This is an intriguing question of human mind that has been asked eternally from time immemorial. Who taught the ants to build their underground elaborate township? Who taught the birds and the bees to build their own intricate homes? All these and numerous other questions made human beings to think of a higher intelligence behind these creations. In nature there must be a creative force working behind the scene that helps to program the animals before birth. How can a duck swim spontaneously as soon as they are born, while a human baby cannot? The answer is obvious; they have been programmed this way prior to birth, during cell division and differentiation towards maturity.

So, the answer to your question is as follows.  The ideas of those magnificent ancient buildings were in the minds of the ancient inventors (as built-in or innate knowledge) and the geometrical precisions and intricate mathematical calculations for the building came later (as acquired or intellectual knowledge). Albert Einstein put this in a very poetic way, “The universe is pure geometry, and pure geometry is pure mathematics, and pure mathematics is pure thought. Therefore the universe is a giant thought, and we are created in God’s image because we think.”  

Dear Tushar,

Thank you very much for your constructive comments.

My personal opinion is that Geometrics is human-created aimed to represent the patterns in nature in a simplified way. How much time/pages would it take for a top specialist in mathematics/geometry to represent a simple bird nests in all its detail, e.g. taking the shape and position of each nest fiber/twig/branch into account?

I think correct answering the original question needs differentiation between (a) instinctive and conscious, (b) intuitive and systematic, and (c) empirical and rational ways of creation. I do believe that instinctive, intuitive and empirical creation may lead to surprising results. But conscious, systematic and rational creation may lead to avoiding surprises with 'magnificent architectures'.

Mayas,  Egyptians     .... similar constructions without physical contact and cultural exchange? Spiritual connectivity, mental influences, dream exchanges????

Dr. Lambrechts, I do not think the appearance of the theory of geometry (or that of physics) can be connected to any particular date, as you know, they are historical developments. Anyway, there is an interesting list of the (extant) oldest buildings in the world in Wikipedia, not including natural shelters and single-chamber megalithic tombs. Please see: http://en.wikipedia.org/wiki/List_of_the_oldest_buildings_in_the_world . Regards, I.H.

This is a good question with many possible answers.  

Obviously, there are pros and cons about the absolute necessity of geometry versus a completely naive, intuitive approach in the design and construction of great architectures.   It is also obvious that that birds with their construction of variously shaped hemispherical nests with great strength, bees with their incredibly functional and beautifully designed hives and spiders with their magnificent yet subtly constructed webs, have no knowledge of what we call geometry and yet these animals are highly successful architects.    On the other hand, the many long-lasting architectural wonders such as the Parthenon in Athens, Notre Dame cathedral in Paris, and the Blue Mosque in Instanbul bear the imprint of a deep understanding and usage of geometry.

So this question brings to light a marvellous dilemma and intriguing dichotomy between the obvious successes of natural architectural wonders and the incredibly successful, long-lasting and beautifully designed historical buildings.  

Although nature is a magnificent mathematician of precision and complexity, actions of humans in doing sophisticated architectural buildings in ancient civilizations all over the world  that still puzzle us today have to be results of strong but intuitive geometrical understanding, the concept of symmetry and solid knowledge of measurements to design lasting and stable structures of aesthetic flavor.     

What about the design of crystals? It is aesthetic, symmetric, stable.... No human-made geometry theory of the creators but magnificent?

I think this will lead us to state changes, equilibriums and situated entropy ...

Why not mentioning attractive forces bringing particles/molecules together to construct magnificent architecture? These forces might be biotic or abiotic in nature. E.g. Birds are attracted to natural substances in such a way that it will end up in a bird nest? Molecules are attracted to other molecules in such a way that it will end up in a crystal.... etc...?

Architectural design is inspired by functionality and beauty. Crystal design is related to  stability and beauty.

Sorry Colleagues, I have seen ugly crystals. Also buildings...

Dear Imre,

what is called 'ugly' is not more than a human interpretation. There are still these attractive forces that also make what you call non-aesthetic shapes? 

Dear Marcel,

I fully agree with you. Seeing something 'beautiful' or 'ugly' (not only by the eyes, but also by the mind) is humane. This is valid for all natural formations and produced artifacts. And the judgment is more or less converging or the same for the overwhelming majority of people. Just think of it: has anybody said to his or her newborn baby that 'you are so ugly'?. I am not trained sufficiently in aesthetics, as the branch of philosophy, to see and reason about what is behind and in the depth - and I am also curious if it has been explored and agreed upon at all. However, most probably, human aesthetic judgment is a historical development, perhaps related to survival as many other things, and it has by now become coded in our genes. I do not know.

Kind regards, I.H. 

