  We establish a pseudoisotopy result for embedding spaces in the line of that
of Weiss and Williams for diffeomorphism groups. In other words, for $P\subset
M$ a codimension at least three embedding, we describe the difference in a
range of homotopical degrees between the spaces of block and ordinary
embeddings of $P$ into $M$ as a certain infinite loop space involving the
relative algebraic $K$-theory of the pair $(M,M-P)$. This range of degrees is
the so-called concordance embedding stable range, which, by recent developments
of Goodwillie-Krannich-Kupers, is far beyond that of the aforementioned theorem
of Weiss-Williams.
  We use this result to give a full description of the homotopy type (away from
2 and up to the concordance embedding stable range) of the space of long knots
of codimension at least 3. In doing so, we carry out an extensive analysis of
certain geometric involutions in algebraic $K$-theory that may be of
independent interest.
