Scientists who analyze these things say that the Andean Condor, soaring in the upwelling air currents over the mountain ranges of South America, can travel farther, for less expenditure of energy, than any other creature.
        But, those same scientists assert, even the condor is surpassed by a human riding a bicycle on a level road.
        In my younger years, my bike had one speed. To get up hills, I stood on the pedals and grunted. To stop, I pedalled backwards. If the chain came off – something it did with unpredictable regularity – I hurtled downhill until I fell off or hit something. Hopefully, something soft, like someone's prized hedge or flower bed...
        Today's bicycles have 24 gears, shock absorbing suspensions, and brakes that can pitch you over the handlebars.

Mathematical formula
        Yet all this development happened almost by chance. Just the other day, a group of mathematicians announced that they had finally found a formula to explain a bicycle's stability.
        You've all given a bicycle a push and let it go, I imagine. Even without someone steering it, the bike will coast along and stay upright. Until finally it slows down too much, and falls over.
        "Since the bicycle's invention some time in the 1860s," wrote the London Telegraph's Science Editor, Roger Highfield, "mathematicians have tried to sum up bike riding with equations based on Newton's laws of motion.
        "In the journal Proceedings of the Royal Society, a conclusive mathematical account of bike riding is described in a dense 28-page paper by Professor Andy Ruina of Cornell University, Jim Papadopoulos of Green Bay, Wisconsin, Jaap Meijaard of Nottingham University, and Prof Arend Schwab of Delft University of Technology, the Netherlands."
        A bicycle's stability used to be attributed to the gyroscopic effect of the rotating wheels. But that's not so, the authors found. The wheels on an untended bicycle, pushed off to fend for itself, turn too slowly to keep it upright.
        There are more complicated elements to factor into a formula.

Just do it!
        Of course, you don't have to be a mathematician to ride a bicycle. You just do it.
        The bicycle demonstrates that something can work, even if you can't explain why.
        For example, the ancient Hebrews didn't know that trichinosis is caused by tiny parasite called a nematode. But they knew that eating pork had something to do with it. So they avoided pork.
        Biologists have developed elaborate models to explain apparently self-sacrificing altruistic acts among animals. But the animals don't consciously calculate that defending eight cousins is as valuable for protecting their family's DNA as defending your own offspring – or whatever the genetic formula is. They just do it.
        The Golden Rule – treat others the way you would want to be treated – is found in every major religion. We knew that it – or its negative formulation, don't do anything to others that you wouldn't want them to do to you – generated social harmony long before modern psychology could offer an explanation.
        You don't always have to know why it works, to know that it works.