Firstly, I will reassemble the uncut shafts to see if it is possible to rearrange them in the way they were intended, and secondly, I will seek the governing geometric principles in that arrangement. I offer two approaches to discover what happened. The sorrow is that they weren’t, because the height of the doors had been changed so the shafts carved from the time the templates were made would no longer fit when the next crew came to install them. If the twenty truncated shafts had not been cut there would have been enough to complete the colonnettes if they had been correctly arranged. Indeed, twenty out of forty-three have been shortened. Yet many have been butchered and shortened without any apparent rhyme or reason. Some of the most intricate and careful carving in the portal is found in the thin colonnettes between the column figures. By the time the built the portal foot units were not required, and instead the masters relied on a practical man's geometry so he and his men would know exactly what to do. This is where geometry took the place of measure. Yet masons still had to issue precise directions if stones from the quarry were to fit snugly on site.

It was not a matter of confidence, of which there was no shortage, but of an institutional disintegration that followed as the decline of Roman jurisdiction, and with it rules of measurement faded from use until there was no authorized unit of measure. The portal shows the master's comprehensive inability to share either their designs or their measurements in a way that would enable a successor to complete the work as begun. The misplacements and hacked sculpture reflects their bold attempts to complete the portal without documentation. The former includes the fundamental phrases of Christianity written into the dimensions, including the dedication of the cathedral. It was set out from two sets of ratios, one sacred and the other mundane.

All three lintels were reduced in length as the masters changed, four times.

Mont saint michel and chartres summary