Age of Invention: To the Drawing Board

How mathematics transformed shipbuilding

Last week I described the ever wider application of geometry in sixteenth-century England to fields like agriculture, navigation, fortification, and ballistics. (If you missed it, you can read it here). One application that I did not mention, however, was shipbuilding. The key innovator was one Matthew Baker.

I’ve briefly mentioned Baker before, when I cited a list of English innovators of international renown from the 1590s. Baker “has not in any nation his equal”, boasted the writer of the list, “for his skill and surpassing grounded knowledge for the building of ships advantageable to all purpose”. In fact, even earlier, in 1581, another writer put him on par with two of the other greatest applied mathematicians in world history: what Vitruvius had done in the first century BCE for architecture, and what Albrecht Dürer had done for applying new rules of perspective to drawing and painting, Matthew Baker had apparently done for ships.

So what did Baker do, exactly?

Since about 1500, an Italian and Portuguese method of making ships had come into ever wider use in northern Europe. This was to construct the ship’s skeleton first, and then lay the planking around it. This contrasted with the older “clinker” method, by which the planks were laid from the keel upwards, with each plank slightly overlapping the one below - the rest of the skeleton was filled in later to strengthen it. The new “carvel” method, instead of having overlapping planks, allowed for a smooth hull. But it also required more planning.

The master shipwright had to first design full-sized templates, or frames, which were placed along the keel to determine the width and height of the hull, like cross-sections up and down the length of the ship. To the edges of these frames were then fixed ribbands - long, pliable boards running down the ship’s length. Altogether, the frames and ribbands formed a temporary, basket-like structure, to guide the moulding of the ship’s permanent hull around it.

But calculating the size of the frames at each point was tricky. After the placement of the first few, which might be pre-specified in size, the next ones along were typically determined according to the curve of the ribbands. Calculation was certainly involved, but it took place in the form or marking and adjusting the wood itself. Design and construction both took place in the shipyard, and through the medium of wood.

What Matthew Baker did in the 1570s was to take the design process out of the shipyard, and onto paper. He drew his ships, to scale. And by using pen and paper, with geometry to make such drawings possible, he opened up grand new possibilities for design. His process allowed him to jot down the latest innovations from the Mediterranean, to speculate about the designs of Noah’s ark and the ships of the ancient world, and to cheaply conduct his own experiments. He drew out new designs for frames, using geometry to work out how any variation would affect the overall shape of the hull, as well as its weight and carrying capacity - all at the cost of only time, ink, and paper, and avoiding the huge potential waste of conducting experiments at full scale in wood. His process allowed him to innovate more easily, and even to design new measuring instruments.

And it changed the nature of being a master shipwright. Baker could design a ship on paper, but leave it to a subordinate to make. All shipwrights had to acquire the tacit, hands-on skill of working with wood, but the master needed the additional mathematics. Baker’s pupils, in addition to future shipwrights, even included noblemen like Sir Robert Dudley, who would have considered the manual side of the profession beneath his station, but for whom the drawing and geometry would have been appropriate. By becoming more mathematical, the master shipwright thus rose in class. In fact, in a 1572 proposal for an academy for the children of the nobility, the shipwright’s art was deemed an essential subject, with a mathematician to be hired to teach it.

Baker’s application of geometry to shipbuilding also had the effect of interesting the more academic mathematicians. One of the leading mathematicians of the day, Thomas Harriot, soon applied his mind to improving ships, and even sent some of his notes to Baker. And Baker’s pupil, John Wells, would soon apply the latest labour-saving advances in calculation - the invention of logarithms - to the practice too. By the 1580s, new English ships were among the most technically advanced in Europe, and even in the mid-seventeenth century, ship plans were apparently still unknown in France. Having once lagged far behind, geometry began to give English shipbuilding the edge.

P.S. If you’re interested in reading more about Baker and sixteenth-century shipbuilding, one of my main sources for this was chapter 3 of the 1994 PhD thesis of Stephen Johnston, a curator at Oxford’s History of Science Museum.

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