The pasuk tells us that the techeiles string on the tzitzis is central to the reminding function of the tzitzis. How? For the gemarra (Menachos 43b, cited by the Ibn Ezra here 15:38) writes that the techeiles colour is to remind us of the sea, which, in turn reminds us of the sky, which in turn reminds us of HaShem’s throne – which means we remember to do the mitzvos! Rav Leuchter pointed out from here that the Torah expects one to exhibit joined-up thinking/thinking via association. We are supposed to associate the techeiles with the sea, etc. to get to an increased awareness of HaShem. The same goes for Rashi’s explanation (15:39) that the gematria of ‘tzitzis’ plus the knots and strings add up to 613 – we are supposed to use such mental exercises to spur us on in our avodas HaShem.
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