Hi Mads,
I have no idea about the entropies. I think though that you are calculating some sort of cumulative string. If you do it per number:
s = Table[N@Entropy@
StringDelete[StringJoin[IntegerName[#, {"Words", "English"}] & @i], {FromCharacterCode[
8208], " ", ","}], {i, 1, 1000}];
ListLinePlot[s, GridLines -> {Range[1, 1000, 10], Automatic}]
Here's a (very badly plotted) image
entropyspeech = Entropy[SpeechSynthesize[StringReplace[IntegerName[#], "\[Hyphen]" -> " "]]] & /@ Range[1000];
Show[ListLinePlot[N[Entropy[StringDelete[StringRiffle[StringSplit@IntegerName[#, {"Words", "English"}], " "], ","]]] & /@ Range[1, 1000], PlotRange -> All],
ListLinePlot[entropyspeech // N, PlotRange -> All, PlotStyle -> Red],PlotRange -> All]
I cannot really tell yet what that means. Perhaps if I plot it better, and fix the problem I mentioned in the reply to Henrik...
Cheers,
Marco