Tag Archives: geometry

Taking Apart and Putting Back Together in a Repeatable Process

The greatest thing about relational databases is they store everything loose in some kind of homogeneous level playing field. It is only be establishing relationships between data that anyone is able to see anything in context. Without context, they are just data. In context they are messages, thoughts, ideas, studies, results, and work products.

If an idea is very complex sometimes it helps to break it down into component parts. Systematically taking it apart to understand what makes this idea tick.

DesignIT Studios

Starship ModelerWikicommons Watch Movement

Taking an idea apart can be very informative. Especially when various parts need to be updated and optimized, continually changing like software releases. If the watch above was wordpress, the Swift theme, and the internet each gear changes sooner or later but the whole watch still needs to work together if it is to continue functioning.  Putting things back together offers it’s own set of challenges.  There is an opportunity to purge elements that are no longer useful during this process. Like a hoarder moving everything out of their house onto the curb then back into the house, maybe some of those items are not worth saving after all. Or fixing a car engine, or someones medical condition, when it is unclear exactly what the problem is but simply by taking it apart and putting it back together, whatever was not working gets repaired.

IDSA Materials and Processes Section

Instructions are needed, parts need to be labeled. A sequence of reassembly is needed to ensure the reassembled whole still is the same. It can be difficult to see how the parts fit together when viewed too close.

Carol Padburg

Because everyone’s perception and experience is different, the exact same elements, in almost exactly the same combination may be understood a different way from different points of view. The receiving end may be “reading something into” what the sender intended. It may not be possible for two different people to consistently see the same things the same ways.

Put Back Together Pictures

However, this is not true for machines like computers or networks like the internet because machines have no prejudices, emotions, or previous experiences.  They simply process the information, break up whole ideas into packets, send them somewhere, another machine puts them back together. For this to be reliable everything on both ends needs to be a repeatable process. It would be so helpful to have a mold with the end result packed in with every packet to ensure consistency. MIT has just started a project to map controversies that may be useful to understand multiple interpretations of the same information.

MIT Mapping Controversies Project

This project is important today because we are surrounded by so many controversies, and so much data, it’s difficult to sort out which parts are actually valid, worth processing, keeping in the information houses where we store things. For example the Washington Post had an article today about the disconnect between science and the general public entitled “Not Blinded by Science, but Ideology” where global warming is a perfect example.

To avoid using information the wrong way, or putting together messages, thoughts, and ideas that may be different than original authors intended, especially while processing the data in emotionless machines – repeatable processes are needed.

BZen Consulting

Info-Sight Partners Actionability Index

Global Wonderware

Today the primary representation of how pieces of information are to be put back together need to work with SQL. Looking at the relationships is usually just miles and miles of code. However, there is a company at http://mkweb.bcgsc.ca who makes Schemaball, a Schema Viewer for SQL Databases where the relationships themselves can be put under a microscope and examined across the whole database in one glance.

It’s curious why geometry proper is not used more often to direct the arc, layouts and relationships. Something like a mold could be useful to ensure the reassembly is 100 percent correct on the receiving end, to match exactly, what the sender intended.


But how would you store and encode that geometry?


Digital Continuity



ABOVE: Nature-2 (rough).jpg @ 50% (Gray)
BELOW: Untitled-1 @ 33.3% (Layer 4, Gray)

Both by Bruce MacPherson, work-in-progress sketches for the MathFactory, for Gallagher & Associates Design Proposal



Below is the introduction from Time & Bits, Managing Digital Continuity edited by Margaret MacLean and Ben H. Davis, an eternity ago in 1998 for the Getty Research Institute.  The Getty Research Institute is dedicated to furthering knowledge and understanding of the visual arts and aesthetic appreciation through the advancement of long term digital preservation and information exchange techniques to protect our common cultural inheritance.  The book is about an early workshop pondering over new problems with obsolete media and machines impact on the cycle of: capturing, preserving, distributing, representing, and unlocking a real understanding of the meaning of stored data. See the Long Now Foundation Projects for follow on work such as the Rosetta Project.


Workshop Figure 1

This was a very unhappy interface. And small wonder. No doubt this entire virtual environment was being encrypted, decrypted, reencrypted, anonymously routed through satellites and cables, emulated on alien machinery through ill-fitting, out-of-date protocols, then displayed through long-dead graphic standards.  Dismembered, piped, compressed, packeted, unpacketed, decompressed, unpiped and re-membered.  Worse yet, the place was old.  Virtual buildings didn’t age like physical ones but they aged in subtle pathways of arcane decline, in much the way that their owner’s did.

