### Shape as Memory: A Geometric Theory of Architecture

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Shape as memory : a geometric theory of architecture. Shape as Memory : a Geometric Theory of Architecture.

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All rights reserved. Remember me on this computer. Cancel Forgot your password? Year 3 24 1 1 Language English 26 Italian 3. Displaying Editions 1 - 10 out of La forma come memoria : una teoria geometrica dell'architettura by Michael Leyton. You should get,.

## Vitruvius - Wikiquote

Subdivide a square of side 1 into two equal rectangles. Then lay out a distance equal to the diagonal of one of these half-squares, plus half the side of the original square. The ratio of this new distance to the original side, 1, is the golden ratio. Let's now return to the pyramids. If we take a cross-section through a pyramid we get a triangle.

If the pyramid is the Great Pyramid, we get the so-called Egyptian Triangle. It is also called the Triangle of Price, and the Kepler triangle. The dimensions, to the nearest tenth of a meter, of the Great Pyramid of Cheops, determined by various expeditions. The Egyptian triangle thus has a base of 1 and a hypotenuse equal to.

Its height h , by the Pythagorean theorem, is given by. Solving for h we get a value of. Project: Compute the value for the height of the Egyptian triangle to verify that it is.

## Computational geometry

Thus the sides of the Egyptian triangle are in the ratio. The astronomer Johannes Kepler was very interested in the golden ratio. He wrote, "Geometry has two great treasures: one is the theorem of Pythagoras, the other the division of a line into mean and extreme ratios, that is , the Golden Mean.

The first way may be compared to a measure of gold, the second to a precious jewel. We recognize this as the sides of the Egyptian triangle, which is why its also called the Kepler triangle. Project: Prove that If the sides of a right triangle are in geometric ratio, then the sides are.

A British railway engineer, Robert Ballard, saw the pyramids on his way to Australia to become chief engineer of the Australian railways. He watched from a moving train how the relative appearance of the three pyramids on the Giza plateau changed. He concluded that they were used as sighting devices, and wrote a book with the grand title of The Solution of the Pyramid Problem in He also noted that the cross-section of the Great Pyramid is two of what we have called Egyptian triangles. He then constructs what he called a Star Cheops , which, he says, " Now we'll look at his other claim, that the Great Pyramid's dimensions also show squaring of the circle.

But just what is that? There were many attempts to square the circle over the centuries, and many approximate solutions, some of which we'll cover. However it was proved in the ninteenth century that an exact solution was impossible. The perimeter of the base of the Great Pyramid equals the circumference of a circle whose radius equal to the height of the pyramid. Does it? Recall from the last unit that if we let the base of the Great pyramid be 2 units in length, then. Since the circumference of the circle 2 nearly equals the perimeter of the square 8.

The area of that same circle, with radius equal to the pyramid height equals that of a rectangle whose length is twice the pyramid height and whose width is the width 2 of the pyramid. Suppose that the Egyptians didn't know anything about but laid out the pyramid using a measuring wheel, such as those used today to measure distances along the ground.

Take a wheel of any diameter and lay out a square base one revolution on a side.

## Shape as Memory: A Geometric Theory of Architecture

Then make the pyramid height equal to two diameters. By this simple means you get a pyramid having the exact shape of the Great Pyramid containing perimeter-squaring of the circle and area squaring of the circle and, for no extra cost, the golden ratio! Project: Use a pizza cutter or a similar disk to construct a pyramid similar to the Great Pyramid. A transformable, formless, relational nature of a diagram and its fluctuations around the points of the archive, are derived from the notion of intensive properties and their dynamic variation — through the analogy to differential theory and theory of movement and continuity in reference to Ciric, , note Diagrammatic search logic enables maximization of a memory space deepens territories and fissures of digital data-storage and matter by symmetry breakings and bifurcations — a kind of fractal regular or irregular involutions, convolutions, and evolutions , while that of an archive based on stratification stacking and classification always requires more space and therefore Figure 5.

