Finite VS Infinite

THE FINITE VERSUS THE INFINITEArchitectural studies

Architectural Reflections

N. Nadareishvili Tutor: Jorge Mejia Hernandez

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FINITE VS INFINITE

Finite - having limits or bounds

Infinite – limitless or endless in space, extent, or

size, impossible to measure (dictionary)

Introduction

In the dictionaries the word capriccio is mostly defined as:

an instrumental work with an improvisatory style and a free

form, or as a prank, a caper or a whim.

In painting, a capriccio means an architectural fantasy, plac-

ing together buildings, archaeological remains and other ar-

chitectural elements in fictional and often fantastical combi-

nations, perhaps with staffage of figures. For example: The

Capricci, the series of etchings by Gianbatista Tiepolo pub-

lished in 1743, reduced the architectural elements to chunks

of classical statuary and ruins, among which small groups

of exotic and elegant figures of soldiers, philosophers and

beautiful young people go about their enigmatic business.

No individual titles can explain these works; mood and style

are everything.

As mentioned, capriccio is a sort of imaginary prank of com-

bining two or more entities, which in real life would have

never been combined, due to several and/or many reasons.

What will happen if we translate this “prank” into architec-

ture? How can we combine two entities and let them grow

together? How will they change each other? Will they mutate

into one? Or, what will happen if you plant a building in a

foreign location, like a seed in the unknown?

Fascinated by the drawings of Tiepolo mentioned earlier, I

decided to make my own Caprricio, to try and answer above

questions. For this reason I chose to combine Guggenheim

Museum of Frank Lloyd Wright and Museu Picasso in Barce-

lona. (Image 1) Two totally different buildings, in sense of ar-

chitectural appearance, locations, surrounding environment

and tissue of the city, style and period when they were built.

Guggenheim museum is one of my favorite buildings. I was

thrilled to see, despite its modest size, how magnificent it is.

The façade has little communication with people outside (for

example unlike Centre Pompidou, where the façade acts like

continuation of public sphere, similar to a street that you can

walk up and down on), but the fact that you are able to par-

tially see the spiral ramp from outside makes you anxious to

go in, curious for whatever awaits you there. This gives you

an enthusiasm to enter and explore.

Museum Picasso fascinated me with its appearance, or rath-

er with its lack of appearance. (Image 2) It combines 5 old,

Image 1 Collage: Guggenheim in Barcelona

Image 2Carrer de Montcada

neighboring buildings. These buildings are very similar to

their adjacent ones. They do not stand out. It is almost

surreal when you walk in the small alley and see lines and

lines of people going into the door that looks exactly like

the one next to it. The museum basically doesn’t have an

exterior. It is mostly an introvert building.

The courtyard plays an important role in the complex; all

five buildings are concentrated around them and these

courtyards serve as an entrance to each. All courtyards

are surrounded by the galleries, which act like transition

spaces between inside and outside.

As much as Guggenheim is different from this complex,

there is one similarity that drew my attention, and triggered

my interest to investigate further.

After close examination of both buildings one can con-

clude that Guggenheims ramp can be compared to those

galleries of Picasso museum and the open space in be-

tween the ramp can be paralleled to the courtyard.

The following part of this essay is concentrating on how

building (in this case Guggenheim museum) can influence

the surrounding environment, once it’s placed instead of

other building (Picasso museum) considering its scale, ap-

pearance, program, and how can the surrounding space

change the building. It provides the hybrid of two entities

and analyzes how can this hybrid develop further as one.

Picasso museum, Barcelona

Location

Museu Picasso is located in the old part of Barcelona. It

occupies five large town houses (palaces) on the medi-

eval street- Carrer de Montcada. (Image 3) The original pal-

aces are from 13th to 14th centuries, occupying a total

area of 10,628 m2. They are an example of Catalan civic

gothic style palace. In medieval architecture, the palace

had larger front facade than regular dwellings, and was

characterized by having a courtyard in the center, which

was accessed through a portal. This courtyard contained

a main staircase, and galleries, usually open or half open.

In XV and XVI century noble families and rich merchants

who had earned their fortune from sea trade inhabited the

street. Today Carrer de Montcada is the most important

area of medieval civic architecture in the city.

