Synchronicity in Samarkand …

I had intended my next post to continue the story of inorganic carbon in freshwater but a holiday has intervened. However, as is often the way with my travel, I have found some unexpected associations with my professional life.

I had wanted to show, using a graph, how much influence inorganic carbon supply (which freshwater biologists refer to, confusingly, as “alkalinity”) had on the types of diatom that are found in rivers. But the simple act of plotting a graph with Excel had, I realised, some unexpected resonances with my current location in Central Asia. I am in Samarkand, in Uzbekistan, a city with a very long history and which numbers Omar Khayyam (1048 – 1141) amongst its previous inhabitants. Omar Khayyam is best known in the West as a poet but was also a noted mathematician and astronomer. Khiva, another ancient city in Uzbekistan, was the birthplace of Muhammad ibn Musa al-Khwarizmi (c.780 – 850) regarded as one of the founders of algebra. Both, in other words, laid the groundwork for the equation y = mx + c, the equation for a straight line that allows me to express the relationship between the diatom assemblage and alkalinity in quantitative terms.

The relationship between the Trophic Diatom Index and alkalinity in a dataset drawn from UK rivers. More about this will follow in a future post but, for now, it is presented as an example of how biological data often fit y = mx + c, the equation for a straight line (indicated by the red line on the graph)

The point of algebra is that you can work out general principles that apply to a situation regardless of the quantities involved. An equation is simply a means of replacing these quantities with letters or symbols so that you can work out the value of something that you don’t know in terms of things that you do know. One of these ancient mathematicians – we don’t know who, but I am giving Uzbekistan the benefit of the doubt – decided to use the Arabic word “shay” (which means “thing”) to represent the unknown in his equations. When the early algebraic treatises were translated to Spanish in medieval times, “shay” became “xay”, which eventually was shortened to “x”. That, at least, is the legend, and no-one seems to have a better explanation. Whenever we use “x” in an equation, in other words, we should reflect that we are part of a tradition that extends back over 1000 years to the plains of Central Asia.

The straight line equation, however, bucks this neat theory to some extent as, in this realm of algebra, “x” represents the known rather than the unknown entity. The unknown, by convention, is indicated by “y”. “Why “y”?” you might ask and, I am afraid, I cannot help. It may be that there is no sensible explanation (“quarks” are, after all, named after a nonsense word in Finnigan’s Wake) but the etymology of “x” is, you have to admit, too good to waste. Especially when writing from Samarkand.

Timurlane’s tomb (Gur-i-Amir) in Samarkand. The photograph at the top of the post shows part of the Registan madrasah complex.

And, finally, I could not resist including this image of decoration on the Sher Dor Madrassa at the Registan: evidence that Medieval Islamic scholars knew about centric diatoms?

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This post really is about Christmas turkeys

Back to the subject of turkeys: real turkeys, this time, rather than bad science.

In the days leading up to Christmas, as the country gradually shut down and real news dried up, so the newspapers filled their space with advice from celebrity chefs on how to roast the perfect turkey.   Strip away all the suggestions to brine, baste, cover with foil and more, and most can be reduced to the very simple formula that I learnt from my mother: 20 minutes per pound, plus 20 minutes.   Which, if you think about it, is basic algebra: y = mx + c, where y = cooking time, x = the weight of the bird and c, the constant = 20 minutes.   I spend much of my working life battering data into forms that can be expressed as lines on graphs and, it seems, I cannot switch off, even when I cook the Christmas dinner.

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The relationship between cooking time and size of turkey, based on the formula 20 minutes per pound plus twenty minutes, but re-calibrated to a metric scale.  The line is the hypothetical relationship; the open circles indicate the reality – read on …

Any cook knows that this relationship is just a guideline, that the best way to determine when the bird is cooked is to pull it out of the oven and poke it with a fork or skewer.  Given the shortcomings of oven thermostats, constant opening and closing of the oven door to put in vegetables as well as variations in the birds themselves, we cannot reduce cooking a turkey to a reductionist formula.   That’s why I put the open circles onto my graph: to show that sometimes the bird is ready sooner, sometimes it takes much longer than we expect.   At some point, the scientist in me has to stand back and let the inner craftsman take over to decide when the turkey is ready to carve.

Back in June I talked about the philosopher William Wimsatt’s work to understand complex systems (“Ecology in an Age of Austerity“), suggesting that it was often better to collect several bit-size nuggets of information, rather than rely upon a single strand of evidence.  My point back then related to ecology, suggesting that the effort spent refining existing approaches to assessment might be better spent looking at alternative sources of evidence.   Cooking a turkey offers a fine example of just that: it may be possible to include more variables and produce a more precise formula for cooking a turkey.   But would it be worth the effort?   We can go only so far with predictive models before we will want to reach for a fork in search of corroboration.  .

The irony is that, pushing my analogy a little further, scientists make their reputations by innovation and a paper entitled A multivariate model for predicting temporal parameters in domestic poultry roasting  will probably be accepted and published by a journal somewhere .  Science will have advanced, albeit incrementally, even if no-one ever puts the elegant ideas developed in the paper into practice.  Lesson #1 from 2013: just because it is in a peer-reviewed journal doesn’t mean that the ideas are superior to the status quo, especially when that draws upon an individual’s experience and wisdom.

Happy New Year