When we code, we code in numbers - doubles, floats and ints. Those numbers always represent real world quantities. For example, the number of people in a room can be represented as an integer, as can the number of chairs.
Dimensional analysis ensures adding or dividing the quantities is meaningful. It can prevent costly mistakes like the Mars Climate Orbiter incident, where mixing units caused a crash on arrival at Mars.
Compile time dimensional analysis can catch errors before they occur, as shown with rocket physics simulations aiming to implement safety measures through dependent types.
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