A Geometric Gesture

January 15th, 2008

Three illustrations from Andre Vandenbroeck’s Philosophical Geometry.

Philosophical Geometry contrasts with axiomatic geometry: the latter “discipline is founded on a group of propositions considered self-evident or necessary, from which a chain of further propositions can be deduced” (p3), whereas Philosophical Geometry is a “property of mind in general and not a specialty of the analytic mind… For example, in ‘Meno’, Plato shows geometry as a birthright of mind in general: Meno’s slave, unhampered by his lack of background, comprehends a geometric necessity with which Socrates confronts him” (p4).

Philosophical Geometry consists of theoria and practica. “Theoria is the adequate expression of geometric experience. As such, it is dependent upon the perception of the geometer; it is a subjectPractica is a necessary structure of two-dimensional events and is independent of the geometer’s perception. It is the object of the discipline… The aim of Philosophical Geometry is the individual elaboration of theoria… Theoria depends upon practica through the perception of the geometer, and it is due to the variance in perception that differences in practica occur” (p12).

Therefore, geometry is the product of geometric gesture.

“On a homogeneous two-dimensional field best termed a plane, the stylus is posited in a gesture of inscription. The contact of stylus with plane breaks the homogeneity of the undifferentiated surface into a heterogeneity of the point of contact and the remainder of the plane… Whatever the final complexity of inscription, the [practica] must pass through this initial stage: the contact of stylus with plane” (p17).


Practica can progress beyond the point only by motion of the stylus. Motion of the stylus produces an inscription best termed a line” (p17-8).


“To qualify the line as a two-dimensional element is a contradiction in terms. A line cannot be a surface. And yet, contrary to the point, it cannot be considered an ideal indivisible marking. Although, as line, it cannot be a surface, it clings to the plane by a dimension of length and thus forces upon contemplation a second dimension of width which is the thickness of the inscripting stylus” (p18).

“To examine the line, motion of stylus has to be arrested… If the motion of stylus is not arrested, a continuous line results. This uniform, indefinitely prolonged motion of stylus finds its perfect representation only in the circle” (p18-9).


8 Responses to “A Geometric Gesture”

  1. Anthony Mistero Says:

    This is the first time I post a comment here (I do it very seldom anywhere,to be sure), but by no means my first visit (I sometimes follow the track of my verbose friend PolyMathicus. Our interests partially overlap).

    From your previous post, “Squaring the Circle”, I got something of great value. While I was doing the construction, I realized that the very act of going through the steps with the mind and the hand was conducive to the proper meditative state for absorbing the necessary hermetic experience (in that case, squaring the circle).

    Although I always knew that hermetic diagrams are alive, I also understood well that they must be drawn
    to be properly absorbed, for the reason specified above.

    As clearly stated by AVB, practical philosophical geoemetry is, first and foremost, a practice. An exploration, an experiment, in which the subject is actively involved.

    May the Ones-Who-Know-And-Are help us unravel the misteries of Sacred Geometry


    Anthony Mistero

  2. Polymathicus Says:

    To me this post was a double happy surprise:

    1) I see you are NOT wasting your precious time in 2008
    (veering to EXPERIENCE is always a good move)

    2) Seeing my old acquaintance Tony Mistero’s comment here was even more of a shock. As he has qualified me as verbose (and correct he is, although someone has to DO the talking, right? Not to mention that his own comment is not exactly a 2 liner.), I shall refrain from my usual, long comments (also because he has made the case already).

    Just a small note: Andre & Goldian are a prototypical, almost ICONIC, hermetic couple (they are all modeled after that most sublime of them all, the legendary Nicolas Flames and his “wife” Perrenelle, yet another “field trip”, to Paris, this time).

    Andre’s talents are perfectly matched by his wife’s hand and skills. She too has a book on sacred geometry,
    less abstract but by no means useless:


    Worth a look.

    My Very Best


  3. Greg Pass Says:

    Dr. M —

    Thanks for de-lurking.

    How heartening to hear you DID the experiment! And then properly realized the connection between “the mind and the hand”.

    The PHYSICAL gesture is a doorway — through perception, through awareness of the ACT — to an “understanding” of MIND, SPIRIT.

    AVB called this initiation “the contact of stylus with plane” within the context of geometry. But it applies to many of the arts we’ve discussed: taiji form, yiquan standing, alchemical laboratory, hex, yantra. All negotiate an immediate physical context within which to penetrate.

    Of course, it’s a lot more WORK to do it this way…

    PMac —

    Beaten to the punch, for once! I’ve added Goldian to the queue.

  4. Anthony Mistero Says:

    Yes, I did the experiment (successfully).
    How else can one hope to understand?
    Knowledge is one thing,
    Understanding another.
    All understanding, bar none,
    requires 3 components:
    body, feeling, and mind.

    Three in one, in the present moment.


    A. M.

    PS Allow me to emendate one word in your reply:
    -it applies to many of the arts-
    should be replaced with
    -it applies to all of the arts-

    There is only one Art, with so many faces:

    The Great Hermetic Art
    of the Perfect Gesture

  5. Stephen Fitz-Gerald Says:

    “Visceral Learning “is the term I apply to the aforementioned phenomena. The ancients knew there was something intrinsically contained WITHIN THE ACT ITSELF of making the models,and thus any serious neophyte was required to do so.
    As my previous post illustrated, in regards to squaring the circle,I found another layer of meaning that emerged only upon fabricating the bronze cube within the stainless sphere and just simply being with it for a few days (much physical contact as well).
    I realize the original exercise was a two dimensional effort,but I am not particularly good at following rules where my curiosity is concerned…

  6. Greg Pass Says:

    Stephen —

    Thanks for this.

    The palpable (to borrow your word) difference between analytical and contemplative geometry surprises me every time: a little jolt when thinking-awareness turns to feeling-awareness.

  7. Junior Says:

    Hi guys just like to say that I am deeply taken by what you are talking about here, I do not fully understand but would love to learn more, if you can I would like maybe a list of books or website that I can look at.



  8. Greg Pass Says:

    Hi Junior —

    All my posts include references to the source material and related web sites. Dig in!

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