when taken to a empire's home world, wrecks said empire.

One of the two explorers wants to steal the Oracle and take it back to Earth, rigging it to answer only his questions. The other wants to head back empty handed and warn Earth. They fight. The first guy dies. The second realizes that he is now stranded, since their ship required two men to operate. But the Oracle could tell him how to save his own life, so….

In one of the Foundation stories, Asimov makes a swipe at what happens when you trade science for scholarship, i.e. when you stop experimenting and just look up the answers. I never bought that argument. Nobody verifies everything that they are told under the authority of science, to attempt to do so would result in another end state—where science keeps reinventing the wheel, over and over again.

However, "Perfect Answer" gets the reaction of the two explorers correctly, or, more specifically, the one that wants to monopolize the gizmo. That is how it would actually work, so our travelers should not have found a happy-go-lucky decadent society, they should have found an authoritarian state in the grip of those controlling access to the answers from the Oracle.

Now you can replace Oracle with "simulation model." But you still need that infrastructure that I spoke of earlier. In science, the infrastructure consists of scientists and the community of science. The community of science is not command-and-control oriented, as many have discovered, to their discomfort.

There is a difference between authoritative and authoritarian, which some people get and some people do not. Authoritarians don't get it. They never do.

Working the System

“Systems Biology Calls for New Way of Training Doctors” – sidebar headline in Chemical and Engineering News

The first feedback control device was probably the float valve, used in ancient water clocks. I’m discounting biological and other feedback systems, obviously. Those are usually called homeostasis.

Prior to the 20th century, there aren’t a lot of examples of feedback devices. Watt’s governor is the one most commonly cited, and its 18th century origin was close to concurrent with the steam release valve, which is also a feedback device. The governor is also of note because it is an example of proportional control. It didn’t just shut the steam on and off; it throttled the steam by varying the size of an aperture.

On/Off control is the sort that you get with a thermostat. When the temperature drops, the furnace kicks on at full force, then it stops when the temperature rises. That produces a limit cycle because the process is non-linear. If the furnace heating were proportional to the difference between the room temperature and the thermostat’s set point, then you’d have proportional control. That also produces a cycle, but the cycle is sinusoidal, and the process is termed linear, because of the type of equation that describes it.

The 19th century invention of a torpedo control system by Robert Whitehead was probably the first mechanical invention that addressed the oscillation problem. The first torpedo designs used a simple hydrostatic valve to adjust the control fins, but this caused “porpoising,” an up-and-down motion that sometimes put the torpedo above the surface of the water. Whitehead realized that something was needed to damp out the fluctuations, so he devised a pendulum that crudely measured the torpedo’s angle and modified the control in the direction to reduce that angle. This added a rate-of-change term (aka, a derivative) to the control equation, and reduced the depth fluctuations of the torpedo from 40 ft. to less than 6.

The problem with a proportional controller with damping is that the system often settles to a point of stable error, because the small error signal is damped out by the derivative signal. The solution to that is to add what is called the integral term, so a small error signal is integrated over time, and thus builds to a large enough signal to move the settling point.

The first example of a full PID (proportional-integral-derivative) controller comes in 1922, when N. Minorsky devised an automatic controller for the steering of ships. The mathematical characterization of control systems was also advanced enough by then to properly analyze such systems.

The “feedback loop” as it came to be called, seemed to offer some benefit to another, more general problem, of the sort that a wide variety of scientists and others were facing, that of the reductionist trap. When someone says, “We’re nothing but a bunch of atoms that think we’re alive,” that’s voicing the reductionist trap. A bunch of atoms we certainly are, but it doesn’t seem accurate to say that we’re nothing but a bunch of atoms. There are, after all, a lot of bunches of atoms around, but none of them behave just like me. I rather doubt that any of them think they are me, either.

Another way of addressing the problem is to use phrases like “emergent phenomena,” which is a fancy way of saying that the whole is more than the sum of its parts. Since a feedback loop is also more than the sum of its parts, and since homeostasis (feedback, remember) is a general characteristic of living organisms, there came a general belief that feedback analysis might offer some insights into biology, or psychology, or sociology.

Thus was born the Cybernetics Movement, which included some folks like A. H. Maslow, whom I mentioned in a recent essay, as well as Margaret Mead and Gregory Bateson, plus some heavy hitters like Claude Shannon, John von Neumann, and Norbert Weiner, whose 1950 book, The Human Use of Human Beings: Cybernetics and Society became a best-seller. I’ll mention in passing that Claude Shannon had just pretty much invented information theory, which, aside from revolutionizing electronic communications, also became part of the cybernetics movement.

Later, Cybernetics became General Systems Theory, which was not exactly a cult and not exactly a movement. But it did have some Believers, and I was probably one of them. The systems guys were of the belief that systems theory could be applied to, if not everything, an awfully big part of everything, and that it could and would revolutionize everything it was applied to.

In my own case, as I’ve previously written, I was attracted to the idea of simulation modeling of large scale biological, environmental, and social systems. I started off doing lake ecology, then slid over to atmospheric chemistry with barely a hiccup, because the methods of analysis were so similar. So that part of the program worked pretty well, at least from my viewpoint. However, I hit the downside of it all pretty quickly.

The downside was first, that while the tools of analysis were top notch, to use them in real world situations, you need a lot of data, and the methods of data collection weren’t really up to it. I hit that first in lake ecosystem modeling, where data from sunlight, nutrients, and plankton were pretty good, but the data we had for fish populations were horrible. And, oddly enough, the fish were important. After that experience, atmospheric science was wonderful; there was so much data available.

The second drawback was the real killer: analysis isn’t enough. In order to “change the world” you have to change the world. You can have the right answer, but if people aren’t willing to use it, what good is it? And, if your way of doing things is different in any way from what people are already doing, what they are, in fact, trained to do, you’re not going to make much headway.

It doesn’t help to blame the other guy, either. Everyone thinks their job is hard and everyone else’s is easy. No, what they are is different. Getting the correct engineering analysis isn’t the same as getting the right policy analysis, and neither of them make getting the policy adopted that much easier.

The worst of it was with the physicians. They go through hell getting their medical education. If you want medicine to change, you’re going to have to wait for an entirely new cohort. Worse, because medical education is also controlled by those same people, you’re actually talking about many generations. I watched more than one systems engineer bash his head into that brick wall, over and over again.

The quote at the beginning of this essay is from July, 2006. It could just as easily have been from 1976. Or 1956 Maybe it will happen, but I’m not holding my breath.

Chaos

Edward Norton Lorenz died on April 16, 2008. Lorenz has been called "The father of Chaos Theory," and it was he who delivered the paper, "Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas" at a AAAS Conference thereby creating the conditions for the phrase "The Butterfly Effect." It helped that a graphing of the "Lorenz Attractor" looked sufficiently like a butterfly.

I myself used Lorenz's butterfly image when describing a storm in SunSmoke, not realizing that I was just ahead of an avalanche of such usages. It wasn't a cliché when I used it in 1983, honest.

It's also been noted that Ray Bradbury used a crushed butterfly to set off all the change-the-past stuff in "The Sound of Thunder." From a scientific point of view, Bradbury was far too conservative. He had meddling in the Jurassic merely change human history; it could have erased human history entirely.

People have as much trouble with chaos theory as they do with quantum mechanics and parallel worlds. There is a tendency to underestimate the effects, to bring them down to human scale, for example. But the point is that small changes in initial conditions can have, under certain circumstance, large changes in outcome. It's also important to understand that this isn't always the case. Not all systems are chaotic.

Suppose you have a very round ball bearing and a very smooth surface. Drop the bearing straight down onto the surface and you can be pretty sure that once it stops bouncing, it is going to be very close to where it first hit the surface. If there is a depression in the surface, you can be even more certain. The bearing is going to wind up at the bottom of the depression.

Now put another ball bearing down below the first, and drop the one onto the top of the other, as best you can. Where will it wind up?

