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28 December 2001

Paleontologists Discover Transistor Radio in Jurassic Sediments... 

by Art Winfree

Several weeks ago (23 November, then more on 30 November) a question arose due to magnitude estimates not fitting together plausibly in context of the visibility of stars under full moon. Maybe you stewed on this a bit and came to a testable conjecture. My own is simply that night vision, using rod cells of the retina with more sensitivity and coarser resolution, has a different and larger "pixel" than daylight vision, which uses cone cells. So any point source has to stand out against more sky glow captured in its larger pixel area. This is clearly a matter that lends itself to quantitative refinement by clear thinking and simple experiments with equipment everyone has. One value of doing so is that it probably won't quite work out: something unexpected will be Discovered. I leave that Adventure in Discovery to you. 

Also in those columns we explored the counting of stars by magnitude classes, and found fewer stars than expected at increasing distances (taking diminished brightness as proxy for greater distance),  and wondered if that could reveal the presence of an obscuring fog. Best estimate from the limited data was "no, not unless you are ready to interpret a plainly straight line as a logarithmic curve, and then also accept that distances as short as a couple hundred light years snuff out as much as a full magnitude" Having taken this one as far as I care to on my own, I looked on the web and found that such departures from the expected inverse square law as we independently encountered had also vexed professional astronomers long ago. Wilhelm Struve played a similar game in 1846, and reported that 1000 parsecs (3260 light years) snuffs out 0.1 to 3.8 magnitudes in various directions. Robert Trumpler conclusively proved the existence of interstellar fog in 1930 and refined Struve's estimates to about 1 magnitude per 3260 light years in the galactic plane. But his fog is still an order of magnitude thinner than the one contemplated on 7 December  (unless I made some silly arithmetic error: there is plenty of opportunity for SAS readers to detect such blunders and report them). So this little mystery also remains to be solved. Presumably others solved it long ago, but we have not, and that is what matters most under "do it yourself" game rules that entitle us to engage Nature with such tools as we actually have here and now, instead of apologetically leaving inquiry to more sophisticated authorities. I have no more thoughts on the matter just now, but you probably have and you are welcome to bring them forth.
 
 

Prior Inventions of the Wheel Excavated

On 7 December we examined the riddle of visual perception that arose in the 9 November column. I recklessly volunteered my possibly-insane view of the curvature of lines in the sky, asserting personal "mystical experience" of a non-Euclidean space, then quantifying it. The conclusion (mine, at least) was that there must be a 2d something like “monocular visual space” distinct from objective 3d space, and that this subjective space is strongly and positively curved. Its metric is not dimensioned in meters but in radians. The rainbow is a denizen of that space, having no "real" position, size, or distance, but being defined entirely in terms of angles; and so are horizons, Sun rays, and the lines visually connecting remote objects. That was my daily "Game's-Worth" of intellectual exercise for 23 October and several following days, and so it naturally provided fresh grist for the new mill of this column when I drafted several that week to get this series started on 9 November. 

Once the follow-up column finally appeared last week, I called it quits and went to the web to find out what others had made of the same obvious facts.  See http://www.mmi.unimaas.nl/people/Veltman/books/vol3/ch3.htm. This tells that similar concerns passed through the minds of a long series of very distinguished philosophers and scientists, culminating perhaps in the works of Ernst Mach and Ewald Hering in the late 19th century. They, too, coined terms "optical space," or "sight-space," or "visual space" to make the distinction from objective Euclidean space. 

Thus I learned yesterday that Ernst Mach's 3-year old daughter, Caroline, declared in wonder during her first trip from the city to a country meadow (1876): "We are in a ball. The world is a blue ball!"  (Analysis of Sensations, XIV.5). This is remarkably close to the the import of  the first figure on 7 December (see below). The only real difference is that she thinks of the blue ball as being out there, whereas we, like her father, think of it as a mental space having no tangible presence in 3d. 
 
 
 

 And excavating even deeper, this archaeological mission to the library turned up Norman Daniels (1972: Philosophy of Science 39, 219-34) "Thomas Reid's Discovery of  Non-Euclidean Geometry" in Reid's Geometry of the Visibles (1764).  This seems to be pretty much what we came to above, about a mental space of two dimensions, resembling a sphere topologically, having a metric of angles, with intrinsic positive curvature everywhere. I don't know whether the 19th century psychologists were familiar with Reid. A modern statement of the same is found in R.B. Angell (1974:  Nous8, 87-117) "The Geometry of the Visibles". He states that this view conflicts with the views of most psychologists and philosophers, but he defends it vigorously. It would be instructive to learn what kind of evidence can inform such divergent views. 

Is it bad that we completely independently reinvented the wheel? I don't think so. That is really the best way to get acquainted with the wheel. Far from lamenting that it is so hard to come up with anything unprecedented (and I guess strictly impossible if our public forum embraced the libraries of ancient civilizations throughout the galaxy), I find the experience is almost necessary for really understanding the archaeological precedents and for appreciating the instructive ways they differ. Public innovation is not our objective in the small world of this Adventures in Discovery column. The objective here is to cultivate agility and resourcefulness in kindling our own personal Discovery of the universe, to cultivate a frame of mind in which things get noticed and implications get drawn, leading to experiences and insights new to us. It does not matter that the results may have been familiar to children a century and a half ago, if their perspective was not familiar to us.  I believe this frame of mind can be depended upon to develop insights unfamiliar in the public forum (among the other insights ... but discoveries cannot be pre-filtered.) 
 
 

Looking to the Future

These "sky" topics (curvatures, magnitudes) ignited from noticing the Moon wrongly oriented during a 23 October run. But attention to the Moon arose from a  non-experience several months earlier. This pyromaniac moves on next time (two weeks hence) to introduce the Mystery of the Missing Rainbow Moon.