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Blue sky problem
|A 2007 revised and somewhat poorly re-subtitled English translation of German historian Götz Hoeppe’s popular 1999 Blau: Die Farbe des Himmels (Blue: the Color of the Sky), which gives a rather detailed and comprehensive historical and scientific journey on the various ways people in different times and places have explained why the sky looks blue, starting with ancient Greek philosophers, who thought that blue was a mixture of black and white, through Arabic commentaries on Aristotle, medieval treatises on painting, Newton's experiments with prisms, Goethe's color theory and on up through the nineteenth-century development of the theory of Rayleigh and Mie scattering, that eventually provide the correct physical explanation for the blue color of the sky. |
“Although ideas about the origins of the sky’s blue color can be traced back to Greek antiquity, the first concerted effort to reach a plausible explanation is attributed to Leonardo da Vinci. The Italian master was followed by Newton, and later by Bouguer and de Saussure. Tyndall wrestled with the problem around 1869, but the definitive explanation would be proposed only in 1899, by Lord Rayleigh.”
The blue sky puzzle, prior to its complete solution in 1899 by English physicist John Strutt (IQ=190), the vacuum debate aside, was the longest-standing unsolved puzzle in science, worked on by the biggest thinkers of all time: Aristotle (IQ=190), Da Vinci (IQ=205), Newton (IQ=215), Goethe (IQ=230), Clausius (IQ=205), Maxwell (IQ=210)—in fact every single genius in the IQ=205+ range (see: genius IQs) worked on the blue sky problem, prior to its solution by Strutt. The best summary of the blue sky solution is given by James Maxwell himself, where, specifically, in a 15 March 1871 letter to his Cambridge friend mathematician Cecil Monro (1833-1882), he gives the following snapshot of the state of the solution to the blue sky problem during this year: 
“I think Strutt on the sky-blue is very good. It settles Clausius’ earlier vesicular theory to explain the blue sky.”
German physicist Clausius, to give some historical context, completed his PhD dissertation in 1847 (1848?), entitled "On those Atmospheric Particles that Reflect Light", under German mathematician and physical chemist Johann Schweigger, which proposed, as Maxwell states, a "vesicular theory" explanation for the blue color of the sky, the red colors seen at sunrise and sunset, and the polarization of light, at the University of Halle, Germany.  In this sense, Clausius might well be the "true" solver of the blue sky problem, in the sense that although he did not complete the exact final solution, his theories were the main road work or construction outlines to the final solution, and the same sense that the 1690 Papin engine design, by French physicist Denis Papin, was the blue print or actual invention draft to the final "working" 1698 Miner’s friend, built by English engineer Thomas Savery.
The Greeks, supposedly, were the first to speculate about the blue color of the sky, as embodied in Greek physicist-philosopher Aristotle's Meteorology, which supposedly the later Arab commentators read and supposedly Leonardo Da Vinci read or had a copy of in his library. 
In circa 850, Arab savant Al-Kindi (c.800-873) attributed the azure of the sky to “a mixture of the darkness of the night with the light of the dust and haze particles in the air illuminated by the sun.” 
|Opening page image of the 2004 article "A Blue Sky History" by American aerosol physicist Pedro Lilienfeld, which details the short history of the blue sky problem, from Aristotle up to its 1899 complete solution John Strutt. |
Italian polymath Leonardo da Vinci’s circa 1508 72-page Codex Leicester, which to note in 1994 sold for an unprecedented $31 million dollars (to Bill Gates), making it the most expensive book ever sold, written in his trademark mirror hand writing, contains the first modern speculations on the blue sky color, containing insights into the sky’s blueness.  In his notebooks, he states:
“You know that in an atmosphere of equal density the remotest objects seen through it, as mountains, in consequence of the great quantity of atmosphere between your eye and them appear blue and almost of the same hue as the atmosphere itself when the sun is in the East. Hence you must make the nearest building above the wall of its real color, but make the more distant ones less defined and bluer; thus, if one is to be five times as distant, make it five times bluer. And by this rule the buildings which above a [given] line appear of the same size will plainly be distinguished as to which are the
most remote and which are larger than the others.”
In another writing he comments on the sky’s whiteness: 
“And if the sky, as you see it, ends on a low plain, that lowest portion of the sky will be seen through a denser and whiter atmosphere, which will weaken its true color as seen through that medium, and the sky will look whiter than it is above you, where the line of
sight travels through a smaller space of air charged with heavy vapor.”
Da Vinci also became aware that the sky darkens as one ascends the Alps, about which he theorized: 
“I say that the blue which is seen in the atmosphere is not its own color, but is caused by the heated moisture having evaporated into the most minute imperceptible particles, which the beams of the solar rays attract and cause to seem luminous against the deep intense darkness of the region … above them. And this may be seen, as I myself saw it, by anyone who ascends Mon Boso [Moute Rosa], a peak of the Alps that divides France from Italy … And I saw the atmosphere dark overhead, and the rays of the sun striking the mountain had far more brightness than in the plains below, because less thickness of atmosphere lay between the summit of this mountain and the sun.”
|Blue sky theory timeline: 1400s-1700s, from the 2004 article "A Blue Sky History" by American aerosol physicist Pedro Lilienfeld. |
Newton, supposedly, in his 1704 Opticks, had the following to say on the matter:
“The blue of the first Order, though very faint and little, may possibly be the Colour of some Substances; and particularly the azure Colour of the Skies seems to be of this Order. For all Vapours when they begin to condense and coalesce into small Parcels, become first of that Bigness, whereby such an A so this being the first Colour which Vapours begin to reflect, it ought to be the Colour of the finest and most transparent Skies, in which Vapours are not arrived to that Grossness requisite to reflect other Colours, as we find it is by Experience.”
