About this column

14 December 2001

Possible Worlds of Discovery 

by Art Winfree

Each column in Adventures in Discovery is intended to spark involvement in an investigation guaranteed to reward modest effort with at least small personal Discoveries. Those happen in the energetic and inquisitive reader with no further need of input from the column, so the column will generally not  (unless report of exceptional Adventures should arrive) ramble on and on about avenues of Discovery that interested readers can better find for themselves. But for getting things started, I give examples drawn from the past two columns. In the past several weeks these Adventures proved instructive to me about how ideas evolve, and I find it exciting that a totally ignorant person with no sophisticated tools (that's me, 23 October to 6 December ... and possibly you) can learn surprising things about the world and about the mind by merely being observant and inquisitive.

Before deciding whether to peruse this week's column, be aware that it will foreclose your possibilities of independently Discovering these particular tidbits. As CNS poison, the following paragraphs resemble neurotoxic competitive inhibitor molecules that will occupy receptor sites in your brain cells, preventing Adventures in Discovery. So you might want to go read some other column and defer this one until it can better serve your purposes. 
 

First regarding "Trouble at Full Moon" (30 November):

Johannes Kepler and Galileo Galilei exchanged letters about the dark areas of the Moon. From Pythagoras through Plutarch then through the Middle Ages the best guess was that they are seas. Four centuries later, we still call them "maria" but we know they are rocks. On 30 November we engaged a similarly speculative debate, this time to decide whether the whiter "highland" areas are or  are not like any rocks we have seen on Earth. This Adventure in Discovery arose by noticing 

 
1) that the full moon is entirely as bright around its edges as in the middle (of course excepting the dark maria), and 

2) that it is surprisingly brilliant relative to just a few days earlier or later when the lighted disk's area is hardly less. 

Seeking answers in a typical property of the lunar soil ("regolith") we had to guess that regolith in the lunar highlands may be optically peculiar. In fact I found today in the log of the first manned Moon landing (20 July 1969) that Buzz Aldrin says of the soil: 
 

"It's pretty much without color. It's gray and it's a very white chalky gray, as you look into the zero phase line [this means with the Sun behind you, looking near the shadow of your head], and it's considerably darker gray, more like ashen gray as you look up 90 degrees to the Sun." 

That confirms, close up, our own observation from greater distance. On 30 November  I mischievously proposed that this gray-white soil may contain glassy spheres such as used in reflective paint or movie screens. Though modeling with 3 mm glass balls did not encourage this fantasy, archived Moon dust indeed turned out to contain glassy spheres. The remaining question, not to be overlooked, and left implicitly for you to notice, is "Are they responsible for the observed dramatic peculiarities?"

This was a deliberate set-up for you to exercise your Discovery skills by thinking up alternative interpretations. Such is the spirit of this column. For example, how about some alternative kinds of retro-reflector, e.g., moon-flowers covered like chenopodium with tiny spheres of exudate, or dew on moon-grass, or minerals containing cube corners? Or more plausibly, what if the surface of the Moon were eons deep in friable dust, never compacted by wind or rain or even by much gravity? Of course, there is extreme heating and cooling daily, and there are vibrations from meteor impacts, and a fullness of time, so we don't know whether this is a plausible speculation. Anyhow if regolith is isotropically crumbly and flocculent like packing material then from any direction the sunlight may penetrate through the interstices between grains to illuminate surfaces visible only from that angle. And we would see them illuminated only when peering in line with the Sun: at full moon. At any other time, looking somewhat from the side, all but the most superficial illuminations would be hidden. Such stuff presumably would look dark from other directions relative to the sunlight. If so, there seems no need for retro-reflectors to account for the two remarkable peculiarities of moonlight noticed (unless it was overcast where you are) during the 30 November full moon: a sudden brightening at full moon, and the absence of systematic darkening toward the rim of the ostensible disk!

Did you at least contemplate this microscopically-textured alternative and look for an observation capable of distinguishing it from the reflecting balls interpretation proposed as a catalyst for your personal discoveries?  One needed observation: are the glass balls in lunar regolith samples transparent? I deliberately didn't mention this caveat. Transparency is essential, since light must twice traverse the interior. Turns out not so: according to reports found on NASA web sites they are mostly dark orange or black. Another needed observation: if regolith brightens at zero phase on account of its loose architecture, it might not do so any more after being scooped up and transported to museums. This could be found out by requesting from NASA a sample to examine optically. I have not done so.
 

