Tangerine Seams

Where I grew up "tangerines" was a collective noun for satsumas, mandarins and clementines. They were always a Christmas treat, making this a festive post :)

Of the three satsumas were my favourite. Partly they just tasted better and partly because they were so much easier to get into. A stiff thumb into the bottom and up the central column usually split the skin and spread the segments nicely. A twist and tug would simultaneously separate the segments from the peel and splay them ready to be pulled out. Contrast that with mandarins, where the above procedure would kinda-sorta work but usually leave the segments mashed and your hands covered in pungent peel-sweat. Tougher mandarins and virtually all clemantines would resist hand peeling completely and need either quartering with a chef's knife or painstaking removal of dozens fingernail sized pieces of peel. No 10-year old has that kind of time.

So then, why is this? What are the differences between the three?

To my mind citrus fruit break down into three relevant parts, the segments, the skin, and the pith binding them together. By "strength" in this case I mean something like "resistance to tearing".

Skin strength. This varies with the thickness and rigidity of the skin. I'm going to assert that this is pretty much the same for all my tangerines (though I couldn't get away with this if I was considering oranges too). So while it might set a scale for some of the behaviours it can't explain the differences between the three and I'll leave it out of the remainder of this post.

Segment strength. This is the integrity of any particular segment.

Pith strength. The integrity of the pith itself, and in particular its ability to bind the skin to the segments and the segments to each other (I'm assuming that these are more or less the same).

Since I slyly ditched the skin strength I only have one combinatorial ratio to worry about - the segment to pith strength. Variations in this single parameter can explain our three test cases. For segment strength>>pith strength we have satsumas, for segment strength<<pith strength we have clementines, and somewhere in the middle we have mandarins.

Essentially I'm saying that the segments (and peel) are semi-independent entities coupled together by the pith. Where the coupling is weak the segments interact weakly and are easily separated. Where the coupling is strong the peel and segments act almost like a single entity that must be cut as a whole or chipped away with a knife. In between the two extremes is more complicated behaviour where many solutions are equally sub-optimal. Segment strength/pith strength is the coupling constant for the system. What I'm doing here is pretty close to a static consideration of a typical simple harmonic oscillator approach (making the "strengths" we are talking about the analogous to the inverse frequencies, the square root of the co-efficient of the restoring acceleration).

Why am I writing about tangerines anyway? Well, I was at a medical conference a few weeks ago when I suddenly thought of tangerines. A urologist was talking about new endoscopic techniques in holmium laser surgery for prostate cancer. Modern treatments for prostate cancer involve destruction of the prostate gland in a wide variety of ways. Now, the prostate is divided into several lobes with membranes in between. The novelty of the technique that the surgeon described, as far as I understood it, was that a remotely manipulated endoscopic laser enabled him to separate and cut out the lobes of the prostate. This used to be easily done in open surgery, but commonly with unfortunate collateral damage to the bundles of nerves that run through that area of the body. There was some compelling video shot from the tip of the endoscope that showed the ease with which he could burn away the membranes and separate the lobes. You see the analogy I'm sure. What stuck me though is that the advantage of one technique versus another is a question of how well they exploit the existing segment to pith ratio.

I was also reminded of a different conference a few years back when I saw a presentation about the epidemiology of stomach and esophageal cancer. ICD-10 coding lumps the upper, middle and lower part of the esophagus together and separates them from the cardia and the rest of the stomach. However, in terms of tissue types (which strongly affect the aetiology of cancer), the lower esophagus is closer to the stomach than it is to the upper esophagus. Here the physical segmentation of the body has acquired a parallel histological coding and the choice between them is the difference between clay and chocolate.

So generalising... applying coupling theory is a nice mini-narrative for considering systems with complex inter-dependent parts, and the possible interventions in them. Happy holidays.