"Wildstyle" is a form of graffiti composed of complicated interlocking letters, arrows, and embellishment. Like all forms of graffiti art, it is spray painted on walls, trains, and other public surfaces, frequently illegally, and is intended to impose on public visual space, and to challenge viewers' ideas of who has the right to represent themselves publicly, and what art is. It is created both for, and in defiance of, the audience, which is made up of other writers 1 and both supportive and unsupportive members of the public. The reasons why people write are diverse and ever-evolving. Some motivations cited are resistance and rebellion, fame (literally making a name for oneself), and the desire to create beauty and share art with their community. Most writers fall somewhere on a continuum blending these desires and more. Wildstyle is intentionally hard to decipher. Dondi, from New York, has said that when he writes for other writers he uses wildstyle, and when he writes for the public he uses straight letters (Chalfant, 1984, p.70). Part of the thrill of the creation of wild letters is the mental and artistic challenge presented both for the writer and the reader. The passion for patterns is one of the binding forces of the community. Copious amounts of time are spent by writers in sketching, piecing, tagging, and bombing 2, examining pictures in graffiti magazines, trading flix (photographs) of graffiti art, and meeting to pass around sketch books filled with one's own and others' art to fill with more sketches. Another excitement of wildstyle is its subversive implications; it is a way of writing messages in huge letters on walls that is translatable only by a very small population of cohorts. Vulcan proposes, "The whole meaning of the art is that it's a communication language... My main thing is taking letters and distorting them, changing them, mutating them. It's about evolving the alphabet. Just because somebody said this is the way it's supposed to be, it doesn't mean it has to be; you can individualise the alphabet. You can make it your own" (Miller, 1993, p. 32). Usually, perhaps eighty percent of the time, what is written is the artist's name; a way of gaining fame and recognition within the community of graffiti writers and aficionados. Other messages are also communicated, sometimes the name of a loved one, or a concise personal philosophy. The letters themselves, it is hypothesized, are a reworking of Arabic lettering incorporating African and Latin rhythms, signifying motion and flow (Miller, 1993). While these theories about graffiti's roots and meaning are generally written by academically inclined graffiti artists and outsiders, any non-academic writer will tell about the synonymous "funk" in wildstyle lettering, meaning movement, vibrance, spirit.
My intention in this paper is to discuss the forms of mathematics that have been developed in the design, painting, deciphering, and evaluation of wildstyle. The brief preceding background presents a basic summary of the driving purposes of this form of expression, from which the technical elements valued in the art take shape. Mathematical forms of thought have been both appropriated and adapted from formal math, and, even more pervasive and significant, have been invented to serve the functions of this community. This is what has been termed "street mathematics" (Nunes, 1993). Nunes, Schliemann, and Carraher convincingly summarize the relevance of street math as follows:
"Sociologists will be interested in analyzing the social conditions under which street mathematics appears and what relationship it bears to variables commonly used to describe a society. Anthropologists will be interested in street mathematics as cultural practices that have an organization surpassing the level of the individual and that are in some way transmitted within the culture. Educators will be interested in such questions as whether children at a given grade level are likely to know particular mathematical concepts from their experiences outside school, whether the new knowledge they gain in school can increase the power of their knowledge outside school, and whether classroom teaching of a novice and a street expert should be different. Finally, psychologists will be interested in the organization of knowledge in street mathematics, its forms of representation, its power to generate solutions to problems, and its acquisition.