The street was declared an artistic-historical heritage site

in 1947. (Picasso, 2008)

The establishment of Picasso museum brought other mu-

seums and art galleries to the neighborhood.

The street kept is original appearance as a very narrow al-

ley, surrounded by the medieval stone palaces. The main

functions surrounding the street on the ground level are

art galleries, museums, and couple of old shops that have

been there for centuries.

Image 3Model: Museu PicassoWith indication of Carrer de Montcada

Concept

During my stay in Barcelona I lived near by Carrer de

Montcada and visited this part of the city almost every day.

Barcelona is a very touristic city, always full of people. It

amazed me to see how crowded these small streets can

get. Even when those limited number of shops and enter-

tainments are closed. The most remarkable thing that I have

witnessed was when I saw a huge line of people waiting to

enter the museum. As mentioned above, the museum build-

ings are pretty much similar to their neighboring ones, both

in typology and appearance. Thus, they do not stand out. It

was a magical feeling to walk in the small alley and suddenly

encounter lines of people going into the regular door that is

neither in any case special nor outstanding from neighbor-

ing ones. It was hard to understand what I was going on

and only when entered I realized that I was standing in this

incredible, breathtaking patio of medieval palace.

Space

Since the complex consists of five buildings and each one is

independent medieval structure, each has the courtyard in

the middle. Each building has an individual entrance through

façade that leads to courtyard and gallery surrounding it.

The patio of palau meca plays important role in the complex;

Surrounded by old gallery, it is the main entrance to the mu-

seum.

Palau Agular (Image 4)

Palau Agular is the first building occupied by the museum.

The courtyard of the Palau Aguilar is one of the Museu Pi-

casso’s most distinctive spaces; it has a grand staircase

leading up to the first floor, the balcony on the first floor and

the various doors and windows, which date from different

periods.

Major parts of the palace were built in the 13th century, and

the coexistence of Medieval, Renaissance and Baroque

styles helps to determine long life of the building, one of the

oldest on this historic street.

Palau Baro de Castellet (Image 5)

This palace is also from medieval period. It is built around a

central courtyard, which has distinctive façade with reli-

gious themed reliefs. The main floor interior is executed in

the neo-classical style of the mid-18th century, including

elements of marble and polychrome reliefs. Its courtyard is

considerably smaller than those of the other noble houses

on carrer Montcada, and has no external stairway giving

access to the upper floors.

Image 4Palau Agular

Image 5Palau Baro de Castellet

Image 6Palau Meca

Image 7Palau Finestres

Image 8Casa Mauri

Palau Meca (Image 6)

Similar to the other palaces, it contains a central courtyard.

Highlights include the medieval polychrome-coffered ceil-

ings of the main floor as well as unique ceilings from the

19th century. This palace is the largest one on the block.

The courtyard of Palau Meca serves as a main entrance to

the Picasso museum.

Palau Finestres (Image 7)

This is one of the best-preserved courtyards of a medieval

residential building in the city of Barcelona. The mullioned

windows with their distinctive arches date it approximately to

the thirteenth century, as does the stairway, one of the most

expressive examples of Catalan Gothic. Arcades surround

courtyard on the ground floor. The building is currently used

as an exhibition space.

Casa Mauri (Image 8)

Casa Mauri is one of the few example buildings from medi-

eval period in Barcelona with its unique wood facade. It is

like other buildings set around the courtyard. The big part of

the building is used for industrial purposes.

Structure

To analyze the whole complex together, here below I want

to refer to Adolf Looses “Raumplan”, specifically the essay

“Adolf Loos – patterns of town houses” where Loos provides

the patterns for analyzing the buildings. Because the com-

plex consists of palaces, which were initially built as a liv-

ing space, I believe that above-mentioned type of analyzing

system is suitable fin this case.

The complex consists of five different (build in different

times) buildings, with five patios in the center of each build-

ing. (Image 9)

Living plan

The difference between up and down

During renovation of the museum in 1978, the long avenue

was created on the ground floor of the five palaces, parallel

to Carrer Montcada and of a long avenue on the ground floor

crossing the street through to garden behind. This space is

open to public. (Image 10)

Elevator and staircases carry the movement from down up

and from up to down.

Upper floor of the complex consist of a corridor, which just

like one on the ground floor forms a longitudinal connection

between the buildings.

