David Vance

Numbers in history

One of the givens in all historical studies and, by extension, in the documentation of museum collections is vagueness. Some facts are known more exactly than others. Therefore, objects may be attributed to a person, a workshop, a local school or even a national school, and dated variously to the day, year, quarter century, reign or century. The ultimate goal of the study of history is to trace the growth and consequences of ideas and perceptions, or words to that effect, and, in any case, to see the big picture. But the big picture is a jigsaw with many pieces missing, others fragmentary. Thus a prime objective of museum scholarship is to place those objects we do have as accurately as possible in time and space, and hence in relation to one another and to historical persons, events and documents. A vaguely known fact, such as an imprecise date, is like a piece broken at the edge. To assemble the big picture, we have to place it as best we can in relation to the pieces that do fit together, which means deducing facts about one thing from what we know of others. This article focuses on the problem of doing so in a context of varying ignorance and precision, but only where numerical data are concerned. Attention is drawn to practices that unnecessarily hamper deduction, and an alternative technique is suggested. Logical deduction in our discipline tends to be simple: a mural cannot be older than the wall on which it is painted, nor much later than the death of its artist-even if finished by assistants. Logic is not the problem: the real source of trouble lies in finding the facts upon which to base a deduction. Regardless of whether information is stored manually or electronically, locating relevant facts depends upon two related elementary processes, sorting and searching. Both are tedious and time-consuming, the worse use of a scholar’s time and the best use of a computer’s. It is the present author’s thesis that a major part of the difficulty arises from conventions of notation. It is the way we write down numbers (and other facts) that makes research so slow and boring and actually prevents computers from being of much use-even at what they do best. Illustrative cases in this article use one category of numerical data: dates of origin, to an optimal precision of one year, stated in terms of the Gregorian Calendar, even for times and places where that calendar was not in use. The principle, however, is applicable to all numerical data where uniform precision is impossible and yet it is essential to sort and retrieve in meaningful ways. Customary notations for dates of origin include:

Of quantity and quality

A quarter century ago students of comparative literature and musicology seized upon the computer to advance the quantitative aspect of their studies. At the most rudimentary level this means investigating such properties as sentence length, the frequency and distribution of articles and prepositions, etc: the side of literature that has no apparent bearing on style, authorship or literary merit but which, it was suspected, might reveal hidden truths-if only the tabulation could be accomplished without pain or confusion. Far more sophisticated analyses of texts have evolved. It would be out of place to discuss them here but the interested reader is referred to the journal Computers and the Humanities (CHum), now in its twenty-first year of publication. Until recently scholars of the visual arts have been spared the rigors of statistics, for it has not, as a rule, been feasible to capture the necessary numbers of numbers. A short story of perhaps ten pages may consist of 50 000 or fewer characters (i.e. key strokes); and, once these have been transcribed to machine-readable bytes, all counting and calculation can be automated. Even major literary monuments do not tax the storage and processing capacity of readily available computer systems. In contrast, the digital representation of one picture requires from 500 000 to more than six million bytes, depending upon the precision of spatial and tonal discrimination or resolution. The sheer quantity of data has precluded the capture, storage, transmission and analysis of images. The bad or good news is that advancing technology has removed the obstacles or, if the reader prefers, breached the humanist’s defenses. A device called a stunner can capture an image in digital representation. The digital optical disk (not quite the same as the videodisc) has the capacity to store a library of images economically. Optical fibers, having more bandwidth than even a television channel, can transmit an image to any distance in reasonable time. Much analytical image processing is within the reach of today’s miniand supermicro computers, while a new class of machine called The Connection Machine (TM) is ideally suited to more esoteric image processing without the costs associated with very large systems. Finally, modern bit-mapped screens are able to display an image at nearly photographic resolution. Some can do so in color. A digitized image is, of course, nothing but a series of numbers. In this series one or three numbers correspond to each componentpititrre element orpixel of the image, three being needed for color. The entire image consists of a rectangular array of tiny pixels, usually between 250 and 1000 in each dimension. This is more than adequate for viewing and all foreseeable statistical analysis. The minimal representation of a pixel is a single bit indicating white or black. The maximal color resolution, to date, requires three 16-bit numbers per pixel, able to specify up to 65 356 intensity levels for each of three primary colors. Obviously this is far too many but most computers are happiest doing arithmetic with 16-bit numbers. Three-dimensional images of sculpture and other solids cannot be digitized directly