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Polychotomy: Discussing a Rather Nifty Word

This is a re-post from my older blog GeodesicPolychotomy [LINK]

Recently I have been interested in the odd little words that people often either gloss over or just don’t use very often. Words such as schism, epoch or polychotomy. Here I thought I’d have a look at this odd but interesting word to understand the reason why it was circled and ultimately cut from a recent paper I submitted. In terms of language use I have to admit I struggled to see the problem.

The question is should a word be cut, when it provides a way of saying the same thing but using one word rather than many. Is not science about being concise? Is there not an understanding that if a scientific reader doesn’t understand the word they have the capacity to look it up? One doesn’t want to confuse the reader but we don’t want to make a presumption of their cognitive ability? When a conference has stipulated a very short paper format, is it not expected that publication becomes an effort to maximize knowledge transfer? Would it be right to use superfluous words in one paragraph only to have to cut some actual content later? Likewise do we not assume that a field has a consistent language and common paradigm despite that language differing between fields?

So back to this particular conundrum.

Many readers will have heard of the word dichotomy. The Oxford dictionary defines it as “a separation between two things that are opposed or different: the dichotomy between good and evil”. Derived from the Greek word “dikhotomia” meaning a cutting in two. Helpfully we can instantly see the prefix in the word, “di” again coming from the Greek prefix for two. By the very virtue of having a prefix one begs the question, could we have a trichotomy, a tetrachotomy or a decachotomy? If we abstract to any separation of any of ‘n’ objects is it valid to use the word polychotomy? Which here we will define as the the splitting into many rather than just the two in the classically understood dichotomy.

After a discussion with a computational linguist a few weeks ago they came back with a point that is rather important in terms of modern classification of words and indeed our archival of those words. If a word is made up of a prefix, a stem and a suffix, would you list every single variant in the dictionary? Here I’m thinking of the variants, plurals, and tense endings, “ing”, “ed”, “s”. Or would the dictionary list the stem, a section on prefix and suffix grammar (often found as an extra section) and possibly list a few of the more common prefixed versions of the word? Certainly we already have the words hexagon, pentagon and polygon. These words effectively show we have an ability to abstract up the numerical prefixes towards an overall generalization using the “poly” prefix.

After further digging the word polychotomy is in fact not in the Oxford dictionary. However the word trichotomy is listed clearly at Oxford Dictionary Online (Trichotomy – Oxford Dictionary Online). An interesting discussion with a pure mathematician yielded another point. Is it valid to talk about a prefix-stem and the generalization of that word if the stem is not in the dictionary? Lets take the example of a hexagon, pentagon and polygon. Each of these words are in the dictionary, but is the word “gon” in the dictionary? In the full Oxford dictionary it does, but is listed only as a combining form. “-gon” with the definition of “in nouns, denoting plane figures with a specified number of angles and sides: hexagon, pentagon”. See here: “-gon” Oxford dictionary Online. The listing then goes onto say, “from Greek -gōnos ‘-angled'”. We therefore effectively have a stem that is never used either in modern language or indeed in the Greek, its always used in the combinatorial form, indicated by the hyphen at the start of “-gonos”.

Coming back to our word of choice in this discussion, does a “chotomy” exist, the answer is yes but in a slightly different form. From the original Greek “dikhotomia”, there is the combinatorial form of “-tomia”, or the modern version, “-tomy”. Interestingly, this ending is still in use as evidenced by the listing for “botany” a “[mass noun] Botany repeated branching into two equal parts”. Its nice when things link up isn’t it. Having said that, the exact specific linguistic process where a spelling is able to morph (-tomy to -tany) is beyond my field. For completeness the listing for “-tomy” is here: “-tomy” Oxford Dictionary Online, effectively listing it as a combining form meaning “cutting, especially as part of a surgical process: episiotomy”, “from Greek -tomia ‘cutting’, from temnein ‘to cut'”.

So to summarize briefly, we do indeed have a stem, we have the prefixes and we have dictionary listings for certain common forms of the prefix-suffix combination. We also have a useful prototype in the use of the prefix-stem use of the combining form “-gon” and not to forget we have the similarity between the usage of the combining forms “-gon” and “-tomy”.

From further discussion with various language students and mathematicians we now have to deal with the tricky subject of contemporary word usage. And the even more difficult discussion of whether people can conceptually leap from “dichotomy” to “polychotomy”.

