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On the risk of making it all tangible
From virtual reality to data visualization to memory palace there is a plethora of tools and techniques trying to leverage the efficiency of our visual system. The human brain is able to sense and process visual information very efficiently. As a society we are constantly pushing this exaption from basic daily life activities, e.g cycling while respecting road signs or transforming our spreadsheet data to charts, to the most important part of being in a society, e.g comparing election voting results to analyzing the efficiency of the most complex tools ever built like the extreme ultra violet lithography machines used to make processors used in the very device you are using right now.
It became so evident that we rarely step back to consider how visualization came to be, what is its actual usefulness but also as importantly its limits. In fact we are more and more trained from the youngest age to represent abstractions in a more tangible way. We learn to count on our fingers. We compount some numbers with other objects like a hand. This has been recognized for a while in pedagogical research as an efficient way to start. We also rely for a while on geometry and often plot mathematical functions in order to literally see them. Only later on do we use other techniques, like functional analysis, where mostly then only manipulate symbols, abstraction without visualization.
Here then comes the challenge : are visualizations always useful or can they become counter productive? The main idea here being that not everything can be visualized and yet still be interesting. The trendiest example at the moment being machine learning and its reliance on highly dimensional spaces. We can easily represent a dataset in 2D or in 3D, conceptualize somehow 4D using the animation of a hypercube, but in 10000 dimensions our ability to imagine breaks. Yet, plenty of innovations today come from machine learning so clearly it is useful. The pedagogical question then becomes : will people who rely heavily or even entirely on visualization struggle when they will have to work on abstractions or even conceptualize new ones?
This alone is an important question, intellectually but even pragmatically as the place of mathematics is so central in our lives, from the running of our infrastructures to the gadgets in our pockets to our ability to understand the World at any scale. What makes it arguably even more important is its potential impact on the emerging media that are virtual reality, augmented reality and really anything allowing us to leverage space. Beyond visualization extended reality or XR allows us to move in space. We are able not just to see objects, from text to data visualization to 3D objects, but also walk among them. This opens up new avenues for exaption where beyond just visualization we can rely on navigation. For examples one can consider the memory palace technique where one must remember a long list of items, e.g the chronogical list of all French presidents, by placing them in a familiar place like the rooms of their house. This has already been explored in XR yet now prompt the question : despite, or even due to, its efficiency, will navigation in XR hinder our ability to manipulate abstraction?