The Original Step Counters of Ancient Greece
Bematists in Ancient Greece
The ancient Greeks were known for their fascination with physical activity and exercise, and one of the professions that emerged from this culture was that of the Bematists or Bematistae, who were essentially ‘step counters’. These individuals were responsible for measuring the distance of various routes, such as roads and racecourses, by counting the number of steps it took to traverse them.
Bematists specialized in geometry and arithmetic. They were the first to use mathematical proofs and theorems to solve problems, and their work was instrumental in the development of mathematics.
The Bematists were experts in measuring distances and areas. Their job was to measure distances by counting steps or strides, which they used to determine the length of a journey, the distance between two locations, or the size of a plot of land.
The Bematists were highly skilled individuals who had to undergo extensive training in order to accurately count their steps. They would have to walk a predetermined distance over and over again until they had perfected their stride length. They would then use this stride length to count the number of steps taken to measure the distance between two points.
Bematists made significant contributions to the development of mathematics and its applications. Their work was instrumental in the development of modern mathematics, and their ideas and techniques are still used today.
Etymology
The word ‘Bematist’ comes from the Greek word “bēmatistaí” ‘step measurer’. From the Greek ‘bema’, which means ‘step’ or ‘pace’ and sometimes also translated as raised platform or ‘stepping’. This term was used to describe someone who counted their steps while walking.
The earliest known bematists were members of the Pythagorean school of thought, which was founded by the Greek philosopher Pythagoras in the sixth century BCE.
Pythagoras and his followers were interested in the study of geometry and the relationship between numbers and shapes. They believed that the universe was composed of numbers and shapes, and that mathematics could be used to understand the world.
Bematists were employed in ancient Greece to measure distances for a variety of purposes, including the construction of roads, the laying out of racecourses, and the marking of property boundaries.
Bematistae
In ancient Greece, bematists or Bematistae learned to measure their steps to calculate distances. They would often publish their calculations in books, which listed distances between well-known points as well as reports of empirical customs and natural findings.
The use of Bematists in ancient Greece dates back to the 5th century BC when they were employed by various individuals, including the government, to measure distances and land. The Greeks believed that the most accurate way to measure distances was to use a person’s stride length.
The stride length was calculated by dividing the distance travelled by the number of steps taken. This method of measurement was used in ancient times because there were no standard measures of distance or area, as we have today.
Bematists used a variety of methods to solve geometric and arithmetical problems. They relied heavily on the use of diagrams and geometric constructions. They also used a variety of different tools such as compasses, straight edges, and rulers.
Bematists accompanied Alexander the Great on his campaign in Asia. Their measurements of the distances travelled by Alexander’s army show a high degree of accuracy to the point that it had been suggested that they must have used an odometer, although there is no direct mention of such a device:
“The overall accuracy of the bematists’ measurements should be apparent. The minor discrepancies in distance can be adequately explained by slight changes in the tracks of roads during the last 2,300 years. The accuracy of the measurements implies that the bematists used a sophisticated mechanical device for measuring distances, undoubtedly an odometer such as described by Heron of Alexandria.” – Engels, 1978
Bematists were also responsible for the invention of several mathematical concepts and the introduction of the concept of zero from India and of negative numbers, and they were the first to use algebraic equations. They were also responsible for the development of trigonometry, which is the study of angles and their properties.
The Bematists played an important role in ancient Greek society, as they were responsible for ensuring that roads and racecourses were properly laid out and measured. This was crucial for the efficient movement of people and goods throughout the country.
The accurate measurement of racecourses was also important for sporting events, as it ensured that races were fair and that records could be properly recorded. In fact, the ancient Greeks were so obsessed with physical competition that they even measured the length of jumps in various sports, such as the long jump and the high jump.
The work of the Bematists also had significant cultural significance, as it helped to reinforce the idea of order and structure in ancient Greek society. The Greeks believed that a well-ordered society was essential for the proper functioning of government and the preservation of civilization.
Famous Step Counters
The most famous bematists were Thales of Miletus and his pupil, Anaximander. Thales is credited with introducing the concept of geometry to the Greeks and is considered to be the “Father of Geometry”. He was one the first few people to prove the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. Anaximander is credited with developing the theory of infinite space and time, and is considered to be the “Father of Astronomy”.
Another earliest known Bematists was a man named PolyKleitos, who lived in the 5th century BCE. He was responsible for measuring the distance of the famous racecourse in Olympia, which was used for the ancient Olympic Games. Polycleitus also wrote a treatise on the art of measuring distance through the counting of steps.
Another famous Bematist was a man named Herodotus, who lived in the 4th century BCE. He was commissioned by the Athenian government to measure the distance of a proposed road from Athens to Corinth. Herodotus used a device called a stadimeter, which was essentially a large ruler with markings that allowed him to count steps more quickly and accurately.
Eratosthenes, who lived in the 3rd century BC was known for his calculation of the circumference of the Earth, which he did by measuring the angle of the sun’s rays in two different locations and using geometry to calculate the distance between them. Eratosthenes was also a skilled Bematist, and he used his knowledge of distance measurement to create the first accurate
Pausanias, a Greek traveller and geographer who lived in the 2nd century AD and who travelled extensively around Greece, is known for his meticulous attention to detail and his ability to accurately measure distances.
He would often walk the same path several times to ensure that his measurements were correct. He also used landmarks, such as trees or rocks, to help him remember where he had been and to ensure that he did not double-count any steps.
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