# Fields

Fields are an imaginary concept where, at every point in space (be it 2d, 3d, or any-d), there exists a value at that point. What this value represents is up to you, as fields are only imaginary abstractions! (yes, including electric fields too).

## Scalar Field

Assunme you have some object at a point in space, , and that object has a property you'd like to measure which varies depending on where you are. This scalar property is part of a scalar field, as every point on the plate has a temperature you can measure just the same. It's as if you placed an invisible number at every point in space. In this case, a function, exists, which maps the coordinates and to a scalar.Scalar fields are used for measuring simple, one-dimensional quantities such as temperature, pressure, sound pressure level, or color.

## Vector Field

What if what we are trying to measure has a little more dimension to it? Let's say for example, the air flow at a point near an airplane wing. This measurement will be a 3d vector, with components in the , , and directions. is our vector field, which maps the coordinates , and to a 3-vector.This means for every measurement point in 3d space, there exists a 3 dimensional value (a 3-vector). We give the our measurement function a vector and it returns a vector! This is a vector field. Vector fields are incredibly useful for measuring things like flow, electric fields, gravity, acceleration, or anything else where there is force, or directional information of some kind.