Many mathematicians before Galileo had dealt with the
problem of statics – how forces are transmitted by structural members.
Galileo proposed a new science, the study of the strength of
materials, that considered how the size and shape of structural members
affects their ability to carry and transmit loads. He discovered that as
the length of a beam increases, its strength decreases, unless
you increase the thickness and breadth at an even greater rate. You
cannot, therefore, simply double or triple the dimensions of a beam, and
expect it to carry double or triple the load. This led Galileo to
recognize what we now call the scaling problem – there are limits to how
big nature can make a tree, or an animal, for beyond a certain limit, the
branches of the tree or the limbs of the animal, will break under their
own weight.
The illustration of a cantilever beam demonstrates Galileo’s
discovery that the breaking force on a beam increases as the square of its
length.
