“As hangs the flexible line, so but inverted will stand the rigid arch.”

So, the funicular form itself – a hyperbolic cosine function delineating the most efficient and minimal form under self-weight – is not easily described by geometrical drawing, but derived instantaneously with a chain – a material proficiency!  The word catenary means “relating to a chain”.  The German term “Kettenlinie” means literally “chain-line”.  So, this formative structural logic for minimal forms in masonry is approximated by a drawing convention – graphical analysis – which may translate between design and construction, yet is most wholly represented by a material line under self-load – a chain.

Thus, the 4-Dimensional Masonry Construction is the relationship and the act of translation between design drawing and material drawing.

Guastavino, Cathedral of St. John the Divine.

The 4-dimensional drawing is embedded within the act of construction itself, and is an integral principle of the way in which a masonry structure (as opposed to any other type of construction) is built by craftsmen.  Now, all sorts of constructional methods involve a registration of sorts so that building components ‘line up’ in their fully assembled state.  But masonry is particular, insofar as the builder must ‘see a surface’ through all stages of construction, carefully laying bricks in position so that the geometry of the entire system is not compromised by a poorly placed brick which cascades into system error.  This is particularly important when building with techniques derived from Spanish timbrel vaulting, where bricks are set by cantilevering into space off of the last course, and are set very rapidly on account of the use of high compressive strength and rapid-set plaster mortar.  When a surface then curves into space (in two directions nonetheless), how does the mason know where each brick should be positioned so that the structural form is not lost?

Many different types of tools are used by the craftsman to ‘draw in space’ the ideal registration for a masonry surface.  Mason’s line or chain, plumbs, line-levels, levels, squares, angles, templates (paper, wood, or traits), compass (or dividers) and rule.  In a constructional system, certain of these tools may combine with the greatest registration tools of the mason – the hand and the eye – to systematically describe where the masonry surface wants to be in any particular position.  One such system is the cintrel, a central pole with mason’s line connected at the top, which may be rotated about the pole to register bricks in the construction of a dome.

But still – these masonry tools occupy a grey zone between drawing as an act of building and building as an act of drawing.

The board below – long since the desired theme of the 4-Dimensional Masonry Construction – will come to be tested as analytical research, design and construction overlap.  These examples – stereometrical drawing, Islamic Mucarnas drawing, and the ruled-surface hyperboloids of Gaudi – are drawing systems which are made to translate into a 3-dimensional space, as registration of masonry surface in the temporal act of construction.  Pencil lines on paper become drawings on materials and construction surfaces, extended by the tools of the mason into space. This is the 4-dimensional drawing, a critical translator between masonry design and construction, drawing and building.

_ Where do concerns of ‘craft’ lie in relation to contemporary computational design?

_ What is the threshold of computation in the domain of human and material error?

_ What are the implications of the distinction “building a sketch” (as opposed to the “illustration of a geometry”) suggested by Nader, and how does this apply to notions of the 4-dimensional constructive drawing?

_  Can the customized treatment of an industrially produced unit be ascribed to the domain of the craftsman or builder, by virtue of the attention to idiosyncratic details of fixed and predictable systems?  Likewise, may the variability of unitized systems be ascribed to the domain of the designer?  May one utilize the former in the service of the latter, exploiting this knowledge of the hand towards new applications – not merely fastidious craftsmanship, but crafted design?

_ What might reconcile the apparent incommensurateness of (increasing) complexity in rule-based logics and the synthetic, sensory responsiveness and intuition of contemporary craft?  Is design itself not positioned as antithetical to such sensory responsiveness?

_ Can one say that stereotomy was a product of geometric practices associated with renaissance architecture?  According to Robin Evans, stereotomy evolved from geometry just as it did from constructibility:  Cutting would be thus a geometric and constructional “reciprocity between masonry unit and method of assembly” (Nader).  I like this phrase.

_ Is such practical geometry not by nature a reconciliation of geometry and material, theory and praxis?

_ Is it possible for a masonry unit to generate states of in-situ structural stability?

_ There is an Irish word – ‘tomhais’ – which means both ‘guess’ and ‘measure’.  Can such a concept be represented by the intuitive measuring and accounting of the craftsman?  How can an intuitive accounting – synthesized knowledge of the hand, the eye, the body – come to be analytically represented through such a system as reductive computational analysis?  How can this intelligence be extracted in application to a computational ‘craftsmanship’, a synthetic and analytic constructive sensibility?

_ What are the limits of analytical methodologies in computational programming?

_ Is the greatest weakness of computation that it considers all things as rule based logics, where rule-based logics have an inherent limit to the number of variables or parameters to maintain the coherency of a problem?  Can sensory responsive logics of craftsmanship intuitively synthesize a great many more variables?

_ Does ‘computational determinacy’ exclude the reconciliation between what may be computationally generated and how it is resolved in construction?

_  Is most computational design motivated by a desire for the transcendence of the concerns of labor (ie. Gramazio + Kohler, Mark Goulthorpe), the elevation of automaticity in construction over the intelligences of the hand and the eye?  How do latent class concerns play out here?

_  What in my own method is most similar to the tendencies of contemporary computation?  Perhaps a methodological approach that proposes that mistakes – variations from normative logic sets – provide the opportunity for a new design intervention?

_ How may one embed this intuitive problem-solving back into the design process?  Can this occur by problematizing errors – which exist already in the context of craftsmanship – within a different paradigm for resolution?

The chain, string, plumb, line level, straight level, template, compass and rule, angle and tape, cintrel…

All serve their purposes in the registration of the masonry system.

These spatial drawing tools will be considered throughout the design process, constituting a 4D masonry drawing projected on the plane of design representation.