Murray Gell-Mann once whispered (in a typically mischievous Murray way) to me during an @sfiscience seminar, "biology is not ready for maths."

I don't agree but I am sympathetic. Moving forward requires triangulating bw diff types of representations. Even as we approach the end of a problem I think what actually crystalizes is not just an equation but mappings + isomorphisms, with understanding residing inside the triangle—a position that is akin but not identical to one of Roger Penrose's, and captured in his three-world's diagram.


Lots of discussion lately about the value of math + formalization, particularly for problems at the boundary of science + philosophy. Formalization can help to clarify as long as we remain aware of its + our limits.

Triangulation (mine—data, mathematical formalisms, natural language) in no way implies some biological problems are not describable mathematically or are better described by natural language. Rather I am suggesting that understanding resides in triangulation itself, with no specific type of representation *necessarily* dominating although some forms might be more generative. The power is in establishing isomorphisms + mappings.

WRT to Murray's point. I reiterate he was being cheeky. He did after all found
@sfiscience. At the time he made the comment, probably around 18-20 years ago, microscale data was less common than it is today. And the divide between modelers + theorists in biology was large. That divide is still large although it is improving. And today we have much higher quality microscale data, which allow derivation of macro from micro and hence checking to make sure our macroscale variables are fundamental, not the result of observe bias. Murray's point was about attending closely to patterns in nature + finding principled ways to describe those patterns, understanding when a phenomenological approach is a valid one, + having humility about what we don't know.

Another yet more profound take on triangulation says it's not just the cause of understanding but the causal dynamic underlying existence. This version comes from Wheeler, who in claiming that observer-participancy is the basis for "it from bit" invokes a triadic interaction à la Peirce, whom he cites towards the end of his it from bit paper. The existence of a photon is confirmed when it collides with + is absorbed by an electron. This event is registered by a measurement device, which in Wheeler's telling, is a third-party to the event (the apparatus in an experiment) but it could also be the electron itself, which in absorbing the photon moves to a higher energy state. These two possibilities entail somewhat different causal networks but both have a triadic character. According to Wheeler, the universe is a loop born out of this very simple dynamic.