The question of size provides a clear example of the relevance of biology and mathematics to design thinking.
For a given shape of house or organism, there are physical limits to its possible size. This is because as the length of a structure increases, its surface area increases proportionally to the square of its length, and its volume proportionally to the cube of the length (although Gordon (1978, p.311) suggests that, for animals, the critical Griffith crack length is more significant).
For insects respiring through their body surfaces, this rule means that beyond the sizes to which they have evolved, the volume of body cells can no longer be served by surface respiration.
Gould (1980, p.171) relates it to mediaeval church architecture.
Bateson (1979, p.66) dramatically illustrates the problem in his "Tale of the Polyploid Horse". This poor creature, twice the size of a Clydesdale horse, had to push eight times the normal equine diet down an oesophagus only four times the normal calibre.
This issue can easily be seen to apply to buildings. Gifford (p.235) discusses the immensity of New York's World Trade Centre, which he says would be uninhabitable and unworkable without electricity for heating and cooling. It also applies to Cloud Structures Analysis.
In Critical Path, p.233, Fuller mentions a maritime application of the principle:
"Inasmuch as the cost of driving progressively bigger ships through the water at a given speed increases in direct proportion to the increase in friction of the wetted surface, the eightfolding of payload volume gained with each fourfolding of wetted surface means twice as much profit for the same effort each time the ship's length is doubled."
Fuller considers size as a function of frequency in Synergetics 528.00.
The principle can be applied to Spaceship Earth itself: see Gould's "Planetary Sizes and Surfaces" (1980, p.192).
© Paul Taylor 2001