In Croatia, the first two consonants in many river names are 'k' and 'r', respectively: Karašica (two rivers with the same name), Krka, Korana, Krbavica, Krapina and Kravarščica. Mainstream linguistics considers that to be a coincidence, that those river names are unrelated. But what is the probability of something like that happening by chance? Does anybody know how to calculate that?

I have published a paper in both Valpovački Godišnjak and Regionalne Studije that tries to do just that. It is basically this text, just edited differently.

To summarize, I think that I have thought of a way to measure the collision entropy of the different parts of the grammar. The entropy of the syntax can obviously be measured by measuring the entropy of spell-checker word list such as that of Aspell and subtracting from that an entropy of a long text in the same language (I was measuring only for the consonants, I was ignoring the vowels, because vowels were not important for what I was trying to calculate). I got that, for example, the entropy of the syntax of the Croatian language is log2(14)-log2(13)=0.107 bits per symbol, that the entropy of the syntax of the English language is log2(13)-log2(11)=0.241 bits per symbol, and that the entropy of the syntax of the German language is log2(15)-log2(12)=0.3219 bits per symbol. It was rather surprising to me that the entropy of the syntax of the German language is larger than the entropy of the syntax of the English language, given that German syntax seems simpler (it uses morphology more than the English language does, somewhat simplifying the syntax), but you cannot argue with the hard data. The entropy of the phonotactics of a language can, I guess, be measured by measuring the entropy of consonant pairs (with or without a vowel inside them) in a spell-checker wordlist, then measuring the entropy of single consonants in that same wordlist, and then subtracting the former from the latter multiplied by two. I measured that the entropy of phonotactics of the Croatian language is 2*log2(14)-5.992=1.623 bits per consonant pair. Now, I have taken the entropy of the phonotactics to be the lower bound of the entropy of the phonology, that is the only entropy that matters in ancient toponyms (entropy of the syntax and morphology do not matter then, because the toponym is created in a foreign language). Given that the Croatian language has 26 consonants, the upper bound of the entropy of morphology, which does not matter when dealing with ancient toponyms, can be estimated as log2(26*26)-1.623-2*0.107-5.992=1.572 bits per pair of consonants. So, to estimate the p-value of the pattern that many names of rivers in Croatia begin with the consonants 'k' and 'r' (Karašica, Krka, Korana, Krbavica, Krapina and Kravarščica), I have done some birthday calculations, first setting the simulated entropy of phonology to be 1.623 bits per consonant pair, and the second by setting the simulated entropy of phonology to be 1.623+1.572=3.195 bits per consonant pair. In both of those birthday calculations, I assumed that there are 100 different river names in Croatia. The former birthday calculation gave me the probability of that k-r-pattern occuring by chance to be 1/300 and the latter gave me the probability 1/17. So the p-value of that k-r-pattern is somewhere between 1/300 and 1/17. So I concluded that the simplest explanation is that the river names Karašica, Krka, Korana, Krbavica, Krapina and Kravarščica are related and all come from the Indo-European root *kjers meaning horse (in Germanic languages) or to run (in Celtic and Italic languages). I think the Illyrian word for "flow" came from that root, and that the Illyrian word for "flow" was *karr or *kurr, the vowel difference 'a' to 'u' perhaps being dialectical variation (compare the attested Illyrian toponyms Mursa and Marsonia, almost certainly from the same root). Furthermore, based on the historical phonology of the Croatian language, I reconstructed the Illyrian name for Karašica as either *Kurrurrissia or *Kurrirrissia, and the Illyrian name for Krapina as either *Karpona or *Kurrippuppona, with preference to *Karpona. Do those arguments sound compelling to you?

I understand that I probably should have asked this question before publishing that paper in two journals, but I guess that now is better than never.

  • 1
    My main question is, why would the collision entropy of characters in a written representation be a good measure of this?
    – Draconis
    Commented Apr 26, 2023 at 15:18
  • @Draconis Well, Croatian has a very shallow orthography, so I don't think that's a problem. Commented Apr 26, 2023 at 15:29
  • 3
    The Wikipedia pages for several of the rivers you mention give different possible etymologies. What is the basis for the claim that mainstream linguists consider the pattern to be coincidental?
    – Keelan
    Commented Apr 26, 2023 at 15:40

2 Answers 2


I'm not sure entropy is the right measure for this, particularly collision entropy. Instead I'd recommend a simple frequency analysis.