Image 9Museu Picasso floor plan/courtyards/facade

Image 10Public avenue on the ground floor

The difference between front and back

Front facades of five buildings form the front façade of the

complex. They relate to the street, the street front is most

public and contains entrance. The façade is more magnifi-

cent and festive, embellished by stone and beautiful win-

dows.

Functions close to the front of the building are more public,

than on the back where more private facilities like the hall of

events is located

The interesting feature of the “difference between front and

back” is that building is located between the two public

spaces: the street and the garden and has a gradient of:

public to more private facilities

The difference between left and right

On both levels of the building the movement from left to

right and the other way is linear. Central corridor on first and

second floor provides circulation line with gallery rooms at-

tached on both sides. Gallery rooms are stacked around the

courtyards.

The centrifugal use of space (Image 11)

Just like Adolf Looses arrangement of the rooms around

empty space, in Picasso museum the spaces (exhibition

rooms) are arranged around courtyards, which are on the

other hand arranged around linear circulation corridor.

Space plan

Exterior

The exterior of the complex is executed in the classical me-

dieval style, with thick stonewalls and small windows.

The difference back and front

Front façade of the building is kept as close to original as

possible. Back façade is more open for new additions and

has been renovated into contemporary structure with con-

crete finishing.

The difference between in and out

The building from inside is very different from what you see

from the outside, After entering, classical structure is tuned

into modern, white clean interior.

The compound interior (Image 12)

The interior is composed with cube shaped rooms. Larger

exhibition spaces have big windows that provide daylight.

Some of the old walls inside are restored and create nice

contrast against modern white walls.

Image 11The centrifugal use of space. Museu Picasso

Image 12-13The compound interior. Open staircase. Museu Picasso

Open staircases (Image 13)

Open-air staircases provide entrance to the galleries from

courtyards.

Eccentric Circulation

Circulation perimeter is placed in the middle of the building

with long corridor connecting left to right.

Material Plan

Supporting construction

External thick walls are load bearing. The construction is

made of stone, like most medieval buildings. The floors are

made of stone as well.

Exterior cladding

Stone finish is used for exterior cladding, at some places

showing brick, usually at the top of the arches.

Interior cladding

The inside surface is plastered in white; some parts of the

old construction in stone are saved and contrasted against

modern interior.

On the first floor floors are finished with marble and on the

ground floor with stone

Solomon Guggenheim museum, New york

Location

Guggenheim museum is located in New York City, in the

heart of the city- corner of Fifth Avenue and has a view on

central park. (Image 14) It is clear that museum is unlike the

buildings around it, which are straight walled extrusions

from rectangular ground plots. Guggenheim makes its mark

through non-standard devices, (Foundation, 2009) The mon-

umental character of the museum based on its three dimen-

sional sculptural form erupting from the restricted framework

of the grid.

Concept

Designed by Frank Lloyd Wright to be “a temple of spirit, a

monument!,”(Richard Cleary, 2009) the museum is a round

building spiraling around an empty space/void/atrium.

(Image 15) From the street the building looks like a white rib-

bon rolled into cylindrical shape, slightly wider at the top

than at the bottom. Initially Wright designed the routing in a

way that visitor would go up by an elevator and come down

Image 14Location of Guggenheim museum

Image 15Circulation and gallery spaces. Guggenheim Museum

Image16-17Inverted ziggurat concept

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3.1. Space within a space2. Interlocking spaces3. Adjascent spaces

1. Space within a space2. Interlocking spaces3. Adjascent spaces

Centralized OrganizationA central dominant space about which a number of secondary spaces are grouped

Linear OrganizationA linear sequence of repetitive spaces

Centralized OrganizationA central dominant space about which a number of secondary spaces are grouped

Linear OrganizationA linear sequence of repetitive spaces

by ramp while going thru a collection of paintings. Today the

routing had been changed; the visitor has to walk up the

ramp while seeing works of art.

