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of mathematical formulae, but their further development did not require 

 more than the standard methods of calculus. It is possible that the new 

 electronic computers will in the future contribute significantly to the develop- 

 ment of biology, where the highly complex interrelationships between con- 

 stituent parts, whole organisms, and environment require equally complex 

 mathematical treatment. 



It would not be correct to mention the increased use of statistics as an 

 example of the impact of mathematics on biology. It is rather the other way 

 around. Biometricians, such as Galton and Pearson, developed statistics; 

 Johansen applied it to genetics; and in agriculture the great variability in 

 field experiments required special methods to evaluate results. This led a 

 number of mathematicians to develop the theory of probabilities further 

 until now it is an important tool in all biological research where for one or 

 another reason one is dealing with variable material. During the last quarter 

 century statistics has been used increasingly in plant physiology, almost to the 

 point where it has become a fad, and a number of cases can be cited where 

 the statistical treatment of the experiment has taken precedence over con- 

 sideration of the physiological significance of the data. 



In physics the quantum theory, now just 50 years old, has overshadowed 

 probably all other developments in theoretical significance and has caused 

 the rapid development of many new branches of physics as well as of chem- 

 istry. As such it also has influenced biology in a secondary manner. However, 

 the first direct applications of quantum theory to photos3mthesis by Warburg 

 touched off a whole new development in this field, particularly here in America. 

 Now, using these energy considerations as a basis, physicists like Franck, 

 chemists like Calvin, and plant physiologists like Emerson, French, and 

 Arnon are on common ground in their attack on the most important single 

 reaction on earth: the photoreduction of carbon dioxide. 



Other developments in physics of basic significance, such as the theory of 

 relativity and the problem of elementary particles, have had no direct applica- 

 tions in biology, except inasmuch as they led to new techniques. Electronics 

 has brought us a new era of measuring and of instruments, which in the hands 

 of technicians produce wonders of accuracy. For the new generation of plant 

 physiologists it is hard to imagine what a pH measurement or spectral de- 

 termination involved 30 years ago. Fortunately the budgets of plant physiolo- 

 gists have increased so that they can take at least partial advantage of the 

 availability of commercial meters and recorders. We should not lose sight, 

 however, of the dangers involved in fancy instruments. They all have been 

 designed for specific purposes, and thus one may not be measuring what one 

 wants but rather what the instrument can. Thus the investigator is exposed 

 to the risk of becoming a slave of his instrument instead of the instrument 

 being the slave of the investigator. Even such universal instruments as the 

 Warburg manometer are not free of this evil, and I cannot escape the feeling 



