Wednesday, 7 October 2020

Jigsaw Puzzles

In 1766 the mapmaker John Spilsbury made an educational aid of a new kind: a map of Europe, mounted on wood and dissected by cutting around the borders of the kingdoms. Children would learn the countries' shapes and borders by reassembling the original map. Dissected pictures soon became—and still are—very popular as puzzles. For childrens' puzzles the dissected pieces usually correspond to identifiable components of the whole picture. For adults the dissection is arbitrary: the pieces are much smaller, usually linked by the familiar blob-and-socket device.

Solving jigsaw puzzles invites informal analogies to many intellectual tasks. The informality is itself an advantage, freeing an active mind to find fresh perspectives and understandings. Michael Polanyi [1] likened the distributed work of scientific research groups to solving a gigantic jigsaw puzzle. Each group works to assemble what they believe is one identifiable coherent part of the whole picture. As the work progresses, mismatches are recognised between the groupings and the emerging structure of the whole problem. Groups A and B are working on distinct but adjacent parts of the same house; group C proves to be working on two cars, not one; groups D and E discover that they are working on scattered subsets of the same windmill. Group F discovers that the recalcitrant pieces of foliage that won't fit into their tree are in fact fragments of a large garden hedge that merits a group to itself. The shape of the task evolves as it progresses.

Closer to home, jigsaw dissections can be compared to software engineering structures. Requirements intended to describe system behaviour are often defined as stimulus-response pairs: "If Set Ratio mode is not selected, Set Ratio mode shall be selected if the Control Panel SR switch is pressed." If this is a piece of the puzzle, how many pieces would make the whole picture? Is the whole picture provided, or will it appear only when all the pieces are assembled? Where are the blobs and sockets connecting each piece to its neighbours? How might this piece's picture fragment continue on a neighbouring piece? Are these the only pieces, or are there pieces of other kinds that provide a matrix and a frame? Can the stimulus-response pairs be grouped into larger more meaningful structures—like Spilsbury's kingdoms? What would such structures correspond to in reality?

One of Spilsbury's jigsaws, with its ornamented title "Europe divided into its Kingdoms", can be seen at the British Library [2] in London. Inevitably—in a non-formal reality—the structuring in kingdoms is not perfectly simple. The physical boundaries of most kingdoms are too irregular to be precisely represented; parts of the kingdom of Spain are tiny islands, embedded in the Mediterranean sea and too small to form separate pieces; Sardinia (a disconnected part of Italy) and Corsica (a disconnected part of Spain) are combined into a single piece. As a cartographer, Spilsbury could identify these anomalies and deal firmly with them: he had the whole map in front of him as he made his dissection. At a requirements engineering workshop a senior consultant from a car manufacturer proudly announced that his company's leading product line had 200,000 stimulus-response requirements. Were they dissected from the complete picture? Or were the developers hoping to infer the whole picture from these 200,000 pieces? The consultant didn't tell us.

[1] Michael Polanyi; The Republic of Science; in M. Grene ed, Knowing and Being, pp50-1, U Chicago 1969.

[2] [https://www.bl.uk/learning/timeline/large104695.html] accessed 7th October 2020.

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