Shammai and the three pillars on which the World stands

The only mishnah in Avot that is attributed to Shammai is found in the first perek, at Avot 1:15.  There, he teaches three things: (i) one should make one's Torah "fixed", which is usually taken to mean either that one should fix regular times for one's Torah learning or that one's fulfilment of its precepts should be constant rather than wavering in accordance with the company one keeps or other influentual variables; (ii) one should say a little but do a lot, and (iii) one should greet other people with a happy, smiling face.

It occurred to me that these three pieces of stand-alone advice somewhat mirror the content of another, earlier mishnah in Avot in which Shimon HaTzaddik lists the three things: (i) Torah, (ii) avodah (literally "service", meaning one's service to God) and (iii) the performance of acts of kindness (Avot 1:2). 

These two mishnayot actually complement each other quite neatly, though this is not a point that seems to have been picked up by earlier commentators [can readers please get in touch if they find anyone who has already made this point?]. "Torah" and "fixing" one's Torah are obviously on the same topic; acts of kindness and greeting people cheerfully both involve an element of respect and concern for other people. That leaves only "service" and saying little but doing a lot. If "service" in context is taken to mean serving God by performing his mitzvot, it makes sense to teach that service of this nature is rendered by doing, by real action, not by talking at length about what one plans to do. This forges a three-ply link between the two mishnayot.