Zero Essay

UNBUILDING
An essay for Dutch architecture magazine, A10

    The award of the 3rd Jaap Bakema Fellowship for my traveling research project ZERO amidst the Great Recession opened up a reflexive space for me to question the current limited opportunities in the architecture profession and its role in society.

    A critique of the architectural profession today is inevitably a criticism of the global free market phenomenon (in which architecture is complicit), and of the unbridled capitalism practised worldwide, which has enormous economic and social consequences. As early as 1998, John Gray warned of the dangers of the global free market system. In False Dawn, he wrote that ‘global markets are engines of creative destructions. Like the markets of the past, they do not advance in smooth, steady waves. They make progress through cycles of boom and bust, speculative manias and financial crises.’1

    Sociologist Richard Sennett has described the loss of sociality in modern-day consumption, where a fixed-price policy for goods and services has done away with the reciprocity of haggling and bargaining.2 In so-called less developed countries, such interactions between seller and buyer in a market or bazaar still retain this social dimension. For Sennett, consumption as a discursive activity has become an abstract, impersonal monetary transaction. Similarly, drawing on Sennett and his reading of Marx, the process of dematerialization separates production from consumption – how a thing is made from its use – leading to the devaluation of things and a diminished role for craftsmanship, and promoting a desire for future consumption through advertising and marketing. Rather than focusing on the present and the practical, the shift from actuality to potentiality, as described by Sennett, gives the consumer an illusion of freedom and choice because they are no longer concerned with how a thing is used now, but with its future possibility.3 Reduced to objects of consumption and uncontrolled fantasy, architecture faces similar challenges, as exemplified by that former playground of architects called Dubai. Architecture is mistakenly perceived to be progressive, and heralds a new future. In reality, what it does is merely to perpetuate and stimulate the thirst for an untenable culture of consumption and excess at the urban level. Architecture becomes a search for newness and is reduced to a spectacle.

Contrariness
    As an architect with a deep affinity for the arts, and who also teaches in an art school, I am inspired by artists who have discovered the manifold expressions of zero as a rich ground for experimentation. Their activities, ranging from making works that are formally incomplete to adopting subversive inaction and radical unmaking as strategies, challenge our comfortable and cherished view of what art means and by extension our own assumptions, prejudices and perceptions about the world. This is especially significant for me as an architect, since use and economic values are so closely tied up with architecture that they can sometimes create a myopic view of the architect’s role in society.

    As far back as the 1970s, Robert Smithson and Gordon Matta-Clark were making works that ran contrary to accepted notions of art as a formally complete work. In the process, they overturned our attachment to objecthood, aura, presence and authorship in art; values still clung to by many architects and perpetuated by academics in spite of overwhelming evidence that they are reserved for an elite group of iconic architects. Robert Smithson’s 1970 work, Partially Buried Woodshed, on the campus of Kent State University, where an excavator dumped loads of soil onto the shed until the centre beam cracked, exemplified his theory of entropy, which situates art on the inexorable path towards ‘the outer edge, the flat surface, the banal, the empty, the cool, bland after blank’.4 Through a combination of time, the natural process of weathering and human intervention, the work eventually ‘returned’ to the land where it once stood.

    Gordon Matta-Clark, on the other hand, reacted against his formal architectural education at Cornell through his brief but compelling oeuvre. His works exposed the ideology of professional architecture that legitimized the stranglehold of experts and their abstract ideals. By cutting up abandoned and soon to be erased buildings, Matta-Clark also questioned the assumption of utility and the misplaced belief in property and ownership. Both Smithson and Matta-Clark eschewed traditional materials and techniques of art-making. Instead of creating objects to be placed on the land, Smithson’s Land Art and Matta-Clark’s Building Cuts re-inscribed art in the site, steering it away from the hermetic and rarefied environment of the museum.

Strategy
    It is with this spirit of inquiry, reclamation and re-examination, reinforced by a dose of art-inspired resistance that I wish to introduce the strategy of ‘unbuilding’ in this essay. I interpret unbuilding as a gradual erasure from something to nothing, the necessary ‘other’ of building and a creative act within the cycle of creation and destruction. With cities declining and buildings becoming obsolete more quickly than ever before, the process of unbuilding, which opens up new spaces for different opportunities and engenders the emergence of an alternative practice, will necessarily become part of what an architect does. In Detroit, where city authorities demolish two to three thousand buildings a year, companies specializing in demolition works became much sought after.5 However, since architecture as taught, practised and regulated is squarely situated within the narrow bandwidth of design and creation of an artefact, it will take significant effort and a major shift from a business-as-usual attitude to embrace the notion of ‘de-sign’.

