Information Entropy

A formal definition of functional load was given by Charles Hockett . His calculation was based on a measure of the entropy \citep{Shannon1948} in the language in question, the formula for which can be seen in Equation \ref{eq:entropy} (for each phoneme \(\phi\) in the language’s phoneme inventory \(\Phi\)) where the probability of a phoneme is calculated as its relative frequency.

\[\label{eq:entropy} H(L) = -\sum_{\phi\in\Phi} P\,(\phi)\text{log}_2P\,(\phi)\]

The idea was simply that the amount of work done by a given contrast is the amount of information that would be lost if this contrast is neutralized. His formula thus requires the comparison of the language \(L\) with a theoretical language \(L_{x,y}\) where the contrast between phonemes \(x\) and \(y\) is neutralized.

\[\label{eq:hockett} FL(x,y) = \frac{H(L) - H(L_{x,y})}{H(L)}\]

Work on this formality was later expanded to include any type of contrast imaginable within the phonology of a language. Hockett’s formula was designed specifically to calculate the functional load of a contrast between two phonemes, but its basic principles can (and have) been extended to featural, syllabic, and even whole-word contrasts \citep{Surendran2003,Surendran2006}.

This measure has been used and compared with the simple minimal pair counts method as a predictor for phoneme loss \citep[cf.][]{Wedel2013}, DISCUSSION OF RESULTS FROM THIS PAPER.

An important issue with the entropy measure is its sensitivity to phoneme frequency. The more frequent two phonemes are, the more likey they are, by chance, to form minimal pairs in the lexicon. This means that their functional load might be artificially inflated compared to a measure that extracts away phoneme frequency. Indeed the question of frequency is discussed in Wedel et al.’s article. Once frequency is allowed to affect the measure, a decision must be made whether the additional factor of token frequency should be taken into account. We find this dissatisfactory and therefore rejected information entropy as an appropriate measure of functional load.

An additional issue with Hockett’s method is the results that it gives. After implementing Hockett’s method, the resultant data are a series of values measuring the functional load of each feature. The voicing feature will have one value, and the place feature another. It is, however, very difficult to compare these values to one another. As can be seen in Table \ref{tab:surendran}¹, there are patterns in the differences between the various features (place has a higher value than manner which has a higher value than voicing in all four languages Surendran & Niyogi tested). We are incapable, though, of saying to what extent these differences are important. We cannot easily determine to what extent place is more important than manner in a given language, nor if these differences are important cross-linguistically. Note also that the values we obtained for French are much higher than those reported for other languages.