Stadtarchäologie - Workshop 7

Permutations of the Multilinear Stratigraphic Sequence: Nature, Mathematics and Consequences

The phrase "permutations of the multilinear stratigraphic sequence" was introduced in 1984 by Edward C. Harris . Since then the notion has entered into the collective awareness of stratigraphers, though no author has so far been willing to confront permutations head on. Harris noted that the notion was "not acceptable for publication in 1982" And less than a decade ago (1993) Triggs elegantly understated that when "a single deposit is held constant and other deposits are moved in relation to it, the permutations ... ... can be on an exponential scale for even a small site."
This contribution discusses the nature of "permutations of the multilinear stratigraphic sequence" and suggests ways of calculating those permutations. It will be necessary to look at the mathematics appertaining to the stratigraphic sequence in some detail to understand how permutations may be calculated. Then, in conclusion, to discuss the consequences of this explicite knowledge about the permutations of the mulilinear stratigraphic sequence. For the phasing of a site is closely related to the reduction of the possible permutations of a stratigraphic sequence to a number less than the maximum. This takes place under inclusion of non-stratigraphic criteria such as finds-dating, dendrochronology etc. Phasing does not change the relationships of contexts on a common lines of the sequence. Rather, is fixes the relationships to each other in time, of contexts on different lines, whose relationships cannot be ascertained on purely stratigraphic evidence, thereby assigning them to phases and periods. The reduction of the permutations to less than the maximum therefore has a direct relationship with the interpretation of a site and with the definition of phase- or period-interfaces. At its simplest, accepting the maximum permutations would essentially be the same as admitting that the site is unphasable. Conversely, a single possible permutation would indicate a perfectly phased site where everything fits into place. The analysis of permutations might therefore not only be an archaeological tool which can facilitate the phasing of a site but also an analytical one with which the criteria used in phasing and thus interpreting any site can be critically examined.

David Bibby
Landesdenkmalamt Baden-Württemberg david@bibby-online.de

Permutations of the Multilinear Stratigraphic Sequence: Nature, Mathematics and Consequences The phrase "permutations of the multilinear stratigraphic sequence" was introduced in 1984 by Edward C. Harris . Since then the notion has entered into the collective awareness of stratigraphers, though no author has so far been willing to confront permutations head on. Harris noted that the notion was "not acceptable for publication in 1982" And less than a decade ago (1993) Triggs elegantly understated that when "a single deposit is held constant and other deposits are moved in relation to it, the permutations ... ... can be on an exponential scale for even a small site." This contribution discusses the nature of "permutations of the multilinear stratigraphic sequence" and suggests ways of calculating those permutations. It will be necessary to look at the mathematics appertaining to the stratigraphic sequence in some detail to understand how permutations may be calculated. Then, in conclusion, to discuss the consequences of this explicite knowledge about the permutations of the mulilinear stratigraphic sequence. For the phasing of a site is closely related to the reduction of the possible permutations of a stratigraphic sequence to a number less than the maximum. This takes place under inclusion of non-stratigraphic criteria such as finds-dating, dendrochronology etc. Phasing does not change the relationships of contexts on a common lines of the sequence. Rather, is fixes the relationships to each other in time, of contexts on different lines, whose relationships cannot be ascertained on purely stratigraphic evidence, thereby assigning them to phases and periods. The reduction of the permutations to less than the maximum therefore has a direct relationship with the interpretation of a site and with the definition of phase- or period-interfaces. At its simplest, accepting the maximum permutations would essentially be the same as admitting that the site is unphasable. Conversely, a single possible permutation would indicate a perfectly phased site where everything fits into place. The analysis of permutations might therefore not only be an archaeological tool which can facilitate the phasing of a site but also an analytical one with which the criteria used in phasing and thus interpreting any site can be critically examined.