The cake slicing conundrum

In 1906 a gentleman scholar was confronted with a significant problem for his wife and himself – how to cut a round cake to serve two people at afternoon tea, and preserve the remainder for the next day in good condition.

The classic method is to cut it into wedges. However, the problem with removing wedges is that it is difficult (even with our high-tech cling wrap) to protect the remaining cut surface from dehydration.

Galton aged-75The gentleman who offered a solution to this conundrum was the Englishman Francis Galton (1822-1911). He is considered to be the father of modern statistical mathematics, and developed the mathematics of correlation and of the normal distribution.

But he did more than that: he founded psychometrics (the scientific measurement of mental action); developed the classification system for human fingerprinting that was used by forensic science; and was a pioneer in meteorology (creating the first ever weather map). He even applied scientific principles to the study of prayer, finding that there was no statistically significant difference in longevity between those who were prayed for and those who were not. He lived at the end of the age when it was possible to know something about nearly everything. He was knighted in 1909.

On top of all that, he liked his afternoon tea.

Galton was sufficiently excited by his practical solution to cake slicing that he wrote a letter explaining the method to the most prestigious scientific journal of his time (and of our time) – Nature. By 1906, Galton was a highly respected scientist and mathematician with over 300 scientific publications. Nature published his letter. Presumably the editor liked afternoon tea too. There’s a facsimile of it here. For perspective, Einstein had published his paper on special relativity a year earlier.

His method was to cut a slice out of the middle of the cake, then join the two cake-sections together to protect the cut surface from drying out. Each day, the cake is rotated 90 degrees and the process continues. He assumed that the cake only lasts 3 days and therefore only requires 3 steps, each taking out about a third of the cake. He also assumed the cake was iced, so only the cut edges needed protecting.

Cake Cutting Figure

Science is not just about Large Hadron Colliders and Higgs bosons you know…