(Nunes, et al., 1993, p. 6)"
The community of graffiti writers exhibit particularly rich, sophisticated, efficient, application-specific forms of street mathematics, from which educators can learn much. Nunes et al. consider the significance of studying street mathematics to be in understanding the conditions under which it arises, how educators can use outside math understandings in teaching of formal math, and how these knowledges are developed, used, and transmitted through communities and to novice members. All of these are extremely interesting phenomena which I will at some point examine relative to this community. There is an additional, and particularly important significance of street mathematics, though: what it implies about formal intelligence. Many graffiti writers are unsuccessful and uninterested in school math; qualities which, when perceived by outsiders, may be interpreted as ignorance. Some artists are notable exceptions to this, and I will discuss them and their merging of street and school intelligences; but for the purpose of improving education it is critically important to look at the people, disturbingly the majority, for whom school education fails. When people "fail" at school math, yet utilize street math in a sophisticated way, we must interrogate why school math is not reaching them. It may be methods or content or student motivation, or some combination of these. Whatever the cause of discontinuity, much is implied about the nature of formal and sanctioned knowledge. School math is valued as a universal, generalizable set of tools to apply to any situation, yet for most people it is a source of disempowerment, as they feel unable to recall or apply formal algorithms in "real-world" situations. When this is so often the case, educators need to question why this happens and what can be done to value types of mathematical power that students already have, and not only relate "real" math to street math to strengthen student's real-life uses of math, but broaden school math to incorporate the strengths, flexibility, and creativity of street math. An analysis of math use in the graffiti community is particularly compelling because it is a counter-cultural group composed of people and an activity that is generally conceived of as criminal and unintellectual. The results, then, are particularly challenging to common conceptions of intelligence.
It is interesting to note the ways in which writers themselves speak of the mathematics of graffiti. It is common for there to be discussion of balance, flow, and symmetry as mathematical elements, as well as perspective visualization (letters are frequently drawn three-dimensionally). However, I have not, in my interviews or readings, heard any mention of the value of school/formal mathematics in learning these skills. The informal mathematical elements used in the practice of their art seem to be conceived of as learned within and specific to the application. Super LP Raven in Bomb the Suburbs says, "[Wildstyle] is mathematical... graffiti is mathematically constructed... It's about proportion, balance, syllabic distribution... It should be, after you study someone's wildstyle once, you should be able to read anything they do in that style - if the style makes sense" (Upski, 103-104). Giant has talked of his use of "axonometric architectural renderings" 3 and the pyramidal form he uses to construct his pieces; there is "inherent balance, strength, and power associated with pyramids", he says. Delux and Eskae and members of their crew, the Aerosol Syndicate, study sacred geometry and incorporate the "natural" proportions, symmetries, and patterns prescribed by it to create their artwork. Delux, who studies mechanical engineering, has also found that his engineering and graffiti skills symbiotically enhance each other, enriching his skills in both domains. Interestingly, the mathematically inclined artists that I have interviewed became interested in mathematics after they began graffiti, and then began to incorporate these formal knowledges into their work. This intellectual and theoretical angle to their artwork seems to be highly respected by other community members, which may have powerful implications for motivation in school education.
Additionally, there are numerous informal mathematical skills employed by writers that they do not conceive of as mathematical. This may be because it is uncommon for people to think of skills that are learned and used independent of school as "real" mathematics, or, as Nunes, et al., say, "The mathematical skills involved in everyday activities go unrecognized. They are so embedded in other activities that subjects deny having any skills" (1993, p. 11). Specifically, those in use here include pattern creation and deciphering, and tools and practices of measurement and proportional translation utilized in production of pieces. Subsumed in these categories are the specific talents of spacial visualization, symmetrical and geometrical design and reasoning, and precise, consistent, and coherent application of pattern.
Difficulty of deciphering by the uninitiated is a primary intent in the creation of wildstyles. To achieve the goal of being undecipherable to lay people while legible to other writers, there must be coherence and commonalities within the domain that are transmitted to new members of the community. It is common for a writer to be able to read a piece relatively easily that an outsider may not even realize has letters in it.