    As history shows, the perceived permanence of buildings can be erased within minutes by a natural or man-made disaster, government actions and a civil or international conflict. The 2004 Boxing Day Tsunami caused widespread destruction to the coastal towns of eleven countries, stretching from Asia to Africa.6 The haunting physical emptiness of the A-bomb dome of the Hiroshima Peace Memorial serves as a searing and lasting symbol of the devastation caused by the dropping of the atomic bombs in Hiroshima and Nagasaki during the Second World War, where many hectares of buildings were reduced to a horrific wasteland. In more recent times, the destruction of the World Trade Center Towers in New York City, the devastation accompanying the continuing conflict in Iraq and Afghanistan are other examples of the violence buildings are subjected to.

    Despite its apparent negativity, I would dispute that unbuilding is concerned only with demolition or destruction. If demolition and destruction are akin to fast food, then unbuilding is slow food: a careful and delicate process of disassembling, cataloguing, re-purposing and erasing an existing building. Furthermore, the process of unbuilding as in deliberately making something absent, also overturns the accepted role of the architect as a creator through design and accumulation. Ultimately, unbuilding and building co-exist as two sides of the same coin. The following examples highlight how the process of unbuilding can be a meaningful act across different scales, cultures and purposes.

Ise Shrine, Japan
    The Ise Shrine is a well-known Shinto site that is disassembled and rebuilt every twenty years. In contrast to accepted notions of architectural preservation and of buildings as cultural artefacts that will bear witness to the course of human history through their enduring presence, the ephemeral nature of the Ise Shrine serves the same purpose in reverse, through the process of unbuilding and rebuilding. Besides the significance of spiritual renewal in Shinto belief, unbuilding is also necessary for more practical reasons, as Svend M. Hvass pointed out in Ise: Japan’s Ise Shrine, Ancient Yet New.7 The twenty-year span is also the lifespan of the timber beams, columns and thatched roof. Shorter than the lifespan of a person, the twenty-year cycle permits the older generation of carpenters to pass down valuable knowledge to the younger ones during the process of rebuilding. If the shrine buildings had persisted as an enduring presence, these older craftsmen would have died out, together with their construction wisdom and expertise. The timbers from the dismantled shrine are reused for different elements within the shrine compound, such as the vertical poles of the Torii gateways and as replacement timbers for the less important shrines. The remaining timbers are distributed to shrines throughout the country for the same purpose. The thatch roof, which is not reusable, is burnt and any metal elements are melted down and recycled.

Unbuilding Beppu: Building Dismantling School and The Materials Bank
    The slow economic decline of the Japanese city of Beppu has resulted in many houses that are either completely abandoned or demolished or that are slowly deteriorating around their occupants. Since the old traditional timber houses were built close together, forming a dense network of narrow footpaths, small open spaces and residential units, the removal of a single house causes the compact organization to fall apart and the houses that remain standing are left without the protection from the weather offered by the proximity of neighbouring houses. The common practice is to use the readily available and cheap corrugated metal sheets to cover the ‘open face’ of the surviving house. Two interdependent proposals by architect Kenta Kishi, entitled ‘The Building Dismantling School’ and ‘The Materials Bank’, offered bottom-up strategies for creating jobs, recycling materials and reprogramming the many vacant buildings for new uses. The Building Dismantling School offers an unconventional approach to teaching the skills needed for the careful unbuilding of abandoned houses that cannot be reused. The Materials Bank, on the other hand, provides a dedicated space in the city where salvaged recyclable building materials can be stored and where they can be given away or exchanged.

Material Harvesting: The Work of Murco Recycling Enterprises Inc.
    Murco Recycling was founded by Chicagoan Jodi Murphy, who pioneered an ingenious business that combines material harvesting, recycling and public auction in the process of unbuilding a house.8 Ironically, whereas architecture and interior design are professionally separated in the course of building, Murco Recycling reunites them, since the flotsam of architectural elements like timber beams, frames, furniture, fittings and interior decorations need to be sorted and recycled, either as usable materials or rubbish. The social activity of buying and selling of the traditional marketplace returned with the auctioning of the furniture, fittings and building materials harvested by Jodi’s company. Instead of the anonymity associated with online auction sites and the more formal real-life versions, the auctions of Murco Recycling are celebratory and performative events filled with laughter, teasing and serious haggling and bargaining, which owe much to the exuberance, energy and sharp business acumen of the company’s founder. She plays multiple roles – as auctioneer, organizer, publicist, broker, provocateur, networker and, last but not least, a business person driven to do her part for the environment. To ensure that the materials and fittings are affordable, successful bidders at Murco Recycling’s home salvage auctions are required to return to the house and carefully remove the material themselves. In one of the company’s projects, as much as ninety per cent of the building materials, finishing and fittings are reused in new contexts.

