"A border is a completely imaginary line on a paper or cybernetic map that has no genuine counterpart in the real world. Do not mistake it for a property line. It is possible, in some instances, for a border to be congruent with a property line, but they are not the same thing at all. One represents the geographical limit of a military and political claim to authority over a given territory. The other is part of the description of something - in this case, land - lawfully owned by an individual or a voluntary and contractual association of individuals." (L Neil Smith, "Only Nixon", 2010)
"[...] maps, like many other kinds of visualizations, distort the 'truth' to tell a larger truth. The processes that abstract, schematize, supplement, and distort the world outside onto the world of a page, filtering, leveling, sharpening, categorizing, and otherwise transforming, are the same processes the nervous system and the brain apply to make sense of the barrage of stimuli the world provides."
"This is always the case in analogical reasoning: Relations between two dissimilar domains never map completely to one another. In fact, it is often the salient similarities between the base and target domains that provoke thought and increase the usefulness of an analogy as a problem-solving tool." (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)
"Graphics, charts, and maps aren’t just tools to be seen, but to be read and scrutinized. The first goal of an infographic is not to be beautiful just for the sake of eye appeal, but, above all, to be understandable first, and beautiful after that; or to be beautiful thanks to its exquisite functionality." (Alberto Cairo, "The Functional Art", 2011)
"In each branch of mathematics it is essential to recognize when two structures are equivalent. For example two sets are equivalent, as far as set theory is concerned, if there exists a bijective function which maps one set onto the other. Two groups are equivalent, known as isomorphic, if there exists a a homomorphism of one to the other which is one-to-one and onto. Two topological spaces are equivalent, known as homeomorphic, if there exists a homeomorphism of one onto the other." (Sydney A Morris, "Topology without Tears", 2011)
"It is ironic but true: the one reality science cannot reduce is the only reality we will ever know. This is why we need art. By expressing our actual experience, the artist reminds us that our science is incomplete, that no map of matter will ever explain the immateriality of our consciousness." (Jonah Lehrer, "Proust Was a Neuroscientist", 2011)
"If maps are essentially subjective, interpretative, and fictional constructs of facts, constructs that influence decisions, actions, and cultural values generally, then why not embrace the profound efficacy of mapping in exploring and shaping new realities? Why not embrace the fact that the potentially infinite capacity of mapping to find and found new conditions might enable more socially engaging modes of exchange within larger milieux?" (James Corner, "The Agency of Mapping: Speculation, Critique and Invention", 2011)
"Making a map is the physical production including conceptualization and design. Mapping is the mental interpretation of the world and although it must precede the map, it does not necessarily result in a map artifact. Mapping defined in mathematics is the correspondence between each element of a given set with each element of another. Similarly in linguistics emphasis is on the correspondence between associated elements of different types. For designers all drawings are maps - they represent relationships between objects, places and ideas." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)
"Mapping is based on our perceptions of what we are experiencing and our conceptions framing how we interpret sensorial input. The map isn’t ‘real’ but the objects in the map are at some point in the world or of the world. Just as we have to disabuse ourselves of the idea maps, as semiotic texts are value neutral, similarly mapping calls into question how we interpret perceptions." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)
"Maps are parenthetical - maps frame what you want to hold apart from the real in the world. Maps do this by creating conceptual representations of the milieu using symbols and relations between symbols. [...] Maps, any map and every map, begin with a frame. This is the literal and conceptual demarcation between what is in the map and what is not. Making a map begins with an observation which is both a thought about thinking and the object of thought itself. The undifferentiated world cannot be apprehended, therefore; all maps have a frame whether a concept or a cosmography." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)
"The utility of mapping as a form of data visualization isn’t in accuracy or precision, but rather the map’s capacity to help us make and organize hypothesis about the world of ideas and things. hypothesis-making through the map isn’t strictly inductive or deductive, although it can use the thought process of either, but it is often based on general observations." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)
"Using maps as communication tools masks their complexity as a mode of thinking. Maps act like language: we attribute the signs or marks in the map to a natural extension of thought. But post-structuralism exposed maps (like language) as artificial signs whose meaning is tethered to time, place, culture, gesture, smell - in short, a plethora of cognitive and phenomenal attributes of our communication ecology." (Winifred E Newman, "Data Visualization for Design Thinking: Applied Mapping", 2017)
"Maps also have the disadvantage that they consume the most powerful encoding channels in the visualization toolbox - position and size - on an aspect that is held constant. This leaves less effective encoding channels like color for showing the dimension of interest." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)
"The relationship of math to the real world has been a conundrum for philosophers for centuries, but it is also an inspiration for poets. The patterns of mathematics inhabit a liminal space - they were initially derived from the natural world and yet seem to exist in a separate, self-contained system standing apart from that world. This makes them a source of potential metaphor: mapping back and forth between the world of personal experience and the world of mathematical patterns opens the door to novel connections." (Alice Major, "Mapping from e to Metaphor", 2018)
"We cannot draw a complete map, a complete geometry, of everything that happens in the world, because such happenings - including among them the passage of time - are always triggered only by an interaction with, and with respect to, a physical system involved in the interaction. The world is like a collection of interrelated points of view. To speak of the world 'seen from outside' makes no sense, because there is no “outside” to the world.
"A neural-network algorithm is simply a statistical procedure for classifying inputs (such as numbers, words, pixels, or sound waves) so that these data can mapped into outputs. The process of training a neural-network model is advertised as machine learning, suggesting that neural networks function like the human mind, but neural networks estimate coefficients like other data-mining algorithms, by finding the values for which the model’s predictions are closest to the observed values, with no consideration of what is being modeled or whether the coefficients are sensible." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)
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