My chavrusa and I are currently up to Megila 25a, where we learn that 
one should not daven "Modim Modim", nor "Shma Shma", because it 
appears that the duplications are directed towards different deities, 
chas v'shalom. Rishonim and acharonim (see Orach Chaim 61:9 and 
121:2) mention that this applies whether one repeats only the first 
word, or even the entire sentence.

We are trying to understand the logic here. In modern English, one 
who says "Thank you, thank you" or "listen, listen", does so for 
emphasis, not in order to address different people. There is no 
presumption that these would be addressed to different audiences 
unless the speaker would do something to indicate that, such as 
repositioning himself so that the repeated phrase is clearly directed 
elsewhere. I would understand banning "modim modim" and "shma shma" 
if it were clearly directed at different audiences, but I have not 
seen that inside.

(In fact, even if the two Shma's *were* directed at different 
audiences, I'd still have extreme difficulty understanding the 
problem, because it would be talking about two Yisraels, not two 
HaShems. Where is the polytheism in saying Shma twice? Even if "Modim 
Modim" thanks one deity and then another deity, I just can't figure 
out why this problem even exists in the case of the Shma.)

Furthermore, Lashon HaKodesh has a clear standard of using repeated 
words to show emphasis. The repeated word often is in a different 
grammatical form than the first, but that is not always the case. In 
fact, if we are on the topic of using repeated words to suspect 
someone of heresy, can there be a clearer example than the repetition 
of Hashem's name in the 13 Midos? HaShem Himself did not shy away 
from this phrasing, despite the interpretations that the 
first "HaShem" and second "HaShem" have different connotations (such 
as HaShem before I sinned vs. HaShem after I sinned, whatever). If we 
don't worry about possible polytheistic implications there, they why 
would we worry about it when someone simply says, "Listen listen"?

My chavrusa and I suspect that this halacha (not to say "modim modim" 
or "shma shma") is based on linguistic realities which existed in the 
time of the Mishna and Gemara, but are not found in Modern American 
English, and that's why we can't understand it -- the concepts simply 
(and literally) "get lost in translation". Can anyone suggest a 
different way of understanding this topic? Or, can anyone point to a 
similar function which does exist in English?

Thank you
Akiva Miller