A “ziggurat” - Babylonian temple pyramid, inverted, inspired

the museums design. Ziggurats were Mesopotamian tem-

ples built for high priests to praise the God and make sac-

rifice on top of it, where it is believed that temple was lo-

cated. Basically Ziggurats were houses of Gods, and were

built to be infinitely high to reach the sky. The idea behind

the Guggenheim form is both Wrights fascination with an-

cient architecture and his ambivalence toward the modern

city and its paradigmatic morphology - skyscraper. With

Guggenheim, Wright chose to transform the ancient Ziggu-

rat, by turning it over. This can be easily seen at close inves-

tigation: in the design of the museum the base is narrower

than its top. (Image 16-17)

Wright makes circulation internal to the building, and uses its

spiral circulation as the museums prime organizing system.

(Image 18-19)

By inverting the ziggurat-based setback form in Guggen-

heim, Wright critiques forms used by skyscraper design-

ers. Museum does not simply adapt the form of the Tower

of Babel (ziggurat) but with new inverted ziggurat form, and

its possibility of endless growth upwards – (the “optimistic

ziggurat” as Wright would call it) generates an alternative for

the modern city.

Interior

The interior consists of central spiral ramp going up and

secondary spaces connected to the main spiral space. The

entrance slowly leads visitors to a path where the artworks

are exposed along a spiral ramp lit by a large skylight at its

zenith divided in the shape of a citrus fruit. “The museums

interior space with its spatial continuity, counters the isolat-

ing, repetitive and boxlike quality of the metropolis and the

skyscraper. And with this Wright created a new hybrid form

of the museum, where tradition and innovation stand in bal-

ance”.(Foundation, 2009)

Space

Guggenheim is very different from the museum buildings

that we are used to, because of its spiral shape, manifested

by the merging of triangles, ovals, arcs, circles and squares,

which correspond to the concept of organic architecture

used by Wright in his designs. (Image 20)

If you stop for a moment and look toward the center of the

spiral you realize how impressive this building is, reminiscent

Image 18-19Centralized Organization & Linear OrganizationGuggenheim Museum

Image 20Space organization. Guggenheim Museum

of a snail, which allows us to see the center of the rotunda

and various levels of exposure of the spiral ramp downward.

At any place on the ramp, one is able to see where one was,

and at the same time, where one is going. Like this, the ramp

provides a sort of “time-space continuum, a sort of “when

past is future”. The very nature of the ramp itself suggests

change and motion.” (Richard Cleary, 2009)

Structure

The building has a spiral structure featuring a large exhibition

hall lit by a skylight. More than any other form spiral signified

both spatial and temporal continuity for Wright(Foundation,

2009)

Finite vs InfiniteFrom here I want to introduce the notion of finite and infinite

in both buildings.

Although the patio space in Museu Picasso is magnificent,

it is still limited; it has clear beginning and the end. It starts

at the exact point when you enter the gate, because you

do not have any idea about it before. You experience space

while going up the stairs, through a gallery. And then it ends.

Exactly when you enter the door of the museum. Your ex-

perience of the courtyard space, your excitement suddenly

disappears. You jump into different world, and your interests

and excitement shifts to a new space (museum), forgetting

about the older one, like a child forgets about old toy when

he gets a new one for Christmas.

This I believe is a finite space. The space that has borders:

physical and/or mental.

On the other hand, the definition given above about the ramp

of Solomon Guggenheim museum gives an idea behind the

spiral ramp. In contradiction to finite perimeter circulation in

atrium of Picasso museum, here the spiraling, rotating ramp

can go on forever, to infinity.

Based on all above mentioned I tried to imagine how building

like Guggenheim museum will develop in the environment of

Barcelona, if it was to be planted instead of museu Picasso.

Here below I want to propose two: Horizontal and Vertical

development scenarios for Guggenheim Museum in Barce-

lona based on two reference projects.

Horizontal development

Museum of unlimited growth (Le Corbusier)

In 1929 Le Corbusier produced his first design for a museum

of contemporary art the “museum of unlimited growth”. (Im-Image 21

The Museum of unlimited growth. Le Corbusier

age 21) It was a square spiral that would eventually devel-

op and grow according to the needs of the project. Based

on golden section, floor plan illustrates a design in which

continuous circulation dominates the museum’s spatial or-

ganization. This scheme later appeared as a basic idea for

the Guggenheim Museum, presenting restricted circulation

around a central core. (Kaynar)

Le Corbusier proclaimed the failure of the museum as he

saw it in an essay of 1925 “Other icons; the museums” he

rejected the design of 19th century classical museum by

calling it “a Liar” and proposed new, “transcendental Geom-

etry” of spiral routing which will grow infinitely depending on

how much space museum will need. Le Corbusier’s design

was, like many other of his works utopian. But the “museum

of unlimited growth” was an inspiration behind Guggenheim

design.

