Listening to Triad, one has to believe that there is a very specific reason why Maynard chose to not put vocals to it. If he can put vocals to Lateralus and Schism, he can do so for Triad, a 3/4 song all the way through.
From observation, it seems to me that the Lateralus album as a whole is thematic towards spiritual progression. I think Triad has no words to it because speaking is unnecessary. You don't need to speak to experience something. The band is possibly saying that one of the final steps towards spiritual evolution is completely living for your experiences, and flowing through them without judging them or corrupting them. This is the way Buddhists live, and it's a way I agree with, and apparently, a way the band agrees with.
No clapping, no belting along the chorus... just... listen.