- It is the ratio between these two sets of values that is important; the ratio of the amount of surface area available to service the needs of the internal volume of the protoplasm, will DECREASE."
A glimmer of insight flicked across Master Kolreuter's face. He was not an unintelligent boy, so he raised his hand. Mendel turned to him at once. "Yes?" he asked.
"Please sir," Kolreuter said, "does this mean that at some point there will not be enough surface area to supply all the needs of the internal volume, so the cell will either have to stop increasing in size, or die!" There was no denying a minor note of triumph as he made the last statement. Kolreuter had his pride and he hoped this input would redeem him in Mendel's eyes.
"Excellent," Brother Gregory exclaimed, "Master Kolreuter has grasped the essential point. "These tiny living spheres are prisoners of mathematics. Two different formulae determine the two essential quantities of internal volume and external surface area. But in life, these two values are vital components of each cell and are inevitably linked together. If a cell were to grow to three times its radius ..." He did the calculations rapidly in his head, "... then ratio of surface area to volume would decrease from a value of three down to a value of one."
Kolreuter raised his hand again, and when called on said, "It is a bit like the barges on the river - remember. In my grandfather's day all wool was brought into Brno by barge, but the river was too narrow and as they built more and more textile factories, the amount of wool reaching the town was not enough. That is why they had to build the railroad. The river was a bottleneck it could not service the needs of the factories in town."
Mendel was beaming. "Perfect! A bottle neck - of course. At a certain cell size there will not be enough surface, through which the juices must flow, to feed all the internal protoplasm."
"Well, of course," Makyatta agreed, but not out of any conviction. Like other mortals, he needed time to digest the ideas that sprang fully formed from the minds of geniuses. In his ex-pupil he saw clearly a truly original mind at work. He knew that Mendel was very adept at making connections between numbers and ideas, after all his whole research project into plant hybrids and how the ratios of flower color in offspring related to inherited 'elementes' depended upon seeing ratios and relationships hidden to normal men.
Which created a connection in Makyatta's own mind.
"Brother Gregory, I don't pretend to understand the complexities of the relationship, but ..."
Mendel didn't hear him. "Which also explains some of the ideas exposed by Doktor Virchow. In his book Cellular Pathology, which was published only a few years ago, Doktor Virchow strongly indicates that disease should be considered to be a dysfunction of cells, not pathologies based on gross structural changes in organs. If cells swell, as in inflammation, then they will not be able to function properly."
"But ..."
"However, Doktor Virchow also makes other claims for cells that may be harder to substantiate," Mendel continued. "He writes in his book that all cells arise from already pre-existing cells, which, if true, means that all life on this planet is cellular in nature - a fact hard to accept if one reads the work of the French scientist Pasteur."
"This is interesting, but ..."
"Pasteur ..."
"Brother Gregory!" Makyatta was able to interrupt at last. "Please, you are going too fast! I am still trying to work out the relationship between the size of cells and barges on the river. Slow down!"