Since the museum of unlimited growth was an inspiration

and an idea behind Guggenheim museum, I found it logical

to apply this concept in exaggerated manner to he hybrid

development of Guggenheim museum in the new environ-

ment of Barcelona.

This is how I imagine it:

Based on the fact that the “museum of Unlimited growth”

develops infinitely in horizontal layer, the Guggenheim mu-

seum most logically has to do the same. Lets imagine, the

ramp structure of Guggenheim being pilled of like an orange

skin from the structure, dismembered and turned into one

long striped corridor. Just like the existing Picasso museum,

this structure will have no distinctive façade. The structure

from outside will consist of old existing buildings and streets,

ordinary doors that are no different from each other and the

doors next to them. Like Howl’s moving castle from Miyaza-

kis famous animated movie: The ordinary façade, non-dif-

ferent form any other one on the same street, but only be-

fore you enter and see white, sleek, contemporary interior

of Guggenheim museum. (Image 22) White long corridor goes

on spiral circles around the city. The feeling of “time space

continuum” is lost in smaller scale but obtained in larger, city

scale. (Image 23)

This long corridor in a way also forms a courtyard, which is

much bigger scale than in museums of Picasso or Guggen-

heim. In this case the part of the city, which is inside the

corridor perimeter, can be considered as a giant courtyard.

(Image 24) This space will obtain all the positive features of the

courtyard. It will become the cultural hart of the whole city,

because literally this space is enclosed by culture itself.

Note here that: infinite spiraling development of the building

might provide the feeling of confusion, in a sense that one

Image 23Infinite spiral horizonthal development / Diagram of main streets

Image 24Infinite spiral horizonthal development. Space in Between

Image 22Unexpected door to Museum in the alley

doesn’t understand anymore, is he inside or outside? Which

part of this enormous structure is interior and which is exte-

rior? This characteristic can later be linked to the notion of

indefinite.

Can Guggenheim museum develop this way? If the idea of

the museum scheme by Frank Lloyd Wright was based on

museum of unlimited growth than this development scenario

is quite logical.

Vertical development

The library of babel (Jorge Luis Borges)

“I remember its circularity.. Light was entering through a glass dome, they

told me, and I perceived it over my head, as if we weren’t inside the build-

ing but in open air, and I wondered in anguish if it would all end abruptly in

the void and I would fall over the edge”

Jorge Luis Borges about Guggenheim Museum

“The library of Babel” is a short story by Argentinian author

Jorge Luis Borges, conceiving of a universe in the form of a

vast library. Library consists of hexagonal planes with book-

shelves that are connected with spiral staircases and go ver-

tically to infinity.

Despite their obvious differences buildings like libraries, mu-

seums and archives have similar identity. They are all spaces

that contain and influence knowledge and culture. (Psarra)

Although Borges story is fictional, it describes very solid ar-

chitectural structure/space, which doesn’t have beginning

or end. But can the endlessness of the libraries, museums

and similar facilities be considered as an endlessness of

the knowledge that they are capable of giving? And than

interpreted this idea into endless infinite construction of the

tower, which is like a tornado, black hole in the city. (Image 25)

It spins and goes up to infinity of knowledge. Isn’t “ziggurat”,

another inspiration behind Guggenheim museum, based on

Image 25Infinite vertical development of Guggenheim

Image 27Collage of public triange/Tension between monuments

Image 26Collage new skyline of barcelona/tension

the idea of infinite tower/temple (temple of knowledge?)

that goes to the Gods in the sky?

In this case limitless or finiteness of Picasso museum inner

space is turned into infiniteness of spiral tower. You do not

need to enter the space and exit it. You are in the space

all the time. The experience of space and art/knowledge

is united.