Bruce Sterling, in Holy Fire. Science fiction writer and founder of the Dead Media Project.


Workshop Figure 2

Below from the article Storage Knowledge by Doug Carlston, page 28 Time & Bits: Managing Digital Continuity

– process information is everywhere and, with increasing frequency, it will not be possible to perceive the full expression of the content-creator’s intent if the ability to perceive the process information is lost.

Imagine, if you will, that we are talking about process content that represents the instructions for building a virtual space and populating it with still and animated images tied to sounds.  Even if one could disambiguate the various data forms and figure out what was image, what was sound, and what was descriptive code, the author’s expression is virtually impossible to deduce absent its interpretation via his original processing device.  If in the future it becomes common to create digital wire models of complex inventions and other devices in lieu of written words, we will have an entire body of obviously important process data held hostage to its original interpretation device.

Perhaps in these areas we just have to give it time.  We do seem to have some movement towards standards, numerical bits have been translated in a reasonably consistent way into numerals and letters of the Roman alphabet (and others), a necessary first step toward a process Rosetta Stone.  And there appears to be a compelling universal interest in standardizing the operating systems and chief applications of commonly available computers, although these standards themselves continue to evolve at a hazardous rate.  Perhaps this process will not continue indefinitely, in which case we are confronting merely an interim problem while the universal standards are finally worked out.


All of this was written before the explosion of the semantic web, online services, and the large scale development of open standards.  Nevertheless, many early concerns raised at the Time & Bits workshop are still valid.  The documentation of places and buildings together with the public information they generate has only just begun.  When will the process information be mature and standardized enough to tell the story of all these people and places over long periods of time?  There are many arguments on OntologForum regarding the utility, accuracy, and even the possibility of universal standards for such large scale processing. Like buildings in the real world, some digital architectures are better than others, some data deserve to be taken better care of and

“there is no constituency representing that body of information”

Margeret MacLean, Setting the Stage, page 33 in Time & Bits: Managing Digital Continuity.

3 images below are from the central garden at the Getty Center in Los Angeles. You can go anywhere, touch anything, get led in directions you want to go anyway, and have tremendous vistas open up around unexpected angles.  There are curves and corners. Only the best materials are used and they are taken care of.  The combination is gorgeous together.  This level of spatial design, execution, and maintenance is needed for an equivalent level of high quality, long term, takes-forever-to-build, semantic web spaces made expressly for the general public.


File: Getty Center Central Gardens Wiki Commons




Companion Post: Trace Continuous Threads



Talking About Spirals

Context Driven Topologies are mathematical groups of ideas and information transmitted over computers and networks.  Their form and process are expressed using drawings and specifications.  Their purpose is to organize and drive network topologies to answer questions and derive meaning from data collections of any size, particularly in open source environments.  The purpose of answering questions and deriving meaning is to foster Collective Intelligence. Refer to Wikipedia Unassessed Systems for related work.

CItypes (131)

The default form envisioned for storage mode is a spiral.  Groups of ideas and information can be rearranged infinite ways while working with or distributing to and from precise locations. Locations can be physical, conceptual, or a combination of both.  Assuming constructing exchanges and working this way is possible, what shapes and topologies would be most effective?  What are their properties? What do they have in common? What would a computer and network language about these pathways, densities, colors, transparencies, forms, linkages and exchanges look like?


Its too complicated to wonder about ALL possible forms, the question can be simplified by just concentrating on spirals for an example. Therefore, a previous post Spiral Model is expanded to incorporate slides prepared by A&A Director Vera W. de Spinadel for a Postgraduate class on Form and Mathematics which focuses on logic and technique. Dr. de Spindel remarks “Of course this has a lot to do with the subject of Context Driven Topologies“. Lets see what this means to computers and networks, starting with :

spiral model

Spiral Model, Boehm, 1988, Original Creator: Conrad Nutschan

According to Wikipedia on November 22, 2006: The spiral model is a software development process combining elements of both design and prototyping-in-stages, in an effort to combine advantages of top-down and bottom-up concepts. What a perfect shape spirals are to portray complex evolving relationships. Just imagine the possibilities using spirals as a base structure.


A Equiangular Spiral and its Secants from the Visual Dictionary of Special Plane Curves

Now for Vera’s slides:











English captions to be completed at a later date – this slide says “Carrying out some modifications in the process of construction of this spiral, we are going to build other linked with the Numbers of the FNMPP. In the following figure details of the construction are shown.”