In 1725, French scientist Pierre Bouguer (1698-1758) quantified the light attenuation of the earth’s atmosphere. 
In 1789, French physicist Horace de Saussure (1740-1799), noted for his age 19 thesis “Dissertation on the Nature of Fire”, wrote two papers, in which he described a cyanometer, an apparatus used to quantify the degree of blueness of the sky, concluding that the “the color of the sky determined by the cyanometer is the measure of the quantity of concrete vapors [particles in suspension] in suspension in the air.” 
In 1809, French physicist Francois Arago (1786-1853) discovered the polarization of daytime skylight at 90 degrees to the direction of the sun. 
|Blue sky theory timeline: late 1700s to early 1900s, from the 2004 article "A Blue Sky History" by American aerosol physicist Pedro Lilienfeld. |
In 1826, German polymath Johann Goethe was working out a law to explain the blue color of the sky (see: Goethe timeline) via his Newtonian-alternative color theory.
German physicist Rudolf Clausius, whose 1848 PhD dissertation, as noted, was on sky color problem, pointed out that refraction within macroscopic droplets could not explain the color of the sky, he postulated the presence of minute atmospheric water bubbles; this theory, however, supposedly, was inconsistent with Arago’s results. 
Others to work on the problem, in the context of the 90 degree polarization data, include: William Herschel, James Forbes (c.1868), and John Tyndall who in 1869 concluded:
“When the air was so sifted as to entirely remove the visible floating matter, it no longer exerted any sensible action upon the light, but behaved like a vacuum.”
The next frame in the history of sky color theory involved the search to provide a mathematical solution of the scattering of light by particles with dimensions smaller than and comparable to the incident wavelength, the precise solution of which involves a cast of characters including: Alfred Clebsch, Ludwig Lorenz, James Maxwell, John Strutt, Gustav Mie, Peter Debye and others.
In 1871, Strutt published his first paper “On the light from the sky, its polarization and colour”, followed immediately by another entitled “On the scattering of light by smaller particles”. A 1873 letter from Maxwell prompted him to investigate the phenomenon further. In 1899, Strutt published what some have called his most-famous article "On the Transmission of Light Through an Atmosphere Containing Small Particles in Suspension, and on the Origin of the Blue of the Sky," which thus solved the problem. 
In 1908, German-born American physicist Albert Einstein, building on the earlier theories of Polish scientist Marian Smoluchowski, calculated the size of the density fluctuations in a gas, and then calculated the scattering of a light beam incident on these density fluctuations; as a byproduct of his calculations, he found, supposedly, a better explanation for the blue sky color, in solution to those who had objected to the flaw in Strutt’s explanation that if the air is uniformly distributed throughout the atmosphere, the scattering of a beam of light by the air molecules should exactly cancel out. Einstein, supposedly, rescued Strutt’s explanation from this disaster. 
Experimental confirmation that air molecules do scatter light was apparently achieve for the first time by Jean Cabannes (1885-1959 in 1913.
1. Lilienfeld, Pedro. (2004). "A Blue Sky History." Optics and Photonics News, 15(6): 32-39.
2. (a) Maxwell, James. (1871). “Letter to Cecil Monro”, Publication.
(b) Maxwell, James, Garber, Elizabeth, Brush, Stephen G., Everitt, C.W. Francis. (1986). Maxwell on Molecules and Gases (pg. 506). MIT Press.
3. (a) Cropper, William H. (2001). Great Physicists: the Life and Times of Leading Physicists from Galileo to Hawking (pgs. 104-05). Oxford University Press.
(b) Rudolf Clausius – Mathematics Genealogy Project.
(c) Johann Schweigger – Wikipedia.
4. Ohanian, Hans C. (2009). Einstein’s Mistakes: the Human Failings of Genius (pg. 126). W.W. Norton.
5. (a) Codex Leicester – Wikipedia.
(b) Newman, Sharan. (2005). The Real History Behind the Da Vinci Code (§: The Codex Leicester, pg. #). Penguin.
6. (a) Al-Kindi – Wikipedia.
(b) Lilienfeld, Pedro. (2004). "A Blue Sky History." Optics and Photonics News, 15(6): 32-39.
7. Strutt, John. (1899). "On the Transmission of Light Through an Atmosphere Containing Small Particles in Suspension, and on the Origin of the Blue of the Sky", Phil. Mag. Ser. 5. 47:375-84.
8. Hoeppe, Gotz. (2007). Why the Sky is Blue: Discovering the Color of Life (translated by John Stewart). Princeton University Press.
● Gribbin, John. (1998). Q is for Quantum: An Encyclopedia of Particle Physics (blue sky, pgs. 48). Simon & Schuster.
● Rayleigh scattering – Wikipedia.
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