Having just read “Stairway to the Mind” (by Alwyn Scott) I feel compelled to write some comments. I admit to having enjoyed the book for its coverage of various ideas, but I agree with Lee Corbin that he attacks a form of reductionism that I have never encountered. Even the atomic physicist agrees that one cannot practically calculate the spectrum of Lithium (3 electrons) from QM. At several points he emphasizes that the whole universe could not be harnessed to build a computer fast enough to leap some of the steps (on the stairway) that he enumerates. I agree. I even agree that it is an important observation. But I have not met a reductionist who ever claimed that you could. He seems to be battling a caricature of a reductionist.

I will come out with it and say that my ontology is relative. When I do math I will claim that there exist composite Mersenne numbers. When I argue about biology I do not claim that. It will strike some as Bizarre to deny the existence of a number just because I am considering another field. It may indeed not be necessary in that case but I suspect that is in others.

Some years ago I had the good luck to work with an engineer on the design of a modem. I was very familiar with time domain representations of the signal over a phone line and he with the frequency domain. At first I presumed that he agreed that the time domain was the real world and that he merely knew many useful theorems and had many useful intuitions about the frequency domain. It soon was evident that he thought the same about my view—that it was merely a peculiar formal way of looking at things. The good news is that many problems were obscure to one of us and entirely clear to the other. The most dramatic (in my favor) was a very peculiar property of filter that could be proven by fancy mathematics in the frequency domain. The same theorem in the time domain merely stated that a signal can’t begin to emerge from a filter until it has begun to enter it. There are many examples where the opposite applies and the frequency domain makes things clear. In this particular case one mathematical construct, the Fourier transform, mapped from either domain to the other. I found it to be dangerous to mix time and frequency domain arguments. I wish I could remember the nature of the pit-falls. An interesting situation here is that neither view claims to be the lower one. I learned this only after meeting someone that thought my view was not the fundamental one.

Another particular experience with abstraction is in the construction of computers with some well defined instruction set. The correctness of a program written for that instruction set is in no way dependent on the manner that the instruction set was implemented in wires. Creatures implemented in software have no hope of determining the nature of the circuits of the machine, or even their existence.