Today, we do experiments in our heads. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

The late 19th-century German philosopher Ernst Mach added a phrase to our language. It was "thought experiment." It's a wonderfully contradictory idea.

One scientist observes and measures nature. Another writes mathematical theories. Experiment and thought seem to be separate roads to learning. Mach walked the experimenter's road. But he said we can also experiment in our heads, not just in nature.

He said, look what Galileo did. Aristotle thought heavy things should fall faster than light ones. He thought a stone should fall faster than a feather. So Galileo said, "Let's glue a feather to a stone and drop it. Together, they weigh more than either the feather or the stone alone. If Aristotle's right, they'll fall faster together than either would fall alone. But who could believe the feather wouldn't slow the stone? Aristotle has to be wrong."

That's what we call a thought experiment. Galileo did the experiment in his head. Mach made a funny argument to justify doing that. He said our intuition is accurate because evolution has shaped it. We shrink from the absurd. That's what Galileo was doing when he said a feather can't speed the fall of a stone.

Enter now the grand master of thought experiments, Albert Einstein. Einstein was Mach's disciple. He created a great theater of thought experiments to explain relativity. But relativity flies in the teeth of our intuition. He talked about throwing balls and reading clocks on railroad trains and elevators. His conclusions had nothing to do with intuition.

Mach finally cracked under the weight of Einstein's admiration. Relativity theory was, he wrote, "growing more and more dogmatic." For Mach, a theory was only a framework for our measurements. Einstein figured that you first wrote correct theories. Then the data would simply fall into place.

In 1919 Einstein shrugged off an important telegram. Someone wired that they'd seen rays of light bend under the influence of gravity. That's what relativity predicts. Einstein was unimpressed. If light hadn't bent, he said, then "I'd have been sorry for the dear Lord. The theory is correct!"

So Einstein took Mach's thought experiments and used them in ways Mach never intended. He used them to show us a world that's far more subtle and surprising than anything our intuition ever prepared us for. Mach's ideas about thought experiments finally faded because the world is much stranger than our capacity to imagine it.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

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Sorensen, R., Thought Experiments. American Scientist, Vol. 79, May/June 1991, pp.250-263.

For more on the implications of thought vs. physical experiments, see Episode 1213.