Often times when people think of maps, they imagine a visual representation of a certain physical area optimized for navigation. This may be a paper map of a city or more recently, digital, interactive representations such as Google Maps.
There are a couple reasons that may suggest why most people default to this representation. The general use of the word “map” in comparison to what people mean by it often correlates to this representation, and due to the nature of word usage frequencies, more popular words and their corresponding meanings have a snowball effect on mass adoption. (An aside, but this video on Zipf’s Law goes more into this and is overall an interesting watch). This leads to more and more people using the word “map” to mean the same thing.
Another tangential reason is the more recent use of this representation of maps on mobile devices. The popularity of smartphones (at this point we can probably just call them “phones”) and the widespread availability of the internet provided the affordance for map apps such as Google Maps to really take off. Now, Google Maps is a default app preinstalled on the majority of phones. This further probes at the idea that most people imagine visual representations of a physical area optimized for navigation.
Looking at this more generally, the factors that are important to notice is that the most common understanding of “maps” is tied to the notion of the mathematical concept of mapping. Wikipedia describes “the term mapping, usually shortened to map, refers to either a function, often with some sort of special structure, or a morphism in category theory, which generalizes the idea of a function.” What this means is that there is an input set, typically referred to as the domain, which has elements that correspond to elements in an output set, typically referred to as the range.
More generally, a map conveys a relation. It says that there are some things in a category X that have a relation to some things in a category Y. Looking at all the individual relations between X and Y can provide us a higher order understanding of the relation between the entire sets X and Y.
Stepping back into the common understanding of the word “map,” we can apply this formality to identify that the set of visual features on Google Maps are based on a set of features that exist in the physical world that are selectively chosen to help with navigation. In other words, let the set X consist of all the IRL features that are used for navigation (roads, intersections, exits, one way signs, etc.) and let the set Y consist of visual cues on Google Maps (graphical representation of roads, arrows for one way signs, icons for points of interest, etc.). The collection of each relation on this mapping from the physical world to the one represented in Google Maps signifies the overall relationship between the two categories.
Now that we have generalized a conceptual framework for thinking about maps and mapping, we are free to detach any preexisting notions that maps have to deal with visually representing physical areas used for navigation. This lets us think of maps in terms of a relation between two sets, which paves the way for the different types of maps Harmon presents in You Are Here. In NYC Mapping the Soul of the City, Harmon shows maps that are still tied to the physical representation of NYC, but convey different messages that aren’t used primarily for navigation. For example, the city smellscapes map resembles the relation between the set X consisting of physical locations in NYC to the set Y containing different odors.
In Personal Geographies, Harmon transcends the common notion that maps have to be based off of physical areas and maps from entirely different input sets X. The image below is a mapping between human characteristics and overarching aspects of society and life to a visual representation based on a person’s head.
By taking a step back and incorporating the mathematical/category theory based definition of a map, we are liberated to expand the boundaries on what a map can visually represent.
A further analysis on synesthetic artists
In class, we watched a video on a synesthetic artists. Synesthesia is a condition defined by “the production of a sense impression relating to one sense or part of the body by stimulation of another sense or part of the body.” The artist was able to see music. She described that different songs had different colors and that certain riffs and melodies and different genres presented different tones. In that sense, her art is a mapping from such features of music to the arrangement of color on a 2D space.
However, the artist also remarked that her paintings depend on her mood at the time of painting. If this is also a factor, then the mapping function to describe the relation between the factors that influence the painting and the painting itself must include more parameters than just the music itself. Formally speaking, if the paintings solely depended on the features of the music, our mapping function can be represented as y = f(x) where y is the painting and x is the music. However, since it seems that other factors such as her mood are involved, the mapping function must be multivariable, i.e. y = f(a, b, …).
This is important to consider as it helps us do a more mathematical analysis. One thing to consider is whether the mapping function is pure. A pure function always yields the same output given the same input, regardless of external conditions. In the artist’s case, what that’s asking is whether the artist always sees the same colorful image every time a certain song is played. If so, we can give a lot of weight to her synesthesia in terms of how strong its relation to the final painting is. However, if we find that the mapping function is impure, i.e. the artist produces different images every time a song is played, and in theory, there are other parameters that play a significant role in the output painting, then we can determine that her synesthesia only accounts for a small part of what goes into her paintings. Furthermore, if we find that there are other parameters that have a stronger correlation with the output painting than what we notice from her synesthesia, we may be able to conclude that the artist is using her synesthesia as an excuse to paint whatever she pleases. But until we do a formal scientific experiment and statistical analysis, let’s give her the benefit of the doubt =)