Writers employ a common schemata in the deciphering of wildstyle pieces. When coming to a piece by an unfamiliar artist that is not easily read, the first step is always to look for the signature 4 mentioned before, a wildstyle piece will usually spell the artist's name, so if the signature is present and legible, the reader has a good idea of what the piece may say. It is still frequently no easy feat to see the letters, though. The subsequent step is to look for any relatively obvious letters in the piece. It is difficult to characterize the various directions this may take, as it is dependent on the particular codes of the piece and the strengths of the reader. Sometimes one or more letters can be found relatively easily, and from there, it can be guessed that they will be of approximately the same size and evenly spaced, and so it can be guessed where other letters should fall; features are then looked for in those spots. Another frequently useful strategy that may follow or be concurrent with the aforementioned involves following a line as it weaves above and below crossing lines and distractions, to see if it is an embedded letter shape. This is useful in the frequent case that a letter is formed by only one continuous line, but sometimes the shape is instead implied by several unconnected lines touching. This is observed in the comparison between the first and second E's in Figure 2 5.
It is of course key to know what shapes to look for; this is part of the knowledge of the practices of the domain. A knowledge of the standard shapes of upper and lower case Arabic letters is a basis, and from there writers become familiar with different common styles of letters employed and adapted by wildstyle writers. These are sometimes particular to regions, although regional variation is dissipating with the emergence of the internet, widely distributed international graffiti magazines, and writing on freight trains, which then exhibit regional styles across the country. Also, many times a writer will be familiar with the styles of known artists, and may be able to recognize consistent patterns across pieces that help in deciphering. Following Super LP Raven's comment cited earlier, stating that if the logic of a style can be determined, it should be easy to subsequently read anything else in that style.
Finding the letters in a piece becomes an obsession for writers; Delux calls it "obsessive-compulsive pattern disorder". It goes beyond wanting to know what a piece says; it is a game, an intellectual challenge, to find the words. Ambiguity is acceptable; that is, for there to be sections that look like letters but actually aren't, or that may imply several letters. That is part of the complication and the "background noise". An important component of deciphering is being able to sort between letter and embellishment. Susan Farrell at Art Crimes 6 sees wildstyle deciphering explicitly as a form of problem-solving: she speculates that the difference between people who can "deal with" wildstyle and those who can't is due to their problem-solving ability. Practice, as well, is a key component. Readers come to automatize the variety of deciphering strategies they may try, and can sense when to terminate one line of analysis and try another, a typical quality of skilled mathematicians and problem solvers.
Other factors helpful in reading wildstyles are patience and use of collaboration. Reading complex pieces may take twenty minutes, or even revisiting over several days. It is frequently a collaborative process, where people verbally speculate about what letters certain shapes may indicate, as they jointly attempt to decipher. This is interesting in light of Alan Schoenfeld's research showing that it is a commonly held student belief about mathematics that if one is capable of doing it, it should be done in less than five minutes, and that it is a solitary activity. In school mathematics, most students will quit quickly if they don't see a known solution strategy, believing a problem to be impossible for them. In this form of street mathematics, however, multiple solution strategies are tried, and if they don't at first succeed, new ones may be invented. Collaboration is frequent also in deciphering, as well as in aesthetic and technical evaluation.
Coherence of pattern within a piece is a very important factor in its evaluation. The patterns should be consistent throughout a piece, and not random or done to look interesting or complicated without having a precise pattern or design in formation of letters throughout. It is commonly noted that when novices first come into the graffiti world, they usually want to do wildstyle, and they may start drawing designs that look intricate and tricky, but actually have no solid foundation. There should always be a strong "ghost" of a letter underneath the distracting extra lines, shapes, and fill-in (colorful designs which fill the letters in a piece, and may contribute to obscuring the lettering). What makes a coherent pattern and what doesn't is a complicated topic that I don't at this point have a solid enough understanding to go very deep into. I will explore this more in future research. [ed. note: See especially Metamagical Themas: Questing for the Essence of Mind and Pattern by Douglas R. Hofstadter, which is one of the most entertaining and thought-provoking books I've ever picked up.]
