### Density of Soap

The fall term began with a laboratory that introduces measurement through the measurement of the density of soap.

I began the laboratory with the Freeman Dyson quote:

For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created... ...equations are quite miraculous in a certain way. ... the fact that nature talks mathematics, I find it miraculous. ... I spent my early days calculating very, very precisely how electrons ought to behave. Well, then somebody went into the laboratory and the electron knew the answer. The electron somehow knew it had to resonate at that frequency which I calculated. So that, to me, is something at the basic level we don't understand. Why is nature mathematical? But there's no doubt it's true. And, of course, that was the basis of Einstein's faith. I mean, Einstein talked that mathematical language and found out that nature obeyed his equations, too.

The day before I had noted that if the density of an object was less than one gram per cubic centimeter, the object would float. If the density of an object was more than one gram per cubic centimeter, then the object would sink. The density would be determined from the slope of the graph later in the class period.

In the second half of the laboratory the class moves to the computer laboratory to work on the laboratory report, determining the slope of the linear regression.

The laboratory always includes Ivory soap in the mix, which floats in water. This surprises some students who have never used Ivory soap. This allows me to repeat after Dyson, "You predicted the soap would float and the soap knew what to do." I