Dr. Lewis Kausel, the same from another angle: Is the shape of the ancient Egyptian pyramids dictated by the fact that its builders had easier job with the majority of the weight closer to the ground, or because pyramid as a geometric shape is so nicely symmetrical and proportional? We know that ancient builders had great difficulties with working against gravity in all contexts. The idea of a wide base might originate in the analogy of sand piles. Regards, I.H.

Dr. Lewis Kausel, I resonate very much with your reasoning. However, concerning shape (geometry) I can add something starting out from my engineering background. The possibility of producing and using flat facets or surfaces in buildings was very much influenced by the available technologies. Rocks/stones were split or sawed and the obtained orthogonal, brick like parts were used as building blocks. I think this applies to pyramids.

I learnt from my architect colleagues that single-curved surfaces came in much-much later. Just our modern technologies allow us to produce double curved (e.g. saddle) or twisted surfaces for buildings (e.g. in concrete, or glass). Arbitrary geometries need additive manufacturing (like 3D printing) technologies.

The Tumulus of Bougon is a group of five Neolithic barrows located in Bougon, France. The oldest structures of this prehistoric monument date to 4800 BC (see link below).

It seems to me that the plan of Bougon complex has aesthetic features.

http://en.wikipedia.org/wiki/Tumulus_of_Bougon

http://en.wikipedia.org/wiki/List_of_the_oldest_buildings_in_the_world#By_age

Are flower/fruit designs (e.g. pine apple design) also aesthetic examples of nature's architecture not taking human-made geometry into account?

Dear Talib,

Tumulus: I seem to perceive circles or tubes? Where did the inspiration come from? Mushroom shapes, tree trunk shapes, the shape of the moon or the sun..... ?

Not more than copying nature without understanding the mathematics behind the shapes?

Thank you Marcel.

I am not specialist in aesthetics philosophy, But I feel that the builders of Tumulus inspired by their feeling in curved boundaries and symmetry in addition to how to geometrically make harmony with nature.

Dear Cecilia/All,

Each individual animal construction is physically unique in design. Two bird nests will never be the same. What is the relative importance of imagination, e.g. variation that was wanted as an individual signature, versus constraints, e.g. living beings are physically unable to make an exact copy of an existing creation?  

What is imagination, e.g. an mental image of a construction before it is built, versus a template, e.g. a genetically-based brain organisation that influenced attractiveness towards and organisation of chosen building material to be used for the realisation of a construction?

Can imagination have a genetic basis?

Dr. Lambrechts, related to your last question: Let me call your attention to a paper (probably you know it) written by Simon Baron-Cohen. Though this does not address what I would call, the historical genetic basis, but I think he adds a lot to our understanding of how the brain and imagination are possibly interrelated. See attachment. Kind regards, I.H.

Can birds imagine nest constructions they cannot build themselves? They perceive and memorize existing physical structures including nests from other species.....?

Scientists claim that animals dream, so perhaps animals might dream from imaginary nest constructions they cannot build? 

@Cecilia: Gorillas create beddings of leaves to rest. Can they imagine more elaborate constructions when they dream? I can dream from fantastic buildings I can not build myself in this biology-based life. I can dream from fantastic buildings of which the details are not always memorised, which implies that I can not make a detailed copy on paper. However, I can let my imagination work to propose a construction from a dream?  

@Imre: How scientifically demonstrate that autistic childs do not have imagination, despite the fact they can have photographic memory?

I would hypothesize that the decorations of bowers in bowerbirds partly result from imagination.

@Marcel

slaudividni namuh naht sessecorp gniylrednu tnereffid yletelpmoc evah nac ruoivaheb lamina taht mialc stsigolohcysp laminA

Animal psychologists claim that animal behaviour can have completely different underlying processes than human individiuals.

Yes indeed! But can they truly read their minds?

Marcel, no, or at least not sufficiently. Overall, still very little is known about the secondary and tertiary activities of human or animal minds and the related innate cognitive (and perceptive and attentive) processes. Likewise, the genetic basis and mechanisms for formation of shapes of plants, vegetables, etc. are only poorly understood. With regards to morphological formation of organic structures what is assumed is that it is influenced by chances as much as by conditions. That implies to me that we first need to know all the genes that were and are involved in that process and then after a long while we will possibly be able to piece together a descriptive or an explanatory theory. Regards, Imre

The question then is: how much detail do we have to know to understand a process which allows you to make reliable predictions, but this is another  question. We are deviating from this thread, or not? 

Marcel, for me, making reliable predictions cannot be separated from contextualization. What is the specific context you have considered?. The forerunning discussion pieces reflect a generality (and an unclear teleology, if it is there at all). Regards, Imre

You don't need to know the (details of) theory in geometry or mathematics to make magnificent constructions is the summary. 

Dear Cecilia,

I was also thinking about the thousands of paintings of constructions accepting that a drawing or a painting also represents an expression of architecture. 

