Page 59 - Special Topic Session (STS) - Volume 3

STS515 Jim R. et al.
Those who view mathematical science not merely as a vast body of abstract
and immutable truths, whose intrinsic beauty, symmetry and logical
completeness... entitle them to a prominent place in the interest of all
profound and logical minds, but as possessing a yet deeper interest... this
science constitutes the language alone through which we can adequately
express the great facts of the natural world... will regard with especial interest
all that can tend to facilitate the translation of its principles into explicit
practical forms. Lovelace (1843, p2).

1. Lessons for young minds from histories
Let us visit Victorian England for some lessons for young minds – these
include lessons that go beyond sciences and technologies themselves. We
derive our lessons from the lives of Charles Babbage (CB) and Ada Augusta
King, Countess of Lovelace (AL) in the period 1833-1852. CB is often credited
as the designer of the first computer; AL as the first programmer. CB’s
Difference Engine was designed to create tables of numbers relevant to
astronomy, navigation and mathematics, and was based on calculating
successive terms in a given series using the method of differences which was
built into a mechanical system of cogs and levers. His even more brilliant
insight was the idea of a general purpose device with a store, a mill (CPU), a
printer, and operation cards (for the program and numeric input) that would
not need to be reset mechanically for each new table. Both the Difference
Engine and the Analytical Engine were to be driven by steam. CB received huge
amounts of state funding for the Difference Engine (more than the cost of
building 2 battleships (a measure of research funding no longer used in the
UK)). He realised that a successful Analytical Engine would do everything and
more than the Difference Machine was capable of, and so devoted his energies
to the Analytical Engine. A fully-functioning version of the Difference Engine
was never built. The development of the Analytical Engine was never properly
funded.
• Technologies change – and contemporary technologies can present
barriers to brilliant ideas
• Funding streams depend on delivering what you (more or less)
promised
If the state of technology was a limitation, what of the state of
mathematics? Hot topics of the day included early explorations of non-
Euclidean geometry (imagine that! – but why bother?), and imaginary numbers
(again – surely impossible?). William Frend was a university mathematician and
sometime tutor of AL who did not believe in negative numbers; he ridiculed
the idea of zero. Along with some other mathematicians, he rejected the idea
of using undefined symbols in algebra. Boolean algebra was first set out in
Boole’s (1854) The Laws of Thought – two years after the death of AL. By way

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