A Topology of Ideas: Beyond Visuals
The launch of the Dynamicland website / front shelf at the end of last week was revelatory to many, if not all, who have followed the journey of Dynamicland and the work of Bret Victor, as well, of course, for all those who are new to the work of that fascinating laboratory.
Other than the stunning interplay between technology, environment and community that takes place in the democracy of objects that Dynamicland facilitates, there is much more to the heart of what Bret Victor has been working on in that space for many years - check out his talk on 'The Humane Representation of Thought' from 2014 in which he brilliantly elucidates a trajectory of how thoughts and concepts came to be represented in increasingly visual ways.
The first example Victor gives is the manner in which Scottish engineer and political economist William Playfair, in 1876 created graphical methods of statistics - instead of representing data in tables, he visualised it across X and Y axis, like a map:
In my domain, working in neurodivergent education settings and developing workshop content to transmit concepts about inclusion, we talk about visuals a great deal - visual supports in the environment to facilitate receptive and expressive communication, visual ways of rendering academic school concepts in a concrete manner to remove the difficulty of abstraction, and ways of visualising the relationships between ideas in workshops.
One conclusion I've come to over the years is that it can be a misnomer to just rely on the idea of visual information as the best way to consider how information can be rendered and shared - not least from an accessibility standpoint, for those who are blind or with vision impairments, but from limiting the boundaries of how we might structure representation.
There are three flags on the map, so to speak (an intentional phrase), that I refer back to with regard to this notion of thinking beyond visuals within our consciousness / subjectivity -
While this is a topic that could be rendered across a great deal of space, I'm going to be purposefully brief here just to highlight the key points, that we can go into in more depth later.
Gerald Murnane lives in Goroke in the Wimmera region of rural Victoria. A monolith of Australian writing, he is best known for his 1982 masterpiece The Plains, which contains ideas related to the relationship between landscape and human thought that he would explore across most all of his books and in his talks, such as this one, The Still Breathing Author, given at the Goroke Golf Club in 2017.
I have been fortunate to discuss these concepts with Murnane in letters, as the principle endlessly fascinates me. In brief, at the risk of mispresenting Murnane's ideas, my interpretation is that he considers his mind a landscape that he moves around in - when he reads about a character in a story walking up a hill, that hill really exists within the landscape of Murnane's mind, and while beyond the hill might not be discussed in the story, it still exists, somewhere in the internal landscape of Murane's subjectivity, perhaps related to another hill in another story read many years before.
Murnane extends this to the idea of time, too - in his first letter to me, he says, "I know that I've written at least once in my published works that time has no existence: that what we call time is our confused perception of place after place."
This is a portrait of ideas that do not exist in a readily visualised way, plotted on a graph or rendered as a graphic - this is a representation of thought as a topography of inner-land, a moving across a map, similar to Playfair's revelation about 'mapping' data, using the tools of cartography to move one's thoughts across physical space, a literal trajectory of cognition.
How does this idea relate to pedagogy, to how ideas about neurodivergent learning principles could be transmitted in a workshop? Perhaps it is less about what is shown on a sequence of slides at the front of a room and more about how participants move about that room, to the sort of practical activities they do - creating space, using Lego to represent the environmental questions that a classroom raises, going for a wander and letting ideas move.
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Keep the idea of landscape as subjectivity in mind as I attempt to introduce Slovenian philosophy Slavoj Zizek's ideas on how different geometric topologies can represent the domain in which our ideas take shape. It doesn't hurt to have read enough Kant and Hegel to get the bones of what he's going for here, or this terrific lecture he gave in 2017 on the topic (in which he is surprised at 3:33 in the clip to realise he's still writing his notes while everybody is silently waiting for him to begin..!).
Take a look at the shapes above - the M?bius strip, for example, in Zizek's telling represents the trajectory of our thought despite apparent oppositions: it’s a surface with only one side, symbolising how our subjectivity can appear split (inside vs. outside, conscious vs. unconscious) while actually being part of a single, twisted structure. This captures some of the relationship between how much of our consciousness is informed by the external world and how much is internally mediated, and how much is both at the same time, as a singular form.
