In these notes we revisit the tachyon lagrangian in the open string field t
heory using background independent approach of Witten from 1992. We claim t
hat the tree level lagrangian (up to second order in derivatives and modulo
some class of field redefinitions) is given by L = e(-T) (partial derivati
veT)(2) + (1 + T)e(-T). Upon obvious change of variables this leads to the
potential energy -phi (2) log phi (2)/e with canonical kinetic term. This l
agrangian may be also obtained from the effective tachyon lagrangian of the
p-adic strings in the limit p --> 1. Applications to the problem of tachyo
n condensation are discussed.