Embedding the diamond graph inLpand dimension reduction inL1

We show that any embedding of the level k diamond graph ofNewman and Rabinovich [NR] into L_p, 1 < p 2, requires distortion atleast . An immediate corollary is that there exist arbitrarilylarge n-point sets such that any D-embedding of X into requires. This gives a simple proof of a recent result of Brinkmanand Charikar [BrC] which settles the long standing question of whetherthere is an L₁ analogue of the Johnson-Lindenstrauss dimension reductionlemma [JL].