Mid 20th-Century questioned, “why he designed Square Buildings? – accomplished Architect Erno Goldfnger’s abrupt response was ”only Pygmy and Zulu live in round houses!”. Expressing racial and derogatory stereotypes then prevalent in Western Society, a bald assertion made its geometric point. A duality, evident in a rectilinear installation and advancement of ‘Civilised’ society, was everywhere constructed from a recent-organised [Neolithic Era – 10,000 B.C.] control over the cyclic roundness of our primordial origins – everyone’s biomorphic ancestral roots.

How Architectural Geometrics Have Conditioned Our Society – ref: 2009 Consciousness Studies –

1964/5 saw my ‘Final Year’ urban design presentation at Kingston School of Architecture. A college-task was to survey and ‘modernise’ the layout of an ancient-established rural community – Diss, in Norfolk, UK.,_Norfolk

The previous school-year had completed its survey of V. Gordon Childe’s [1930’s] ‘revelatory’ excavations at Neolithic Era Skara Brae, Orkney Isles – the far-north of Scotland.

Exceptionally well-preserved, those most-ancient of Europe’s dwellings had appeared as rounded – but their internal layout and ‘stone-age’ fittings were well-crafted rectilinear, as any 1930’s ‘Bauhaus’ or ‘Goldfinger’ concept. It prompted me to consider that same question – why do we ‘civilised’ peoples so ‘squarely’ design our elegant and comfortable homes – whereas tribal peoples intelligently construct their comfortably convenient round environments?

Our small Art School Library came-up with the answer – in less than an hour. “Black-Elk Speaks * told how “when the White Men came to our land” we Native Americans were forced from our rounded homes and an efficient mobility of a “Tepee” encampment, to be permanent-imprisoned in their squared confinements. So, not only ‘Pigmy & Zulu’ but nature-dependent ‘nomadic’ peoples everywhere – from ancient times till now – require (and deeply desire) their homes to be rounded! The Mongol Ger/Yurt is desirably ‘Modern’, a portably effective ‘machine-for-mobile-living’ – as is an “Airstream” camper-van. *,ack_Elk_Speaks

Why do those so-want/need their own living geometry? US researcher Prof. Roger Sperry [same time – mid-1960’s] revealed the answer via his surgically invasive split-brain investigations.

He showed ‘Time-logic’ is left-brain-made cyclic variable – bi-laterally separated from a right-brain ‘fixed-Space-logic’ well-evident in mammalian and avian make-up. That base-duality is fundamental to promoting advanced existence. Ref – 2013; Two distinct forms of functional lateralization in the human brain (

In the bio-rounded bird-nest or fire-placed birth-homes of the mobile lifestyle a female-predominant (left-brain specialist) time-logic controls a centralised (but protectively moveable) security of that ‘sacred territory’.

Diss is a small market-town – an agricultural-trade settlement in its post ice age river-valley, well built on a hill-side above its unique crafted ‘Mere’. A ‘gem’ is immediately experienced as a self-confined ‘sacred territory’ – remote as a very long walk away from its eastern railway connection to Urban Modernity or a southern road that bypasses it.

In studying a forced ‘modernised’ redevelopment of its ‘iconic’ prospect saw me concerned – how to preserve and advance a unique, ages-assembled, fragile charisma?

Diss has its obvious ‘organic’ layout that set my thinking on biomorphic lines. Cell-morphology dictates our biological origins and living presence. D’Arcy Wentworth Thompson’s ** Classic study “On Growth and Form” set-out how geometrics condition the science of cellular bio-evolution; so my “Space-Cell Systems” project was instant initiated. Its geometric impulse was to formulate a ‘Natural Architecture’ – design an evolution-generative Metabolism – as then demanded for advancing an unprecedented Cosmic mobility and a new World re-ordering, 1957 evidenced in ‘Sputnik’ orbit.**

A ‘Space-Cell’ approach to renewed urbanism was radical – but soon ‘nationally’ vindicated via the ‘Observer‘ Sunday newspaper. Their renowned Architectural Critic was Ian Nairn. He gave an authoritative review of that Diss Project’s presentation – then showing at London’s ‘Building Centre’. Nairn observed that among all those proposed gridded-out schemes mine alone showed a different formal-appreciation of the town as a unique masterpiece – to cellularly contain its organic extension.

But Erno Goldfinger’s contrasted ‘incompatible’ relationships between round and rectilinear form in Architectural Geometrics (as evidently definitive in home-setting everyone’s life-style) had yet to be science-explained. What inherent logic (evidently critical) was needed as diversely effective?

