The Music of Nomography – Laurence Hewes’s & Herbert Seward’s ‘Design of Diagrams for Engineering Formulas’ and John Cage’s scores

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

Laurence Hewes’s and Herbert Seward’s manual on the design of nomographs, published in 1923, is an unintentional masterpiece of analogue calculation aesthetics. The topologies and contours of these charts echo the systems they encapsulate. Fluid lines plot the parameters of hydrodynamic flow. Arcing parabolas delineate ballistic trajectories. Most lead double lives as (unperformed) musical scores.

Invented in 1884 by the French engineer Philbert Maurice d’Ocagne, nomographs are graphical analogue calculating devices that allow the computation of linear or non-linear functions. Now superseded by computers and electronic calculators, these diagrams were once the preferred method for calculating solutions to practical problems when a few variables were already defined within a complex system. Ron Doerfler’s The Lost Art of Nomography is a good essay on the history of these charts, it also explains exactly how they work.

The musician/performer David Tudor used the term nomograph to describe a notation he created for the performance of John Cage’s Variations II – we might wonder if Cage ever used the term himself ? Cage created scores that not only bare an uncanny resemblance to nomography but also use a nomographic process to generate musical events within his partially deterministic musical space-time. The projection of lines into two and three-dimensional space, and their resulting intersections with other lines and points, were used to define musical events in his works of the 1950’s such as Concert for Piano and Orchestra [1958].

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

manual of nomographsIllustration from The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

In the visual arts Agnes Denes used nomographs for the basis of some of her philosophical drawings which she argued represented the metaphysical aspect of mathematics conveyed through aesthetics. She wrote, “I love mathematics because I could humanize it, and in turn it gave me perfection and beauty”. In her work The System [1970], she embellished the well known Smith Chart – a nomograph designed for solving radio frequency problems with transmission lines and matching circuits in radio frequency engineering.

Score Page from Concert for Piano and Orchestra - John CageScore Page from Concert for Piano and Orchestra – John Cage [1958]

Score for Fontana Mix - John CageScore for Fontana Mix – John Cage [1958]

SmithChartSmith Chart – Phillip H. Smith

Further Viewing/Reading:

The Design of Diagrams for Engineering Formulas and the Theory of Nomography – Laurence Hewes and Herbert Seward [1923]

The Lost Art of Nomography – Ron Doerfler [PDF]

David Tudor’s Realization of John Cage’s Variations II – James Pritchett

48 seconds on Mathematics – John Cage

Manifesto Mathematics – Agnes Denes [PDF]

Agnes Denes: Early Philosophical Drawings, Monoprints, and Sculptures

4 Responses to “The Music of Nomography – Laurence Hewes’s & Herbert Seward’s ‘Design of Diagrams for Engineering Formulas’ and John Cage’s scores”

  1. Andrew writes:

    Another excellent post. Congratulations on your wonderful website. Keep up the job work!

  2. Robin Parmar writes:

    I’m in love with nomographs. Excellent post!

  3. cocky eek writes:

    thanx Paul, since a long time im looking at your blog again, and it gives me a very nourishing feeling, as if coming home:)

  4. 08/16/2016 – Comics Workbook writes:

    […] From the Archive: Data is Nature: Everything You Wanted to Know About Nomographs But Were Afraid to … […]

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Cypraea mappa – The Mollusc Cartographer

CypraeaCyprea (Cowry) Shells from Thesaurus Conchyliorum – G.B Sowerby (Cyprea mappa shown in center)

Remi Rorschach, one of a few dozen or so characters in George Perec’s immensely complex and ingeniously constrained masterpiece ‘Life a Users Manual’, has a series of seemingly incongruous occupations –  first a clown and circus manager, then an international shell trader before finally becoming a TV executive. As a cowry shell trader he travels across Africa hoping to make his fortune by off loading a cache of Cypraea to local tribes where the shells were (really) used as money.

Rorschach’s surname might have been all the more appropriate if Perec would have chosen Cypraea Mappa (The Map Cowry) for his trading enterprises as this subspecies is named for its shell patterns being perceived as resembling antique maps. Using groups of activator inhibitor cells this marine gastropod mollusc secrets pigments incrementally into its shell row by row, as it grows, like an inkjet printer rendering a pointillist reaction-diffusion facsimile of a faded ancient map. Study the faded contours of these shell maps and you will find rivers, estuaries and peninsulars, Some shells may even represent the terrains Remi Rorschach journeyed in pursuit of his fortune.