You can be pretty sure that you aren't going to get two ball bearings stacked onto each other. Past that, well, it's anybody's guess, and guess is the operative word. Conservation of momentum says that the two bearings will ultimately be on opposite sides of your starting point, but they could be very far apart if there isn't much friction in the system. The smallest offset between the centers of the two ball bearings get multiplied very quickly by the bouncing.

Multiply this situation by a few dozen orders of magnitude and you have atoms colliding in a liquid or gas. Look at the system in fine enough detail and you can see "Brownian movement," the effect of bunches of atoms randomly hitting one or the other side of something preferentially for brief periods of time.

In truly chaotic systems, like those showing fluid turbulence, the small effects can magnify as time progresses, and produce major, macroscale phenomena. It's not just the butterfly wing that can set off the tornado, Brownian movement can also. So can a single quantum fluctuation, the radioactive decay of a single atom, the ionization shower from a single cosmic ray, the heating of a single molecule by a single solar photon.

Or maybe not. Sometimes things do cancel out, perhaps. We don't have access to all those alternate quantum universes, so we don't know how many there are, nor do we know how different they would have to be to no longer be here. Identity is a slippery thing, after all.

But weather is chaotic, so all possible weather events probably happen in the Great Beyond. Read any history and count the number of times when weather played a big role in the life of a nation, a people, or just individuals. Crops fail, and famine is a chaotic event.

War is chaotic, of course. Every soldier is a fatalist, knowing that the difference between life and death is often a matter of seconds, or inches, or a single random impulse. Plagues are chaotic, with disease vectors jumping around (literally sometimes) like fleas.

That's three of the Four Horsemen. The fourth one is Death, and he looks like Chaos to me.

But Life is also chaotic, even at the beginning. It's sometimes said that the fastest sperm gets to fertilize the egg, but in fact, it takes a mass of sperm, containing enzymes that break down what is called the "zona pellucida" to allow a single sperm to get through. So it's more like "We're taking the 3,887,996 caller."

Every conception is a random throw of the dice. Every birth is a door from chaos into chaos. Every individual creates a myriad universes, just by existing.

Is that enough? I mean, what more do you want?

See How It All Fits Together

In my essay, "The Scientific Method," I described (and bragged a bit about) some work I once did on the photochemistry of toluene, which has the unusual property of, under some very special conditions limiting the amount of ozone that is generated in a smog system. It's a weird effect, and I was bragging because I'd predicted it, then designed an experiment to show that its weirdness was real.

In a more recent essay, "PAN", I noted that there were some features of the chemistry of that compound that I'd gotten right because of a detailed analysis, a I-knew-what-I-was-doing sort of thing, which is more bragging, of course, but I noted that, science being what it is, I was only a little bit ahead of the curve. The rate constants that I'd had to adjust to make my simulations work were routinely measured as being what I'd needed only a little while after I did my work, and the ordinary workings of science would have produced models that did the right thing, even if no one was paying attention.

In "The Linear Hypothesis," I remarked that sometimes (in fact, pretty often) scientific models are used for purposes of policy and decision making, and a model is often chosen to make that task easier, because, well, that's the purpose at hand. Sometimes this is done for good reasons, like selecting a conservative model in order to observe "The Precautionary Principle," where we are dealing with asymmetric error; if an error in one direction is vastly more costly than an error in the other direction, then simple caution suggests using the more conservative model, even if there is some weight of evidence on the other side.

Anyway, I've just been talking to an old colleague, who tells me that one major smog kinetics model has been "fixed" so that it no longer shows that weird toluene behavior that we actually proved to exist. The experiment that proves it is now considered "old" (as if chemistry somehow goes bad with age), or "sloppy," or the result of experimental error. Not that anyone is bothering to replicate it, you understand.

I expect that it has to do with it just being too confusing to have models tell you that sometimes adding one pollutant can produce less of another pollutant. Or something like that. The rationalizations sound pretty sad, however.

We've been hearing a lot lately about the ways and methods that various players in the Bush Administration have been tampering with scientific reports, muzzling scientists, and twisting the system to their own ends. This is, of course, despicable. What I am saying here is that I've seen a lot of this sort of thing throughout my entire scientific career, coming from every policy quarter. Yes, the Bush Adminstration does it, and has been totally shameless about it. But they had plenty of precedent from the Tobacco Industry, the Oil Industry, the Pharmaceutical Industry, and, I will add, Environmental organizations and regulators. When people have an ax to grind, they will first grind it on the facts of the matter, or at least the theories and models that are used to codify the facts.

The "Probability Engine" that the time meddlers found in Destiny Times Three by Fritz Leiber was originally a simulation engine, developed by advanced beings to calculate the probable results of various actions, and to avoid the worst actions and their consequences. The horror of the story is that the device came into the possession of humans, who, with the best intentions (but insufferable arrogance) used it to create those dystopian worlds, rather than simply model them.

I do so hope that this is not, ultimately, a metaphor for science in the hands of human beings.

Stamp Collecting

A while back I picked up Motivation and Personality by A. H. Maslow from the free book table outside the Berkeley Public Library.

M&P is one of those books I’d never read, but is still so familiar that I might as well have read it. It was published in 1954, based on papers written during the 1940s, and it’s full of such phrases as “self-actualization” and “synthesis of holistic and dynamic principles.” Maslow isn’t really responsible for the ways in which those ideas were later turned into buzzwords and catch phrases; he used them first, and he was driving at something.

The couple of chapters constitute a long essay on the philosophy of science, because Maslow was dealing with a phenomenon in the psychological sciences that is nowadays called “physics envy.”

When I was a lad, close to the time of the publication of M&P, in fact, the popular image of the scientist was in the process of moving away from a guy in a white lab coat pouring the contents of one test tube into another test tube. What replaced it was a guy with a particle accelerator. Granted, the guy in front of the blackboard scribbling incomprehensible algebra bridged the two other images, but nevertheless, the image had changed from chemistry to physics.

The sci-fi magic wand changed, too. The old school method was the magic potion, or, in the case of Frankenstein (and even older tale from the dawn of electricity) the lightning bolt. The tame lightning bolt was accomplished by the special effect of the Jacob’s Ladder, you know, the gizmo with the electric spark crawling up between the two metal rods. But Steve Rogers gets to be Captain America by getting injected with the magic potion.

The new school was radiation. Radiation grew giant ants, woke up Godzilla, and gave Peter Parker spider powers. The magic potion became the magic ray.

It doesn’t take much reflection to uncover the source of the change, at so many levels. Hiroshima and Nagasaki went up in nuclear lit flames and suddenly physics is a much bigger deal, with big, big budgets The Manhattan Project was bigger than any corporation of its time, and the national lab system that grew out of it was likewise gigantic.

The number of jobs for physicists likewise increased enormously, as did the money available for education in the sciences, again, with physics being the glamour field.

I don’t think I’m going to single out the academic physics community for becoming all snooty about their sudden increase in worldly status; all academics are snooty, given anything like an excuse (and just being academics is usually enough). Being snooty is part of the academic job description.

Nevertheless, academia is always a status competition, and the physics guys suddenly had a lot of extra moxie. So all of the old canards (“All science is either physics or stamp collecting") got some more muscle behind them. Hence, physics envy.

I will grant that, since much of Maslow’s work was done before the end of WWII, physics envy was obviously in the making long before the post-war physics swarm, but why should I let an inconvenient time-line spoil a good narrative? Besides, I’m not saying that this is cause and effect, just that the effect was given a booster shot. Maslow gives a perfectly good description of the intellectual history of what he calls “atomistic and reductionist” thought; I’m just adding a sociological footnote.

Maslow, of course, was concerned with psychology, and his main point is well-taken, that science is too often centered on the means whereby something is studied, and the problem itself may be given short shrift for this reason. Thus, because physics uses certain kinds of mathematics to solve problems, other fields try to mimic the mathematical fireworks. Physics attempts to avoid teleological interpretations in its theories, because such interpretations are contaminated by the projection of human desires, etc. But psychology is about motives, desires, and purpose. In that way it is teleological at its core. Any attempt to avoid interpretations of motive, desire, and purpose make psychology into something other than what it is.