Excerpt cabinet. From Placcius , p. So in a way this is similar to the use of Zotero or other citation management systems, but instead uses loose sheets of paper on hooks. The strips are hung on poles or placed into hybrid books. Transition from logic of sort in boxes toward interactive logic of search in a Big Data network — example of linkedin network created by Linkedin Inmap tool; c.

Here he explains the emergence of big data science and marginal cases that prove the unsustainability of those grand narratives and concepts being phenomenology influencing the change of the way we think as carried out by the second always present and operative autonomously within those big universal historical style generation of digitally intelligent architects, designers, creatives within the paradigm of the declarations Foucault, DeLan-da.

The first one is attached to the concept of an archive, and second digital turn manifested as a global social project, phe-nomenon, and strategy. This move, the second one, or the one that results from that breakage of discoursive constructs originating he claims, caused a major shift in scientific methods of research and inquiry as the primary model in the free-structure relational state of all the pure information, attached to the concept of a for logical operations - the move from the imperative of sort, to-wards that one of the search diagram.

In this telligible entities suitable for immediate and clear knowledge transmission, negotiate connections framework, it is not the question that one which guides the data but the data guides the question among entities whose relations they recognize as relevant. Miessler, almost completely heuristically. More information as this collection of everything opens up new insights, implies new problems and triggers new questions. The convergence of neurosciences and information sciences in recent history starting from the second half of the 20th century until the latest innovation in the ield of their cross-disciplinary hy- Digital transcriptions of the idea of the complete world knowledge in the present moment, largely bridizations produced distinctive models for data-processing.

Paradigms of connectivity and difering from the one that existed from ancient times taking form of diferent architectural objects communication, transmission, and dynamics present in biological mechanisms of brain activity, libraries, memory temples, theaters, and tower, etc. These might be performed in diferent ways — we may use analogy, but also a direct vious rules of information charting, categorizing, and retrieving; a new intelligent relational entity precise scientiic method of transposition and relational dependence model as in complex adaptive emerged.

Virtual ields, besides provision of vast, almost ininite space for documentation, enabled systems which make connections between biological aspects and processes in organisms, envi- creative formation of a new system by which digital citizens and societies behave and function. This ronment, and social forms and aspects of existence in order to deine or predict matter formation includes laws and strict regulations, but also possibilities of unlimited diagrammatic restructuring as which will at the end have its spatial result, eventually architectural one.

The given explanation introduces abstract, virtual and digital terms, and real physical one. Functional connectivity measuring and re- the way to investigate a governing structure — network and geometry — of these search metacogni- cording by recent fMRI advanced imaging have proved some of the assumptions of brain activity tive connectivities; of the geometry that organizes and orders our thoughts and imagination.

While speaking about basic thinking mechanisms as those that guide and direct our But visible parts of architectural intellectual and intuitive practices of reasoning and representation.

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A the aim here is to evade any stylistic categorization in order to be able to produce novelty or inno- discovery and explanation of how architects think, act creatively, progress, and produce innovation vate our visual and architectural domains. It appeared that diagrammatic scriptures may ofer an interesting perspective follow classiication principles or principles of the archive.

But, as we might tend to innovate and and answers to these questions. Referring to the previous section which dealt with astute, and pleasant. Their speciic ield of application might be related to ideas of the extended visual cosmopoiesis, we recognize that traditional models of the world found their virtual data-dou- mind Clark and Chalmers, , or intelligence strategies dealing with biological-artiicial and in- bles and contemporary data-architectures, closely resembling each other, but they also recorded terior-environment coupling in thinking processes, concepts of multiple and integrated intelligence signiicant alterations and improvement by the inclusion of the most advanced scientiic discoveries Gardner, , , , and move from his concepts of intelligence fragmentation spe- and modelling e.

Kolatan and isms as direct materialization of data. But this method is just one of the possible architectural interpretations of data-space, the one not to be taken as architecture per se but architecture of statistics. It might be rather taken as the bridging condition from traditional or classical architectural mnemotechnics, across scientiic augmentation of real space by additional statistical data, their direct transposition into computer language or retrieval from its algorithms, inally l eading t oward a ppropriate r esearch m ethodology a nd v irtual instrument investigated in this paper.