Motor City Blight Busters
    The Motor City Blight Busters (MCBB) is a not-for-profit organization led by founder John J. George.9 Following its motto, ‘Fight Blight, Stabilize, Revitalize’, the more than twenty-year-old organization has carried out thousands of community-based projects, ranging from simple house painting and trash removal from empty lots to securing abandoned houses and demolishing those that cannot be restored for living. Although the unbuilding process is not unlike a commercial house demolition operation, one major difference is the way MCBB harnesses the strength and volunteer spirit of the community in carrying it out. By using sledgehammers, power tools and small crawler loaders for tougher tasks, the unbuilding of abandoned houses and the removal of ‘negative energy’, a term often used by John J. George, becomes an act of collective catharsis for the community in Detroit. It restores community pride and confidence, as well as giving those who are still living the city a sense of hope. Through unbuilding, the new emerges in the form of a community garden, a playground or a new home.

Unbuilding and Obduracy: The Dutch Experience
    In Unbuilding Cities. Obduracy in Social-Technological Change, Anique Hommels draws attention to the tension and contestation among stakeholders as they struggle to reconcile renewal and preservation.10 She researched the phenomenon of obduracy in the city through an analysis of spatially distinct case studies in the Netherlands, using a combination of three conceptual frameworks: frames, embeddedness and persistent traditions. For Hommels, unbuilding is a natural process of change in the city as the new replaces the old. However, because what is built is layered through time with traditions, memories and political agendas, new initiatives are met with strong resistances. Of particular interest are the four unbuilding strategies for overcoming obduracy she identified in her case studies. The first strategy involves acknowledging and engaging the multiple voices of social actors and communities in the redesign process. The second strategy recognizes urban structures as embedded in a network of relationships rather than existing as discrete elements. Unbuilding therefore entails a thoughtful search for and negotiation of elements that can be unbuilt. The third strategy involves identifying the specific role traditions play in the obduracy of urban structures and discovering ways to overcome them. The last strategy places emphasis on material and technological characteristics in the belief that the ills of obduracy will be eliminated by new and innovative design ideas and planning.

    The selected examples and strategies of unbuilding form the necessary first steps towards reclamation, recovery, restoration, renewal, recycling and rebuilding. As Hommel’s book shows, this process is neither easy nor smooth. Nevertheless, the process of unbuilding questions what has been categorized as waste and prompts its revaluation in economic, social, ecological and spiritual terms. Unbuilding empowers residents to action and self-determination. It is a conduit through which tradition and wisdom are passed from one generation to another. It opens up new opportunities for a more socially and environmentally focused business. Finally, unbuilding can be a new and practical skill set. The process from something to nothing reveals the potent act of subtraction and the positive value of de-sign. Design is no longer focused solely on accumulation, novelty and the arbitrary distinction between the cast-off and the retained. To expand the work of an architect or a designer to include the deliberate act of unbuilding, especially at a time of economic recession, opens up new opportunities where existing knowledge can be deployed in meaningful and sustaining ways.

1. Gray, John (1998). False dawn: The Delusions of Global Capitalism. London: Granta Books, p. 210.

2. London School of Economics (17 November, 2009). ‘Cities, Design and Climate Change’ [Video File].  Retrieved 9 April 2010 from http://www2.lse.ac.uk/publicEvents/events/2009/20090825t1340z001.aspx

3. Ibid.

4. Ibid., p. 13.

5. Time Online. (April 1989) ‘Crime: Dismantling Detroit’. Retrieved 11 November 2009 from Time website: http://www.time.com/time/magazine/article/0,9171,957494,00.html

6. ‘The Deadliest Tsunami in History?’ (7 January, 2005). National Geographic News. Retrieved 24 April 2010 from http://news.nationalgeographic.com/news/2004/12/1227_041226_tsunami.html