Bird's Nest Stadium, Beijing, China.

Dear Talib/All,

How do you know that the architects of the bird's nest stadium in Beijing did not use (complex) geometry and mathematics in the design of this construction?

Marcel, to your previous question, They certainly did. The BNS in Beijing is a multi-objective and multi-purpose optimized construction. According to the literature, this artifactual bird’s nest can withstand an earthquake of up to magnitude 8 on the Richter Scale. Were or are birds thinking about this? But they definitely provided a case for an attractive analogy. Regards, Imre

Do you need to know the (details of ) theory in geometrics and mathematics to make constructions that resist against the physical forces of nature, e.g. Eskimo ice-based constructions (iglou, igloo)? 

How much is learnt without theory, e.g. through cultural transmission?

Tank you Marcel & Imre,

Up to my general engineering knowledge, I see that ancient (pre-mathematics) magnificent architectures includes functional, aesthetic and structural stability aspects. Functional and aesthetic aspect could be inspired by ancient builders feeling to satisfy their needs taking into consideration symmetry,..., and harmony with nature. Structural stability aspect could be satisfied by over sizing (not optimum or minimum required) structure sporting dimensions. I think that the role of mathematics is only to predict the best design. Most of modern inventions (telephone,  voice recording, airplanes) have been done initially by inventors have no experience in mathematics.

But is it not instinctive? (or sub-conscious, if you like)  I am on this side ... If we reason this way we might reduce the gap between animal creativity and the spontaneous (imaginative) creation of humans, as entailed by the last, very good comment of Dr. Abbas.

Do not ignore that construction of magnificent design in humans is (often) the outcome of the contributions of more than one individual, and that each individual has her/his own individual-specific characteristics. Who is the leader in socially accepted creativity/inspiration? Socially-based instinct, or not?

Evolutionary biologists would consider humans as animals, so why making a clear cut distinction in the underlying biology-based mechanisms involved in the development and realization of magnificent design between human and non-human vertebrates? 

"why making a clear cut distinction in the underlying biology-based mechanisms involved in the development and realization of magnificent design between human and non-human vertebrates? "

Dear Marcel, I was not arguing for a clear cut distinction. Actually, I am not sure if we need to strive for it. However, I share your view: creative act does have a social dimension, in addition to the historic one.

Are the biology-based personality profiles/hormone profiles of architects truly known and can they be linked to design?

Any quantitative studies available, e.g. men and women perhaps differ in how they design constructions?

Perhaps sex differences in architecture are also reflected in the shape of bottles addressed to men versus women? Should men design for men and women for women, or not? For instance, if men would design for men versus women for men, would the architecture end product be different, and how would men and women observers appreciate these end products?

If taste would be the key to success in architecture, why not involving citizens in the choice of architecture, e.g. exposing drawings/plans of architecture in open-access web-sites to vote for the most appreciated one(s)? Those that obtained the most up-votes could then be built?

Did clothes design inspire building architecture or did building architecture inspire clothes design?

As a common citizen of the World, I presently apreciate the architectural efforts to integrate in Nature, and the environmental demands.  It is a question of survival of the Planet, even if some of the aestetic perfection might be lost. But geometrical questions may also become quite useful in calculating the best environmental integration.

I was amazed, last April, when I visited Petra, in the Southern desert of Jordan. And to notice how well integrated the rock carving caves wre, without loss of aestetics, or geometry, and nevertheless with full environmental integration.

We should thrive to learn m,ore from our ancestral predecessors  They knew their jobs well.

Dear Michel and Dear RG Fellows, 

It is possible and it is proved by the wonderful examples which follow:

Gaudì - Sagrada familia in Barcelona

Niemeyer - Revello's auditorium

Le Corbusier - Chapelle de Ronchamps

Two extreme examples are:

Michelucci's Saint John the Baptist's church in Florence (along the Sun motorway) where the mathematical framework is only apparent since the actual computations were performed by the engineers according to the drawings of the architect.

On the opposite, there are the "Cretti" of Burri which cover and include the ruins of Gibellina (Sicily's earthquake of 1970) where the performers are the nature and the artist. 

Have a nice Sunday!

Ting Fa Marg

First I would like to state that "geometry" in a practical sense, was already present in ancient times. Pyramids, is a characteristic example. Parthenon, however uses a lot of theoretical geometry, golden sections etc. Furthermore Aegean architecture is a magnificent architecture, and it is dome by common sense and the needs of the islands. 

Dear Dr. Diez-Pastor, Lasting things obey certain rules, no matter if we are or not aware of these at the time of creating things. We apply many soft and firm rules not only explicitely, but also implicitely in engineering. In this line of reasoning, your above comment: "Of course architecture can be done ignoring all the laws." does not seem to be defendable in my reasoning model. Kind regards, I.H.

