probable microstate.In specific,even at a temperature of 1 000 000 K.a about entropy,but it holds only for the microcanonical ensemble.The sample of helium is more likely to be in a particular crystalline microstate definition Eq.(Al)is harder to understand but is also more general,ap- than in any particular plasma microstate.However,there are so many plying to any ensemble.The two definitions are logically equivalent.See, more plasma than crystalline microstates that(in the thermodynamic limit) for example,Richard E.Wilde and Surjit Singh,Statistical Mechanics: the sample occupies a plasma macrostate with probability 1. Fundamentals and Modern Applications (Wiley,New York,1998).Sec. The definition of entropy in Eq.(1)is the best starting place for teaching 1.6.1. COMPUTERS IN THE CLASSROOM I've paid my dues in physics and astronomy,and in those basic sciences,computers have nothing to do with learning. No computer can help someone understand the meaning of a wave function,angular momen- tum,or the relativistic-twins paradox.Software can simulate these on a glass screen,but these simplifications depend on someone else's understanding,which may be quite limited. Up and down the line,computer programs feed us someone else's logic,instead of encouraging us to develop our own.When confronted by a quandary,we're fed someone else's rubric rather than creating our own assaults on the problem. Clifford Stoll,Silicon Snake Oil (Doubleday,New York,1995),p.121. 1096 Am.J.Phys.,Vol.68,No.12,December 2000 Daniel F.Styer 1096probable microstate. In specific, even at a temperature of 1 000 000 K, a sample of helium is more likely to be in a particular crystalline microstate than in any particular plasma microstate. However, there are so many more plasma than crystalline microstates that ~in the thermodynamic limit! the sample occupies a plasma macrostate with probability 1. 34The definition of entropy in Eq. ~1! is the best starting place for teaching about entropy, but it holds only for the microcanonical ensemble. The definition Eq. ~A1! is harder to understand but is also more general, ap￾plying to any ensemble. The two definitions are logically equivalent. See, for example, Richard E. Wilde and Surjit Singh, Statistical Mechanics: Fundamentals and Modern Applications ~Wiley, New York, 1998!, Sec. 1.6.1. COMPUTERS IN THE CLASSROOM I’ve paid my dues in physics and astronomy, and in those basic sciences, computers have nothing to do with learning. No computer can help someone understand the meaning of a wave function, angular momen￾tum, or the relativistic-twins paradox. Software can simulate these on a glass screen, but these simplifications depend on someone else’s understanding, which may be quite limited. Up and down the line, computer programs feed us someone else’s logic, instead of encouraging us to develop our own. When confronted by a quandary, we’re fed someone else’s rubric rather than creating our own assaults on the problem. Clifford Stoll, Silicon Snake Oil ~Doubleday, New York, 1995!, p. 121. 1096 Am. J. Phys., Vol. 68, No. 12, December 2000 Daniel F. Styer 1096