But I did try smaller balls. First with 1 mm eggs of smelt or flying-fish ("masago" at a Japanese restaurant) I noticed that retro-reflection from a high halogen lamp requires the egg, adhering to a toothpick tip, to be suspended at a critical distance from a white tablecloth. Too far or too close, or against an absorbing surface, it doesn't work. Maybe this distance is the focal length, about 1/2 radius. Then in my lab using 300-mesh Dowex ion exchange resin from a chromatographic column, I observed the same. And then spray-painted a ping-pong ball flat black, followed with spray adhesive (which made it shiny), then dusted with resin balls. Guess what? It brightens up remarkably and shows no edge-darkening in light arriving from almost the viewpoint!  But unexpectedly the retro-reflected brightness ends quite abruptly when viewpoint and light diverge by about 17 degrees, corresponding to about  1.5 days from full moon. And unexpectedly, the transition is not synchronous for all colors:  the bright time has a rainbow fringe.  This suggests some interest in a closer measurement of the Moon's brightness and color at phases near full moon, perhaps to exclude such interpretation. (The graph below had data only at 1 day increments, without attention to color, and averaging white highlands with dark maria.) 
 
 

 

Figure 1

Rubbing dowex beads into the fuzz of a tennis ball as suggested 30 November did not make it resemble the Moon. Maybe because fuzz threads provide inadequate background to reflect the focused beam from behind each ball?

Glass beads of the sort used for sand-blasting to polish metal and for roadway sign and stripe marking (300 mesh, 1/10 mm "ballotini") perform about the same. They reflect wonderfully, and only near zero phase, as a monolayer on white background, as in movie screens. Adhering to the surface of a ping pong ball they perform so in the middle of the visible disk, but nearer the rim without background in line of sight, they don't, so the rim is darker, much as with the 3 mm balls two weeks earlier. Maybe this result would change if they could adhere to cliff faces near the rim. In any case they serve poorly when deeper than monolayer, and I suspect they would serve poorly were the glass not clear and colorless.

All this raises a question: has anyone ever provided at least one candidate material which, made into a rough ball and exposed to a distant lamp, quantitatively duplicates the very strange dependence of moonlight on phase? Such should be invented and tried, not just vaguely imagined. Are there many such materials or none?

Our encounter with Phong illumination was not a set-up. I invented this trap by falling into it. But it could lead an Adventurous soul to another little Discovery, as follows:

If you try to learn about illumination models you pretty soon realize they are all about surfaces and angles. 

Light comes off a surface by specular reflection at the same angle as its incidence (both measured from the surface normal), with intensity, color, and polarization depending on two material parameters (absorbency and refractive index as functions of wavelength, or if you like, a wavelength-dependent complex-valued speed of light). Exactly how? Just as needed to satisfy Maxwell's Equations at a planar interface: you probably remember this as an undergraduate physics homework exercise. 

And light comes off also by diffuse scattering in all directions, which I suppose is an ad hoc description of multiple reflections within a rough surface. Here three angles relative to the surface normal may be crucially implicated: the angle of incidence and two angles to characterize the outgoing light or the viewpoint. (or at maximum generality, four angles for anisotropic materials: two characterize the input vector and two characterize the output vector.) Clearly what we see in moonlight is such scattering, so it is tempting to formulate the problem in terms of an integral over the spherical surface. 
 

I fell into this trap while trying to anticipate the integrated brightness of half moon (as 1/, rather than 1/2). But here is the little Discovery:  all this is irrelevant because there is no "surface"! The Moon is a pile of rocks, and a rock is an almost-fractal aggregate of smaller lumps. This realization is clearly not material for newspaper headlines, but anyway we call it a Discovery in the spirit of this column because in one abrupt stroke it revolutionizes our way of perceiving and thinking about the Moon. And because without it we would wander in a house of mirrors involving ever more complicatedtrigonometric fantasies. And because with it we approach the problem altogether differently: in terms of finding candidate materials whose reflectivity depends on only one angle: that between viewer and Sun, as viewed from the Moon (which is called the lunar "phase angle"). And depends on it in the peculiar way of Figure 1 . 

Of course it is necessary that moonlight integrated over the disk must depend on only one angle, because the lunar phase angle is the only thing that distinguishes one view of the Moon from another. But we ended up imputing this property and the peakedness of Figure 1 to each handful of local moon dust, too, and in that context it is a strange anomaly that seems to require some marvelous interpretation.