7. Hvass, Svend M. (1999). Ise: Japan’s Ise Shrine, Ancient Yet New. Copenhagen: Aristo Publishing, pp. 40-41, 96.

8. Murco Recycling. Retrieved 24 April, 2010 from http://www.murco.net/what_we_do.php

9. Motor City Blight Busters. Retrieved 24 April, 2010 from http://www..blightbusters.org/about.html

10. Hommels, Anique (2005). Unbuilding Cities. Obduracy in Social-Technological Change. Cambridge, Mass.: The MIT Press.

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Cardinal

0, zero, "oh" {{IP

Ac-en|ˈ|oʊ}}, nought, naught, nil
Ordinal0th
(zeroth, noughth)
Divisorsall other numbers
(except itself)
Binary02
Ternary03
Quaternary04
Quinary05
Senary06
Octal08
Duodecimal012
Hexadecimal016
Vigesimal020
Base 36036
Arabic٠,0
Bengali
Devanāgarī
Chinese零, 〇
Japanese零, 〇
Khmer
Thai

Zero is a specialnumber.[1] If there are zero things, there are no things at all. There are none. For example, if John has zero hats, that means he does not have a hat at all.

Symbol[change | change source]

The symbol for the number zero is "0".

Arithmetic with zero[change | change source]

  • Adding a number to zero results in that number. For example, adding zero to three gives three. In symbols:
3 + 0 = 3
  • Subtracting zero from a number always gives that number. For example, subtracting zero from three gives three. In symbols:
3 − 0 = 3
  • Subtracting a positive number from zero always makes that number negative (or, if a negative number is subtracted from zero, it makes the number positive). In symbols:
0 − 3 = −3
  • Multiplying a number by zero always gives zero. For example, multiplying forty-three by zero gives zero. In symbols:
43 × 0 = 0
  • Dividing zero by a number always gives zero. For example, dividing zero by forty-three gives zero. In symbols:
0 ÷ 43 = 0 43 ÷ 0 has an undefined answer.
  • Zero divided by zero has no answer. In symbols:
0 ÷ 0 has no answer.

Below are all of the above examples with a few others in a condensed, and generalized form in a tabular layout.

Here in the table below, x represents any number.

OperationRuleExample
Additionx + 0 = x3 + 0 = 3
Subtractionx - 0 = x3 - 0 = 3
Multiplicationx × 0 = 05 × 0 = 0
Division0 ÷ x = 0 , when x ≠ 00 ÷ 5 = 0
x ÷ 0  is undefined5 ÷ 0 is undefined
Exponentiationx = 005 = 0
x 0 = 150 = 1
Root√0 = 0 
Logarithmlogb(0) is undefined 
Factorial0! = 1 
Sinesin 0º = 0 
Cosinecos 0º = 1 
Tangenttan 0º = 0 
Derivative0' = 0 
Integral∫ 0 dx = 0 + C 

History of zero[change | change source]

The idea of zero was first thought about in Babylon, India and in Central America at different times. Some places and countries did not know about a zero, which may have made it harder for those people to do mathematics. In India, zero was discovered by the 7th century mathematician Bramhaguptha.

Over hundreds of years the idea of zero was passed from country to country. From India and Babylon to other places, like Greece, Persia and the Arab world. The Europeans learned about zero from the Arabs, and the word is from the Arabic language.

The place of zero as a number[change | change source]

Zero is almost never used as a place number (ordinal number). This means that it is not used like 1, 2, or 3 to indicate the order, or place, of something, like 1st, 2nd, or 3rd. An exception to this is seen in many programming languages.

Some other things about zero:

Any number divided by itself equals one, except if that number is zero. In symbols:

0 ÷ 0 = "not a number."

In time, zero means "now". For example, when a person is counting down the time to the start of something, such as a foot race or when a rocket takes off, the count is: "three, two, one, zero (or go)". Zero is the exact time of the start of the race or when the rocket takes off into the sky.

0 as a number[change | change source]

0 is the integer that precedes the positive 1, and follows −1. In most (if not all) numerical systems, 0 was identified before the idea of 'negative integers' was accepted. It means "courageous one" in hieroglyphics.

Zero is a number which means an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight. If the difference between the numbers of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result.

While mathematicians all accept zero as a number, some non-mathematicians would say that zero is not a number, arguing that one cannot have zero of something. Others say that if one has a bank balance of zero, one has a specific quantity of money in that account, namely none. It is that latter view which is accepted by mathematicians and most others.

Normally speaking, there was no year zero between 1 BC and 1 AD. More exactly, almost all historians leave out the year zero from the proleptic Gregorian and Julian calendars (that is, from the normal calendar used in English-speaking countries), but astronomers include it in these same calendars. However, the phrase Year Zero may be used to describe any event considered so important, that someone might want to start counting years all over again from zero.

0 as a numeral[change | change source]

The modern numeral 0 is normally written as a circle or (rounded) rectangle. In old-style fonts with text figures, 0 is usually the same height as a lowercase x.