CypraeaCyprea (Cowry) Shells from Thesaurus Conchyliorum, or, Monographs of genera of shells – ed. G.B Sowerby

CypraeaCyprea mappa, The Map Cowry

CypraeaCyprea (Cowry) Shells from Thesaurus Conchyliorum, or, Monographs of genera of shells – ed. G.B Sowerby

Cowries of all subspecies are common finds in archaeological digs. Aside from their importance as currency, they have been used in tribal masks, worshipped as fertility emblems, used in fortune telling and divination. In India they have been used in astrological predictions. They are considered precious enough that clever fakes have been made by etching elaborate patterns using chemicals or creating less sophisticated hybrid morphologies by glueing fragments of different shells together.

Further Viewing:
Thesaurus conchyliorum, or, Monographs of genera of shells – ed. G.B Sowerby
Historic shell illustrations, found in the Biodiversity Heritage Library collection

Related Posts:
The Writing of Stones – Roger Caillois

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Selected Tweets #24: Aural Topographies, Byzantine Vaults, Cybernetic Notation

Max NeuhausMax Neuhaus: Sound Works [1994]

Selected tweets from my Twitter stream @MrPrudence:

Max Neuhaus: Sound Works [1994]. Drawings, sound poems, aural topographies [PDF]

The Time of Roland Kayn’s Cybernetic Music – Thomas Patterson [PDF]

Animated musical notation/scores using algorithmic processes for rule based composition – Ryan Ross Smith.

The Cybernetic Brain, Sketches of Another Future – Andrew Pickering [PDF].

Hyper-geological structures generated with X-Gen by Lee Griggs. Elongated cubes en masse on mesh.

Adaption_KayneAdaption – Roland Kayne [1972-1974]

Deconstructions and extensions of human forms using growth algorithms – Cen Pekdemir.

Processing particle sketches revealing refractive geologies – 414c45’s Emergence set

Jole de Sanna on the Metaphysical Mathematics of de Chirico’s paintings [PDF, translated].

Mathematical surface models and other sculpted and knitted surfaces – Alexander Crum Brown [1900].

William Turner’s Perspective Diagrams at Socks Studio. Pedagogical diagrams as visual aids for Turner’s lectures.

Alexander_Crum_Brown Surface – Alexander Crum Brown [1900]

Plates from Auguste Choisy’s ‘L’Art de bâtir chez les Byzantins’ [PDF]. Geometrical construction of Byzantine vaults.

A New Elucidation of Colours – James Sowerby [1809].

Color Problems: A Practical Manual – Emily Vanderpoel [1903].

The Commander’s Radiation Guide & other fission fragment fallout decay slide-rules.

James-SowerbyPlate from A New Elucidation of Colours – James Sowerby [1809]

Aerial tuning inductor – Rugby Radio Station, 1943-1966.

12-minute Mandelbrot Fractals on a 50 year old IBM 1401 Mainframe – Ken Shirriff.

Xenakis’s Spatialised Music – ‘Meta order’ from chaotic systems.

Richard Giblett’s Architectural Algorithms. Axonometric projections of over developed dystopias.

Geometric ruleset drawings with Rorshach symmetries – Laura Battle.

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Form Constants of Optical Mineralogy

form constants of optical mineralogyChromatic Polarisation of Light (German, unknown) [1895]

The Virtual Museum of the History of Mineralogy contains a large collection of scans from monographs on crystallography and mineralogy, arranged by author in alphabetical order, from 1450 to 1912. The chromolithographs of optical interference figures, mostly from the 19th century, record the passage of light through crystal lattices to reveal a corresponding geometric figure. Visualising the interference and chromatic polarisation of light during short mineral detours allowed mineralogists to decrypt the chemical constitution and locate the geological origin of each wafer-thin sample; photons moving at light speed were coaxed into perusing time-spans of billions of years. The proto-op art configuration of the figures echo the morphologies of Kluver’s Form Constants, Purkinje’s taxonomy of visual subjective phenomena and Chladni’s figures (which are, after all, also captive remnants of the properties of wave vibration). These intelligible ornaments deserve a place in collective unconscious for optical and spectral phenomena.

