50 Years of the Roche Biochemical Pathways Poster

See Roche Biochemical Pathways - A legacy in scientific education.

I used to work at the University of Cambridge Computer Laboratory, where it was my job to maintain the software on people's personal computers. In order to stay sane I spent most of my spare time at the gym or cycling. I used to have an A2 printout of this poster on my wall. I loved it because it was presented as a kind of circuit. You could imagine simulating cellular metabolism on a computer by modelling reaction rates, concentrations etc. in π-calculus and plotting the physical evolution of the system in terms of some series of, what? Graphs of concentrations, temperatures, and reaction-rates? But they would have to be spatially represented somehow, ... how would you do that? How would you know what these processes you had modelled were actually doing physically? When you think about it this way, you actually find that you are asking yourself "How did they produce this abstraction?" What materials did they have in their labs? Were they looking through microscopes at individual e-coli cells and measuring infra-red radiation and refracted light to see what temperature it was at various places in the bacterium as it moved around through its environment? Seems unlikely. I was having enough trouble maintaining computer software, ... how does a cell maintain this laboratory which constitutes its being? I guessed it was pretty much by doing lots of exercise and cycling to work every day. See Popper's Non-dualist Theory of Objective Knowledge.

Joe Hurd was a PhD student of Mike Gordon, then was a postdoc at Cambridge for a few years, then went to Oxford, then came back to Cambridge and the last I heard he went to work for Galois Connection in Portland, OR. Joe's PhD dissertation was on formalising proofs in Higher Order Logic of number-theoretic properties of cryptographic protocols. He did a clever thing which was to write the arithmetic evaluator of the HOL theorem prover in such a way that every computation of an arithmetic operator on integers was represented by a proof of the result. So every calculation of, say m=1,234^153 + 567^153 was a proof that m was indeed equal to that sum of 153rd powers.

Joe and I once had a conversation about the halting problem, and I said something like "how do you know that machine exists?" and his reply was "because I just described it!" That was pretty much the end of that leg of the discussion.  Then one day we had another conversation about intensionality in the definitions of mathematical functions, I think, and in biological systems. He said that when he sees me cycling down the road in Cambridge he can tell my intention: I am going to work or going home, or something. I replied and said no, I have lots of other intentions. I am thinking about something, I am exercising my calf muscles, releasing endorphins, etc, etc. I wasn't intentionally working on the next edition of the Roche Biochemical Pathways poster, though I suppose I could have been at some point, ... it depends what the Roche corporation think is the purpose of life. The following full-size drawing is the Biochemical Pathways chart drawn up by Gerhard Michal of the Boehringer Mannheim company, according to a Reddit post:

So how do we know this machine exists? Just because it's effective in some sense? What is an effective method as far as a mathematician is concerned? Doesn't it inevitably involve in some way an act of representation of a problem in a formal system and an act of interpretation of the result? Like HOL proofs of arithmetic calculations, for example? See Fredrik Nordvall Forsberg on Linear Logic.