Of course spirals are seen in nature and architecture. Rough translation “Finally, in the country of the Architectural Design, fits to mention the interesting antecedent of the Spiral building, built by the Arq. Fumihiko Maki in Tokyo, Japan in 1985. Maki gue prizewinner with the Prize Pritzker in 1993 and in its Spiral building has utilized the geometry of the curve, that conjugates marvelously the concepts of fragment and unattainable center. The geometric figure is an evocation of the ones that are found in Kyoto, in the famous Temple of Ginkakuji (Silver Building) 1338-1573 and in the Temple of Kinkakuji (Building of Gold) 1398, reconstructed in 1955. Though these denominations of Gold and Silver have religious and historic meaning, they would be able to serve of example to design making use of so much, metallic spirals flat curves like helicoides metallic.”


The question Vera is looking for is geometrical interpretations of the members of the family of metallic means – which she discovered in 1997. She found a relationship of the golden mean with the pentagon and another of the silver mean with the octagon. And that was all, there were no more relationships with polygons. So, she began trying to construct metallic spirals, generalizing the well known golden spiral – and was successful! She introduced a family of metallic spirals and continues intensively working with the silver spiral. There will be more to see when she presents at the International Conference on Geometry and Graphics ICGG-2008 in Dresden Germany.


Other computer and network systems that may be interesting to study in terms of forms, dynamic properties, geometry and graphics to streamline information that have been highlighted in recent discussions include:

Artificial Neural Networks

Pattern Recognition

Single Instance Storage

But what is even more interesting is


Collective Intelligence


the Information Economy Meta Language IEML see the paper “Collective Intelligence Protocol Semantic Metadata Exchange Standard (CIP-SMES)” by Michel Bietzunski and Steven Newcomb 18 July 2007. A commentary on this paper and Chapter 3 of Topic Maps by the same authors, edited by Jack Park is here IEMLcomments









Capturing and Communicating Flow

penderecki1 penderecki2 penderecki3

Krzysztof Penderecki communicates flow in his musical compositions through his own annotation system. Eventually his drawings are translated into traditional notes and lines so performers can play the work. But for his own purposes, and maybe to explain the details and overall patterns to performers and patrons – Penderecki’s own system captures his ideas best.

The scores above are from wood s lot, Sinepost, and the gallery of music at WFMU.
A set of images from Mattmo‘s Inspiration Set on Flickr are presented in contrast below. They also capture flow. At one point maybe only to the artist or mathematicians but at some point later, perhaps to others interpreting or performing the work…..maybe even machines performing work that has a flow.



The Persistence of Geometry

From the Cleveland Museum of Art


Constructivist Portrait, Ellen Carey 1983


Male Antelope-Anteater Headdress (chi wara-sogoni kun)
Africa, Mali, Bamana, Diaura or Djiumu Area, 1920s


Untitled, Sonia Delaunay


Gray Scramble (Single), Frank Stella, 1936


Creative Therapy, Jacob Lawrence, 1949

The Persistence of Geometry exhibition was organized by the Cleveland Museum of Art in collaboration with MOCA Cleveland and was made possible through generous grants from the Kulas Foundation and the John P. Murphy Foundation. Additional support was provided by The Contessa Gallery. The Cleveland Museum of Art and MOCA Cleveland receive support from the Ohio Arts Council. Promotional support provided by 90.3 WCPN.


Social Justice and Peace

There is a place in Washington DC called Busboys and Poets that believes social justice and peace are achievable goals.

What does this mean today? What data structures need to be built to further this goal? What geometry works best to distribute and streamline the information flow?

Peace Education Image by D@dalos
Today, there were 1000 monks and nuns in Myanmar seeking social justice in a quiet, peaceful manner. The Washington Post Express reported concern for the monks and nuns safety. The author noted the monks and nuns are the conscience of their country. Every country could use a group of people thinking, and acting, together like this for peace and social justice. This is what the monks look like.


AP Online via the Washington Post

Archiv-Burma, source reference www.asiatours.net

Here is where Myanmar, that was once Burma, is located:

East Asia Blog Spot

What are the optimal, most efficient paths for quiet, peaceful, social justice people to get the word out?


Social Network Diagrams and instructions available at Group10


Context of Codes

According to sustainable design architect William McDonough, in the world of building codes, context is all.


