Now a remarkable feature of the quasicrystalline tiling patterns ... is that their assembly is necessarily non-local. That is to say, in assembling the patterns, it is necessary, from time to time, to examine the state of the pattern many, many 'atoms' away from the point of assembly, if one is to be sure of not making a serious error... (This is perhaps akin to the apparently 'intelligent groping' that I referred to in relation to natural selection.)...
     Normally, when Nature seeks out a crystalline configuration, she is searching for a configuration of lowest energy... I am envisaging a similar thing with quasicrystal growth, the difference being that this state of lowest energy is much more difficult to find, and the 'best' arrangement of the atoms cannot be discovered simply by adding on atoms one at a time in the hope that each individual atom can get away with just solving its own minimizing problem. Instead, we have a global problem to solve. It must be a co-operative effort among a large number of atoms all at once....
     Let me now carry these speculations further, and ask whether they might have any relevance to the question of brain functioning...
     -- Roger Penrose (1)

     The new media environment is a shared and sharing environment in which users "put in and take out" from the system. Returning to the origins of the term broadcasting, I suggest that the new media environment is reminiscent of an agricultural milieu in that it is a productive environment, an on-going process of creating, using, and sharing information, an electronic reaping and sowing. Therefore, rather than view the NII as a superhighway (with all its connotations of linearity, transportation, progress and speed) I suggest we consider the converged telecommunications infrastructure as a parcel of farmland to be cultivated.
... [E]lectronic agrarianism creates a "new context" informed by the potentials of emerging technologies, and the need to shape these technologies in a fashion that recalls the values and beliefs of agrarianism, the cornerstone of Jeffersonian democracy (Black, 1962, 38). It is through the synthesis of two, seemingly incompatible concepts, advanced computing and telecommunications technologies, and agricultural self-sufficiency, that the Information Age might be reconceptualized in a manner that is consistent with the potentials of both man and machine.
     -- K Howley (2)

Rhombic series

The Thing

Rhombus, n. A parallelogram with all sides of equal length. Pl. rhombi or (U.S.) rhombuses. Rhomboid, n. A parallelipiped with rhombic faces.

My interest in rhombic and rhomboidal tiling was inspired by D R Nelson, "Quasicrystals," Scientific American, Aug 1986, pp.43-51; P Ross, "Buckyballs," op. cit., Jan 1991, p 14; as well as by Roger Penrose, whose mind seems to be as quirky as mine.

Another application of the geometry is described by Al Globus, et al, in [Machine Phase Fullerene Nanotechnology]:

Recent advances in fullerene science and technology suggest that it may be possible,
in the far future, to design and build atomically precise programmable machines
composed largely of functionalized fullerenes. Large numbers of such machines with
appropriate interconnections could conceivably create a material able to react to the
environment and repair itself. This paper reviews some of the experimental and
theoretical work relating to these materials, sometimes called machine phase,
including the fullerene gears and high density memory recently designed and simulated
in our laboratory. 
[...] One author suspects that genetic programming may be a fruitful approach to the software control problem.
Just think, if we could use certain primitive (but widely available, and generally stable) genetic programs to process human phase materials, sometimes called communications, to design and build a near-future environment which repairs itself!

The Map

The sitemap, adapted from the (interactive) [Quasitiler], is composed of two remarkable rhombi which are defined by the diagonal to edge ratio (the 'golden mean,' 1.6180339..., known as phi, in the 'fat diamond,' and its reciprocal in the 'thin diamond' ). In the partial outline here, some of the local and not-so-local symmetries are highlighted as 'macro-rhombi' which follow a Fibonacci series, e.g.
1,     phi,

phi + 1

2*phi + 1

3*phi +2

5*phi + 3

Or, starting instead with the square root of 5 = phi + 1/phi =

2*phi - 1

phi + 2

3*phi + 1

4*phi + 3

7*phi + 4

The last reaches clear across the page to catch its own tail, as the map replicates itself left and right (as well as top and bottom). Now, while the source image was modified to 'macro-tile' in just this way (actually, to serve as Windows wallpaper), it isn't actually necessary for the E-Lekh to do so, although, as the number of posts grows, it might seem as though this one page would be insufficient. No, we need merely to declare the 100 or so tiles in 'Big Pink' (say) to be contained 'within' a single tile on this identical map! ( C18 is an instance of this kind of nesting.) Indeed, as each poster draws on numerous experiences, allusions, interpretations and implications as hyr word-cultivars, each contribution may already comprise a 'map' of itself in this way.

In short, this kind of hyper-topography perfectly complements 'plain' hypertext, if we can only learn to domesticate it. Like Dr Penrose, I believe this task must be a co-operative effort among a large number of participants all at once, or rather, in this asynchronous medium, as an on-going affair.


(1) Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds and the Laws of Physics (New York: Oxford 1989), pp 436-7. Reviewed by [TLS ]

(2) Kevin Howley, "Electronic Agrarianism or, Thomas Jefferson Gets a Modem" ([abstract] at Principia Cybernetica)

(3) Although how to count the rhombi which lie across the line is a legitimate question, it is no different from the question of what the 'boundary' of even a single field means. Does a line not depend on there being an outside as much as an inside?

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