  • Lets first deal with the conceptual leap. Whenever we use language we make an assumption. We assume, quite rightly, that the reader or listener is of normal intelligence. We should never talk down to someone or presume we are of higher intelligence. To do so is a very easy way to lose respect, friends and alienate colleagues. This becomes heightened in academia as you have to assume that the reviewer of your paper/manuscript is probably higher up the academic ladder than you. Certainly it bodes well to have a healthy respect for authority, I’m just a lowly PhD student trying to persuade a number of peer reviewers, doctors and professors that the content deserves publication. With constructs such as hexagon, pentagon and polygon in total contemporary use and indeed taught from a very early age, one must assume the reader can use normal prefix-stem grammar. It does help that while the Latin and Greek languages are rather niche these days, their influence litters our language. Here is a nice link to numerical adjectives and prefixes, Phrontistery Numerical Adjectives. We can then move away from spoken language use and into mathematics. The ideas of counting, sets and abstraction are a regular feature of both university level and school mathematics. Concepts such as geometric series or the Taylor expansion or the interpretation of infinity should not be new to many people, although they may not know or may have forgotten the actual names for the concepts. They will still remember that we can write the integer set as {1, 2, 3, 4, 5, …, n} or that we can use a summation over a set. If these concepts are so ingrained in us from an early age and are reinforced continually as an individual progresses through education, can we really assume they are too “dumb” to make the conceptual leap from two to many or from “di-” to “tri-” to “poly-“. My personal feeling is that assuming your reader is stupid or purposely dumbing down language is a very slippery route and should be avoided at all costs. The fact that the final version of the sentence in the paper was longer, added to my frustrations.

  • Lets now deal with contemporary word use. At what point should we self-regulate and cut a word if its contemporary use is really very rare? For polychotomy it doesn’t take long to amass quite a few uses of the word. O the magic of Google. I was quite interested to see a Wikipedia entry Polychotomy at Wikipedia which helpfully does two things. Firstly it nicely defines the word as a generalisation of dichrotomy, explicitly stating the splitting into many parts or classes. Secondly it nicely links to “polytomy”, meaning “many temporal based branches”. One of the interesting things in modern language use is the linkages and differences between multiple world dictionaries. While the Oxford Dictionary doesn’t include polychotomy, via the website the word polychotomy is listed in the Webster’s New World College Dictionary with the definition of “division or separation into many parts, classes, etc”. Why one dictionary lists it and another dictionary could be a feature described earlier by the redundancy of listing all combinations of the prefix-stem-suffix for a particular stem.

Polychotomy has also been listed on the International House of Logorrhea blog, a rather nice compendix of rare words, purely for the joy of language Polychotomy: International House of Logorrhea.

The contemporary use of the word can be further verified by a very quick Google search, and hence my frustration at being told to cut such a wondrous word. In the world of decision and classification mathematics comes the concept of the Polychotomous key, defined as the number of alternatives from a decision point. From economics we have “polychotomous choices” simply defined as a multiple choice where the dependent variable has more than two possible values.

A close friend of mine has weighed in on the contemporary usage and publication debate by asking if the word has been used in recent publication either in my own field or in related academic circles. While the work published does rely on some statistical analysis and not high level statistical constructs, from the domain of statistics itself we find polychotomy being used in Polychotomous Stepwise Logistic Regression. For the benefit of any statistical mathematicians reading this, a usage of the word from the front page of Google obtained the 1996 paper by Kooperberg “Polychotomous Regression” found here Polychotomous Regression: Kooperberg and the paper “Bayesian Analysis of Binary and Polychotomous Data” by J Albert, S Chib Bayesian Analysis Binary Polychotomous Data: Albert

The next point then, after the word has clearly been shown to exist, is its use in my personal field and whether the target audience has ever had the opportunity to see the word, outside of the arguments above about the stem, prefixes, other combining forms or the conceptual frameworks already available for the word. Within the wide world of engineering, my field could be pretty much described as microelectronics, opto-electronics, the detection of light, using that light for optical signalling but also I should really include optical generation and in fact all fields relating to topics discussed in the proceedings of the target IEEE conference.