As it happens, I tend to get a little distracted by something that falls to the wayside. When it was all potions and funny smells, science was centered on chemistry. With the rise of the status of physics, chemistry lost status. And there I was, naturally attracted to chemistry.

Still, tastes and conventions change. The image of the heroic physicist has waned, particle accelerators have become prohibitively expensive (and what have they done for us lately, anyway?) and now biochemistry and genetic engineering have become the new magic wands, all the way to taking over the retconned origin of Spider-Man. And the most visible image of science in popular culture is the crime lab technician.

By the way, the author of the “physics and stamp collecting” quote was Earnest Rutherford. Who won the Nobel Prize in Chemistry.

PAN

PAN is fascinating stuff if you’re an air geek, and it’s maybe interesting to other sort of people. PAN is the acronym of peroxyacetyl nitrate. It’s got two parts to it, peroxyacetyl:

CH3CO-OO*

And nitrogen dioxide:

-NO2

The asterisk (*) on the peroxyacetyl is one of the conventions used for indicating that it is a radical; it has an unpaired electron that plays well with others, especially if they also have an unpaired electron.

Now a bit of history, in an attempt to lose anyone that I haven’t already lost with the chemical formulae.

Los Angeles was known to have a smog problem even before WWII, but during and after the war it got much worse, partly because of the massive expansion of oil refineries, and the attendant expansion of automobile travel. L.A. smog was known to be different from “London smog,” in that the L.A. sort was oxidizing, and London’s was reducing. Ozone was identified as a major component of L.A. smog, but the ozone alone couldn’t account for “plant bronzing,” damage with a characteristic yellow-brown splotches on the leaves of plants. A guy by the name of Haagen-Smit (mentioned in a magical incantation in SunSmoke), managed to replicate the plant damage by using the product of some smog chamber reactions, but could not identify the compound that was responsible.

Some researchers at the Franklin Institute in Philadelphia (Stevens, Hanst, Doerr, and Scott), used a technique called long-path infrared spectroscopy on smog chamber products and spotted a set of IR bands that were particularly strong in the results of a biacetyl-NOx run. They dubbed the responsible agent, “Compound X.” Compound X turned out to be PAN, and how cool is that?

In the mid-1970s, PAN was discovered to thermally decompose, i.e. at elevated temperatures, it rapidly changed back to a peroxyacetyl radical and nitrogen dioxide. That made everything much more interesting, because PAN gets formed early in the day, when it’s cooler, then, as the air warms, it can decompose and feed radicals and NOx back into the smog formation system, producing more ozone. The thermal behavior of PAN is one of the reasons why smog is worse on hot days. PAN can also assist in the long range transport of oxidizing smog, serving as sort of an ozone storage system.

The thing is that PAN and its constituents/products form a steady-state at constant temperature, with PAN existing in balance with peroxyacetyl and NO2. Change the temperature and the balance changes. At higher temperatures, PAN decays and if there is still sunlight around, ozone goes up. But this process is dominated by the behavior of peroxyacetyl radicals.

If NO2 were the only thing that peroxyacetyl could react with, this wouldn’t happen. But peroxyacetyl also reacts with nitric oxide (NO), and that is one of the reactions whereby ozone is generated, by converting NO to NO2, which then photolyzes to ozone (note: the entire system is ‘way complicated, which is why I spent 20 years studying it). By the same token, if something reduces the amount of peroxyacetyl, relative to other peroxy radicals, then PAN concentrations decline, NO2 comes back into the system, and ozone can increase.

Peroxyacetyl radicals also react with other radicals, and that alters the balance. In the early 1980s, looking over the set of chemical reactions we had available, I decided that the cross-reactions between radicals were set too low. Fortunately, there was a paper by a fellow named Addison that had measured them higher that the generally accepted values, so I used Addison’s numbers. I can still remember the combination of excitement and satisfaction that came when Addison’s numbers led to a simulation that just nailed the PAN decay data. Since then, rate constants have been measured that are even higher than Addison’s; when I used the new, higher still numbers, the results was almost exactly the same. There seems to be a point of diminishing returns, a gating function, call it what you will. Once you get above the critical numbers, there is little additional effect.

So even without my own insights into PAN decay, mostly the result of my paying attention to that particular problem, it would only have been a few years until the problem was solved by better measurements, and correct PAN decay would have been achieved in simulations anyway.

On the other hand, there were several features of the system, such as the specific products of some of the radical-radical reactions that have not been addressed to this very day, to the best of my knowledge, and, nearly as I can tell, no one is looking at those problems and no progress is being made. Sometimes the great grinding engines get it and sometimes they don’t. There’s room for a ton of lessons here, I’m just not sure what they all are.

The Linear Hypothesis

One of the many problems with using "animal models" for estimating human health effects of exposure to various toxins, radiation, etc., is that most animals are short-lived, so the effects of chronic exposure to low levels of the toxin of interest does not become apparent during the animal's lifetime. The method generally used to try to get around this problem is to boost the dosage, which is assumed to shorten the "induction period" of disease progression in a more-or-less linear fashion. The idea is that doubling the dosage will halve the time it takes to get a response, more or less.

That is a pretty kludgy method, of course, but all the methods are pretty kludgy. Using longer-lived animals also has problems, not least being that you have to wait much longer for results. Moreover, the lower the general exposure, the fewer responses you are likely to get, statistically speaking, so the use of realistic exposures and exposure times becomes prohibitively expensive. Also, longer-lived animals tend to be more "charismatic" in the sense that people like them more and animal rights activists pay them more attention, sometimes to the detriment of the researchers.

For the purposes of this little essay, I'm going to use radiation as the example, mostly because there are so many places to get information on the radiation/cancer debate, but also because the chemical/cancer debate gets even more arcane in spots, and I'm doing a once-over-lightly here.

The main alternative to the "linear hypothesis" is the "threshold hypothesis," the idea that a toxin or radiation does not overwhelm the body's cellular defenses until it gets above a certain level, or threshold. There are clearly many, many cases where such thresholds exist; "the dose makes the poison" as Paracelsus claimed, and there are few things that don't become poisonous at a high enough concentration.

There is a variation of the threshold hypothesis, which is called the "hormesis model." This is a somewhat more extreme version of the threshold model, and postulates that low doses of radiation are good for you. This isn't an entirely loopy suggestion; after all, radiation is used to treat some kinds of cancer, because cancer cells are more susceptible to dying from radiation than most body cells. It does, however, contain echoes of the early days of radiation, when things like radium were used as "invigorating" tonics, and that didn't work out well.

There are a variety of arguments and observations made to support both alternatives to the linear model. One of my favorite involves studies that create biological systems that lack the naturally occurring radioisotope potassium-40 and include only potassium-39. This apparently leads to birth defects. However, a high concentration of deuterium in the body (i.e. biological systems using heavy water) also produces severe-to-lethal effects, with no radiation involvement whatsoever. It's not out of the question to suggest that our bodies' enzymes are "tuned" to a particular isotopic weight of the elements involved, and that even relatively small changes in these elements can cause problems. To the best of my knowledge, the potassium isotope experiment has never been performed with some external source substituting for the missing radiation. The result would need to be normal development, obviously, for hormesis to be validated.

Other observations that seem to support various versions of threshold or hormesis include epidemiology in areas of high natural background radiation, which seem to show no excess cancers. Again, matters of the adaptation of local populations, questions of whether or not differences in infant mortality create a "harvesting effect" (where susceptible individuals die before they reach the age where cancers would present), or even simple things like actually getting the exposure levels correctly measured, become important. I've seen claims that the linear hypothesis cannot explain the epidemiology of the Japanese atom bomb survivors, for example, but I know for a fact that the actual radiation exposure to these individuals is a matter of estimation and guesswork, so the "failure" may simply be a matter of not knowing what the true exposure was.