form constants of optical mineralogyPlate from Mineralogia Generale – Luigi Bombicci Porta [1889]

It was David Brewster, ‘the father of modern experimental optics’, who founded the sci­ence of optical mineralogy and first annotated these patterns. Knowing all too well of the allure of the prismatic figures he discovered during his polarisation experiments he invented the Kaleidoscope in 1816. This most famous of all optical toys encodes the laws and properties of light for amusement, as well the mechanics of symmetry and tessellation. Polariscopes and Conoscopes, the more serious utilitarian siblings of the Kaleidoscope, were the optical devices used to view and annotate the interference figures found in this post.

form constants of optical minerologyPlate from Physikalische Krystallographie – Paul Heinrich Groth [1885]

form constants of optical minerologyplate from Mineralogie – Franz Wolfgang Ritter von Kobell [1864]

form constants of optical minerologyPlate from Physikalische Krystallographie – Paul Heinrich Groth [1885]

form constants of optical minerologyPlate from Mineralogie – Gustav Adolf Kenngott [1890]

form constants of optical mineralogyOptical effects during the heat treatment of glass – David Brewster [1815]

form constants of optical mineralogyThe Phenomenon of Light (German, unknown) [1895]

Related posts:
Primal Generative: Form Constants & Entoptic Geometry
The Logic of Crystals – William T. Astbury & Kathleen Yardley’s Space-group Diagrams

2 Responses to “Form Constants of Optical Mineralogy”

  1. Whewell’s Gazette: Year 2, Vol: #03 | Whewell's Ghost writes:

    […] Data is Nature: From Constants of Optical Mineralogy […]

  2. Whewell’s Gazette: Year 3, Vol. #08 | Whewell's Ghost writes:

    […] Dataisnature: From Constants of Optical Mineralogy […]

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Mark A Reynolds – Intersecting the Void by Intervals

Mark A ReynoldsThe 1.111 Series – Mark A Reynolds [2014]

Mark A Reynolds’s constructivism of intersecting translucent planes is created by modulating primitive shapes and lines based on proportional systems such as the golden section and square root series. Tracings of overlays, which record a process of revision over time create spatial illusions; precision cuts in space that represent an architecture of intervals. Reynolds notes that he is interested in ‘how the mind builds things, how it specifically orders space and records the development of an infinite variety of choices and structures because of the ratios and relationships inherent each system.

Cartography is implicit; the geometry of points, lines and their triangulations, in his works, are possible maps or mnemonics for imagined space; refracted cubist psychogeographic trajectories of structured time. No need to be reminded that geometry (from the Ancient Greek: geo- “earth”, -metron “measurement”) means to measure the Earth.

Mark A ReynoldsMinor Third Series, Fine Structure of Matter – Mark A Reynolds [2008]

Mark A ReynoldsMinor Third Series, A Grouping of Root Fives – Mark A Reynolds [2015]

Mark A ReynoldsMinor Third Series, Vortex Sound – Mark A Reynolds [2013]

Mark A ReynoldsGreater and Lesser Dyad Series, Two Ogee Curves – Mark A Reynolds [2011]

Mark A ReynoldsMusical Ratios Series, 6 to 7 – Mark A Reynolds

Mark A ReynoldsPhi Series, Root 5 Grouping – Mark A Reynolds [2015]

Mark A ReynoldsSquare Series Piston Effect – Mark A Reynolds [2010]

Mark A ReynoldsPhi Series, Phi Square Root – Mark A Reynolds [2014]

Many of the works meld disparate ratios together to create unified systems of mathematical counterpoint and resonance by isolating unifying elements that can bridge domains – in in his own words, to join the incommensurable. Since ratio and proportion are key to his structuring process it’s no surprise that there is musicality encoded into his works too.

