Thanks, @Jeremy! Your questions prompted an etymological quest, and herein is what I found.
I have been perplexed by “vertex” as the organ emphasis of the integral structure, as well. In all the time of my studying and teaching biology and anatomy, I have never seen it used in reference to the surface of the skull. In geometry, it usually has one of two meanings: the top of a triangle, where the two legs meet (the third side being the base), or more generally, any point where two lines of a figure meet (in 3D objects, where two edges meet, i.e. a cube has 8 vertices). But, after further delving, I don’t think either of these capture what Gebser is getting at.
Several months ago, I was given an opportunity to “pillage” the library of a retired biology teacher (and anthroposopher). I found, amidst numerous textbooks, field guides, and a nearly complete collection of Barfield’s writings, a small (6” x 7”), handbound, photocopied 1973 edition of Ursprung und Gegenwart (part I). Its from the “Bibliothek der Padagogischen Forschungsstelle Beim Bund der Freien Waldorfschulen”. So, though I don’t read German, I have been (synchronistically) blessed with access to the original language.
(Vertex) is a translation of (Scheitel). My german dictionary is not great, and only gives this to mean the part of the hair. Internet translators are more helpful, though. The single-word translation I got was “apex”, but here are some other, “looser” meanings:
- the line that divides the hair into right and left halves
- the top of the head
- in architecture, the peak, or high-point (scheitelpunkt)
- in astronomy, the zenith
More meaning can be gleaned from these expressions:
- “jemandem den Scheitel mit der Axt ziehen”: roughly translated, to pull(separate) someone’s “scheitel” with an axe; colloquially, to kill someone (seems reminiscent to scalping, though I’m starting to sense its not of the head, but in some way, above it, as if this is a severing of an “umbilical cord”, connecting a person with their “scheitel”, but definitely I’m projecting here)
- “vom Scheitel bis zur Sohle”: a German version of “from head to toe”
Perhaps out of a wish to avoid Mythical associations, or ignorance, Gebser doesn’t mention what I must admit comes to mind for me, that this is the crown chakra. With the usual caveats, one could easily imagine: magical – root/sacral/solar plexus(?), mythical – heart/throat(?), mental – throat/brow(?)
Viscera, heart, and brain are readily thought of as “physical”, while vertex/scheitel are not so easily imagined (for me). Perhaps when the integral structure is concretized, our idea of “physical” will change to include what seems now to be super-physical.
To return to a more geometric consideration, I am minded of pg. 260, wherein Gebser refers to the (projective) geometric axiom that two parallel lines meet at a point-at-infinity. Taking two such lines to be the legs of a triangle, the intersection of two parallel lines is the vertex/apex/scheitel of a triangle. And correlative to our physical limitation, such a point is generally not “conceivable”, at least within the mental structure. But through projective geometry, and the paradoxical thinking it entails, such elements at infinity can be “wared”.
I hope that, more than provide a definition, I’ve at least given you some pictures to play with when pondering (vertex). Its meaning, for me, has certainly expanded (or intensified) in the process. Of course, my understanding is limited by my supeficial understanding of German language and culture; a native German speaker would contribute greatly to our sense of the word.
(source: Duden | Scheitel | Rechtschreibung, Bedeutung, Definition, Herkunft)