Today, a parable of the head and the hands. 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.

One German astronomer in seven was a woman during the late 1600s. One in seven! Those were masculine times. The Protestant Reformation put women in the home, not in the academies. Yet the complex mathematical life of astronomy drew women in. At first that doesn't seem to make sense.

Those were times of radical scientific change. We were building the modern scientific method on experiments. Historian Lhonda Shiebinger explains how, in Germany, women found an odd door into this new life of the mind. That door didn't lead into the academies. It led into the trades. The trade tradition was strong in Germany. Women could take up any work that looked like a trade. The new scientific work had just that look and feel.

University faculties spun theories about the stars, but they left data-collecting to tradesmen. Telescopes and sextants were found in private homes. The observatory was one more cottage industry. It was usually a family affair, and the astronomer's wife was often his assistant. Maybe she worked as a technical artist, making a permanent record of the night skies. Maybe she worked as a human computer, grinding through calculations. But those women also saw the patterns in their work, for the hands lead right back to the head.

Take the case of Maria Cunitz. Her father educated her at home. She studied languages, classics, science, and the arts. Then she married a physician and amateur astronomer. Soon she was the primary astronomer in the family. At thirty she published a set of astronomical tables. In them she simplified Kepler's method for calculating the positions of stars.

It was an important book, and it went through many editions. In the later ones her husband had to write a preface saying it was all her own work. It was so useful that readers assumed he'd written it for her. She herself felt obliged to tell readers that her astronomy was accurate despite being the work of "a person of the female sex" -- her words, not mine.

Cunitz's troubles didn't end with her death. The 18th century was even less hospitable to women. Astronomers of the so-called Enlightenment period couldn't digest her. Forty years after her death, one complained that "she was so deeply engaged in astronomical speculation that she neglected her household."

So the door that'd opened for a while was swinging shut again. But those clear-headed German women remind us how well our hands inform our heads. In the end, not just our technology, but our science as well, must wed head and hands. It must wed doing and thinking. It must also wed male and female.

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

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Schiebinger, L., The Mind Has No Sex? Cambridge, Mass.: Harvard University Press, 1989.