Then there is the fact that when we talk of "radiation" we're not talking about a unitary subject. There are many different kinds of radiation, and many different ways of being exposed to it. These "hypotheses" and "models" that we are talking about are just that: models. A lot of different phenomena are being compressed onto a single, seemingly authoritative graph, but the real, underlying situation is complex and complicated. It's entirely possible that some forms of radiation show some hormesis effect, while others are linear, with no safe levels. The science necessary to make these distinctions is lacking.

Ultimately, however, these models are not some abstract scientific question, but rather, they are used to sort out issues of regulatory policy. And there is where the rubber meets the road. Advocates of threshold and hormesis models are invariably proponents of nuclear power (the reverse is not necessarily true, since there are nuclear power advocates to have no problem with the linearity regulations). There are claims that the public is "radiophobic," which may be true, but then again, that is the public's right. It is not as if there has been a consistent policy of telling the public the truth about these matters, and people tend to get a bit antsy when they know they've been lied to.

Ultimately, the linear hypothesis is the easiest to administer and produces the most clear-cut regulatory framework. It is conservative. Threshold standards tend to create situations where pollutant releases go right up to the threshold and bump against the standard, usually exceeding it from time to time. Linear standards say, "Reduce your impact to the lowest possible level." I find this to be a useful first (and usually second and third) approximation to regulation. But then I am what used to be called a conservative.

On Faith

The online world is a lot like college dorm bull sessions, with a lot of outrageous opinions being expressed, sometimes simply because they are outrageous. Add in the fact that a lot of the discourse is contributed by anonymous or semi-anonymous individuals, and it’s a recipe for a free-for-all.

The upside of that is that it provides cover for “dangerous ideas.” Now some of those aren’t really dangerous at all. I can’t think of anyone who has been sent to jail for being “politically incorrect” in the common usage of that term, though there are plenty who pat themselves on the back for being so “daring” as to express blatantly racist or misogynistic sentiments (usually anonymously) . On Bill Maher’s TV show(s) “Politically Incorrect”, all manner of things were given a pass; then Maher agreed with Dinesh D’Sousa that it might be less cowardly to fly a plane into a building than launch cruise missiles at 500 miles, and huh, that turned out to be incorrect politically. Who would have guessed?

Similarly, hate speech is rarely dangerous to the speaker. The danger is directed elsewhere.

Nevertheless, the overall turbulence of discussion allows some ideas to be expressed more forthrightly than when public discourse is filtered through conventional outlets. That, plus the fact that there are religious wars (both hot and cold) going on, has led to a good many atheists coming out of the closet.

I’m a pretty dovish atheist. I tend to look on religion as one of many rationalizations that people use to justify elevating their own gut feelings and prejudices to the level of absolute philosophy. I’ve found plenty of libertarians who are just as fundamentalist, utopian, and dogmatic as any bible thumper of my childhood, and plenty of communists to pair them up against. Philosophy, of whatever flavor, is more a rationalization than a rationale.

Still, it’s refreshing to see some unapologetic atheists writing about what they find obnoxious about faith. That’s particularly true about atheists who are also scientists, since it’s so often the case that scientists make a big deal about science not being incompatible with religion, etc. I mean, I understand, the apologetics; scientists have to live in the world, and it can get tiresome explaining to people that, no, not believing in God doesn’t automatically send you on a rape, murder, and pillage spree, but if that’s all that’s keeping you from doing that, then, please, by all means, continue to believe in God. More to the point, many scientists are religious, either conventionally or unconventionally. Sometimes it even affects their science, usually, but not always, detrimentally.

That leads to one argument that, contrarian that I am, I will take some issue with, and that is the assertion that there is no place for faith in rational discourse. I could mention The Prisoner’s Dilemma in this context, but that’s a bit of a cheat; one solution to TPD is often called faith, but it’s actually more like commitment. You choose not to defect (with the expectation that the other prisoner will also so choose) because you are committed to them, or to whatever it is that binds you, or even your own sense of integrity. Noble sentiments, but not necessarily dependent on faith.

No, I’m going to say just a little about interpretations of quantum mechanics.

There are really two major interpretations of QM. One, the dominant view, is the so-called “Copenhagen Interpretation.” This holds that a “mixed wave state” can exist until a “measurement” is made of it, at which point the wave function “collapses” to a localized quantum event. This interpretation led to the Einstein-Poldalsky-Rosen experiment and the unpleasant concept of “spooky action at a distance,” that so intrigues quantum mystics. The “wave function collapse” that happens in an EPR type experiment seems to operate faster than light, and that has led to all sorts of sci-fi speculation about how to use it for space travel, time travel, or what-have-you.

The wave collapse is hardly the only effect in physics that has FTL properties; the best known is “phase velocity” that occurs in a traveling wave tube. You can also get superluminal velocities from the moving spot on a cathode ray tube for similar reasons: they are illusions that do not carry information. Point at the sun. Now point at the moon. What you are pointing at has just moved faster than light. But that “what” has changed, hasn’t it?

The “Many Worlds” interpretation of quantum mechanics, first advanced by Hugh Everett III, does not suffer from the confusion between real and virtual events, at least not in the FTL sense. I’ve read the original paper. It’s not actually very technical, in the sense that there isn’t much mathematical jiggery pokery in it. The basic concept is fairly simple. Everett just decided to ignore the “wave function collapse.” Wave functions split at every quantum event, but none of them ever vanish, they become “uncorrelated” with other wave sets. So how does one then interpret an EPR experiment, in which a paired particle set is separated and one quantum characteristic (often spin) is measured at a distance, thereby assuring what the other particle’s spin is? Simple, by measuring one particle’s spin, you have determined what “path” you take if you wish to confirm the other particle’s spin. You can only take a path to the one that is correlated with your measurement. The complementary spin still exists for the “split” version of the other particle, you just can’t get to it because you’re “uncorrelated” with it.

Of course, the existence of the other particle cannot be tested in any way. You just have to take it on faith. That’s the same faith that you must have in the “wave function collapse,” if you are following the Copenhagen Interpretation.

Some people hate the many worlds interpretation though. I was once on a panel with Larry Niven, who is one of those who dislike the MWI and I asked him why. His replay was, “Because I sweat over my decisions, and I resent the idea that I could just as easily have decided the other way.”

Food for thought, and I’m not embarrassed that I didn’t have a ready reply. But I do have a reply now: The guy who made the other decision isn’t you. It wasn’t all arbitrary. By making a decision, you literally create a new and different universe for yourself and those around you. How can you resent something like that? You’re playing God.

Larry’s story expressing his view is the title story in All the Myriad Ways.

One of mine is my story Shiva. Another is Aphrodite's Children. That one is a prequel to Dark Underbelly and Blood Relations. Anyone following those will notice that I've formulated an entire religion based on this quantum interpretation thing. You can take it seriously, or as an amusing SF construct. Either way, it creates new universes, by my way of thinking.

Thinking Outside the Box

I spent a number of years developing what is called a “three-dimensional Eulerian photochemical grid model,” aka the “Urban Airshed Model.” I was one among many, of course, but I did make some significant contributions to the effort.

The “three-dimensional” part of the name says that a volume was divided up into a lot of compartments, “grid cells” in the jargon, and the “Eulerian” part says that the grid didn’t move around, although there was a bit of cheating on that one in that the top of the modeling region rose with the “mixing layer” in some versions of the model. The alternative to “Eulerian” is “Lagrangian” where the model volume itself moves around, usually with the fluid flow, which is to say, the wind. That’s a “trajectory model” and it usually had only a single box, although we developed some multi-box trajectory models to handle plumes like those from power plants. A single line of boxes is “one-dimensional;” a “moving wall” of boxes is “two-dimensional.” A single box, therefore, is “zero-dimensional.”

So-called “box models” are common in air pollution, and other areas of environmental modeling. They can be really simple, especially if you are dealing with pollutants that don’t react. Then all you have to do is have a source input for emissions, a “ventilation rate” for the combination of wind and diffusion that’s removing material from your box, and boundary conditions for what kind of air is replacing what’s in the box. This is the sort of model that you get on first year chemistry or physics courses; it can be expressed in a single differential equation.

