The Origins of Selling Bread "in Dozens" in Medieval Times

The Practicality of 12 and 60 in Medieval Mathematics

In medieval times, the practice of selling bread "in dozens" may seem peculiar to us today, but it was rooted in the practicality of numbers in mathematics during that era. The use of 12 and 60 as preferred numbers in various calculations made them particularly desirable. Let's delve into the reasons behind this intriguing phenomenon.

During the medieval period, all mathematical calculations were done mentally or with pen and paper at most. In this context, the numbers 12 and 60 held significant advantages. The number 12, for instance, has four non-trivial divisors, meaning it can be evenly divided by halves, thirds, quarters, or sixths. In comparison, the number 10 only has two non-trivial divisors, limiting its flexibility in division. This made 12 an ideal number for bakers who needed to divide their loaves into various portions without resorting to complicated fractions.

Similarly, the number 60 was widely used for measuring angles, time, and latitude/longitude. It had ten non-trivial divisors, making it a valuable tool for medieval architects and mathematicians who relied heavily on pen and paper calculations. The ease of dividing 60 into multiple equal parts made it a godsend for these professionals, simplifying their mathematical processes.

The Convenience of 12 in Everyday Life

The convenience of the number 12 extended beyond the realm of mathematics. It found its way into various aspects of everyday life, including the measurement system and household items. For example, the imperial measurement system incorporates 12 in many of its units, such as hours and minutes. The division of time into 12 hours and 60 minutes can be traced back to the practicality of these numbers in dividing and measuring.

Moreover, when considering the size of a bread tray that would go into an oven, a 5x2 configuration would result in a long and thin loaf, while a 3x4 configuration would yield a more natural and desirable shape. The convenience of using 12 as a basis for measurements and quant***** led to its inadvertent adoption in various aspects of life, including baking trays and other household items.

The Addition of the 13th Loaf

The inclusion of the 13th loaf in a baker's dozen has an interesting historical background. Laws were passed to ensure that bakers sold the correct number and size of loaves in a dozen. To avoid fines and penalties, bakers began including an extra loaf for free. This practice ensured that even if a loaf was dropped, lost, or miscounted, the customer would still receive the intended quantity. The addition of the 13th loaf became a protective measure for bakers, guaranteeing their compliance with the law.

Counting Beyond Ten

While counting in sets of ten is the norm today, it is important to note that it was not the only method of counting in medieval times. The number 12 offered more ways of being split evenly compared to 10. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 10 are 1, 2, 5, and 10. Additionally, counting on one hand by using the knuckles of each finger with the thumb allowed for easy counting up to 12. This method was so prevalent that special words for "eleven" and "twelve" were used before entering into the "-teens."

The practice of selling bread "in dozens" during medieval times can be attributed to the practicality and convenience of numbers like 12 and 60 in various mathematical calculations. These numbers offered greater divisibility and ease of measurement, making them ideal for bakers and other professionals of the time. Additionally, the inclusion of the 13th loaf in a baker's dozen was a protective measure to avoid fines and ensure compliance with the law. The adoption of 12 as a basis for measurements and quant***** extended beyond bread, finding its way into various aspects of everyday life.