What are spatial functions? I was reading Einstein's paper 'Concerning an Heuristic Point of View Toward
the Emission and Transformation of Light' and read came across this segment: 

"While we consider the state of a body to be completely determined by the positions and velocities of a very large, yet finite, number of atoms and electrons, we make use of continuous SPATIAL FUNCTIONS to describe the electromagnetic state of a given volume,and a finite number of parameters cannot be regarded as sufficient for the complete determination of such a
state."

What are they? And what does it mean in the context above?
The above context is described in the book "Einstein: His Life and Universe" by Walter Isaacson (Page 97).

By spatial continous functions he refers to electromagnetic fields of the wave theory of light. He also states that theories of particles (like kinetic theory of gases) involve velocities and positions of finite number of particles and a wave theory cannot give this information. 

Above text emphasize differences between wave-particle approaches.
The above context is described in the book "Einstein: His Life and Universe" by Walter Isaacson (Page 97).

By spatial continous functions he refers to electromagnetic fields of the wave theory of light. He also states that theories of particles (like kinetic theory of gases) involve velocities and positions of finite number of particles and a wave theory cannot give this information. 

Above text emphasize differences between wave-particle approaches.