Related Posts:

David Wade’s ‘Fantastic Geometry’ – The Works of Wenzel Jamnitzer & Lorenz Stoer

John A. Hiigli – Layering the Isotropic Vector Matrix

The Constructivist Cosmologies of Richard Lippold

2 Responses to “Mark A Reynolds – Intersecting the Void by Intervals”

  1. Mark A. Reynolds’ Artworks | MythraGallery writes:

    […] via Data is Nature […]

  2. Block Party | ?T H O U G H T S ? writes:

    […] kinds of vision that you want to penetrate and discover new possibilities. We were talking about Mark A. Reynolds, one of the creative geniuses of our time creating cartographs of natural and computational […]

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Thomas Sopwith’s Stratigraphic Models

Thomas Sopwith – geological models Model-XI – Thomas Sopwith [1841]

First produced in 1841 Thomas Sopwith’s wooden models were some of the earliest three-dimensional representations of Earth’s geological strata. Layered, glued, hand carved and polished, his models demonstrate the abilities of a skilled woodworker and isometricist. Sopwith began his apprenticeship as a cabinet maker and so his interests in carpentry and geology collude to create functional objects with sculptural qualities in their own right. Rather than represent specific locations the models were generic visualisations of typical stratigraphy found in the mining districts of England in the early 1800’s. Some of the models could be could reconfigured, like small puzzles, so that subterranean features such as dislocations, inclines and folds could be viewed from different angles reducing the need for multiple drawings.

Thomas Sopwith – geological models Model-X – Thomas Sopwith [1841]

In reality the layering of strata can be a messy business. Often, as an affront to the the law of superposition and general common sense, much older rocks can be found layered above younger ones. These anarchic non-conformist strata present themselves in, what’s known in the business, as thrust faults. Other chronological discontinuities, generated through folding and erosion, complicate things further. The book of stratigraphy is a cut-up novel containing a narrative of cryptic topographies – pages have been ripped out, shuffled, and replaced inside the wrong chapters. Since Sopwith’s models many great breakthroughs in geological cryptanalysis have been made. The grand theories of continental drift and plate tectonics allowed geologists to unravel the puzzle in order to understand how these layers of rock came to be so disordered as if to imply, at times, that the earth’s crust might have been created with time running backwards.

Thomas Sopwith – geological models Model-VII – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-VI – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-IV – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-II – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-VI – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-V – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-VII – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-IV – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-IV – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-V – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-VI – Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-IV – Thomas Sopwith [1841]

Thomas Sopwith – geological models Models Illustrating Denuded Strata- Thomas Sopwith [1841]

Thomas Sopwith – geological models Model-II – Thomas Sopwith [1841]

Related Posts:

Agates – Time Compiled
The Writing of Stones – Roger Caillois
Where Time Becomes Nervous: John Mcphee’s Annals of the Former World
Hypogean Wildstyle: Dominik Strzelec’s Byzantine Geology

 

2 Responses to “Thomas Sopwith’s Stratigraphic Models”

  1. Whewell’s Gazette: Year 2, Vol. #02 | Whewell's Ghost writes:

    […] Data is Science: Thomas Sopwith’s Stratigraphic Models […]

  2. Whewell’s Gazette: Year 2, Vol. #26 | Whewell's Ghost writes:

    […] Data is nature: Thomas Sopwith’s Stratigraphic Models […]

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‘You Really Do Not See a Plant Until You Draw it’ – Botanical Wall Charts at the Academic Heritage Foundation

Stichting Academisch Erfgoed Bontanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed has gathered a massive collection of botanical wall charts that were used as teaching aids in the Netherlands and the rest Europe from 1870-1960. The collection, over 3000 images, includes stylised morphological diagrams, sketches of microscopic anatomy and early botanical data visualisations. It’s clear from this collection that the act of illustrating was as much an act of observing. These lithographs record a kind of meditative microscopy; each a postcard sent from a journey into the minuscule world of tissues and cells. As Goethe is quoted as saying ‘You really do not see a plant until you draw it’. The highly detailed plant morphologies in German botanist Leopold Kny’s Botanische Wandtafeln are virtually cosmic in their nebulous configurations while Dutch geneticist Hugo de Vries’s data visualisations tend towards the lyrical.

Note: many of the thumbnails appear to be missing from the page although the full-sized images are correctly displayed.

