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An Edwardian Banjo barometer. Note the use of vague expressions such as "much rain" and "very dry" alongside exact numbers. The vague words on the barometer have become particularly useful for us now that barometric pressure is no longer expressed in inches of mercury, but in millibars. (31 inches equates to approximately 1050 millibars, for instance.) See Chapter 11 of the book.

"When does modernity start?" (seen on a shop window in Florence, Italy) In a similar vein, one could ask what makes a warm day, a mountain, or an old man. Words of this kind have in common that they allow borderline cases, where it's unclear whether they apply or not: a day when it's somewhere between mild and warm, a large hill, or a man of 63 years old. The existence of borderline cases is usually seen as the defining property of vagueness.

A striking illustration of the context-dependence of vague words: 14 years counts as "very old" for the deer in this picture, for example. No doubt, a 14-year old human would have been described rather differently.

This balance, by John Drew of Glasgow, was used for the weighing experiment described in Chapter 7. It never registers the weight difference between 10 and 35 grains of rice, nor the difference between 35 and 60 grains, but it always registers the difference between 10 and 60 grains, showing that "can't tell the difference" is no transitive relation.

Coffee outlets can be inventive describing the size of different cups. (What counts as "regular" in one place can count as "small" in another and "large" in another.) This Edinburgh cafee distinguished three sizes: "little wicked", "wicked" and "totally wicked". Who wouldn't fall for the totally wicked size?

A picture of two differently sized heaps: a collection of just tree stones (the minimal size of a heap?), with Britain's highest mountain, Ben Nevis, in the background. Historically, the concept of a (stone)heap appears to have been the first to trigger a sorites paradox (discussed in Chapters 7-9 of the book). See also the next picture.

This newspaper header illustrates the Tolerance Principle: half a pill cannot make the difference. The example shows how hazardous this principle is, which lies at the heart of the sorites paradox. (See also previous picture.)

Measurement is relevant to many everyday tasks, not least cooking. This Italian shop offers a tool for the measurement of bunches of spagetti, for one, two, three and four helpings. Although the tool can hardly be said to be precise, it suits its purpose just fine.

This picture shows the structure of the Parisian prototype metre bar, which was long used as the official definition of 'metre' until more accurate metrics became available, which made the concept of a metre less vague (though not totally precise). The profile on the bar, which was made of platinum-iridium, serves to minimise bending due to gravity. See Chapter 3 for details.

Given that people's height is a recurring source of examples in the book, I couldn't resist including this picture, which gives an idea of the range of heights seen in adult humans. Mr Xishun is said to be a record-breaking 7.9ft (2.36m) tall and Mr Pingping only 2.4ft (0.71m). Remarkably, both men are from Inner Mongolia. (Picture from AP.)

Ships offer an intriguing model of communication. The disk depicted here, salvaged from the wreck of an Icelandic trawler off the coast of Scotland, was connected with a second, identically shaped one, which moved in tandem with it (fixed to the same iron rod that went through the middle of the disk). The first disk was operated by the captain of the ship, to issue an instruction to the engine room. The second disk was read off by someone in the engine room, who used its position to decide how hard to let the engine work, in forward or backward (astern) direction. The indications ''full', ''half'' and ''slow'' explain what it meant to turn the disk clockwise or anticlockwise; much the same effect would have been achieved if two arrows had been depicted, saying ''faster (astern)'' and ''faster (ahead)''. It can be argued that words like ''slow'', on these disks, are not vague at all, because all they do is differentiate between clockwise and anticlockwise. In the book, this phenomenon is called apparent vagueness.

Note the words ''attend voice pipe'', which must have indicated that the captain thought the situation tricky enough to merit communication by speech, shouted through a noisy pipe. One wonders what words passed through it on the fateful last day of the ship.

In the book, original sin is used as a metaphor for the way in which vagueness infects all measurement. This beautiful depiction of original sin (on display in the Accademia in Venice, alongside two other biblical paintings by the same painter) is by Tintoretto. Poor Adam doesn't stand a chance! If you peer in the background (on the right), you'll see Adam and Eve's inevitable fate: expulsion from paradise.