You can make the box pretty big, too, provided you’re willing to take these big honking averages of everything. For either non-reactive or “first-order” (those that just decay all by themselves, without reacting with other things) pollutants, your average result for the single box calculation is the same as if you’d done the multi-box calculation and then averaged all the boxes. That’s what’s called “linear” in the biz.

I did a lot of work with box models, partly because it was easy to test chemical mechanisms with them, and the results are easy to understand also. And I got to thinking about that “ventilation rate.” And wind power.

See, if you extract energy from the wind, it slows down, and that will have an impact on the ventilation rate of any area whose air is passing by the windmills. So I did some box model calculations on the amount of energy that was being extracted from the wind at Altamont Pass near San Francisco, plus the degree of pollution that was in the air that went through the Pass. That allowed an estimate of the increase in air pollutants that would occur in San Francisco due to the decrease in ventilation.

Okay, it was a weird calculation to make in the first place, but the results weren’t that deranged. There was an effect, the largest of which was equivalent to the amount of nitrogen oxides that would have had to be emitted in order to generate the excess of ozone seen at the pass. On a per kilowatt basis, it turned out to be a little less than the amount of nitrogen oxides that would be emitted by a natural gas-fired plant, such plants being the cleanest of all fossil fueled power plants. Of course the result depended on the amount of pollution already in San Francisco; a totally clean area would see no pollution equivalent at all, and since I made those calculations, SF has reduced pollutant levels.

I wrote up my results, sent the paper off to a journal, and then received some of the most flagrantly wrong referee comments I’ve ever received on a paper. One of them showed that I was “wrong” with a calculation that was itself off by five orders of magnitude, assuming, among other things, that wind speeds are constant all the way up to the stratosphere. I think he managed to calculate the wind kinetic energy over the entire Bay Area also, rather than just through the Pass.

Well, I know when I’m licked, and it was obvious that I wasn’t going to get anyone to pay attention to that wacky idea. Even in science, sometimes I’m too clever by half, and that’s a rueful comment, not a brag.

Taking Your Lumps

Let’s suppose you want to look at how some chemical compounds react in the atmosphere. We’ll start with butane, a pretty simple hydrocarbon, C4H10, or to give more insight into its structure, CH3CH2CH2CH3. In chem speak, that’s a methyl group (CH3) attached to a two carbon alkyl chain (CH2CH2), terminated by another methyl group. The methyl group is called “primary carbon” because it’s connected to a single other carbon atom, while the CH2 groups are “secondary carbon.”

Now suppose you have a bunch of butane molecules flying around in the air, and the air also has some hydroxyl radicals (HO) in it. Every now and then, in accordance with the laws of statistical mechanics, one of the HOs will hit a butane molecule. Then what?

Well, most of the time, they just bounce right off each other. The hydroxyl is pretty reactive, radicals often are, but unless it hits the electron cloud of the butane in the right spot, with the right energy, etc., it’s just going to bounce. But every so often, it does hit right, and it grabs one of the hydrogens. Which one?

Well again, it will be the one it hit, but some of the hydrogens are more labile than others, so the HO is more likely to bounce if it hits one of the methyl groups, which have “primary” hydrogens because they are on primary carbons, and more likely to react if it hits the alkyl chain, on a “secondary” hydrogen.

Butane is nice and symmetrical, so there are only two possible outcomes. Due to symmetry, any primary hydrogen reaction looks like every other primary hydrogen reaction, and every secondary looks like every other secondary reaction. The hydroxyl always extracts a single hydrogen from the butane, which gives water, and an alkyl radical that immediately reacts with oxygen, and under smog conditions goes through a series of reactions that lead to either buteraldehyde, if the primary carbon was involved, or methyl ethyl ketone (MEK) if the secondary carbon was involved. (Actually, I’m ignoring some other pathways that get more important as molecular weight increases, like the formation of alkyl nitrates, and the times when the molecule fractures in the middle to produce acetaldehyde and an ethyl alkoxy radical. Having read that sentence, I’m sure you can appreciate my ignoring some details).

We can write a bunch of reactions for all this, assign rate constants to the reactions, put in temperature and pressure dependencies, etc. but the thing I want to point out is this: we’re simplifying a lot of events into a small set of descriptive equations. All the bounces are ignored, except insofar as they affect the reaction rate constant. All the different ways the molecules hit each other, along with the different energies of those collisions, all lumped into a few basic equations. We’re also taking advantage of the symmetries, by saying that reactions at either end carbon are equivalent, which they are, unless we had some way of telling the difference, like if one end or the other was isotope tagged.

Anyway, we’ve put all these things together and called them “reactions of the molecule.” That’s what chemistry does.

Now suppose we want to study the reactions of a number of different molecules, say add some pentane, hexane, heptane, and octane to the mix, and put in all the possible isomers of those compounds as well (there’s only one other isomer of butane, called isobutane, but toss in some of that as well). Now, how would you write your chemical equations?

You could try to write the equations for every single molecule—provided you wanted to go crazy, blow your computing budget, and not have the rate constants for even a tenth of what you wanted. You’re going to have to estimate that last one anyway, of course, though you might cheat and get some empirical data describing the reactivity of your mix.

You could look at what you have in the way of a mix and try to come up with some idea of an “average molecule.” That can get a little strange, because you’re going to have equations that account for some fraction of a carbon, for instance, and averaging rate constants is pretty iffy anyway. The fast reacting compounds will react away most quickly, so the “average” rate constant is going to keep changing. Nevertheless, you can do it, either as a constant average rate or as a continually changing average rate. It’s been done, though most often as a constant rate.

You could take your mix and wave your hands a little bit and say that it should look like some other, simpler mix, 45% butane and 55% octane, maybe. Of something like that.

The first one of these has come to be called the “explicit mechanism” approach. The second is the “lumped parameter” method. The third is a “surrogate mechanism” which is an explicit mechanism that is used on a reduced number of “surrogate compounds” to represent a more complex mixture.

All have been used in smog chemistry models, and all have their limitations. The mechanism that I first encountered was a lumped parameter mechanism called the Hecht-Seinfeld-Dodge mechanism. At that time I was coding what is called a Lagrangian Trajectory model version of the more elaborate Eulerian Grid model that had been developed by the research/consulting firm that employed me, then named Systems Applications Inc. One of my tasks was to code up and test the HSD mechanism in the simpler model.

At the same time, Gary Whitten (later to be my boss, because he was the only one who was willing to have me in his group, me being the charmer that I am) was attempting to use the HSD mechanism in an atmospheric application. He quickly ran into the problem that he had no idea what the “average molecular weight” of an average atmospheric hydrocarbon was, and there were parameters in the mechanism that depended upon that average.

What he did have was what are called “flame ionization detector” measurements of total reactive hydrocarbon, “as carbon.” In other words, he knew about how many carbon atoms there were, just not how many molecules they comprised. There were also a few gas chromatograph measurements that could be used to estimate the molar fractions of olefins (there were no real mechanisms for aromatic hydrocarbons at that time), but the breakdown of the alkyl hydrocarbons just wasn’t there.

Then he had an idea. I still think it was brilliant.

It turns out that the reactivity of an alkyl hydrocarbon (like butane, pentane, hexane, et. al.) goes up with increasing molecular weight, primarily because there are more carbon groups. In fact, the reactivity of any given primary, secondary, or tertiary carbon group is largely constant from one hydrocarbon to another, and if you normalize the reactivity by carbon atom, it’s reasonably close (within 20-40%) to constant. (This neglects the very lightest hydrocarbons, methane, ethane, and propane, because they are anomalously unreactive, but that also means that you can ignore them, mostly).

So Whitten devised a mechanism that ignored the idea of molecules for alkyl carbon. Instead it treated each carbon atom as a single “reactive structure” and did all the chemistry from there. He called it the “Carbon Bond Mechanism,” and its descendants are still the primary photochemical air quality chemical mechanisms used in air quality management in the U.S. (and elsewhere).