Stichting Academisch Erfgoed Botanical WallchartsBladstanden – A.A.Van Voorn

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsFixeeren, Accumuleeren, Affoleeren – Hugo de Vries [1898]

Stichting Academisch Erfgoed Botanical WallchartsRussisch Billard Volgens Galton – Hugo de Vries [1898]

Stichting Academisch Erfgoed Botanical WallchartsCurve der Vruchtlengte van Oenothera Lamarckiana – Hugo de Vries [1898]

Stichting Academisch Erfgoed Botanical WallchartsKurkhuid – J.G. Meijer [1880]

Stichting Academisch Erfgoed Botanical WallchartsCelwand Reactiën – J.G. Meijer [1880]

Stichting Academisch Erfgoed Botanical WallchartsKernschede – J.G. Meijer [1880]

Stichting Academisch Erfgoed Botanical Wallcharts Bloei van Knautia Sylvatica – J.G. Meijer [1904]

Stichting Academisch Erfgoed Botanical WallchartsDodel Port Atlas – J.F. Schreiber [1893]

Stichting Academisch Erfgoed Botanical WallchartsDodel Port Atlas – J.F. Schreiber [1893]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Stichting Academisch Erfgoed Botanical WallchartsBotanische Wandtafeln – Leopold Kny [1874-1911]

Related Posts:

René Binet – Esquisses Décoratives & the Protozoic Façade of Porte Monumentale

The Rhetoric of Weird Wonders Gleefully Carousing in Morphospace : The Biodiversity Heritage Library’s Flickr Collection

Floraskin – Eilfried Huth & Günther Domenig

Patabotany #1: [At the Libarynth] The Forest is a College, Each Tree a University.

4 Responses to “‘You Really Do Not See a Plant Until You Draw it’ – Botanical Wall Charts at the Academic Heritage Foundation”

  1. Rob Kesseler writes:

    Hi Paul, someone sent me a link to your feature on botanical wall charts as I had recently been featuring them in a lecture. I am currently in discussion with a botanical institute in Pittsburgh who rescued a collection including some by Kny from a skip. We are hoping to do an exhibition featuring the charts alongside some of my images in 2017. I will let you know if it comes off.
    Great site you you have and beautiful movies. If you are ever passing through London maybe I could tempt you in to give a talk at Central Saint Martins where I am currently chair of Arts, Design & Science.

  2. Whewell’s Gazette: Vol. #51 | Whewell's Ghost writes:

    […] Data is Nature: ‘You Really Do Not See a Plant Until You Draw it’ – Botanical Wall Charts at the Academic Heri… […]

  3. paul writes:

    Rob, I would certainly be interested in the show you mention that may happen in 2017. Thanks for the comment and keep me posted.

  4. Goncalo Reis writes:

    Brilliant architecture of plants.

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‘It Must Give Off and Receive Light Like a Tiny Space Station’ – Kenneth Snelson’s Atoms

titlePortrait of an Atom – Kenneth Snelson [1984]

‘I’ve longed to see a life-sized replica atom, perhaps with robotic controls, to watch it perform its virtuoso assortment of tricks and tasks; of transmitting light and, catching it again, expanding and contracting….to see it demolished only to self-reconstruct…to watch its host of electrons flashing about the nucleus, forming the frictionless perpetual motion machine that a real atom is.‘ From Portrait of an Atom – Kenneth Snelson

From the classic motifs of Rutherford and Bohr’s planetary models to Schroedinger’s electron position probability clouds, the history of visualising the atom is one of a series of models, each one superseding the previous through new insights in quantum behaviour. After Heisenberg’s Uncertainly Principle the visualisation of atomic configurations, in reality unworkable due to quantum indeterminacy, had pretty much reached a dead end.

In the 1960’s sculptor Kenneth Snelson began to model the atom’s electronic structure based on symmetry laws for circles by correlating circle groups with quantum numbers that described the properties of electrons in atoms. Though the hunt for the ‘real’ atom, had been rejected by science it remained in Snelson’s mind that ‘we might one day find out what an atom would be like in a photographic facsimile or a sculptured replica’

‘It must give off and receive light like a tiny space station. It can remain stable and resist collapse under great pressure. It collects and organizes its electrons in shells around the nucleus. It puts to use all of its electrical, dynamic and magnetic forces in it structure. It can attach itself to other atoms in molecules and crystals with astonishing virtuosity. And though its electrons are in rapid and perpetual motion, it can sit in tranquility in a rock for eternity’ – Kenneth Snelson