And, eventually, the recent history revealed the new materi- ality of all the generative bio-informational and previous data-architectural investigations revealing a scope of neural networks design abilities for direct fabrication. But we will still stay in a domain of virtuality for purposes of the proposed research aim and explanation.

As an introduction to questions of virtuality and virtual space, it might be added that artiicial lives created in their spheres represent models in constant quest to get closer or to merge with their emulated prototypes - the originals, those perfect biological ones - to transcend them in skills and abilities, and eventually completely replace them as at the moment they can replace or extend some of their components, functions, or aspects through algorithmic advancements. This includes Figure 6.

Ex machine movie stills and dialogues — Ava questioning herself about her abstract drawings thought recordings of her artiicial brain algorithm — the complex neural network and development of her imaging possible by advanced mathematical explanations of the world by movement from linear to toward iguration and realism of the immeadiate, analogue environment a tree having also references to nonlinear equations to deal with complexities DeLanda, , IT revolution Saggio, , algorithimic and symbolic logic used in programming; , or development of information sciences and data-computing.

New digital literacy b. Fibrus formations with Simulations, Fibro. Yao [Andrasek, A. Spanning period of years of ticity — the one that proves that connection strengths between neurons can be modiied in response development and application starting with the first experiment in the s , now we may to activity and experience — a process that is widely accepted by neuroscientists to be the basis for clearly see their results, nuances in performance and types in constant refinement and learning and memory. Repetitive training enables the neuronal circuits to become better conig- amplification , and some progressive directions.

Virtuality may easily go beyond the traditional Cartesian 3- by predeined design by engineers. And since the biological brain still represents that superior dimensional space and form-matter, escaping physical properties that govern our everyday thinking mechanism with its lexibility, generalizability, and learning capability, the predictions of lives and materi-al immediacy. But, they may also be formulated as not taking space, not alternative to architecture as arbitrary sculpture arguing for the one that is synergistically intercon- taking place, or being explained by the systems that are not primarily spatial as for example topology.

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Besides being the realm of our unfulilled dreams mutations, morphings. Being able to fuse luid nonlinear forces of dynamic data-architecture and the er being used for its coding, content, or logic of structuring and dissemination. Ater a long period of experimentation in the virtual realm, new ways in which matter may evolve and deine itself based on the information it contains, dynamically generates, expands or invents, are established. These dynamic, open-ended structures and processes of endless data-networking and re-networking are taken as universals for features and logic of information paradigm.

Related to memory and narra- Figure 7. Istvan, aka Chaotic Atmospheres, Flowing City Map series, tive consolidation, cognition, and historical or world interpretation and creation through diferent Tokyo and New Yorks visual ields. Istvan, production resulting with a speciic architectural matter formed by information in-formed. This path Chaotic Atmospheres. So, if we which the only limiting condition might be human imagination Viola, Argumenting intelligence being dependent on memory, followed by question of how can an object become a memory store, i. Adding the principle of asymmetry if both Symmetry and Asymmetry taken for inference rules as an evidence of any kind of interaction, Layton make inference of possibility of storing memory only in asymmetries, while symmetries being something that erases memory, — the change of state and form gives us evidence of some kind of action, that something is taking place, it allows us to retrieve the past, the history; the status quo gives us nothing.

But we must be cautious as we might be facing false conclu- sions - symmetry might contain information about previous activity only if being able to completely recover the initial state an absolute elasticity and if expressing invariants on the levels that might not be visible or detectable to us, or that might be incorrectly described. So, we may leave this theory as the question of closer deinition and determination in some kind of speciic application, Figure 8. Datascapes — Metalevel — the ield of information [information chatter], Dragana Ciric, ; retrieval about the past actions and something inscribed within through previous processes of for- b.

We may see that for Villard, the geometric object explaining the logic of messiness and abundance of Big Data systems, we usually have in mind a also represented a memory store — the memory and the key of geometric construction and relation dispersed relational quantum ield of dynamic entities freed from any kind of biased or preestab- of forces, the procedure that makes, forms, and shapes the matter. If the memory takes place by lished narratives.