First, come up with a criterion for what makes a word a "kr"-word (its first two consonants are K and R?). Gather a list of as many Croatian content words as possible. Then gather a list of as many Croatian river names as possible.

Now you can determine the probability that N randomly-chosen Croatian content words will contain at least K "kr"-words. (The simplest way is just Monte Carlo analysis, pick N random words, check if it has at least K "kr"-words, repeat this a few million times, but you can also do more complex probability calculations if you want.)

Count how many river names you've been able to find—all river names, not just the "kr"-ones—and this is your N. Count how many river names are "kr"-words, and this is your K. Use the calculation from the previous paragraph to determine the probability that you get at least K "kr"-words in an assortment of N content words.

That's your p-value, the probability that it's all due to coincidence. The lower the p-value, the more likely there's a pattern behind them. Most people consider p < 0.05 to be "sufficient evidence" but really there's no hard rule for what's "sufficient" and what isn't (sufficient for what purpose?).

  • 1
    +1, but this approach has a serious drawback: the OP presumably looked at a bunch of river names before generating this hypothesis, and a complete list of Croatian river names will include those. Therefore, even if p < 0.05, it's still probably due to random chance! See <en.wikipedia.org/wiki/Multiple_comparisons_problem>, <en.wikipedia.org/wiki/Researcher_degrees_of_freedom>.
    – ruakh
    Commented Apr 27, 2023 at 7:49
  • English Wikipedia lists 32 long (>50km) rivers of Croatia of which 4 seem to meet the KR criterion, plus 13 shorter rivers (1 KR). That may be the highest 2-consonant combination but they do not seem to form an obvious cluster either taking account of vowels or local geography. When testing for it, you need to take account of the point that other pairs could have been the most common.
    – Henry
    Commented Apr 27, 2023 at 8:36
  • If I correctly understand you, your method would lead to a giant under-estimate of the p-value. Do you understand why I was doing birthday calculations? Do you understand why I was using collision entropy instead of, say, Shannon entropy? Commented May 5, 2023 at 17:26

The null hypothesis is that phoneme distribution in words is random. This is quickly falsified by the Syllable Structure Hypothesis, to the effect that in English (for example) syllables can start with kr but not rk.

In Logoori (a different example), after we take into consideration this phonological factor, we then encounter significant correlations that in a corpus of examples, there are very few words that start with [mɪ] and none are nouns, there are very many words that start with [kɪ] most of which are nouns and very few words starting with [ki] none of which are nouns. At some point we arrive at the Class Prefix Hypothesis that says that words are morphologically complex and that words usually start with some grammatical prefix: then we stop looking at words and focus on roots. We manually filter out templatic effects such as the fact that most kinship words have the pattern CVVCV, thought this is analogous to your river example.

In the English dialect around Puget Sound, we find a large number of place names that end is "mish" or "mie", for example Duwamish, thus we discover a statistical anomaly in need of explanation (which is that they derive from a Salishan suffix -mix(ʷ) meaning "person".

The way we conclude that this is non-chance is by controlling variables. The hypothesis is that this mish/mie ending only exists in words derived from Salishan. Step one is to gather all toponyms (west of the peak of the Cascades, east of the Olympics, worry about north/south later). Then eliminate all words with known non-indigenous etymologies (Sand Point, Kent, Mt. Vernon, Des Moines...). Now you just throw the rest into a statistical meat-grinder along with some indications of what you are looking at. In this case, it is the structure of the final syllable: onset consonant, vowel, coda consonant. In the data you will find "claw" (Enumclaw), "lup" (Puyallup), "lie" (Nisqually), "lip" (Tulalip, hmmm), Snoqualmie, Snohomish, Sammamish, Skykomish, Skokomish, Duwamish. The frequency of segments in positions and frequency of particular combinations can be computed, and we see that the frequency of [mɪʃ] at the end is abnormally high (we probably would not even notice "Snoqualmie").

In manually excluding non-indigenous place names, we baked a hypothesis into our data gathering, but we can uncook that by taking all place names and checking whether this correlation is still valid in the face of the larger corpus.

Your hypothesis is (presumably) that #k(V)r words are abnormally more frequent in river names. Obviously you check that there isn't a simple grammatical explanation like a "river noun class prefix". Barring such an influence, you expect that the frequency of #k(V)r river names is the same as the frequency of #k(V)r general words. It is possible that your hypothesis is wrnog, and it has nothing to do per se with river names, it might be hydronyms, or toponym, so you would want to encode for alternative hypotheses.

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