“All exact science is dominated by the idea of approximation …”

I wrote the names of the diatom species I found in Cassop Pond into January 26th’s entry with some trepidation, as I had not followed the usual rubric for identifying these organisms.   I had looked at my samples in their live state at a magnification of 400 times; however, the standard approach would have involved “digesting” my sample with one or more strong oxidising agents, then mounting the empty “shell” of the diatom on a slide and examining it at 1000 times magnification.   What I can say for certain is that the names I used were pretty close to the biological truth, that this was “good enough” for my purpose, and that both of the species I named belong to aggregates that are still not fully understood by specialists.  The second organism I mentioned, Fragilaria rumpens, has moved between two genera over the last twenty five years and has been regarded as either a species in its own right or a variety of another species, depending on which book you read.    I could go through the motions of measuring its characteristics and matching these to the closest description in the latest identification guide.  However, in my heart, I’m not fully convinced that this is yet the definitive account.

These problems came into clear focus a few years ago when a group of fellow diatom specialists from around Europe came together to compare our identifications as part of a wider exercise to ensure consistency in ecological assessments (see abstract).   We all looked at the same nine samples and, between us, we used 701 different names for the species we found.   Yet when we looked more closely at these names, we found many cases where the same organism had been giving different names, depending on who had done the analysis.   Untangling this reduced our list to 546 species.  Whilst there was broad agreement amongst us about the composition of the samples, it was also clear that we were all bringing different preconceptions and ideas to the analyses and that this was influencing the outcomes.  The “truth”, in other words was a slippery and flexible commodity.

I recalled this episode very recently when I came across the following quotation about the fundamental laws of arithmetic from the philosopher Bertrand Russell (quoted in Simon Singh’s book Fermat’s Last Theorum):
“But”, you might say, “none of this shakes my belief that 2 and 2 are 4”. You are quite right, except in marginal cases – and it is only in marginal cases that you are doubtful whether a certain animal is a dog or a certain length is less than a metre.  Two must be two of something, and the proposition “2 and 2 are 4” is useless unless it can be applied.  Two dogs and two dogs are certainly four dogs, but cases arise in which you are doubtful whether two of them are dogs. “Well, at any rate there are four animals,” you might say.  But there are microorganisms concerning which it is doubtful whether they are animals or plants.  “Well, then living organisms,” you say.  But there are things of which it is doubtful whether they are living or not.  You will be driven into saying: “Two entities and two entities are four entities.”  When you have told me what you mean by “entity”, we will resume the argument.

Though written a century ago, Russell was scarily prescient in his use of microorganisms as examples.   We still struggle to identify these smallest of organisms but it is no abstract philosophical debate.  Being able to agree on the identity of “entities” becomes of central importance to anyone engaged in applied research involving the microscopic world.   It is not an easy problem to solve because taxonomy in this realm is far less resolved than that of macroscopic organisms.   At the purely practical level, the differences between these species sometimes lies at or beyond the limits of resolution of our microscopes.  One of the more intriguing findings of recent years is that there are many more species of diatom than hitherto suspected.  Who knows whether our “Fragilaria rumpens” is one species or several?  They all look very similar to the human eye, but maybe we are grasping at the wrong characteristics?  The vagueness in the identification guides, in other words, often reflects genuine gaps in our knowledge.

The story has a happy ending, of sorts, because we found that this very fine scale variation had little effect on our ecological assessments (see abstract).  This meant that we could “lump” our diatoms into categories that we all agreed upon and which, consequently, represented “entities” that Russell could have accepted.   We could marvel at the seemingly never-ending variations that diatoms present to us under the microscope whilst still being able to get on and do something practical with the data we generated.   And, more pertinently, we were, at least, no longer contradicting one of the fundamental axioms of arithmetic.


One thought on ““All exact science is dominated by the idea of approximation …”

  1. Pingback: An inordinate fondness for … algae* | microscopesandmonsters

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