Portrait of an Atom - Kenneth SnelsonRing Assemblies Representing 4 Complete Electron Shells – A Design for the Atom [1963]

Portrait of an Atom - Kenneth SnelsonStudy for a Big Atom – Kenneth Snelson [1965]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1978]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1978]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1978]

Portrait of an Atom - Kenneth SnelsonStudy for Atomic Space 3 – Kenneth Snelson [1964]

Portrait of an Atom - Kenneth SnelsonAtom Piece – Kenneth Snelson [1964]

Portrait of an Atom - Kenneth SnelsonThree Shell Magnet Piece – Kenneth Snelson [1976]

Portrait of an Atom - Kenneth SnelsonStu’s Atom – Kenneth Snelson [2009]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1966]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1966]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1966]

Portrait of an Atom - Kenneth SnelsonAtomic Model Patent – Kenneth Snelson [1966]

Portrait of an Atom - Kenneth SnelsonStudy for Atomic Space 6 – Kenneth Snelson [1965]

Portrait of an Atom - Kenneth SnelsonStudy for Atomic Space 5 – Kenneth Snelson [1965]

Related Posts:
Robert le Ricolais’s Tensegrity Models – ‘The Art of Structure is Where to Put the Holes’
Spatiologies – Vittorio Giorgini

3 Responses to “‘It Must Give Off and Receive Light Like a Tiny Space Station’ – Kenneth Snelson’s Atoms”

  1. Bookmarks for May 26th | Chris's Digital Detritus writes:

    […] ‘It Must Give Off and Receive Light Like a Tiny Space Station’ – Kenneth Snelson&r… – […]

  2. ben writes:

    amazing. thank you for that find! ben

  3. Ross writes:

    Two Words: “Bussard’s Polywell”

    Fabulous work.

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The Logic of Crystals – William T. Astbury & Kathleen Yardley’s Space-group Diagrams

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

William T. Astbury and Kathleen Yardley’s 230 Space-group diagrams, published in 1924, form a complete notation of all possible atomic lattice configurations in crystals (not including quasi-crystals). The figures formed the basis for what eventually became the International Tables for X-ray Crystallography. A crystal is three-dimensional tessellation of ‘unit-cells’. Each cell is a fundamental pattern of atoms or molecules repeated, rotated, folded. Depending on its symmetry, the unit cell of any given crystal can be classified according to one of those 230 space groups.

Deciphering these geometric sigils, without fundamental knowledge of their crystallographic logic, may be tricky but the plates have a rigorous aesthetic that stands up by itself. Non textual oblique strategists may already be mapping these tridimensional diagrams to create irrational marriages; for rendering micro-crystalline morse-code music or for use as guides to direct their psychogeographical drifts. The 230 space-diagrams designed to navigate crystal space might also be used to negotiate space taxonomies of other kinds.

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

Well aware of hidden language of crystals, Shea Zellweger employed their lattice configurations as a model for his Logic Alphabet – ‘a set of symbols that systematically represents the sixteen possible binary truth functions of logic’. Zellweger arranged the letter-shapes according to the structure of a crystal so that their interrelating symmetries could more easily visualised and manipulated.

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

230 Space-Groups - William T. Astbury & Kathleen YardleyPlate from Tabulated Data for the Examination of the 230 Space-Groups by Homogeneous X-Rays – William T. Astbury & Kathleen Yardley [1924]

Inspired by X-ray crystallography, and under the direction of Helen Megaw (a crystallographer who determined the structure of the ice crystal), the Festival Pattern Group developed textiles based on the atomic lattice of insulin, china clay, and hemoglobin for the Festival of Britain in 1951. In 2008, the Wellcome Collection, in London, curated an exhibition on the Festival Pattern Group called ‘From Atom to Patterns’.

Further Reading:
Logic Alphabet Project – Shea Zellweger

Related Posts:
The Melodies and Megaliths of Pseudocrystalline Terrains

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The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction

Indian Temple FractalsKandariya Mahadev Temple [Madhya Pradesh] (source unknown)

The self-similar, cascading architectural forms found in Hindu temple architecture appear to have been pieced together by a hyper-industrious Minecrafter hooked on Hofstadter. Jagged waves of blocky ornamentation, rhythmically repeating, create diminishing echo’s of the temple’s form; tiny versions of itself repeating towards a proposed infinity. Baroque three-dimensional Cellular Automata. Cantor Set masonry. Malevich’s Architectons upscaled and iterated to the nth degree, often smothered with a teeming mass of deities and denizens, each one competing for your retina.

