After writing the previous post I discovered a web site where Sydney Brenner talks about his life on video. He discusses many interesting things which I cannot go into here. I just want to concentrate on one subject which he mentions there, Schrödinger’s book ‘What is life’. A large part of this book, which was published in 1944 and is available online, is concerned with the mechanism of heredity. It had a strong influence on a number of important biologists, including Francis Crick and James Watson. Thus it may be said that, at least on the level of motivation, the book made an important contribution towards the discovery of the structure of DNA. Brenner’s attitude to Schrödinger’s book is rather negative. He is of the opinion that the one who really gained important insights into heredity from the point of view of mathematics or physics was John von Neumann, following up on ideas of Alan Turing on computing. Unfortunately the biologists payed little attention to (or simply did not know about) this work of von Neumann.
Most of Schrödinger’s book is about heredity. He starts by pointing out that because of the universal presence of fluctuations in the real world a mechanical system cannot work in a reliable way unless it consists of a very large number of atoms. A system consisting of only a few atoms is too sensitive to random disturbances. This Schrödinger presents as the answer to the question why living organisms are so big on the atomic scale. Although the fluctuations arise from quantum phenomena this is not crucially important for the discussion. What is important is that there is some prolific source of fluctuations. Now a gene can be estimated to consist of a number of atoms which is not enormous. The question then is how genetic information can be passed on so reliably from one generation of cells to the next. The answer (in my words) is that it is a digital system. The information is stored in discrete pieces and these cannot be routinely affected by small fluctuations. This has to do with quantum theory and the presence of potential barriers which must be overcome to change from one state to another. The information in the chromosomes is encoded (in Schrödinger’s picture, which we of course now know to be correct) in chemical bonds. The stability of this system rests on the stability of the chemical bond and this in turn is really a consequence of quantum nature of atoms.
Brenner’s objection to Schrödinger’s presentation is that while in reality the genetic material only contains the information needed to make a new individual Schrödinger does not clearly distinguish between the information and the machinery required to implement that information to replicate the cell. In modern terms, he does not distinguish between the role of DNA and that of such things as messenger and ribosomal RNA. This, apparently, von Neumann did without of course knowing anything about the detailed mechanisms. I would tend to say that Schrödinger’s picture was not wrong, its disadvantage being that it is at too low resolution.
I enjoyed reading most of Schrödinger’s book but I felt less well when I got to chapter 6 where the concept of entropy takes center stage. Schrödinger writes (on p. 30 of the online text) ‘Let me first emphasize that it [entropy] is not a hazy concept or idea …’ This is not enough to reassure me. I often feel that even if entropy is not ‘hazy’ in principle it often does have that character in the way it is used by many physicists, not to mention others. When in the seventh and last chapter Schrödinger seems to leave the realm of science in the direction of religion I feel that it does not concern me any more. Chapter 6, on the other hand, does seem to concern me and leaves me with an uneasy feeling. There may be some unfinished business for me there.
Hydrobates 
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