It wasn’t my idea, but I took to it like a duck to water. (So much so, in fact, that some people wound up thinking it had been my idea in the first place, something I later recognized as “ageist” since I was the young ‘un of the team. So I always tried to make sure everyone knew it was Gary’s eureka moment). The CBM had exactly the sort of “thinking around the corners” style that I love. And, it was practical. It made everything easier, emissions inventories, comparisons to air quality data, coding the mechanism. It’s actually a bit difficult to conduct “mechanism comparison studies” among other kinds of kinetic mechanisms in the U.S. because practically every emissions inventory is in the form used by CBM, and a fair amount of the differences between mechanisms is how they treat the emissions inventories.

Over the next few years, we devised a lot of twiddles to make the edges work, like an “operator species” that took intra-molecular reactions (like chain breaking) into account. We also extended the mechanism to include aromatic hydrocarbons, and biogenics such as isoprene and terpenes; those wound up being closer to explicit/surrogate mechanisms. I also came up with a cute trick that involved treating very reactive olefins as if they’d already reacted to their carbonyl containing products (aldehydes and ketones) because they reacted so quickly that their products were more important than the original compound. Not to get too egomaniacal, but it was all very cool.

Now let’s take this up a few levels of abstraction.

If you’ve managed to get through all this technical verbiage, one thing you might have noticed is that this sounds more than a little bit like engineering. We were designing a kinetic mechanism, for particular purposes, based on the resources (time, knowledge, computing power) that we had. Our goal was the construction of an atmospheric chemical kinetics simulation model, a tool that could be used for both scientific and air quality management purposes. If science is devoted to the acquisition of knowledge, what do you call something that assists in environmental management? Again, a lot like engineering.

Science operates on the model of “objective reality” and scientists like to think of themselves as dealing with that reality in an impersonal way. You can see that in the way that scientific papers are written, frequently in passive voice, rarely with individual actions described, and even more rarely as anything where the “arbitrary” is even acknowledged. The idea of choices is largely absent, because choices are the product of subjective individuals.

Art, on the other hand, glories in the subjective, the experiential. Choice is part of its very nature. Art is personal, and artists have no problem with the idea that their ego is involved. That’s part of the point of it. But it’s still often the case that some artistic element “has to be that way.” The artist feels like there is no choice in the matter, because making a different choice will lead to inferior, or even bad, art.

I’ve had careers in both science and art, and for a long while I thought that the art was for personal expression and the science was for the satisfaction of my curiosity about an objective world that was entirely independent of myself. I also had the notion that engineering was where the two met, where one applied the objective knowledge of science in service of the subjective needs of human beings, and those needs included the application of artistic principles to engineering, and engineering principles to art.

It’s a good line of patter, and there’s some truth to it, but as time goes on, I see more and more holes in it. For one thing, while art may be personal and expressive, it’s often pretty generic, and it starts looking a lot like other art. No one else would have written Book of Shadows, but if I hadn’t, there might very well have been another novel of “heroic fantasy,” in that publishing slot, and many of the same people might have read it and taken the same enjoyment from it. SunSmoke is a lot less interchangeable, in my view, but that is not necessarily obvious to the reader. I myself tend toward the idiosyncratic both as writer and reader, but most fiction, most art, is average; that’s what average means. And some proportion of popular entertainment is largely interchangeable with its near equivalents.

One the other hand, a great deal of science is more idiosyncratic, less objective, more personal than most scientists would admit. What is studied, how it’s studied, what sorts of theories and models are created, what sort of notation is used, all of that betrays the human face staring at the instruments, drawing the conclusions, writing up the results. Someone has to want to know the answer to the question that is being asked. Science is a human construct, no less than any other human construct, and to deny it is to deny both one’s self, and the truth.

Objective

After we came out of the church, we stood talking for some time together of Bishop Berkeley's ingenious sophistry to prove the nonexistence of matter, and that every thing in the universe is merely ideal. I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I never shall forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it -- "I refute it thus." -- Boswell’s The Life of Samuel Johnson

“Reality is that which, when you stop believing in it, doesn't go away.” -- Philip K. Dick

In Stranger in a Strange Land Jubal Harshaw, as a demonstration, asks one of his secretaries the color of a neighbor’s house. She answers “It’s white on this side.” The idea was that she was a “Fair Witness,” a person with special training who didn’t make assumptions about her observations, so her testimony was given special credence in a court of law.

Sometime when I was in grade school, living on Ironwood Drive in Donelson, Tennessee, I was witness to an unusual atmospheric phenomenon. There was a very low cloud overhead; I think it may have been a contrail cloud from the relatively nearby airport, because the cloud was long and narrow. It was otherwise clear, and near sunset.

We all know how vivid the sunset can be in the last few minutes of light. This cloud picked up the neon pink of the last rays of sun, but it was close. The whole neighborhood lit up with that light. My hair became red; my skin looked dark and sunburned. Our house glowed electric pink.

Our house was actually encased in white asbestos shingles. But for a few moments it was pink—at least on the side that I could see. Truth to tell, though, for me to say that it would have also looked pink on the sides I couldn’t see would have involved fewer assumptions than Heinlein’s “Fair Witness,” was making.

Is this a cheap shot at Heinlein’s expense? I hope not. I’ve seen climate researchers Spenser and Christy refer to their satellite microwave measurements as “direct observations” of atmospheric temperatures, when they most assuredly are not, given that there have been over half a dozen “corrections” to their estimates since they were first published. They are hardly alone is this sort of scientific conceit; I’ve heard such claims many times over the years, as well as researchers referring to various chemical rate parameters (often photolysis rates) as being derived from “first principles,” another nigh onto meaningless phrase used to cloak a welter of assumptions and models of reality.

“What is reality?” appears in a Firesign Theater record as part of a series of audience heckles, and that’s what it often feels like. What we have to work with is subjective experience, which is then denigrated to “mere” subjective experience. In Zen and the Art of Motorcycle Maintenance Pirsig has a nice long exposition on why words like “just,” “merely,” and “only” are out of place in any descriptions of objective reality, including science. They are indicators of a sneaky, subjective value judgment that someone is trying to slip into the mix. Chemistry isn’t merely very complicated physics. Chemistry is very complicated physics. The second sentence reads differently, doesn’t it?

We have a number of tried-and-true methods of “factualizing” subjective experience and most of them have to do with repeated observations, especially different kinds of observations. We believe in the “reality” of a rose because we can see it, touch it, smell it, taste it, and even hear it if it is moving through the air. Things that register on all the senses are commonly thought to be “more real” than something that can only be seen, such as a rainbow.

Objects also are given greater claim to objective reality if they persist, since persistence is one of the ways a single observer can make multiple observations. Objects made of matter have greater weight because they have weight, which persists, and can be felt.

Science takes everyday observations of reality and gathers them together into grand theoretical constructs, like Universal Gravitation, the Standard Model, and Evolution by Natural Selection. Scientific theories make sense of the world, allowing us to make predictions, or construct gizmos (in the largest sense) that give us power over the material and immaterial worlds. As Lester del Rey once said, “Mysticism has been around for millennia, science for only centuries. Science is ahead.”

The danger is in forgetting that our ideas about reality are themselves constructs. We believe that there is a reality, but no one has it on a leash, and no one speaks for it. The danger itself factualizes when someone projects their own subjective needs, fears, and desires upon that construct, making it yet another servant to the unconscious mind. We’re all guilty of that to some extent; paradoxically, it’s the ones who claim to most serve “reality” who are most likely to make their own ideas into yet another simulacrum of God. Then just crank up the dial to eleven, ‘cause it’s time for another episode of Monsters from the Id.

Lunacy

During my first Aikido involvement, I used to repair to a bar in Berkeley after training, to, um, replenish body fluids I’d lost from the exercise. Yeah, that’s the ticket.

