Trail in Namibia Trail in Namibia

The Great Shadow Stick Riddle

Although I occasionally get labelled as Mr. Anti-anything-modern-and-would-rather-eat-a-pair-of-hemp-pants-than-use-a-GPS*, the truth is different. I do use a GPS, quite regularly in fact and always take one on serious walks, even if I don’t use it. I was able to use it to test natural navigation skills in the Libyan Sahara recently.

Soon I am hoping to use technology to solve a riddle that is proving elusive to both natural observation and thought. That is the shape of the a shadow stick’s arc as it goes from one side of an equinox to another. It is too subtle for me to gauge from stick and chalk efforts in my back garden. The answer is not in any of the many books and articles that I have on astronomy, ancient or modern. I have put this little riddle to dozens of good minds over recent months, some of them professional scientists, and no-one has been able to think their way to the answer so far.

The weirdest thing is that I know what the sun does during this elusive period, nothing very dramatic in short, so in theory this should be very straightforward. But it’s not quite. How can the shadow go from a curve one way to a curve the other without a straight line involved? Or is there a straight line, and if so when? Because it is definitely not at the equinox, that has to be a very gentle curve in the same direction as the summer one.

Why does it matter? Well in some senses it doesn’t, it is unlikely to change the fundamental ways of using the sun to find our way, but it would be, well… nice. I have spent hundreds of hours studying the sun and shadows, both physically and academically and it would give a feeling of completeness if I could just find this small missing piece of the jigsaw.

I think it may be possible to solve using a spreadsheet – horror of horrors! – but I would rather understand the world around me and resort to technology on occasion, than pretend the ignorance is somehow uplifting. It isn’t. It’s an intellectual irritant. I’d be absolutely delighted if someone reading this sent me the answer though. That would be a natural solution for me to a natural riddle, they need not tell me that they used some piece of whirring technology to work it out.

* On an almost related note, I do know someone who runs a small company that sells bamboo clothing.

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