This action of implementation and growth will drastically

change Barcelona’s skyline. (Image 26) There aren’t only

two dominant figures on horizon anymore: Sagrada famil-

ia and Tori Agbar is joined by third monument. This third

new monument creates together with two other ones cre-

ates new tension zone, triangle of cultural space, which

feeds on tree cultural monuments and tensions created

between them. (Image 27)

Transition to part two

This essay provided very subjected view of the possible

building (Guggenheim) development in new environment,

based on analysis and reference projects. In both cas-

es the essential two notions that have to be worked out

– linked to finiteness and infiniteness – are those of the

courtyard, and of horizontal and vertical growth.

For the next couple pages I want to reflect more on the

idea of infinity and how can it be applied to architecture

based on above-mentioned projects.

The notion of infinity is discussed, and more or less de-

fined in philosophy, mathematics, physics, ethics and etc.

But how can it be applied to architectural spaces?

Since architecture itself is the game of borders and limits,

can infinity – the notion in its nature the most contradictive

to the limits, be implied within it? What can be the tools

(lubricants, mediators) that can help these two contradic-

tions come together smoothly?

Based on metaphysics, the notion of infinity has couple

structural definitions:

1. Eternity: linguistically the opposite of finite, having no edges,

limits, and an end: mostly used in connection with time: some-

thing that has no end in time.

2. Indefinite: How could God be sure that there is no one greater?

3. Circularity: The line defining a circle does not have an end.

4. Recursion: Like semantic satiation a phenomenon in which

repetition causes a word or phrase to temporarily lose meaning

for the listener, who can only process the speech as repeated

meaningless sounds.

Which of those structures (if all or none) can be incorpo-

rated in architecture? How can these structures be trans-

lated to fit the demands of architecture? Will this create

the utopian architecture, since infiniteness basically will

be just a promise of infiniteness rather than actual state

of it, or there can be ways to truly incorporate them into

design?

While writing the first part of the essay I noticed that in

both projects analyzed by me, one thing was recurring.

While writing, the courtyard was the central element

around which I built my analysis and research.

The courtyard is a shared figure in both designs, but it

functions in different ways. It is so essential, because it’s

an absence (of content, of building), which defines the

quality of space.

The way the courtyard is applied in both presented cases

differs in such a way that the potential of unlimited growth

is opened in the one horizontally and in the other vertically.

The most important operation for the Guggenheim is

the inversion of the pyramid. A normal pyramid cannot

grow vertically because the form unites in a single point.

Through the inversion, however, the form implicit tends to

diverge, in an unlimited widening of the base. It can grow

infinitely as a top-heavy figure—until the weight of history

topples it over. This can also be considered as a circular

structure of infinity.

The vertical walls of the Picasso have no imbedded ten-

dency in form. The do not converge nor diverge. A vertical

extension will just be more vertical walls.

But the courtyard as a center provides the possibility for

the building mass surrounding it to expand to indefinite.

In this case, the generality of the façade is also very im-

portant. The museum, as it is now, is already an assem-

blage of different components that are all in a way simi-

lar. This assemblage has no natural end (infinity). While

in Guggenheim’s museum, the façade is so defined and

characteristic that to put another museum against it would

destroy an essential quality of the building, the Picasso

could theoretically spread to other buildings. The muse-

um could be like a parasite, infesting other buildings with

the same form. In that sense, the border of the museum

as it is now, is actually quite artificial, and it does not need

a specific enveloping line. It can be seen as a kind of

archipelago.

Context is the other notion of the urban fabric that is very

important. For the Picasso museum, the courtyard is ac-

tually essential for it to work in the fabric. Without, there

would be no air, no light and it would be unlivable. The

courtyard is necessity.

For the Guggenheim, however, has the possibilities to

open windows to its outside because it is an autonomous

object not touched by other buildings in its surroundings.

The courtyard (the absence in the middle) is a deliberate

(voluntary) operation in order to create a kind of experi-

ence.

Now, the tension that appears if you would transpose the

Guggenheim into the urban fabric of Barcelona is one of

autonomous object, vs a building subservient to the ur-

ban fabric. The only reason why such an operation would

work, is because the Guggenheim as in itself the court-

yard, which would allow it to work with the fabric.

Essentially, what I am trying to find out and discuss further

is possibility of Infiniteness, for architecture and the tool,

that as a” recurrence” appeared in my previous analysis

as a centerpiece for this infiniteness.

