Machines Who Write

In 1936, Alan Turing remarked that "computing is normally done by writing certain symbols on paper."¹ Although computing was then the prerogative of human computers, Turing imagined that machines might calculate by writing as well. He defined computable numbers as those "whose decimal can be written down by a machine."² In exploring this definition, Turing constructed a thought-experimental mechanism that was "supplied with a 'tape' (the analogue of paper)" on which symbols could be written, scanned, and erased, including binary renditions of those computable numbers and other information that facilitated the calculation process. Turing intended for this notional machine to be analogous to human computers who calculated by writing and manipulating symbols, relying on paper to augment their memories and for sketching "rough notes" along the way.³ But to what extent is Turing's machine actually writing and reading like a human computer? Alternatively, to what extent does this writing machine introduce novel (albeit thought-experimental) practices and processes to the written work of mathematical calculation?

Recent scholarship in the history of mathematics has argued that mathematical thinking and practice are inextricably entwined with the historical development and "epistemic positivity" of different cultures and systems of writing.⁴ As such, if Turing's imaginary machine, or the physical machines later built in its image, are made to put different inscriptions to work differently than their human counterparts, part of their historical significance derives from being agents or sites of transformed mathematical writing. Indeed, historians have stressed the significance of writing and inscription in the making, circulation, stabilization, and destabilization of knowledge across cultural domains. One avenue for exploring the historical interventions of computing technology is therefore to ask how objects of knowledge are being written in and by computers; what novel data structures, digital inscriptions, and associated processes have been developed by computing communities in order to simulate, store, and study their domains of interest by computational means?

But why should historians of computing read digital data inscription and processing as writing rather than with some other conceptual frame? One reason is that computers (notional and physical) are everywhere said to be "writing" and "reading" when they store, manipulate, and processes information. Even if this vocabulary is or was intended metaphorically, it has nonetheless been generative of possibilities and tools for understanding, experiencing, explaining, and deploying what computers can do. Another reason, however, is that computers are often introduced to the work of knowledge production precisely where handwriting obtained before them. Knowledge-making practices that were once constituted by the inscription and manipulation of symbolic systems on the page are now routinely constituted by the computational processing of particularly configured bits. Especially where computers have been used to displace handwritten practices, historians should situate them in longer histories of writing. Handwritten practices informed and shaped different employments of computation, and computers displaced and transformed handwritten practices that preceded them. These histories should be studied in tandem.

Michael Mahoney proposed that communities of computer users strove to "put their portion of the world into the computer" by "translating their experience and understanding of the world into computational models" that could be made into working programs.⁵ If computers are treated as "machines who write," then the implementation of new computational models as working programs is, in part, an act of translation between representational media and inscription practices in which humans learn to write the world vicariously using materials they can't always see and written configurations they themselves might not be able to employ.⁶ Looking at computer writing as writing directs historical attention away from abstract formal representations of hardware and software and toward the materiality of data—how it is inscribed and configured within specific digital media.⁷

Rewriting Principia Mathematica into the Digital

Within a decade of Turing's article on computable numbers, actual physical machines were inscribing and manipulating the objects of mathematics in their various storage media in service of complex numerical calculations. By the early 1950s, computers were also being harnessed for participation in the work of proving mathematical theorems—a nonnumeric domain of mathematical research. In order to make theorem-proving programs feasible, programming...