Mathematical models and measurement | Tangente

Not all measurements can be made directly. For many of them, a model is an essential first step. This is typically the case with astronomical measurements. A mathematical model is then introduced.

Using a model introduces two sources of bias into the results of any indirect measurement. First, the chosen theoretical representation, even if provisionally validated, may involve some approximation. Second, every indirect measurement requires calculations based on earlier direct or indirect measurements, which are necessarily approximate. These calculations may magnify the error.

Eratosthenes' measurement -----------------------

A historical example shows the importance of modelling: the first measurement of the Earth's diameter, made by Eratosthenes in the 3^rd century BC. The story behind this achievement is well known. The scholar realised that at Syene, near the present-day Aswan Dam in Egypt, the Sun was exactly overhead at the summer solstice. He also observed that on the same date and at the same time in Alexandria, about 800 km away, a vertical stick cast a shadow.