Scalar field in the Langdale view

This is the view from the top of Black Fell. I've added numbers to show what the temperature in degrees Celsius might have been at the point shown. Temperature usually falls as you get higher. Temperature is a scalar quantity. It just has a size. It doesn't have a direction. This spreading out of the numbers across the landscape is called a SCALAR FIELD. There is this scalar number defined for any coordinate we can choose in the view. We could go on to calculate the temperature gradient at any given point - how many degrees Celsius the temperature changes per metre moved. But the gradient would be a VECTOR because it would depend on the direction in which you moved. We'd need to redraw the picture with arrows on to show this. The size of the arrow would represent the size of the gradient and thus we'd have made a VECTOR FIELD.