Precision and cleanness are critical in respectable graffiti, both in design and in painting. I have already briefly discussed conventions of letter design; there is an equally strong emphasis on skill and technique in the actual painting. If one is an excellent sketcher but cannot transfer these to walls, a critical element of the art is lost. Enlarging a sketch onto a wall with accurate proportions is no easy feat. Works may be in the range of ten to 25 feet across and three to eight feet tall, and may be extremely complex. Common measuring devices which could be applicable, such as rulers, tape measures, compasses, chalk line, and levels, are never used. The idea is considered quite preposterous; other tools specific to the domain have been invented to produce the precision that is so valued in the community. Certain factors have contributed to the need to develop alternate measuring tools: one is that conservation of time is frequently a factor, as many pieces are done illegally; a second is that artists must carry a large amount of supplies (mostly spray cans) to the sites, and for economy's sake, carrying additional tools is undesirable. In response, writers have adapted the tools they have on hand to serve the functions needed: spray cans, their bodies, features of surfaces, and their mental design, mapping, and measurement skills, developed through extensive practice.
A spray can is one concrete measuring device used. The body of the can is slightly over six inches long, and three inches wide. In some designs, particularly large "straight" (non-wildstyle) letters, maintaining an even bar width is extremely important, and measuring this relative to can lengths or widths is one method of assuring consistency. This is done mentally in many cases, but there are instances where bar width may be three or more feet across, and mental estimations become increasingly imprecise. Another use of cans is in determining straightness of lines. A line may be intended to be straight for, say, fifteen feet, and this is notoriously hard to do. Giant is reputed as being very skillful at this (he is one of few artists who even tries), and to do it with precision he will hold the can vertically along a sketched bar, and observe if there are slight curves relative to the straight edges of the can, performing multiple mental (non-numerical) calculations of relative slopes.
Simultaneously, the body is used as measuring tool. A common concern is keeping bottom and top borders an even distance from the base of the wall. This can sometimes be quite easily done using features of the surface, such as seams on cinder block walls, or bottom edges or lines of printed writing on freight or light-rail train cars. In other cases, where there are no such helping features, an artist may begin a piece at the left edge, and note where the bottom border falls relative to her or his body, and then continue with the height of that body part as bottom border throughout. The same technique can be used as a guide for top margin. Also, similar to the use of spraycan to measure bar width, hand span may be used to evaluate changes in bar width.
There are many more ways that surface features of walls are used in the production of a piece. One practice applied in mapping a sketch onto a surface is similar to historically used perspective drawing tools discussed by Ferguson (1992, p. 80), with the eye as "apex of the visual pyramid", and the picture being drawn on an intermediate screen between the eye and the image being represented. The graffiti writer's use, however, is inverse. The intermediate image is the sketch, held at arm's length, and the artist mentally projects this image onto the surface behind it (see Figure 3). S/he then remembers where features of a sketch fall relative to features of the surface (such as cracks, brick seams, and other paintings). This process will usually be repeated several times during a production. In this way, also, right margins can be approximated as a piece is begun, so that if a piece is a collaboration (where two or more artists will simultaneously compose several pieces on a wall, frequently with edges touching), the next artist to the right knows where their left margin should be.
Some of the quantitative and proportional reasoning used by graffiti artists has been adapted from historically used art, perspective, and design practices, such as those commonly taught in high school art classes. The act of imposing a grid onto a picture to be copied proportionally onto another gridded surface is a standard and historically used representation that many of us are familiar with. While in most cases, this idea would be scoffed at by graffiti artists, one artist I spoke with is actually planning an extremely complicated piece that he would like to put on a cinder block wall, precisely because he can section it into the 2-to-1 offset rectangularly patterned surface. This is certainly an exception.