Universal Existence is in geometricSpace-Time’ – now measured and proven finite from its ‘Big-Bang’ origin and inherent extension at C2 constant-absolute speed of Light. But Time’ has no presence where everything is only radiant – C2 two-dimensional planar – as photo-graphic Space. Gravity is spherical-localised; as Mass accumulates matter to install ‘Time’ G=M=T. So ‘Space’ & ‘Time’ are inherently separated metric-surfaces; those differential geometric potentials engage in organisation of a vibrant discontinuous foaming in the Cosmic Calculus of an existence-generative ‘Space-Time’ Energy/Mass Matrix.

My key-realisation was seeing in Einstein’s 1905 Relativity Theory newly demonstrated revolutionary dual-geometrics of Space & Time. But Classical ‘Space’ was (remains) seemingly a characterless volume; so for Einstein then-too a nothingness – a simple void – as plenum in its neutral containment of ‘real’ material events, with ‘Time’ same-way a notional linear-measurement in past-future connection of those events. His previous maths tutor Minkowski asserted [1908] that ‘new’ view of existence in his four-dimensional matrix-measuring of it. Now three dimensions of volumetric Space were somehow ‘welded’ to a one-dimensional Time-line. But they were both wrong in maintaining/advancing those ‘Classical-set’ linear assumptions. As our present science references yet define them that way, they are that logical impossibility of fixedly “squaring-the-circle” in an unrealisable “Unified Field” – ever a Pi-based Equation.

But Rectilinear Architecture & Agriculture had made a true ‘Space-metric’ Neolithic-manifest; operating a revolution by fixed-installing those uniform planar-space 2-D surfaces of walls, floors, crop-fields and rice-paddy – first-time everywhere the same – so to become productively and predictively extended (mathematically constant accountable) in Goldfinger-defined rectilinear ‘Civilisation’. But ‘Time’ is proven local-closed (mathematically variable) as directly associated with Gravity/Mass; spherical-surface rounded and cyclic in periodic arrangements. So ‘Time’ is ever personal – geometrically individualised. His ‘Pygmy and Zulu nomads’ must momentary depend-on (every instant locally adapt-to) Earth’s daily, monthly and annual variety and Universal Nature’s constant change – immediately fortuitous or dangerously unpredictable – in a motile bio-subsistence lifestyle.

But of course, Planar Form and Curved Form are inherently ever separated. They cannot have a common denominator nor smallest [infinitesimal] particle to same-way make, measure or conjoin them – except as a constant dynamic-ratio ever ongoing in an infinite series Pi22/7. Squaring-the-Circle’ is the Universal Constructive Formula, the ‘Space-Time’ calculus we must adapt-to and Constant-apply. Every architect’s plan-layout or cartographer’s map-of-the-world is a 2-D flat approximation of a curved surface existence, as 1919’s demonstration of Universal Gravity Curvature conclusively proved Einstein’s ‘General’ postulate.

In the same-way, every photo or mirror’s 2-D unified flatness takes Mass – with its ‘Time’ dimension – away from the radiant Spaceit planar-true reflects.

Our body’s construction is cellular-organised via a linear genetic-coding; then Helix-Cycle assembled in DNA. Same way prescriptive/descriptive in writing, the Western Alphabet is based on the ancient origins of Hebrew script – 22–letters/numerals set out in its 7 groupings – as activating the Pi-dynamic in mental-divided configuration of our verbalised/visualised conjectures or logical assertions of ‘existential reality’.

In Conclusive Showing: Every Atom has its characteristic linear-expressed properties installed via a planar-radiant nucleus [Moseley’s series] separated from a periodic spherical-closed orbital electron-cycle [Mendeleev’s series]. In that contained geometric, as a Pi-resolving duality, those are then the interactive building-blocks of us in our material existence.

That geometric duality (as Goldfinger clearly stated it) indicates two opposing outlooks-on and conditionings-of our worldly existence. Since an archaic generation had then installed our adaptive-species’ Neolithic Revolution the Architected resolution of that eternal diversity has been intelligently geometric re-constructed; e.g. in our ‘Modern’ Times from Greek-Roman based Civic/Religious Architecture + Buddhist Stupa – Mecca’s Kaaba. All same way set a world-wide ‘logic’ in every religious or secular construction and our planar-formed homes and work-places. Those force-install a common [non-local] base for standardised time-routines of us as ‘civilised’ occupants, new-disciplined in a Universe-resolving dynamic – along with the time-specific accommodative arena of collective re-creation (a socialised cyclic-revitalisation) in religion, sports and entertainment.

JOHN McCLELLAN – 01-09-2021 – 11-05-22

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