The Klein bottle (on the right, above) goes even further, representing a surface where the inside and outside are indistinguishable. ?i?ek uses it to explain how subjectivity includes an inherent paradox — our interior life is shaped by the external symbolic order, but we can never fully step outside of it to view it objectively. This is a way of capturing the strange, looping relationship between our conscious selves and the societal structures that define us.
I wrote a book on landscape and subjectify a couple of years ago, Antinomicity, in which I wrestled with some of these, and Murnane's ideas, whilst on walks around Newcastle -
"I have come to think of my relationship with landscape as one of subphysicality, beneath conscious association and physical connection, within enclaves that position these landscapes as analogous to the shape of the inland empire that is my subjectivity.
These landscapes are not analogous in an abstract form within my mind; rather, they exist as my mind - subject as object. To look from the ceiling of the gas silo across an expanse of grassland and industry is to recognise the literal silhouette of my own awareness. Environmental declivities and ascensions are carved into the fabric of my consciousness as into an inverted mirror, allowing landscape to pour into the negative space at the foothold of my thoughts, providing to the body a simulation of what division without remainder might feel like."
Douglas Hofstadter gained popularity through his Pulitzer Prize-winning 'G?del, Escher, Bach: an Eternal Golden Braid' book in 1979, in which early tenets of computer algorithms and human consciousness were explored. Recently, he has?been quite distressed?about what he's seeing with AI's advances, notably in its capacity to compose classical music in a cadence that fools seasoned musicians, something Hofstadter sees as a critical bastion of humanity.
One of the most important contributions Hofstadter has made to my own understanding of human cognition is the way he talks about analogy as the core of cognition. In his own words, from a talk given at an analogy workshop in Bulgaria:
"One should not think of analogy-making as a special variety of reasoning (as in the dull and uninspiring phrase “analogical reasoning and problem-solving,” a long-standing cliché in the cognitive-science world), for that is to do analogy a terrible disservice. After all, reasoning and problem-solving have (at least I dearly hope!) been at long last recognized as lying far indeed from the core of human thought. If analogy were merely a special variety of something that in itself lies way out on the peripheries, then it would be but an ittybitty blip in the broad blue sky of cognition. To me, however, analogy is anything but a bitty blip — rather, it’s the very blue that fills the whole sky of cognition — analogy is everything, or very nearly so, in my view."
The more I consider this idea, the more it resonates - an idea or a concept by itself, as singular, is not intelligible, like the first note ever sung: it is only when it is paired with its analogous counterpart, the following note or a gesture or the environmental context of the voice, that the sung note becomes born. Our minds are analogy-making machines, not just for the convenience of explaining ideas through metaphor, but literally as the mechanics of cognition. This relates to that, this mirrors that, this idea exists only in relation to that - it is the analogous connections, the relationships between thoughts, that bring them to representation.
Again, consider the practical implications of this in adult learning - anybody who has ever facilitated a workshop knows that the sage advice is to tell a story in order to elucidate a concept, to give an example: and, what is a story / example but an analogy for the core idea you want people to understand, the vehicle that drives you to your destination (so says the analogy).
We might extend these principles into rich, dynamic fields, of the sort that Bret Victor and Dynamicland are doing - consider a workshop session on Double Empathy in which the communicative experiences of neurodivergent folks are explored not through a table of data on a slide, but rather than the physical mapping of communication trajectories across the physical space of the workshop: one journey starts at point A, another at point B, through towns labelled with social intentions, river systems marked by points of connection and overlap, as participants guide two conversations across the topography of the map towards each other, to understand Double Empathy not just in a visual manner, in a literate manner, but to inhabit it, to move alongside one's thoughts, as analogies guiding each other to new learnings.
This might seem like a long and complicated way of saying that adult learning principles should not be reliant upon didactic lecture stylings, but my point is more nuanced than this - it is about the variety of methods used to really connect with how learning occurs, of the population of thoughts and practices that lead to new versions of ourselves that we can bring into our classrooms and society. This is the subtle nudge of a topology of ideas beyond visuals.