In this paper we improve the bound on the value of Dylan's constant 𝐷. This value, first defined by Dylan [1963], is the number of roads that a man must walk down.

We briefly recap the history of Dylan's constant. Although it is not a priori obvious that a man must walk down a finite number of roads, a relatively elementary nonconstructive proof that 𝐷 is finite, using the pigeonhole principle, was quickly given by Yarrow, Stookey and Travers [1963]. The first explicit bound, a stack of exponentials of height 5, was found by Wonder [1966]. This bound was significantly improved by Baez [1976] to 𝐷 ≤ 420 using methods of higher category theory. Although this bound remains the best known currently, Adams [1980] conjectured that 𝐷 = 42 based on extensive computer calculations.