We now turn to a more concrete example of a mathematical experiment.
Our meta-goal in devising this experiment was to investigate
the similarities and differences between experiments in mathematics and in
the natural sciences, particularly in physics. We therefore resolved to
examine a conjecture which could be approached by collecting and investigating
a huge amount of data: the conjecture that every non-rational algebraic
number is normal in every base (see box). It is important to understand
that we did not aim to prove or disprove this conjecture; our aim was to
find evidence pointing in one or the other direction. We were hoping to gain
insight into the nature of the problem from an experimental perspective.
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