112.

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		2.5.8— Analyzing Data: The Bad News

		We used the patch clamp technique to record the currents through individual ion channels. We then constructed the phase space set from our data to determine if random, thermal fluctuations, or deterministic, atomic forces cause the channel to switch between its open and closed states. Our conclusion: It was very hard to tell which mechanism caused the switching. Thus we move from the Good News to the Bad News.

		1— The Good News

		The good news is that these new methods now make it possible to determine if data were generated by a random or a deterministic mechanism.

		2— The Bad News

		The bad news is that these methods can be difficult and frustrating to use.

		The mathematics of chaos is still being developed. New methods may overcome these difficulties.

		The present state of affairs should not surprise you or lead you to a low opinion of this field. A similar situation prevailed four centuries ago when Newton and Leibniz formulated the calculus. The success of the calculus was haunted by definitions that were not clear and results that could not be proved rigorously. The differentials, Dx and Dy used to evaluate the derivative dy/dx = Dy/Dx were ridiculed as ''the ghosts of departed quantities." Afraid of such criticisms, Newton chose to use less controversial geometric arguments, rather than the calculus, in his great book, the Principia. It took another 150 years until Cauchy's formulation of the concept of limit put the derivative on firmer ground.

		In retrospect, mathematics is clear, rigorous, and obvious. In progress, the crude figures drawn in the sand sometimes look imperfect and unpleasing.

 

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