Wheel invention

Trial and error and.... Eureka in stone age language?!

Perhaps I would have first used slices of wood trunks to be inspired? Perhaps bevers helped with this?

Fact is, that buildings are much more time resistant as theories, because theories are written down on paper, papirus, and other perishable materials. No one will use the wall of some building to write down architectural theories. They are not "good for the folk" as religion and political propaganda are. So it is quite hard to guess if human authors of magnifficent buildings already had some theory about them, but I think  that they already had + a lot of experience with normal buildings.

All of these is different in the case of wasps, ants and bees, to give only some examples. Also in their case the theory was pre-existent, but the support of its transmission seems to be genetic. On a side more perishable than paper, but on the other side much more resistant(!)

Human-produced theory (e.g. geometry as a language) simply describes in a simple way what already exists/what is observed.

Geometry describes the shapes of buildings that have been built by people that did not necessarily received formations in geometry/mathematics.

Archtectures rapidly made from wet sand and built by the hands of children on a beach can subsequently be described with geometry/mathematics

The shapes of the nests/constructions of social living beings can be very aesthetic . One bee worker will make a small contribution to the construction of the nest without having the whole structure in mind. One worker/artist can work on a small piece of a cathedral without having the whole cathedral in mind.

It is true Marcel, the bee have not the whole construction in mind, but the principle of the construction is somehow in its subconstient mind, coming directly from its genes. It is even stronger: a cell does not have the whole organism in mind, but cells build a whole organism, starting with only one cell - and it can be even a human! Molecules sometimes build magnificent cristalls whithout being constient of anything. We must theoretize how a magnificent building can be done by inconstient agents that respect only some principles - but I am affraid that this theory must incorporate both cristallization and morphogenesis, which are both still open problems...

Do you know theory-based geometric figures that are impossible to build?

infinite line

topological one-manifold, 10-dimensional cube, a planar double knot

Perfect geometric figures from a theoretical point of view can never be built?

Example as discussed somewhere else:

That empirical action/construction always differs from theoretical prediction can be illustrated with simple examples. How many figures after the comma are required to match theoretical prediction concerning dimensions of simple geometric figures? Who decides on the precision of measurements required? In other words, how exact is ‘exact’ or how ‘precise’ is ‘precise’? Moreover, simple geometric equations describe cubes, but how well do the theoretical predictions provided by the ancient Greeks match practice? If children or adults are asked to build  the same cube, and they apply mathematical equations describing surfaces or perimeters of that cube, there is definitely an constructor/observer effect. If the true nature of nature is indeed variation, human-invented ‘perfect’ cubes as defined in Mathematics/geometry can never be 100% matched in practice?

I can't imagine (not build) real infinite dimension geometry spoken about.

Marcel, Yes, it is intuitively true. First, physics may work against. Consider a 20 m rope fixed and tensioned at both ends. Can it be made straight? Second, we have (unintended) geometric/structural errors (deviations from nominal) in engineering. Think of Tacoma Narrows Bridge. These biases may appear and act in innumerable forms in real life..

Yes, Cecilia, TNB is an excellent example where engineering errors and natural effects intertwine. If I remember correctly, it was concluded that the reason of the collapse was not only the extreme wind, but also the undersized girders that were designed to keep construction costs low, but were not sufficient to resist the excitation.

Do architects only focus on the design of containers, sometimes called houses, churches, buildings, furniture, boxes, etc...? So sculptors are not architects, e.g. desiging solid material (e.g. a stone) versus containers (e.g. a cave)?

Does increased architecture aesthetics complicates construction maintenance?

Do architects take long-term maintenance costs into account when they wish to maximize their view of aesthetics?

Marcel, just to reflect on the first part of your comment (the question): I think everybody who wants to give a yes or no answer to your question is wrong. This is not a black or white issue. We have a modern definition of what an engineer is (or is seen now) and there was a different interpretation (as well as a role) 100, 500, and, not to mention, 1000 years ago. Now we say an engineer is a learned professional practitioner equipped with knowledge of sciences, mathematics, engineering, and some level of humanities, as well as with competence, ingenuity, and experience. In our modern age they are supposed to be creditable, responsible, responsive, inventive, and open to technical, societal, and commercial challenges. In addition, we should not forget about many other explicit or implicit attitudinal issues. They have to consider not only the possibilities, but also the probabilities, no matter if they develop or implement systems, consumer durables, materials, services, structures, or whatever, in specific contexts, and recognize the limitations and threads imposed by the unknowns, regulations, praxiology, safety, humility, costs, sustainability and societal impacts. Where these things out there 100, 500, or 1000 years ago? Probably not …

Does this imply that the most important role of the architect is to propose creativity/aesthetic constructions on paper to be realized in practice by the multi-competent engineers?