The conjectural parallel subspace distance formula d(X,Y)^2 = ||<XºY>_{m-k-l+2n}|| / ||<X•Y>_{k+l-2-2n}|| has now been proved for 0 <= n < k <= l < m <= 7 : all nontrivial cases from skew to fully parallel in space of up to 6 dimensions. The computation minimises the distance between a point P in X, where subspace X is in general position, and Q in Y, where subspaces Y and Z = meet(X,Y) at infinity are both fixed. Note that under a subsequent isometry moving Y (and Z) also into general position, the right-hand side above would remain invariant. The branch-free polynomial version however was still incorrect, with S -> 1/S accidentally: it should have read d(X,Y)^2 = ||(XºY)(S)|| / ||(X•Y)(1/S)|| S^(m-2) with S -> 0 . Lanco suggests that there is some connection between this stuff and the general meet problem, where the dimension of meet(X,Y) --- not now necessarily at infinity --- exceeds the minimum k+l-m-1 . He may well be right about this; but notice that we do need 2n rather than n in the distance formula, in order to avoid just getting 0/0 whenever n is odd! Similarly, any expression for the universal meet must somehow or other conjure a blade of grade 2m-k-l-n from grators with grades 2m-k-l-2i of fixed parity, irrespective of parity of n . I have uploaded to googledocs a ferocious summary TTT_EGA.txt of EGA as applied to this question. Feedback invited: the URL is https://docs.google.com/leaf?id=0B6QR93hqu1AhZTcyM2EzNzItYWYwNi00NDU3LTk3NzQ... Fred Lunnon