Explaining the Twilight 2

(Picture: Andreas Rabending Fotografie)

(Picture: Falkue)

(Picture: Photo after the 1961 Beckett portrait by Reginald Grey)

(Picture: U.S. Army)

(1.-2.11.2022) »Will you look at the sky, pig!«, Pozzo says to Lucky in Samuel Beckett’s Waiting for Godot, and Lucky looks at the sky, after which Pozzo goes on to give an explanation of twilight that oscillates between being poetic and prosaic. The one or other reader may recall Samuel Beckett from school – his play was published in 1952, and it premiered in January 1953 –, but who does know Edward Olson Hulburt? Because this scientist actually did explain twilight. Because Hulburt did explain why the sky was blue at dusk, and this in a publication, published only weeks after the premiere of Waiting for Godot. Does this sound absurd? Perhaps. But even more remarkable is perhaps to notice that the scholarship Hulburt represents was also helped by the V-2 rockets, developed by Nazi Germany, and available to US scholarship after the Second World War.

Not every human does want to know why the sky is blue (and why it remains to appear as blue at dusk). Fair enough.
But it seems that you want to know, dear reader, so I am assuming that, perhaps, you have been asked by a child recently why the sky is blue.
Or perhaps you have been asked by an already informed child why the sky keeps on to appear as blue during dusk, and if this is due to the Rayleigh scattering only, or due to other effects (like the Chappuis absorption). Sigh.
Maybe you have not yet had the time to consult the internet, so you chose to turn the child’s attention to other things, like poetry, for example. But stop.

All I am writing here is written from a layman’s perspective, and I am not going to suggest that I, myself, do understand it in other than layman’s terms. But we have to start from the beginning: Why is the sky blue? Answer: the sunlight coming down from the sun to the earth gets scattered, and various wavelenghts of the visible light (various colors) get scattered in various ways. Result: the sky appears as being blue (it is the Rayleigh scattering, stupid).
But the Rayleight scattering alone is not enough to explain why the sky, during dusk, keeps on to appear as being blue. The theory would rather demand it to turn towards green and yellow, and grey. But there is something like the blue hour, and the theory does not seem to be complete or even correct. Problem: The blue hour is not yet explained.
Various physicists have contributed to explaining it more fully, and Edward Olson Hulburt was perhaps the one to have explained it almost completely (but, as it seems, not yet fully completely). And, in layman’s terms, the blue hour does appear as blue not only due to the Rayleight scattering (also, but not only), but also due to the Chappuis absorption. In simple words: some wavelenghts of the visible light get absorpted high above in the sky (in the so-called ionosphere) – and it is the ozone who acts here as a main protagonist, taking out some of the possible colorings –, with the sky at dusk appearing as remaining blue (and not green or yellow or grey). Brief: it is not due to the Rayleigh scattering alone, but also due to the Chappuis absorption which has to be included to an explanation of the blue hour (I am neglecting here to ask for the relative importance of each factor).

Now we may turn to poetry for a moment, but, as we know, Samuel Beckett yet had a longing for the romantic, but tended to suppress this longing, which may be the background of Beckett having his one protagonist Pozzo explain the twilight in this bizarre manner (and not necessarily as convincing as Edward Olson Hulburt could, by using the language of science (we come to that in the end). Pozzo is oscillating between the more prosaic and the more lyrical. And the performance Samuel Beckett wrote for Pozzo, in Waiting for Godot, reads as follows (in brackets are given the stage directions):

»POZZO:
(who hasn't listened). Ah yes! The night. (He raises his head.) But be a little more attentive, for pity's sake, otherwise we'll never get anywhere. (He looks at the sky.) Look! (All look at the sky except Lucky who is dozing off again. Pozzo jerks the rope.) Will you look at the sky, pig! (Lucky looks at the sky.) Good, that's enough. (They stop looking at the sky.) What is there so extraordinary about it? Qua sky. It is pale and luminous like any sky at this hour of the day. (Pause.) In these latitudes. (Pause.) When the weather is fine. (Lyrical.) An hour ago (he looks at his watch, prosaic) roughly (lyrical) after having poured forth even since (he hesitates, prosaic) say ten o’clock in the morning (lyrical) tirelessly torrents of red and white light it begins to lose its effulgence, to grow pale (gesture of the two hands lapsing by stages) pale, ever a little paler, a little paler until (dramatic pause, ample gesture of the two hands flung wide apart) pppfff! finished! it comes to rest. But – (hand raised in admonition) – but behind this veil of gentleness and peace, night is charging (vibrantly) and will burst upon us (snaps his fingers) pop! like that! (his inspiration leaves him) just when we least expect it. (Silence. Gloomily.) That's how it is on this bitch of an earth.«

After that performace a long silence is to follow.

Edward Olson Hulburt had already addressed the problem of explaining twilight before the Second World War (just as Samuel Beckett had mused about twilight). But Hulburt’s 1953 publication (see below) could take into consideration more data, and this also due to the collecting of data via rocket flights. These data had to be more convincingly explained. And this is, as far as I can understand it, what Hulburt did. At about the same time Beckett published his play. And one may look at these efforts from various sides here: from the viewpoint of history (the history of technology; but also the viewpoint of the history of postwar mentalities that express in Beckett’s play). Or from the viewpoint of someone who just examines various types of languages. More or less willing languages, more or less able to explain twilight (given that humans want to explain it). And this is why why I would like also to quote E. O. Hulburt, although I may not fully able to understand him (one may say maliciously here: just read it as a kind of poetry). The abstract of Hulburt’s first publication of the matter (published in 1938) reads as follows:

»Abstract
With a calibrated Macbeth illuminometer measurements were made of iz the brightness of the zenith sky and of ig the energy flux across a vertical plane from the twilight horizon for the depression Θ of the sun below the horizon from 0° to 13°. For clear sky conditions the iz, Θ; and ig, Θ; curves did not change within 30 percent with the season from October, 1937, to April, 1938, and were the same for evening and morning twilight. Calculation from the Rayleigh theory of molecular scattering and the observed iz and ig data showed that within ±30 percent the densities of the atmosphere from sea level to about 60 km were those of the density-height relation known to 20 km and extrapolated for a temperature of 218°K. It follows that the temperature of the twilight temperate zone atmosphere is 218°±15°K from 20 to 60 km. The influence of secondary scattering, determined from ig, although small for small values of Θ; increased rapidly with Θ; to such an extent that the twilight zenith sky brightness measures gave no indication of the distribution of density above about 60 km.«
[© 1938 Optical Society of America]

See further:

E. O. Hulburt, Explanation of the Brightness and Color of the Sky, Particularly the Twilight Sky, in: Journal of the Optical Society of America 43, No. 2, Februar 1953, p. 113–118

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