1. Insist on the right of humanity and nature to co-exist in a healthy, supportive, diverse and sustainable condition.

2000 Carbon Atoms in a Diamond Lattice
James R. Morris, C. Z. Wang and K. M. Ho

2. Recognize interdependence. The elements of human design interact with and depend upon the natural world, with broad and diverse implications at every scale. Expand design considerations to recognize even distant effects.


Core by W3C
3. Respect relationships between spirit and matter. Consider all aspects of human settlement, including community, dwelling, industry and trade, in terms of existing and evolving connections between spiritual and material consciousness.


High Sky 2 by Bridget Riley, lives at the Neues Museum, Nurnberg, Germany.
4. Accept responsibility for the consequences of design decisions upon human well-being, the viability of natural systems and their right to co-exist.


Spatial Layout, Deborah MacPherson CAD drawing with SpinnerCropHoudek

5. Create safe objects of long-term value. Do not burden future generations with requirements for maintenance or vigilant administration of potential dangers due to the careless creation of products, processes or standards.


SeaShellCage by Dream Geometry at Midcoast.com, Research & Development Through Free Exchange of Ideas.
6. Eliminate the concept of waste. Evaluate and optimize the full life cycle of products and processes to approach the state of natural systems, in which there is no waste.

7. Rely on natural energy flows. Human designs should, like the living world, derive their creative force from perpetual solar income. Incorporate this energy efficiently and safely for responsible use.

8. Understand the limitations of design. No human creation lasts forever, and design does not solve all problems. Those who create and plan should practice humility in the face of nature. Treat nature as a model and mentor, not as an inconvenience to be evaded or controlled.

9. Seek constant improvement by the sharing of knowledge. Encourage direct and open communication between colleagues, patrons, manufacturers and users to link long-term sustainable considerations with ethical responsibility and to reestablish the integral relationship between natural processes and human activity.

The Hannover Principles should be seen as a living document committed to transformation and growth in the understanding of our interdependence with nature so that they may be adapted as our knowledge of the world evolves.


Form, Shape, Trace, Reckon, Calculate, Represent

The Institute for Figuring

To Figure: To form or shape, to trace, to reckon or calculate, to represent in a diagram or picture, to ornament or adorn with a design or pattern.

The Institute for Figuring does not yet have a physical space. Their location in the conceptual landscape is permanently located on the edge of this iconic fractal.mset_forweb.jpg

Institute for Figuring (IFF) Mandelbrot set location: (-0.7473198, i0.1084649) with detail (color inset.)


Crochet model of hyperbolic plane by Daina Taimina

In 1997 Cornell University mathematician Daina Taimina finally worked out how to make a physical model of hyperbolic space that allows us to feel, and to tactilely explore, the properties of this unique geometry. The method she used was crochet. See [105] Hyperbolic Space Crochet Models for more information.

[105] Hyperbolic Space

[111] It is one thing to know that something is possible, it is quite another to understand what it is. Like the blind man and the elephant, hyperbolic space appears in different guises depending on how we approach it. One way of visualizing this enigmatic space was discovered by the great French mathematician Henri Poincar?. In the Poincar? disc model the entire hyperbolic space is depicted inside a circle.

disc1 Poincare Disc Model of Hyperbolic Space

Image and text above from the website of the Institute For Figuring (www.theiff.org)


Brings to mind topological knots. Images below by Sofia Lambropoulou.


Escher mechanical trefoils


Ancient knots in Berlin museum


Mongolian knots on stamps


Complex Geometry

If attempting to draw the geometry of knowledge changing over time, curves and projection geometry make everything more complicated.

Computers prefer straight lines with nice even units but the geometry of knowledge seems more fluid. Important continuity must be shown and traced, some form of projection is nearly always be involved.

Domes, globes, spheres and spirals pose special problems. A example of dealing with a projections onto a curved dome is the Theatre of Pattern Formation made by James Crutchfield and David Dunn. A visual and auditory articulation of chaos theory designed for the LodeStar Astronomy Center in Santa Fe and planetariums everywhere. At a talk at CUNY December 2004, the authors explained their struggle with knitting together complex fractal imagery to present properly on a curved surface. Sample below:


In this and other examples, artists were able to help scientists see their own work a new way and vice versa.

What can be done today between artists and scientist to create and establish the complex data structures we need today? What is the geometry like? Is it more suited to networks than individual computers working in isolation? Where are curves and projections necessary in such projections?