Indian Temple FractalsKandariya Mahadev Temple [Madhya Pradesh] – RM Nunes

It’s not just that these temples appear to be algorithmically generated, the ancient Vastu Sustra texts provide procedural rules or recipes for their design, layout and build (including the positions of ornaments). The texts transmit recursive programs, by verbal instruction, to masons so that according to Kirti Trivedi, the Hindu Temple becomes a model of a fractal Universe. A model which represents ‘views of the cosmos to be holonomic and self-similar in nature’. The idea of fractal cosmology is no stranger to western academia. In 1987 the Italian physicist Luciano Pietronero argued, in his paper, that the Universe shows ‘a definite fractal aspect over a fairly wide range of scale’ based on correlations of galaxies and clusters, their spatial distribution and average mass density.

‘According to Hindu philosophy the cosmos can be visualised to be contained in a microscopic capsule, with the help of the concept of subtle element called ‘tammatras’. The whole cosmic principle replicates itself again and again in ever smaller scales’ – Kirti Trivedi

Indian Temple FractalsYellamma Temple [Karnataka] – Paul Prudence

Indian Temple FractalsArchitecton Series – Kazimir Malevich [1923]

Indian Temple FractalsTemple Plan for Barwasagar Temple [Uttar Pradesh] from Geometry Measure in India Temple Plans

The initial temple plan is based on a grid form known as the Vastu-Purusha Mandala. Tellingly Trivedi remarks in his paper that the Vastu-Purusha Mandala is ‘not a blueprint for a temple, but a ‘forecast’, a marking of the potential within which a wide range of possibilities are implied’. The significance here, should not be underestimated. A ‘potential for possibilities’ within a predefined rule-set predisposes architecture to be governed by a degree of emergence. While emergence in parametric architecture arrived, recently, with computers and algorithms, India has been enacting emergent masonry for thousands of years thanks to the open rules of the Vastus Sustra.

Indian Temple FractalsShweta Varahaswamy Temple [Karnataka] – Paul Prudence

Using a system of measurement called the ‘Tala’, dimensional relationships of proportions rather than exact structural specifications are defined. Initial decisions (why not call them algorithmic seeds?) combined with rule sets are used to define the final outcome of the building. The ‘Tala’ system is scale invariant, just like fractal mathematics, so that a building of any size can be created, and decorated without compromising the model of self containment. The temple, as a whole, is built by interweaving fractalization processes with repetition and superimposition. An example of a typical recursive instruction, verbalised, is:

The layer of prahara (projection) will be above the chadya (eave of the roof). This is to be repeated again and again on the spire over the spire. A fraction of the prahara is to be constructed and again the spires are to be constructed. Each of the upper spires will be sprouted out with a measurement equal to half the size of the lower spire – Ksirarnava, 7.113

Indian Temple FractalsSri Meenakshi Amman Temple [Tamil Nadu] – Paul Prudence

The Kandariya Mahadev, in Madhya Pradesh, is one of the best examples of recursive temple architecture in India. The rising towers (Shikhara) of this structure are said to mimic the forms of mountains which are themselves self-similar. Shikhara literally translates to the word mountain.

Inspiration by way of a recent trip (one of many) to Karatanka, Tamil Nadu and Kerala.

Further Reading:

The Hindu Temple is a Model of a Fractal Universe – Kirti Trivedi [1993]
Infinite Sequences in The Constructive Geometry of 10th Century Hindu Temple Superstructures – Sambit Datta [2010]

Related Posts:

Stanley Tigerman & G. T. Crabtree – The Formal Generators of Structure
Breed – Driessens & Verstappen: Evolutional Diffusion Lattices
Yuri Avvakumov – Agitarch Structures: Reconfiguring Utopia

14 Responses to “The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruction”

  1. Kevatha writes:

    Can I use this article for my talks and research ?
    I come from the lineage that built with the Vaastu parusha mandala our clan is called the vishwakarmans

  2. paul writes:

    @Kevetha, feel free to mention this post in your research/talks. A reference back to here would be appreciated, if possible. I’m going to look up on the ‘Vishwakarmans’, thanks.