The Courtyard

The main problem that I see with using courtyard, as a

tool around which I want to build up theme of infiniteness

is that, in its most basic character - the courtyard is super

finite archetype. Thus, basically what I am trying to prove

is that: white is black, or, white can be black.

The courtyard is finite notion because it creates the space

that has borders, the space that is surrounded by walls

and is defined by them. It was and still is widely used in

worlds many cultures, if not all of them, for different rea-

sons, for privacy and private meetings with neighbors,

for security, storage, relaxation and etc. This space to-

tally shelters its inhabitants from outside world, surrounds

them with privacy and safety. Courtyard is a super intro-

vert and finite entity. That is why it might be a bit strange to

consider it as a central piece, the mediator for providing

infinite space.

Although, just like in mathematical problems, we can al-

low ourselves to set the rules in the beginning that will de-

termine the consequent process of analysis. For instance,

define the procedure that we will have to apply to a court-

yard to turn it into infinite space.

Firstly define the components and their characteristics:

The figure of the Picasso museum (square) allows for an

indefinite multiplication of an amount of side-placed units.

It can spread, grow, and infest like an archipelago. The

figure of the Guggenheim (circular) allows for an indefinite

extension of one and the same unit. It can only grow as a

singular entity.

As we spoke above, In case of Picasso museum, stacking

buildings on top of each other will just create more walls

(Image 28), expanding the courtyard will create just bigger

courtyard, (Image 29) which will still have walls to border it.

Hence, what will be the operation, if there is one at all?

While working on Guggenheim and Picasso museum

I’ve noticed that besides vertical and horizontal develop-

ment there is third option that can provide ultimate infinite

space. So, what will happen if courtyard develops diago-

nally? (Image 30)

What I mean here is that diagonal development of the

building can provide the possibility of infinite growth and

development of the building.

Diagonally developed courtyard can have the mix of best

Image 28verically developed courtyard

Image 29horizonthaly developed courtyard

features from both worlds. It provides secure feeling of

the courtyard, while at the same time is more open and

provides the ability of breathing and connecting to out-

side world. Here the strict distinction between private

and public is somewhat blurred. One is inside the court-

yard, thus is in the private space, but because of partial

openness of the space one becomes the participant of

the public scenery. This feature makes courtyard become

more inhabited and used, it has “loopholes” which allow

you to sneak beyond them into some larger, further space.

Because of this feature we can assume that the space is

some way indefinite. Which, as stated above, is one of the

typologies of infiniteness.

The scenario of diagonal development feeds from the

several features from the both buildings analyzed earlier.

For example, as we spoke before, the design of Guggen-

heim museum was inspired by turned ziggurat. This shape

exactly corresponds to the diagonal development of the

building. Ziggurat spins from wide base and squeezes it-

self to the top, with this operation setting the limit to its

growth. By turning ziggurat upside down the chance for

unlimited development is provided. Logically, turned zig-

gurat is diagonal shaped and can continue developing

with same direction.

Hereby I want to add, that in relation to infiniteness and

eternity of the space, the reference to ziggurat is a very im-

portant one, considering that, Ziggurat is an archetype of

a temple. Therefore, it references to the idea of an eternal

space, that proves itself to be mediator between the hu-

man and the divine. In this case divine doesn’t necessar-

ily mean the God, but it can be any sort of mediator/tool/

space/place etc. that makes you feel close to it. And the

architecture can be this sort of a tool. That’s when archi-

tecture becomes eternal and infinite, when it becomes the

mediator between human and divine. To clarify, the good

architecture is not simply something that is visual. There is

an invisible, metaphysical, ritualistic order in architecture

that is constructed by the culture’s mythology through its

poetic memories and imagination. Our beliefs and memo-

ries of the past are embedded in architecture, creating a

fourth dimension of time and space.(Ayda Zeinali Farid)

I truly believe that Guggenheim museum by Frank Lloyd

Write is one of those architectural monuments that make

you feel close to that divine once you enter. That’s how

it achieves eternity and infiniteness in real life. Therefore

based on above statement, we can say that architecture

can be eternal. At least derived from presented essay.Image 30Diagonally developed courtyard

