On Twitter, I came across a thread among my friends discussing how to name your child. The issue has to do with alphabetical orders. As Thai children often have to write their name in both Thai and English, how should parents name their children such that they appear among the first few names on a list, given that the list follows the Thai and English abugida/alphabetical order?

In other words, what is the optimal name a child can have order-wise?

I formulated a simple measure, i.e. the sum of the ordinal of the Thai and Latin letter corresponding to the Thai letter based on the system by the Thai Royal Institute. For example, the first letter in the Thai abugida is <ก>, which can be transliterated into the Latin alphabet <k>, which is 11th in the English alphabetical order. The total badness score <ก> receives is therefore $\frac{44}{1}$ (1st in the Thai order) $+ \frac{26}{11}$ (11th in the English order) $= 0.4458$. By this measure, I found that the best letter one can have as an initial is <จ>. The Royal Institute standard transliterates <จ> as <ch>, and only the first letter is considered for the digraph, so <จ> is assigned the total score of $\frac{44}{8}$ (8th in the Thai order) + $\frac{26}{3}$ (third in the English order) = 0.297 The worst is <ย> with a score of 1.734 ($\frac{44}{34}+\frac{26}{25}=1.734$).

But wait, does the “badness” of the position in the order increase linearly as assumed? Perhaps it increases exponentially, then the picture changes. Assuming arbitrarily the exponential badness function $b(x)=(\frac{2}{3})^{\frac{n}{x}-1}$, where $x$ is the ordinal and $n$ the number of letters in the writing system. Based on the total badness (calcuated from $b(x)$ for both Thai and English), the ranking changes slightly but the worst letter is still <ย>.

This simplistic formulation is clearly inadequate. Ideally, we would want a more realistic measure that corresponds to the psychological state of the named and/or the socioeconomic benefits that accompany the position in the sequence. More research still has to be done on a more extensive scope (the second letter, the third letter, etc.). From this point, I envision an ambitious project to arrive at the general form of the Law of Naming.

What would be the implications of this Law I do not know, but the same can be said about a great many legendary mathematical findings at the time they were found. One thing is for sure, though: the possibilities for research in this area are endless.