Being an IEEE conference, its logical to ensure the word has been used in either the title, abstract or text of an IEEE archived paper. Very quickly searching the IEEE xplore server we find: “Decomposition Methods and Learning Approaches for Imbalanced Dataset: An Experimental Integration”, 2010, P. Soda. 2010, that seems reasonably contemporary. “A Fuzzy Rule Learner for Inducing Reliable Classifiers”, E. Hullermeier, 2009. Both include the word in their abstracts. Due to the nature of the word, in engineering its always likely to be in one of the decision analysis, biomedical, computer classification or computer interaction conferences. But I wonder if it has had any use closer to my field?

Being involved with what is essentially a quantum detector for single-photons, it is interesting that the word polychotomy pops up in a quantum mechanics paper on effects relating to the increase in optical intensity in lasers. “Polychotomy, Spreading, and Relativistic Drift in Strong Field Photodetachment”, R. Grobe and M. V. Fedorov, 1993. Here it relates to the splitting into a multi-peaked structure in the higher states in a potential well. Still, being quantum theory, its not entirely related to my field but it at least shows the word is used.

I think then, to close, my original (pre-cut) use of the word polychotomy in a microelectronics paper can be reasonably well justified. It would be nice to see the word in the proceedings to which the paper was submitted but certainly we have seen that not only does the word have a very strong linguistic precedent set by other constructs, it is also in contemporary use by a number of different fields. I’d hope you’d agree that just because a word is rare it doesn’t mean it should be cut and replaced by a physically longer string, dumbing down the original sentence and removing physical space that could be used to include another numerical value or another word into another sentence to increase clarification of a complex topic.

Edit 1: Just to clarify, the conference the paper was submitted to, has seen “dichotomy” used quite widely in published papers, proceedings and archive listings. I’ll see if we can find any direct uses of the “poly-” prefix. Stay tuned.

Edit 2: While we should never confuse a reader, a member of my office mentioned that when publishing you should make the reviewer’s job reasonably easy, heavy on the technical content perhaps but relaxing the heaviness of language used throughout. When a reviewer has perhaps 30 papers to review any words they are instantly not aware of or bad grammar etc will just push them away from the paper. In an ideal world the use of a word like polychotomy should be fine to use in a published context but we certainly shouldn’t assume the reader has the time to look it up (as we have been doing here) if they are not instantly aware as to its meaning. This argument is reasonable enough, but it does seem a shame to restrict language use in order to further the paper through the review process. Not to mention the dumbing down of a sentence will ultimately cause problems for science. Further to this, I’d argue that there is enough bespoke words and field specific language that a reader may in fact come across words outside of their normal vocabulary reasonably often. Certainly the case with papers crossing the divides between engineering, physics, maths, biology or medicine and most likely papers crossing from field to field even within microelectronics engineering. One just needs to look at field specific language use in large conferences such as ISSCC or ESSCIRC.

Edit 3: A friend just sent me this, rather interesting.

At the time, (2012), Becky also left a reply on this blog post:

Becky Price says:

May 8, 2012 at 11:12 pm

This is a well written piece….. and as a linguist I would fully support the usage of “polychotomy”. Granted it probably does not have its own dictionary entry in most if not all dictionaries, but assuming that the reader is familiar with the concept of a “dichotomy”, the cognitive processing would recognize the word as being composed of two morphemes: di+chotomy, but they are bound morphemes which cannot stand alone.

According to the Principle of Compositionality in Linguistics, a complex expression is comprised of the meanings of its constituent expressions, which then combine to form a unified meaning. Assuming that the combination is not semantically anomalous (which is it not here), there is no reason why a new form cannot be comprised from a stem and prefix which both have understandable meaning and can combine to make semantic sense.

A new form which is comprised of two semantically sound constituents in isolation, which do not combine to make a grammatically sound word would be something like *unwalk. The reader is doubtlessly familiar with the prefix un-, roughly corresponding to a reversible process, and the verb walk, denoting the action of walking. However these two meanings cannot combine together because there are lexical restrictions regarding what un- may attach to, namely that which is reversible, and the verb “to walk” is not a reversible process and therefore is not grammatically valid.

However, as you have stated in the above, there are indeed dictionary entries for both poly- and ‘chotomy’, and from my perspective the Principle of Compositionality is easy to apply here, and that the meaning of the word is easy to infer. I daresay the writer is able to think of a new compound word with which to describe the character of the aforementioned moderator of their paper…

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