  3. k p umapathy acharya writes:

    Nice article.

  4. Marta Leite Ferreira writes:

    Mr. Prudence,

    I’m writing about this issue in Observador, a portuguese online journal. Can you give me permission to use your photos with proper credits? Thank you.

  5. paul writes:

    Hi Marta, the three images that were taken by me you are free to use. Feel free to email me for more images.

  6. La fractalidad del universo se reitera en estos templos hindúes (y en estos fractales de templos hindúes) - La Tlayuda News writes:

    […] vía de Data is Nature, encontramos este fascinante concepto de los tammatras, que parecen ser las unidades que componen […]

  7. gregorylent writes:

    the third generation vastu shastri whose family constructed ramana ashram in tiruvannamalai would have recognized your ideas of recusiveness and fractals but his language and understanding derived from mysticism and sadhana .. spiritual practice .. important to remember that these things were created from the “inside out” ..

  8. Templos hindus, cosmologia fractal e uma arquitetura muito peculiar | Alameda 9 writes:

    […] No final de contas, este templo hindu reflete o modelo do Universo fractal, como explica o Dataisnature. […]

  9. Jasmine Shah writes:

    The article by Kirti Trivedi that is quoted here was presented at a Vastu Vedic Trust Conference organized by Dr. V Ganapathi Sthapati of Mamallapuram. It was Dr. V G Sthapati’s father who built the temple inside the Ramana Ashram. Dr. Stahapati has written prodigiously on this subject and worked tirelessly to preserve and present it to the modern world. It is truly thanks to him that today we are discussing this in this contemporary context!

  10. Whewell’s Gazette: Vol. #43 | Whewell's Ghost writes:

    […] Dataisnature: The Hindu Temple as a Model of Fractal Cosmology – Forecasting Architecture with Recursive Instruc… […]

  11. paul writes:

    @Gregory, I take your point here. This post could have expanded on the implicit vs explicit fractalization process in art and architecture. Quite often the explicit use of fractal processes can be quite worn, boring and generic. Fractal ’emergence’ a the result of philosophical ideas or physical constraints are much more interesting not only because of the resulting aesthetics, but also the trickle down effect of how certain ways of thinking can become externalised in form, as you say ‘ important to remember that these things were created from the inside out’

    Other great examples of philosophical or physical constraint based fractalization processes include those found in the Shipibo textiles and African tribal design:

    African Fractals: Modern Computing and Indigenous Design [PDF]:
    http://monoskop.org/images/f/fc/Eglash_Ron_African_Fractals_Modern_Computing_and_Indigenous_Design.pdf

    The Generative Song & Sound Pattern Matrixes of the Shipibo Indians:
    http://www.dataisnature.com/?p=596

  12. paul writes:

    @Jasmine, thanks for the extra info on Kirti Trivedi’s paper and also the leads on Dr. Stahapati’s work.

  13. Mayank_chatur writes:

    Please take a look at these papers….

    http://www.ijsr.net/archive/v3i12/U1VCMTQzMjI%3D.pdf

    http://www.researchgate.net/profile/Dongkuk_Chang/publication/222512493_Fractal_geometry_as_the_synthesis_of_Hindu_cosmology_in_Kandariya_Mahadev_temple_Khajuraho/links/0f31753b21e06bd624000000.pdf

    http://www.ijert.org/view-pdf/13155/role-of-fractal-geometry-in-indian-hindu-temple-architecture

    http://www.akashfoundation.com/Articals/Hindu_Temple_Models.pdf

  14. Dr. Jessie mercay writes:

    This lovely article is right on track with the cosmic understanding of temples per the Vishwakarma tradition. The late Dr. V. Ganapati Sthapati commented in depth about these ideas in his book Temples of Space science. We often think only of Hindu temples but this knowledge has been traditionally applied to Jain, Buddhist, and Islamic architecture as well as early Christain architecture. We like to think of it as “Hindu” but in fact, it is universal and not simply Hindu. Would a Buddhist, Jain or Muslim apply Hindu architecture? No. Hence we must accept that the forms built per Vaastu and Silpa Shastras are beyond religion – they are indeed universal forms that manifest fractals of consciousness for the well being of humanity.

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