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?

Flickr sundog photo by Prof. Bizzarro

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