Following structural definition of infinity, as stated above is

circularity. I am not quite positive If it applies In the case

of Guggenheim diagonal structure, Since, most probably

this translation will be too literal. The courtyard and the

building wrapped around it of course goes in spiral up,

and this can be considered as an circular development,

but the main idea of infinite circularity is that you don’t go

in spirals but in circles. You end where you started, you

do not develop, rise or evolve. I do think that courtyard

in its basic form is circularly infinite, but maybe, and it

is my opinion, the diagonally developed structure looses

its ability to be so, because of its capacity to evolve up/

down/to infinity

From ancient times, recursion and/or repetition of the ar-

chitectural elements was considered one of the known

tools for achieving visual infinity of the space. Starting

from Greeks and Romans, who were masters of designing

endless repetitions of columns, that were as solid as they

were disappearing when repeated (colonnades in ago-

ras, the sides of temples when viewed from certain angle)

to create infinite, dissolving space with spirit of disappear-

ance and at the same time presence, which today we ask

of things in the world (glass)

The knowledge obtained from Ancients was broadly used

throughout the history, during renaissance or even in re-

cent centuries.

Endless repetition of elements with the purpose on

achieving infinity is largely discussed theme of 20th cen-

tury. From copying and exploring ancient traditions in

hope to achieve the infinite spaces by many architects, to

critically analyzing this notion, like Pier Vittorio Aureli did,

in his book “the possibility of an Absolute Architecture”.

Where he states that main task of late modern culture has

been the development of the idea of processing infinity

through endless repetition. This he describes as Hegel’s

“bad infinity”, the infinity where “everything is reduced to

bling faith, to the infinite creation of new finite things just

for sake of new things” (Aureli, 2011)

In case of diagonal Guggenheim, The whole structure be-

comes the endless repetition of itself, which grows verti-

cally and at the same time horizontally. Endless repeti-

tion of stairs, ramps and one might also imagine endless

repetition of exhibited art pieces, which one follows while

going up to infinity, to endless temple of divine.

Conclusion

Finally I want to sum up the observations made while re-

searching and writing this essay.

The most obvious definition of infinity to notice was eterni-

ty. There has been enormous amount of discussion about

eternal architecture; everybody has its own idea of what

qualities make architectural piece eternal, but for me the

architectural piece becomes eternal if as I stated above,

it creates an atmosphere that makes you feel comfortable

once you enter, you feel calm, at the peace of your mind

but at the same time exited, driven to explore and can not

get enough of the space. I am not sure how you achieve

this feeling in architecture but it must have connection with

your memories, beliefs senses. The space has a definitive

quality to touch your senses, and make you think. If the

space has these qualities, it can become eternal. Even if

it turns into ruins you will still (and maybe even more) be

driven to go back and explore it, over and over again.

Indefinity of the space is connected more or less to the

quality of the space to leave its inhabitants “confused”.

In the example mentioned before, diagonally developed

courtyard combined two contrary notions: private and

public. The scenario of combining these two opposite

concepts was not possible until courtyard existed in its

basic form. Projected operation of twisting it diagonally

gave a possibility of the fusion.

And lastly, the recursion: to add to what has been said

before, architecture of presence is suffering from “bad in-

finity”. We are recreating more and more “finite” pieces

just for sake of creating new, false infiniteness only based

only on the quantity.

In this second part of the essay I attempted to analyze

four structural definitions of the infinity, I tried to apply

those notions to the architecture, more particularly to a

building chosen for earlier essay analysis.

After analyzing the chosen buildings, creating capriccio,

developing and reflecting on it, I can conclude that infi-

niteness is a notion that can be achieved in architecture.

This infiniteness will not be the literal infinity, but as read

above almost all structural definitions of the infinity: eter-

nity, indefinity, and recursion can be reached with archi-

tectural piece. The attempt to do a research about infinity

and architecture proved me that it is quite a largely dis-

cussed theme in architectural sphere and it seems like

every architect or non-architect, has its opinion about it. In

this essay I tried to shortly present my observations and

opinion about the theme of infinity in architecture.

BIBLIOGRAPHY

Foundation, S. G. (2009). The Guggenheim: Frank Lloyd Wright and making of the modern museum. New York:

Guggenheim Museum Publications.

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observational and descriptive study of the Ann Arbor Hands-on Museum. Retrieved from http://www.spacesyntax.

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