Pedagogics of Mathematics according to V. Bush

Digital Humanities debates have been enthusiastically -- and for a good reason -- addressing the technologically enhanced research and education situations. Such debates have been asking the question 'what happens when we are able to rethink (I am tempted to say "deterritorialize") our institutional and personal habits when it comes down to processing knowledge'. As such, this is not very new. The long histories of optical technologies as part of the academic and teaching processes are known, and similarly we should look at more recent histories of computing in this light. Indeed, what is curiously often missing is an acknowledgement of cybernetics as a mode of thinking across the disciplinary boundaries. Naturally not without its problems whether pinpointed in terms of the ethics of research (the certain control-based mode of understanding knowledge/systems) or institutional affiliations (military ties for instance), cybernetics however was able to build such islands of crosstalk between disciplines that are now being hailed as new with computational methods in humanities. Other people are pretty much on the ball on this one when it comes down to elaborating the debates - see for instance Ian Bogost's recent writings - and I have been more interested in thinking what is left on the outskirts of the debates; for instance media theory, or more specifically media archaeological approaches.

Whether media archaeology is part of "Digital Humanities" is another question; but at least it can provide further insights into ways of thinking computationally. A good example is the work of Vannevar Bush - well known especially for his Memex-device which surely features in some Digital Humanities self-reflections - and his differential analyzer. Besides being a tool for solving, well, differential calculations obviously, it ties interestingly as part of histories of not only computation but also data visualisation. Bush was occupied with the "integraph" calculating instrument already in the 1920s, for integrating functions, where the method of drawing graphical curves was an essential part of the process (of course, dealing with analog computing). (See Mindell's Between Human and Machine, p.153-154).

Already Mindell flags the idea that we are dealing here, very concretely, with a graphical user interface, but also the wider interest Bush had in graphical notation. For Bush, such modes of calculation+graphics was a way to think in terms of diagrams, and learn mathematics through the mechanical aid. As such, for Bush it was part of a wider pedagogic way of thinking: mathematics could be taught in such machinic assemblages. Such realizations from the 1930s and 1940s serve as good reminders of the various early ideas in terms of methodologies for enhanced learning - and environments of technical learning. We need to keep both eyes open - one for the technical side, the other for the graphic/aesthetic side that often becomes more understandable through methodologies known from visual culture studies -- but also media archaeology.

In other ways too, Mindell's book mentioned above is a great source. It shows the work of pre-cybernetics as a significant platform for signal based technical media cultures. Furthermore, it is able to introduce many forgotten ideas and contexts. One such fascinating one that contributes to a further visual media+computation-link is Gordon Brown's 1938 dissertation on the "cinema integraph" that continued the work in combining graphical methods with mathematics of integration. Again, part of the histories of analog computing, but something that in a fascinating way highlights the reliance on other media materials of its time. In short, Brown's innovation (suggested by N. Wiener) was to continue the work in using photocells for tracking and analyzing curves necessary for the calculation - but enhancing this with the transparency of the film material so as to be able to increase the speed of the operation: "Norbert Wiener, who advised the Bush laboratory on calculating machines suggested a way to speed up calculation by lightening the load, literally, on the mechanisms. Plot images of functions on film, Wiener suggested, shine light through the film and electronically integrate the light passing through it with a photocell." (Mindell, 2002, 164). This idea that never picked up really was however a good example of the various intermedial relations in those earlier cultures of innovation -- already completely "multi-media".