Nonplussed! by Julian Havil

Author:Julian Havil
Language: eng
Format: epub
Publisher: Princeton University Press

Figure 8.5.

Figure 8.6. The cissoid.

In a letter to Huygens, de Sluze mischievously described the solid as

a drinking glass that had small weight, but that even the hardiest drinker could not empty

(levi opera deducitur mensura vasculi, pondere non magni, quod interim helluo nullus ebibat).

Torricelli’s Trumpet would satisfy the more moderate drinker, but the glass could never be wetted! Admittedly, this is fanciful for several important reasons, but the imagery is compelling. Where is the paradox? As ever, our senses have deceived us when we have brought about the confusion which arises when we try to bring to the real world something which cannot exist within it; infinitely long things cannot be brought into reality (Euclid’s parallels postulate reveals the danger in trying to do so) and wine is not infinitely thin.

Galileo’s own view echoes this:

[Paradoxes of the infinite arise] only when we attempt, with our finite minds, to discuss the infinite, assigning to it those properties which we give to the finite and limited.

But we should leave the last word to Hobbes, when he commented on the assertion that an infinite solid of finite volume exists:

To understand this for sense, it is not required that a man should be a geometrician or a logician, but that he should be mad.

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