Yet another application of mathematics in the production of graffiti art is in producing the desired volume or flow rate of paint from the can. This is varied by switching the nozzle, or "cap". There are two types of caps most frequently used: fat caps and skinny caps, also known as phantom caps. Fat caps produce a wide, less dense line, while phantoms make a thinner, dense, crisp line. The standard nozzles that come on spraycans have a quicker flow, which can cause drips if it is not moved fast enough. Artists have a very clear idea of how to produce wide and narrow lines, and opaque or translucent paint density, as well as flares, where a line morphs from thin and dense to wide and scattered. Caps are important, as well as technique with the spray can, including proximity to the wall and speed of hand motion. There are constant calculations being performed to determine: the given volume, width, and density of paint flow; what painting techniques will produce the desired outcome; and if it would be preferable to use a different available nozzle or seek out or invent a new one. Writers frequently experiment with caps from other kinds of aerosol products, testing its qualities, and sometimes even make their own by carving existing nozzles. I am unsure of whether they generally have an idea of what painting effect they want and can predict how to modify a nozzle to make it happen, or whether they carve nozzles in various ways without any predetermined desired outcome, but to test possibilities.
One topic that I haven't covered is the use of perspective in graffiti art. Writers commonly use one-, two-, and multiple-point perspective, which I don't have an extensive understanding of myself, so noting and analyzing the complexities of its use are difficult at this point. The majority of pieces are designed such that they appear three dimensional, for example, by painting a shadow cast onto the wall under the letters. Additionally, it is a relatively new phenomenon for some artists, notably Erni and Sleep, to portray letters as though they are actually three-dimensional figures, like sculptures, weaving around each other (see Figure 6), whereas most wildstyle appears to be two-dimensional letters weaving above and below each other, and casting a shadow.
Also, calculation of the amount of time necessary for a piece and number of cans of paint needed must be performed, as one must balance how long a piece will take with the reasonable amount of time it is possible to work at a site without being caught (if it is an illegal spot). This is one of the more solidly numerical forms of mathematical reasoning, relative to the forms of mathematical thought I have mainly been addressing here.
I would like to further examine the strategies of problem solving within this domain, including what sorts of metacognition are enacted, and what other strategies are used that are similar to or different from those productive in the solution of formal mathematics problems.
One approach I have considered using, and have done informally already, is asking for think-aloud protocols as graffiti writers decipher a piece. This begs for a comparison to "novices", however, and I'm skeptical about the validity of expert-novice studies, given the extreme variations between subjects in addition to their experience with wildstyles. I do think that research of this sort would be extremely interesting, though, if it can be designed in a legitimate way.
Also, as I mentioned, I would like to study in more depth what qualities make a coherent pattern, which is critical in the quality and decipherability of styles. It is widely commented that being able to create a solid pattern is a skill that comes with extensive practice and study. I am acquiring a basic feel for determining a piece's success in fulfilling that criteria, but in many ways it still defies explanation for me. This has also been made difficult by the fact that the vast majority of pictures that are encountered in magazines, on the internet, and in writer's photograph collections, are of pieces that have been judged positively. I would like to tour more pieces in the streets and have artists evaluate the pattern-coherence of works of more varied skill.
Symmetry, more often referred to by writers as "balance", is extremely important as well, and can involve quite complex geometric reasoning. Some artists choose to sometimes make their pieces precisely symmetrical, while usually it is sufficient for the piece to be generally symmetrical, meaning the height, width, and outline will be approximately equivalent around a vertical line of symmetry . Given that, writers have a deep knowledge of the construction of letters, including their reverses. This shows highly developed spacial visualization and, I would say, problem-solving skills, as artists determine how to construct two letters so that they are reverses of each other, while maintaining the integrity of each letter. This is a complex topic that I'd like to investigate.
Wildstyle artists, I have argued, have developed sophisticated forms of mathematical thought specific to the needs of their realm. Pattern observation is now considered critical in the development of functional and innovative formal mathematical thought, and it is apparent that wildstyle artists exhibit this talent flexibly and impressively in the practices of their community. Simultaneously, many forms of quantitative reasoning, primarily non-numerical, arise in situation-specific settings in the production of graffiti. This analysis challenges what is often seen as a dichotomy between intellectual reasoning and creativity, with little overlap realized between the two. Not only is it apparent that there is far more complex reasoning involved than may at first be apparent in this art, but parallel to that, what has formally been conceived of as mathematical thought, particularly in the realm of problem-solving, can be a creative endeavor as well.
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