On the seven-segment displays of calculators, watches, etc., 0 is usually written with six line segments, though on some historical calculator models it was written with four line segments. The four-segment 0 is not common.

The number zero (as in the "zero brothers" example above) is not the same as the numeral or digit zero, used in numeral systems using positional notation. Successive positions of digits have higher values, so the digit zero is used to skip a position and give appropriate value to the preceding and following digits. A zero digit is not always necessary in a different positional number system. Something called bijective numeration is a possible example of a system without zeroes.

The numerical digit zero[change | change source]

0 (zero) is also used as a numerical digit used to represent that number in numerals. It is used to hold the place of that digit, because correct placing of digits affects a numeral's value.

Examples:

  • In the numeral 10, which stands for one times ten and zero units (or ones).
  • In the numeral 100, which stands for one times a hundred plus zero tens plus zero units.

Telling zero and the letter O apart[change | change source]

The number 0 and the letter O are both round, so what is the difference? The difference is important on a computer. For one thing, a computer will not do arithmetic with the letter O, because it does not know that it should have been a zero.

The oval-shaped zero and circular letter O came into use together on modern character displays. The zero with a dot in the centre seems to have begun as a choice on IBM 3270 controllers (this has the problem that it looks like the Greek lettertheta). The slashed zero, looking like the letter O with a diagonal line drawn inside it, is used in old-style ASCII graphic sets that came from the default typewheel on the well-known ASR-33 Teletype. This format causes problems because it looks like the symbol , representing the empty set, as well as for certain Scandinavian languages which use Ø as a letter.

The rule which has the letter O with a slash and the zero without was used at IBM and a few other early mainframe makers; this is even more of a problem for Scandinavians because it looks like two of their letters at the same time. Some Burroughs/Unisys computers display a zero with a backwards slash. And yet another convention common on early line printers left zero without any extra dots or slashes but added a tail or hook to the letter O so that it resembled an inverted Q or cursive capital letter O.

The letters used on some European number plates for cars make the two symbols look different. This is done by making the zero rather egg-shaped and the O more circular, but most of all by cutting open the zero on the upper right side, so the circle is not closed any more (as in German plates). The style of letters chosen is called fälschungserschwerende Schrift (abbr.: FE Schrift), meaning "script which is harder to falsify". But those used in the United Kingdom do not make the letter o and the number 0 look different from each other, because there can never be any mistake if the letters are correctly spaced.

In paper writing you do not have to make the 0 and O look different at all. Or you may add a slash across the zero in order to show the difference, although this sometimes causes mistakes in the number 0.

Zeroes of a function[change | change source]

Functions are explained in the Function (mathematics) article. If the function f(x) = 0, then x is called a zero of the function f. For example, if the function f(x) is x2 − 1, then the zeroes of the function are +1 and −1, because f(+1) = (+1)2 − 1 = 0, and f(−1) = (−1)2 − 1 = 0.

Zeroes of a function are used because they are another way to talk about solving an equation, which is a main goal in algebra. If we want to solve an equation like x2 = 1, then we can subtract the right-hand side of the equation from both sides, in this case 1. Whatever we get on the left-hand side, in this case x2 − 1, can be called a function f(x). The right-hand side has to be zero, because we subtracted it from itself. So f(x) = 0. Finding the zeroes of this function is the same as solving this equation. In the paragraph before, the zeroes of this function are +1 and −1, so they are the solutions of this equation. We got this equation by subtracting the same thing from both sides, so we also have solutions to the equation we started with, in this case x2 = 1. So if we could find zeroes of functions, we could solve any equation.

Related pages[change | change source]

References[change | change source]

  • Barrow, John D. (2001) The Book of Nothing, Vintage. ISBN 0-09-928845-1.
  • Diehl, Richard A. (2004) The Olmecs: America's First Civilization, Thames & Hudson, London.
  • Ifrah, Georges (2000) The Universal History of Numbers: From Prehistory to the Invention of the Computer, Wiley. ISBN 0-471-39340-1.
  • Kaplan, Robert (2000) The Nothing That Is: A Natural History of Zero, Oxford: Oxford University Press.
  • Seife, Charles (2000) Zero: The Biography of a Dangerous Idea, Penguin USA (Paper). ISBN 0-14-029647-6.
  • Tapan Kumar Das Gupta: "Der Ursprung des neuzeitlichen Zahlensystems - Entstehung und Verbreitung." Norderstedt 2013. ISBN 978-3-7322-4809-4.

Other websites[change | change source]

A German licence plate showing zeroes

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