On Isomorphism and Pseudo-Isomorphism
In math and science, isomorphism describes the relationship between two entities (such as two biological organisms, or two crystal structures) that possess a similar form.
It's a useful term for art critics and art historians, too, since it relates to a large part of our intellectual labor. Principally, we look at a work of art and try to imagine how other works, both from the same time and from an earlier or later period, might relate to it: that's how we identify emerging movements and trace an artist's influence throughout history. Also, we make juxtapositions between similar works in order to help our reader/audience better understand how a work, well, works. (One of my favorite strategies is to take an image of a work of art and change one element with Photoshop, like moving the position of an arm, or changing the color of a dress, or deleting a detail. I then put the original and modified images side by side, and the resulting contrast helps people better understand the effect of the element in the original.)
From an art historian's perspective, one of the most exciting things about Artsy's Genome Project is that it facilitates the identification of isomorphic works. A set of images that have been tagged as sharing a particular characteristic or trait can help a researcher generate unexpected but fruitful formal comparisons (an idea embodied long ago by Aby Warburg's "Mnemosyne Atlas"). These comparisons can render visible certain realities that may otherwise lie hidden. For example, surveying the range of works tagged as Cubes plainly indicates the enduring legacy of Minimalism's obsession with that most basic of "unitary forms" (to borrow Robert Morris's phrasing).
However helpful, this tool also carries an inherent risk: it can lead to the identification of pseudo-isomorphism between objects that have superficial formal similarities but lack any meaningful relationship. (An example would be a Minimalist cube and this 18th-century bedside table: both could turn up on a search for "cubes," but thinking about them together won't really help you understand either one.) Thus, anyone hoping to make analytical use of "genomic" databases, like Artsy, has to be prepared to do some significant work--whether through visual analysis or textual research--to ascertain whether any formally similar works share a meaningful connection. Think of pseudo-isomorphism as a "red herring" that suggests connections between works when there aren't any, distracting us from their essential difference.
We can see the value of isomorphism using, again, the example of cubes. When I teach students about Minimalism and Postminimalism, I create a series of slides that function as a "database" of cubes in art from the 1960s and 1970s. These works of art are isomorphic, as they all rely on a specifically Minimalist conception of "the cube" as a visual shorthand for "thingness." But it is precisely by recognizing their profound connection to the idea of the Minimalist cube that we can better recognize what makes each work formally unique. In fact, each work can represent a different aesthetic attitude within Minimalism and Postminimalism: starting with Tony Smith's Die (1962)--a paradigm of Minimalism as defined by Donald Judd--my "database" moves on to Robert Morris's Untitled cubes (1965), which use their mirrored surfaces to position their viewers as embodied subjects in real space, and Richard Serra's One Ton Prop (House of Cards) (1969), which is a real-time demonstration of mass acted upon by gravity. Juxtaposing these three works--all of them basically Minimalist cubes--illustrates not only the genealogical similarities, but also the significant differences, between Judd's "specific objects," Morris's turn to phenomenology, and Serra's elaboration of process art. (This is not to suggest that these are the only important Minimalist/Postminimalist cubes: my "database" also contains the sensual concavity of Eva Hesse's Accession II (1968), the psychedelic refractions of Robert Smithson's Four-Sided Vortex , and the architectural deconstruction of Gordon Matta-Clark's Splitting .)
While both isomorphic and pseudo-isomorphic relationships between images tend to jump out at us, it's usually by identifying the works with real "family ties" to each other that we come to understand their key (if subtle) differences--and it's these differences that reveal how a work "works," on a formal level. If you want to learn about their qualities as fruits, comparing apples to oranges actually makes sense; it's comparing apples to red balloons that doesn't get you anywhere.