struck: Fundamentals of Elastic Interval Geometry

Ken G. Brown kbrown at
Wed Oct 14 02:17:51 UTC 1998

At 21:40 -0700 on 98/10/09,  Alan Kay is rumored to have written:
>The big idea is "messaging" -- that is what the kernal of Smalltalk/Squeak
>is all about (and it's something that was never quite completed in our
>Xerox PARC phase). The Japanese have a small word -- ma -- for "that which
>is in between" -- perhaps the nearest English equivalent is "interstitial".
>The key in making great and growable systems is much more to design how its
>modules communicate rather than what their internal properties and
>behaviors should be. Think of the internet -- to live, it (a) has to allow
>many different kinds of ideas and realizations that are beyond any single
>standard and (b) to allow varying degrees of safe interoperability between
>these ideas.

Perhaps Gerald de Jong's 'Struck' program, making elastic interval geometry
visible, might be of use in exploring the 'interstitial' relationships that
Alan mentions above.
Ken G. Brown

Forward from Gerald de Jong:
>the axioms upon which EIG is based are blindingly simple, and in fact
>represent the culmination of a theoretical journey that has maintained
>simplicity as its guiding principle.  having witnessed the diverse and
>surprising fruits of the Struck project, it is sometimes difficult to
>regain a proper appreciation for the uncomplicated beauty of its
>theoretical underpinnings, and even more difficult to clearly delineate
>their corollaries.
>the prey for which EIG and Struck have been so hungrily hunting throughout
>the past few years is the notion of structural form.  so general is this
>goal, and so often has it been approached throughout history through such
>varying means and metaphors that one might wonder if any fresh approaches
>remain.  how could it be that the great minds of the past century have
>overlooked something?  the reality is not quite so dramatic.  it just so
>happens that we, in our time, have access to unprecedented computational
>machinery, and given the wondrous brute-force of these myriads of
>transistors we are afforded a new avenue of exploration: iteration.
>perhaps the most straightforward consequence of an iterative process in the
>context of structural form is discontinuity.  the process necessarily
>involves jumps as opposed to smooth movement, and it effectively denies
>continuity at a very deep level.  as we know from listening to our
>digitally-stored music, smoothness or continuity reappears as an illusion
>when a sufficient sampling rate is employed.  similarly, and maybe
>surprisingly, the distinguishing characteristic manifested in the
>animations resulting from Struck's simulation of an elastic interval
>network is precisely this fascinating illusion of continuity.  movements of
>the networks seem to flow as if belonging to a natural aquatic environment,
>while the discrete/digital/discontinuous nature of the underlying algorithm
>couldn't be more obvious.
>efforts to strip away all the unnecessary issues and isolate a minimal core
>set of attributes capable of producing something intuitively deserving the
>description 'structural form' has resulted in the amplification of a
>seemingly banal idea: twoness.  the 'interval' is a twonees, or a defined
>spatio-temporal relationship between its two ends.  the word 'interval' was
>carefully chosen to avoid inappropriate permanent associations with space,
>as it clearly applies to both spatial and temporal relationships.  an
>alternative term might be 'span', but i strive to avoid such terms as
>'distance'.  EIG deals with twonesses, but disconnected twonesses are not
>sufficient for producing interesting structural forms.  the twonesses must
>relate to each other in the simplest of ways, which is arguably this: they
>merely share 'ends'.  two twonesses share one or more of their constituent
>'relate-ees' (later we will search for more appropriate terminology for
>these things).
>since we have come this far, it is time to preemptively shed light on the
>first and foremost pitfall that perpetually threatens EIG, and that is the
>puzzling human reflex which tends to immediately overturn the priorities at
>this point.  we seem deeply conditioned to consider relationships to play a
>secondary role to the things that they relate.  we tend to attribute
>'substance' to the nodes, if you will, and then find any number of
>metaphors with which to describe what seems like the secondary information
>contained in the relationships between the nodes.  it is not so much the
>case that EIG intends to overthrow this prioritization, but rather that due
>to its origin in the singular purpose of searching for a minimal
>description of structural form, having 'the interval' occupy the primal
>role seems quite self-evident.  in other words, the burdon of proof falls
>upon those who suggest that the 'nodes reign supreme' (to be somewhat
>facetious).  let this at least be clear:  EIG is about simply-related (by
>means of sharing) binary relationships.
>(to be continued..)
>Gerald de Jong, Beautiful Code B.V.
>Rotterdam, The Netherlands

More information about the Squeak-dev mailing list