Alan Davies discovers that answering that question is much harder than he originally thought after visiting mathematician Marcus du Sautoy to help him find an answer. However, this creates more questions, which requires a trip to a place dedicated to measurement, the National Physics Laboratory.
Finding out the exact length of the string proves even more troublesome when Marcus proposes the string could be infinitely long, thanks to the theory of fractals. After leaving Marcus, Alan visits a physics teacher to see if measuring the string in atoms can help him find an answer. However, this means exploring Quantum Mechanics.
Alan goes to a lab to explore the theory of Quantum Mechanics in more detail to see if his string can be in two places at once, confusing him even further. Still no closer to an answer Alan is introduced to the theory that his string may have multiples lengths at the same time, all with the help of a stuffed cat. Alan doesn't believe Quantum Mechanics is important on a basic scale, but photosynthesis and the ability to smell might just change his mind.
If Alan was to find the most accurate way of measuring his string he could theoretically create a black hole. Trying to find the solution to this question has been a philosophical journey for Alan, but he still visits Marcus du Sautoy to tell him his personal answer.