Solution to Plato’s elements challenge

Analytical and Bioanalytical Chemistry, May 2012

Juris Meija

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Solution to Plato’s elements challenge

Juris Meija 0 ) Institute for National Measurement Standards, National Research Council Canada , 1200 Montreal Road, Ottawa , ON K1R 0R6, Canada - Of all the writings of Plato, arguably none has less engaged the attention of modern scholars than Timaeus. However, one interesting aspect of this dialogue to chemists is the way that Platos elements can be transformed by rearranging the primordial triangles, which might be regarded as an early quasi-molecular theory of matter. More importantly, in Timaeus, we find the first documented example of stoichiometric equations for the transformation of matter. Such transformations are subject to a constraint that the number of equilateral triangular faces involved remains constant. According to Plato, a particle of water (icosahedron) has 20 faces, a particle of air (octahedron) has 8, and a particle of fire (tetrahedron) has 4 faces. Thus, the stoichiometry for the transformation of water into fire and air (for example) is Table 1 Stoichiometries for the transformations of Platos elements as inferred from seven translations of Timaeus 56 d 1 Water ! 1 Fire 2 Air; because 1 20 0 1 4 + 2 8. Likewise, the stoichiometries for the remaining reactions discussed in Timaeus 56 d are as follows: 1 Air ! 2 Fire 1 8 2 2 Fire ! 1 Air 2 4 1 2:5 Air ! 1 Water 2:5 4; 8; The stoichiometries of the four equations stated above, as inferred from seven translations of Timaeus [19], are summarized in Table 1. It is clear that translations [2] and [4] err in regards to reaction 1, whereas translation [6] gives the incorrect stoichiometry for reaction 4. 1 Water1 Fire+2 Air 1 Water1 Fire, or 1 Water2 Air 1 Water1 Fire+2 Air 1 Water1 Fire, or 1 Water2 Air 1 Water1 Fire+2 Air 1 Water1 Fire+2 Air 1 Water1 Fire+2 Air 1 Air2 Fire 1 Air2 Fire 1 Air2 Fire 1 Air2 Fire 1 Air2 Fire 1 Air2 Fire 1 Air2 Fire 2 Fire1 Air 2 Fire1 Air 2 Fire1 Air 2 Fire1 Air 2 Fire1 Air 2 Fire1 Air 2 Fire1 Air 2.5 Air1 Water 2.5 Air1 Water 2.5 Air1 Water 2.5 Air1 Water 2.5 Air1 Water 2.5 Water1 Air 2.5 Air1 Water


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Juris Meija. Solution to Plato’s elements challenge, Analytical and Bioanalytical Chemistry, 2012, 635, DOI: 10.1007/s00216-012-5822-0