--- a/Notes.md	Wed Jun 26 09:45:36 2024 +0200
+++ b/Notes.md	Sat Jun 29 17:04:32 2024 +0200
@@ -21,6 +21,21 @@
 sat(::DifferentialOperator, grid, stencil_set, bc) = ...
  ```
 
+
+### Update 2024-06-26
+We will run into trouble if we start assuming things about the coupling
+between the continuous and discrete setting. We could add representations of
+continuous operators but we will also need representations of discrete
+operators. Ideally it should be possible to ignore the continuous
+representations and only work with the discrete operators without losing
+functionality. The discrete representations does not have to be LazyTensors.
+The could be used as inputs to methods for `sat`, `difference_operator` and so
+on.
+
+To see need for a fully functional discrete layer we can consider the
+optimization of material parameters or something similar. In this case we do
+not necessarily want to handle continuous objects.
+
 ## Reading operators
 
 Jonatan's suggestion is to add methods to `Laplace`, `SecondDerivative` and