Suppose I have a rectangular brick of computer memory. My brick is very thin on one side and contains so much memory that it is just one bit away from being a black hole. According to the holographic limit, the amount of memory in the brick is given by the surface area.
Now lets say I have two of these memory bricks. I should now have twice as many bits. Suppose I stack one of these bricks on top of the other. When I stack my memory bricks along the fat side the surface area of the combined bricks is much less than twice the surface area of an individual brick. Therefore according to the holographic limit, the amount of memory in the stack must be less than twice the memory in an individual brick.
Why do half of my files disappear? What happened to the bits I thought I had?