The bar, Shattuck Avenue Spats, had two entrances, one in the front, the other leading out back to the parking lot. One evening I left by the back entrance and was confronted by a full moon in full “horizon effect,” its image close to the tops of the nearby buildings and looking close enough to reach out an touch.

I stopped dead in my tracks for several seconds, just marveling at it. Then, I noticed what I had just done and got curious.

I went over and got into my car, but I just sat there for another 15 minutes or so, watching people as they came out of the bar. Many of them stopped, just like I did, and gazed at the moon for a second. Others pointed it out to their companions. A few became very animated, even to the point of doing a little dance, or otherwise expressing physical excitement.

There have been a fair number of studies attempting to document the “full moon effect,” the notion that crimes get weirder, emergency rooms more crowded, and things generally just get stranger, around the time of the full moon. To the best of my knowledge, none of these studies has ever found a relationship between the full moon and abnormal behavior.

By the same token, and to the best of my knowledge, these studies never correct for whether or not the moon is actually visible on the nights in question. No one has tested the idea that it is the sight of the full moon that affects people, in other words.

Yet the sight of the full moon clearly does affect people. Songs have been written about it; it appears in art and literature.

This seems to be part of that unconscious, social bias in science that I’ve mentioned before. Certain hypotheses are more easily addressed than others. The bias extends to pseudo-science as well. People have a lot of water; the oceans are water; the moon affects the oceans by raising tides. Maybe the moon affects people the same way. That’s considered an acceptable hypothesis to test (and debunk).

The moon affects people through aesthetic influence does not seem to be a readily acceptable hypothesis. It’s subjective. Science is objective; it doesn’t like being reminded of the subjective.

It’s a blind spot, a lacuna. Rhymes with Luna.

Albedo

A strange alleyway, just off of memory lane.

Q. Why does wet sand look darker than dry sand?
A. Reflects less light."
---Answer Dept., THE GRAB BAG, San Francisco Chronicle, April 26, 1992.

And aren't we glad that that's been explained?

The word "albedo" refers to the amount of light that a surface reflects. When it reflects different colors by differing amounts, we get various colors.

Fresh snow has an albedo of about 0.7, indicating that it reflects about 70% of the light it receives. Carbon black reflects only about 3% light, and that is close to a lower limit for flat surfaces. Special "black body" measurements are made by looking at the opening of dark cavities, like the mouth of a cave is darker than any surface.

Of the planets, Venus is the clear winner in the albedo sweepstakes, with a 76% reflectivity. Despite what it might seem on a night with a full moon, Luna is quite dark, with an average albedo of only 0.07, close to that of Mercury, which is easily the darkest planet. There are a number of objects even darker still, mostly carbonaceous chondrite asteroids, or planetary moons which may be captured asteroids, like Phobos and Deimos, the moons of Mars. It's not easy to measure the reflectivity of very dark objects, but the carbonaceous bodies have albedos as low as 0.04.

ALBEDO OF VARIOUS BODIES

• MERCURY: 0.06
• VENUS: 0.76
• EARTH: 0.29
• LUNA: 0.07
• MARS: 0.16
• PHOBOS: 0.05
• DEIMOS: 0.05
• ASTEROIDS: (0.04-0.5)
• JUPITER: 0.34
• IO: 0.6
• EUROPA: 0.65
• GANYMEDE: 0.45
• CALLISTO: 0.18
• SATURN: 0.33
• MIMAS : 0.7
• ENCLADUS: >1
• TETHYS: 0.8
• DIONE: 0.5
• RHEA: 0.6
• TITAN: 0.2
• IAPETUS (leading side): 0.05
• (trailing side): 0.5
• URANUS: 0.34-0.5
• MIRANDA: 0.34
• ARIEL: 0.4
• UMBRIEL: 0.19
• TITANIA: 0.28
• OBERON: 0.24
• NEPTUNE: 0.34-0.5
• TRITON: 0.7-0.9
• PLUTO/CHARON: 0.5

Although the 0.76 albedo of Venus is very bright, it's still not the most reflective body in the solar system. That honor belongs to Enceladus, the second large moon of Saturn, which has an "visible geometric albedo of greater than 1 (some observations make it as high as 1.4).

Like another moon of Saturn, Mimas, Enceladus is mostly water, with perhaps as much as 40 percent of the mass being silicate, including a small rocky core. The interior temperature is quite warm for an icy moon, perhaps due to tidal forcing from Dione, which is much denser, and has a resonant orbital period twice that of Enceladus.

It's pretty obvious that the high albedo of Enceladus is due to anisotropic backscattering, light being reflected back towards it origin preferentially. Since the light comes from the Sun, and since, from Enceladus' point of view, the Earth is always near the Sun, the Earth always gets more light reflected from Enceladus. Even so, the ice on Enceladus' surface must be very clean, although there have been some suggestions (based on spectroscopy) that there is some ammonia mixed in with it. But there is active vulcanism seen on Enceladus, which suggests that the surface is undergoing constant refreshing.

The surface of Enceladus shows evidence of an active geological history. There are six types of terrain ranging from heavily cratered plains to craterless grooved terrain that is similar to the sulci of Ganymede. The sulci terrain features are on the trailing hemisphere of Enceladus, leading to the suggestion that they have been protected from bombardment by the bulk of the moon as it encountered debris in its synchronous orbit.

Saturn's E ring shows a brightness peak along the orbit of Enceladus, and may consist mainly of ice crystals which would escape from the weak gravity of Enceladus when meteors impact the surface or when some other factor causes water to outgas from the interior. If this is true, then the E ring is similar in origin to the "plasma torus" of Io, another moon that is warmed by tidal forcing.

Enceladus is the second classical moon of Saturn, named by Sir John Hershel after a giant in Greek mythology who figured in a revolt against the gods. Son of Tartarus and Gaea, Enceladus had a hundred arms and was so strong that Athene was forced to bury him beneath Mt. Aetna, and his occasional movements were held to be the source of the volcanic earth tremors that move Sicily. The surface features of Enceladus are by convention named after characters in Sir Richard Burton's "The Thousand Nights and a Night."

The Scientific Method

In my experience and observation, what’s sometimes taught in schools as “The Scientific Method” if fairly rare in the actual practice of science. But I’m going to brag a little about a time when I did get to go through the thing pretty much in the prescribed manner (from the Wikipedia entry on Scientific Method):

• Define the question
• Gather information and resources
• Form hypothesis
• Perform experiment and collect data
• Analyze data
• Interpret data and draw conclusions that serve as a starting point for new hypotheses
• Publish results
  

The question we were working on was the photooxidation of toluene (used as a solvent and a component of gasoline) in photochemical smog. It’s a moderately complicated molecule, a benzene ring with a methyl group replacing a hydrogen, and somewhere in its oxidation process, we knew that the ring had to open, and, well, then what?

What I brought to the problem was systems theory and a familiarity with simulation modeling, something that the previous generation of smog researchers had only intermittently. In articular, I was concentrating on the mass flows in the system, which you’d think that chemists would do as a matter of course, but no, they didn’t. In fact, in most generalized photochemical mechanisms that I analyzed, it turned out they didn’t conserve carbon. In once case the non-conservation was so bad that it actually was an infinite carbon generator; the mechanism alone generated more hydrocarbons than did emissions!

So anyway, I was looking to see how toluene oxidized in the atmosphere. Now smog is basically a “slow burn,” with the “burning” mediated by what are called free radicals, in this case hydroxyl (HO), and peroxyl, the simplest being hydroperoxyl (HOO). The HO and peroxyl radicals cycle back and forth in the oxidation process, and one of the byproducts is ozone.

The source of the radicals is partly burned hydrocarbons: aldehydes, ketone, glyoxals, a lot of things having a carbonyl group (C=O) in them. Some of these are emitted by automobiles directly, but the smog process makes during its slow burn. These compounds are photolytic; the break down in the presence of UV light to form free radicals.

The smog process also consumes the primary “fuels,” hydrocarbons and nitrogen oxides (NOx), with the burn essentially ceasing when the system runs out of NOx.

