Sunday, June 7, 2015

The triple sun


Drei Sonnen sah ich am Himmel steh'n / Hab' lang und fest sie angeseh'n;
Und sie auch standen da so stier / Als könnten sie nicht weg von mir.

I was reminded of this song  from the Winterreise by Schubert when I discovered a set of pseudo-sundogs in the city. Real sundogs are caused by ice crystals in the atmosphere. These sundogs were caused by well-positioned glass.
I am an enthusiastic sky watcher and I like to discover new interactions of nature and city. Last week I was doing a delivery in the evening. Beautiful weather, beautiful sunset. As I stood still on the crossing of the Hoge Filterweg and the Nessedijk I noticed reflections of the setting sun from two different buildings. One apartment building where students live:
And another one with luxury apartments and a view of the river: 
I could also still see the sun through the trees:
After plotting the geometry on Google Maps all the angles seemed to match with my observations:
This was serendipity in action. How large was the chance of me being at the right place at the right time in a sufficiently receptive mood? How hard would it be to find another situation like this? A similar arrangement of buildings?
Would this be a bigger or smaller chance than randomly buying four objects in a supermarket and getting a sum of exactly 10 euro? This also happened this week:
Actually this chance could be 1% if one ignores the combinatorial complexities. Which is relatively large. Is the chance of finding more multiple reflections larger or smaller? And could one find triple and quadruple reflections?

Sources:
Flickr sundog photo by Prof. Bizzarro

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