You might also have come to this Discovery about angles along a different route. The fork in the road lies in the  23 November column at the anecdote of William (alias Friedrich Wilhelm) Herschel's quantifying moonlight by direct visual comparison with a cliff face illumined by the same sunlight. A Sherlock Holmes would follow this up, replacing the cliff rocks by material samples or maybe even (I imagined) by samples of flat gray paper such as Pantone manufactures, or by a gradient strip printed from PaintShopPro 7 or some such graphics utility. The white highlands get darker and darker as the phase angle increases from full moon, so darker and darker parts of the paper are needed to match it. Actually trying this leads to a small conceptual revolution.  Notice that the paper's brightness depends strongly on the angle at which you hold it in the sunlight. Do you want it perpendicular to your line of sight? To the incident sunlight? To the part of the Moon's hemisphere that you are trying to match? At this point even the most ignorant fumbler (that's me) has to realize that smooth surface illumination depends on angles, maybe three of them, while the Moon's (globally, of course, but also even locally) seems to depend on only one. And then to realize another big difference, that the "Moon's surface" is nothing like a "surface" in the sense of optics and paper illumination, perhaps the same in both cases, that there is a "surface" that is  smooth on a scale not much coarser than light wavelenght, spanning visual angles exceeding visual acuity. We don't want to think about moonlight in terms of surface illumination models at all! But without trying this "improvement" on the simple Herschel experiment, this would not likely be Discovered.

So what might be the next project? Comparison with rocks. On my garden wall there is now a row of gray-white dull pebbles plucked from the adjacent ground. Each clear weekend when Moon and Sun are at the same altitude within maybe 15 degrees tolerance (there is a half-hour window for that each day) I see which pebbles are brighter and which darker than the lunar highlands, thus ordering the pebbles. The break will presumably vary somewhat with time in the month, i.e., with phase angle, but not with any "surface" angles.  After a few weeks of watching a very light gray-white quartz sits in the middle, darker than full moon but brighter than half moon.

And having written all the above and having kindled this topic almost as far I care to, this afternoon I felt at liberty to query an astrophysicist, Timothy Swindale at the Lunar and Planetary Lab in Tucson, while seeking access to a sample of moon dust . The sample here at Tucson proves too small to help in this matter, but I learned that this was a really hot topic in the late 1960s when NASA engineers were trying to anticipate what an Apollo mission would land into. And then even hotter when samples were brought back. The key name about moon-dust optics is Bruce Hapke. He developed what is now called  "shadow hiding" or "fairy castles" model to sophistication far beyond our guesswork above, as an alternative to melted glass ball models. The history was similar: glass balls were the accepted basis of thought and no one felt any need for an alternative vision when Hapke championed fairy castles before unresponsive colleagues. So challenged,  he was not content with vague speculation, but worked out all the microscopic details in quantitative terms. "Yes" answers are provided to two questions typed into this column yesterday, "whether this is a plausible speculation,"  ("Yes, in fact so plausible that it eventually became the accepted understanding") and "has anyone ever provided at least one candidate material?" ("Yes, abundantly.")  Look up http://www.discover.pitt.edu/media/pcc010716/moremoon.html, http://www.hq.nasa.gov/office/pao/History/alsj/Fcastles.htm, and http://www.gps.caltech.edu/~ge151/natural_reflection/reflected_radiation_from_natu.shtml

But here is the punch line: my dust-architecture alternative to movie-screen beads, that I smugly hoped you would enjoy looking for and maybe finding by yourself, is also wrong! What I learned only this afternoon is that there is yet another cogent alternative, called "coherent backscatter," based not on shadow hiding in fairy castles built of 40-micron grains such as dominate a close view of lunar regolith, but rather on the wave optics of  bacterium-size grains dusting their surfaces. Unlike me, Hapke did request the sample from NASA as suggested above, and reports what he learned from it in Science 260, 509-11 (23 April 1993). His new optical studies of regolith samples are presented as conclusive proof that coherent backscatter, not shadow hiding, is the dominant cause of the two phenomena that started our Adventure in Discovery. 

But both effects do occur, and one or the other may dominate in different cases. Up to present day the debate continues in the scientific literature. You can find the latest at www.google.com by using  buzz-words from the paragraphs above.

There will be a column later about iron meteorites. If you hope for a present during the coming holiday season, you might drop hints that Ebay is a good place for someone (perhaps yourself) to find a 30-100 gram chunk for you. I will describe what happened when I got one for the first time in my life, and undertook to find out about it on my own before looking in books. You might enjoy a similar Adventure in Discovery, if you can get a piece meanwhile.