What I was looking at was the “stoichiometry” of ozone formed as a ratio to NOx consumed. It varies with conditions, so I put “stoichiometry” in quotes. While running my numbers for various hydrocarbons, it became pretty clear that toluene produced much less ozone per unit of NOx than did other hydrocarbons.

Whitten had already gotten an ad hoc simulation mechanism for toluene by reacting it with a short-lived species nitrogen trioxide (NO3). We figured that the NO3 was reacting with some oxidation product of toluene, which wasn’t a very big leap, partly because the “ring-opened” compounds would have a lot of very active double bonds (C=C) that were known to react with NO3.

I’ll also mention that my systems analysis strongly suggested that toluene was producing something that photolyzed very rapidly to free radicals. That meant that toluene, if added to other hydrocarbons, would accelerate the oxidation process. But the above-average consumption of NOx should then terminate the reaction at a lower level of ozone than would occur from the other hydrocarbons.

We had an EPA contract that let us suggest smog chamber experiments to the University of North Carolina researchers who had a two-sided, outdoor smog chamber that was perfect for controlled experiments. So I suggested that they load one side of the chamber with a standard mix of NOx and propylene (or propene, or methyl ethane, which are different words for the same stuff), and the other side with the same mix, plus some toluene. I told them that it should form ozone more quickly in the morning but produce an ozone peak that was notably less than
the control side.

It’s been called a “daring prediction.” I don’t remember feeling that daring. It seemed pretty inevitable to me, and I would have been mightily surprised if it hadn’t worked. I’ll never know, because it worked exactly as I predicted.

There were other hydrocarbons known to suppress ozone formation. Some like reactive olefins, simply react directly with ozone, so if there’s enough of them around, they’ll destroy the ozone as it’s being formed. One of them, isoprene, produces some very bizarre looking ozone curves in smog chamber experiments, where the ozone first goes up, then down, then up again after the isoprene has all been destroyed, but while the partly oxidized products of the isoprene still can
continue to react. Continuing my brag, I was the first person to get those double peaks in simulations also.

Another class of hydrocarbons suppressed ozone formation by soaking up free radicals. One is called DEHA (diethylhydroxyamine, if memory serves), and it was touted as a smog palliative for a while, until it was shown to boost smog once its radical absorption property was used up.

What we’d done, however, was to show that there was a new class of compounds that could, under some conditions reduce ozone peaks. It wasn’t anything like a smog palliative, because toluene is nasty stuff, and the things it forms are nastier still. But scientifically, it was very cool research.

Later we published a brief communication on the two-sided experiment alone, and also a paper on our toluene photooxidation mechanism. I don’t think that all the products of toluene oxidation have been identified to this very day, but we got the main features of its mass balance and ozone formation behavior twenty years ago. As they say, it was good enough for smog research.

Central Limit

My sister gave me a book titled, The Black Swan (The Impact of the Highly Improbable), by Nassim Nicholas Taleb, whose previous book, Fooled by Randomness, was supposedly a bestseller. Taleb is a former Wall Street trader in derivatives, and he made a lot of money thereby, which, ironically enough, he claims is meaningless, a product of luck and a privileged position (and my readers would know that I agree with him on that one), but which nevertheless is almost certainly why he was given a book deal in the first place.

With similar irony, he spends substantial amounts of print in The Black Swan railing against the human tendency to substitute narrative for data, but, of course, the way he conveys his point is via life stories and anecdotes (some of which are fictional). He also insults the French a lot.

Well, golly, he certainly is "stimulating," by which I mean both wrongheaded and just plain wrong about many subjects that I find interesting. I'm not going to attempt a review of his book, because one simply does not try to swat flies in a barnyard, but I will use Mr. Taleb's book as an excuse to write about a few things that it reminds me to write about. One of them, (and god help you who are reading this) is the Central Limit Theorem (CLT).

Taleb writes quite a bit about statistics and their use and misuse, and I'd be there, dude, were it not for the part about his being severely wrong. Much of the time. Indeed, whenever I'm confronted with someone arguing about the use of statistics, I check to see if they have anything to say about the Central Limit Theorem, because that's were the muckup usually begins. Taleb, it's true, makes almost exactly the opposite error that's usually made, but it turns out that being against people who are wrong is not the perfect path to truth that one might hope it to be.

So here is what he says (note on page 325):

The notion of central limit: very misunderstood; it takes a long time to reach the central limit-so as we do not live in the asymptote, we've got problems. All various random variables (as we started [sic] in Chapter 16 [actually Chapter 15-JK] with a +1 or -1, which is called a Bernoulli draw) under summation (we did sum up the wins of the 40 tosses) become Gaussian. Summation is the key here, since we are considering the results of adding up the 40 steps, which is where the Gaussian, under the first and second central assumptions becomes what is called a "distribution." (A distribution tells you how you are likely to have your outcomes spread out, or distributed). However, they may get there at different speeds. This is called the central limit theorem; if you add random variables coming from these tame jumps, it will lead to the Gaussian.

Ah, where to begin. The example that Taleb refers to is a coin flipping sequence that is actually a "Binomial Distribution" that does indeed converge to a good replica of the Gaussian, but that has little to do with the Central Limit Theorem.

Taleb seems to have learned that the CLT has something to do with addition, and that it says that things tend toward a Gaussian (also called "normal") distribution. From there on it's pretty much (to adapt a phrase from Mel Brooks) "authentic techno-gibberish." It's the sort of thing that someone writes when they are trying to snow you.

Here's the deal. The Central Limit Theorem says that, for almost any distribution of numbers that can be produced (you are limited to finite numbers), if you take a large enough sample of those numbers, and average the samples together, the averages of the samples will form an approximately Gaussian distribution around the true mean of the original distribution.

Here's a quickie example, all pretty pictures generated from a spreadsheet. The original distribution is the some 2000 samples of the Rand() function, a random number from 0-1:


That's actually a pretty severe distribution, flat from zero to one, then zero outside of that range. That's called "discontinuous."

Now let's take another 2000 samples and average them 2 X 2 and plot out that result:


Obviously we're a lot less squared off here. The true mean of the Rand() function, incidentally, is 0.5, and the mean of our 4000 samples is 0.498, with a standard deviation (SD, or sigma) of 0.2.

Now let's do 4 sample averages:


Now the SD has dropped to 0.14, so the edges of the original distribution are over three sigma away from the mean. That's important because, by definition, it's impossible to get an averaged sample of a value greater than 1 or less than 0. It can't happen. So the smaller the standard deviation, the less likelihood that one of those sharp tails will bite us.

By the time we get to averages of six samples:

Sigma is down to 0.118, and the distribution will pass almost every test for normality.

Now maybe Taleb would say, "But that's my point! It passes tests for normality, but it isn't a true Gaussian distribution, so if you try to draw any conclusions from this based on assumptions about it's being Gaussian, you'll make serious mistakes out in the tails of the distribution. You'll misjudge the probabilities of improbable events! That's what my book is about!"

Perhaps, says I. But I'm not the guy drawing conclusions about Gaussian tails based on the Central Limit Theorem, because I know that the CLT isn't about the tails of the distribution. It's about the mean, and the finding of it. And it's about how most of the data from summed processes is going to look more than a little like it's normally distributed. And since most processes wind up having a lot of summation of one sort or another going on, you're going to see a lot of pretty-good-approximations-to-normally-distributed data coming from your instruments, or whatever else you use to gather data.

Good scientists and good statisticians know this. And when the tails of the distribution are at issue, then you see all sorts of arguments about whether or not you're "really" dealing with a Gaussian, or a Gamma, or a Weibull, or a log-normal, or any of a dozen other statistical distributions. That's if you're a statistician. If you're a scientist you try to understand the underlying process in order to assess such things as conditional probabilities, correlations, various discontinuities, non-linearities, and, my own personal favorite, the Something We Haven't Thought of Yet.

Which is to say, I don't think we're as ignorant and stupid as Nassim Nicholas Taleb seems to think we are.