Chronos – Günter Haese [2004]

In Günter Haese’s Chronos [2004] an array of radio antenna appear to be wired for aeolian transmissions. Carried to their receivers by micro bifurcating air vortexes the turbulent noise of air flow is the signal in this instance. In the cubic lattice of Kalogo [1999] an freeze frame animatronic of photons appear to be propagating through a crystal slowed down by a factor of a trillion seen through a compound eye. Yoshiwara II [1972] appears to be a point cloud materialized, but sagging under the weight of its own indifference to the environment and its audience.

German artist Günter Haese made a little over 400 hundred fragile mobile kinetic sculptures from brass wire, cogwheels, coils and clock springs in his lifetime. His wireframes of vibrating constellations and quivering parts were powered entirely by the flow of air. In Golf [1997] it’s clear to see the Paul Klee influences that Hasse was keen to mention in his work, but there are also strong hints of Duchamp enclosed inside this cubic trap.

Golf – Günter Haese [1997]

Quirin – Günter Haese [2012]

Responsa – Günter Haese [1965]

Janus – Günter Haese [1992]

Kalogo – Günter Haese [1999]

Pinkus – Günter Haese [unknown]

Pokos – Günter Haese [unknown]

Pythagoras – Günter Haese [1997]

Transit – Günter Haese [1993]

Yoshiwara II – Günter Haese [1992]

Baghdad – Günter Haese [1965]

Myoglobin [1961] – Irvin Gies

In Irvin Geis’s graphic molecule paintings the lightness of the wireframe structures perfectly counterpoints the cast iron logic of each molecules cryptographic configuration. Myoglobin, his most famous illustration published in Scientific America in 1961, took 6 months to complete. It’s frozen lattice of lushly hued paths abstractly coalesce into a connectionist idol; molecular aesthetics as network idolatry. Ribonuclease, with its graphic specular lighting and constructivist blue and red tones, presents molecules as scaled-up utopian architectural constructs rejecting the tyranny of utility.

Lysozyme – Irvin Gies

Lysozyme 2 – Irvin Gies

Crambin – Irvin Gies

Geis was trained as an architect. But the great depression of the ’30’s threw a curved career ball and he found himself working in the golden age of hand illustration for Fortune Magazine in 1930’s and then with Scientific America in the 1950’s. ‘According to Richard Dickerson, the UCLA biochemist who co-authored a number of major books on biochemistry, Gies’s genius wasn’t in depicting a protein exactly how it looked, but drawing it in a such a way that showed how the molecule worked, an artistic process that Geis called, ‘selective lying.’

Ribonuclease S – Irvin Gies

B-DNA – Irvin Gies

Cytochrome C – Irvin Gies

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

Chromatic 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.

Plate 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.

Plate from Physikalische Krystallographie – Paul Heinrich Groth [1885]

plate from Mineralogie – Franz Wolfgang Ritter von Kobell [1864]

Plate from Physikalische Krystallographie – Paul Heinrich Groth [1885]

Plate from Mineralogie – Gustav Adolf Kenngott [1890]

Optical effects during the heat treatment of glass – David Brewster [1815]

The 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

Plate 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.

Plate 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.

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

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

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

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

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

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

Plate 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

Illustration 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].

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

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

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

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

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

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

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

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

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

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

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

Illustration 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 Cage [1958]

Score for Fontana Mix – John Cage [1958]

Smith 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

Cyprea (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.

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

Cyprea mappa, The Map Cowry

Cyprea (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

Max 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 – 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.

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.

Plate 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.

The 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.

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

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

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

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

Musical Ratios Series, 6 to 7 – Mark A Reynolds

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

Square Series Piston Effect – Mark A Reynolds [2010]

Phi 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

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.

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.

Model-VII – Thomas Sopwith [1841]

Model-VI – Thomas Sopwith [1841]

Model-IV – Thomas Sopwith [1841]

Model-II – Thomas Sopwith [1841]

Model-VI – Thomas Sopwith [1841]

Model-V – Thomas Sopwith [1841]

Model-VII – Thomas Sopwith [1841]

Model-IV – Thomas Sopwith [1841]

Model-IV – Thomas Sopwith [1841]

Model-V – Thomas Sopwith [1841]

Model-VI – Thomas Sopwith [1841]

Model-IV – Thomas Sopwith [1841]

Models Illustrating Denuded Strata- Thomas Sopwith [1841]

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

Ken Rudolph’s film Crystals [1968] is microscopy at its most carnivalesque. A synchronized choreography of shape-shifting shards and opalescent slithers create the mineralized equivalent of a Busby Berkley scene. Dendritic spiracles elongate to form microscopic mega-cities but the isometric skyscraper view is flattened into a fractal flatland. Radial diffusions grow like bacterial colonies – the urbane sprawl of molecular lattices inter-fitting with space-filling intelligence.

The music, simultaneously at odds and perfectly at one with the scenography, implies a drama of multiplicities, city building, contagion spreads, early forms of life decrypting the vectors of their own evolution. Cascades of rising notes annotate the accretions of tiny mountain peaks forming and the fanning of microscopic alluvial terrains.

‘It looks like a crystal’

‘Well, gentlemen, there’s our answer’

‘To what?’

‘How Andromeda functions without amino acids’

‘Yes. I’ve often thought that living matter might be based on crystals of some kind. All these wedge-shaped compartments, they’d serve to separate biochemical functions very well’

– The Andromeda Strain.

Ken Rudolph was known in the academic film world for a series of films that applied synthesizes of sound and video informed by counter-cultural and psychedelic currents of the late 60s and early 70s. No wonder his film is a take on the first person view through the liquid crystal dream of a lysergide adventurer.

Related:
Form Constants of Optical Mineralogy
The Logic of Crystals – William T. Astbury & Kathleen Yardley’s Space-group Diagrams