Computation is like meaning or beauty; it is something that we may see in physical objects but it really isn't in the object; it is in the mind of the observer. When you see marks on a screen, those marks are meaningful only in virtue of conventions that certain marks are to be interpreted in a certain way. The mark "dog" doesn't refer to dogs in virtue of anything physical about the mark itself, but only in virtue of the fact that we have learned that it refers to dogs. Someone who doesn't read English would have no idea what the mark refers to, and no possible examination of the physical characteristics of the mark could reveal what it refers to.
Beauty is a bit different because it isn't entirely conventional. When you see a configuration of pixels on a screen that resolves visually into a picture of some beautiful scene, you don't consider the scene beautiful just because of convention. Convention (or, more properly, social conditioning) may play a part, but there is also an aspect of biological response, so that another human who sees the image can often know that you would see the image as beautiful without knowing what your social conditioning is, but an alien with no knowledge of human biology or psychology would not be able to tell that the image is considered beautiful, and no amount of physical examination could reveal that.
Computation is different yet again, in that it is constrained by logic in such a way that if you can infer what aspects of a physical process are intended to be computational, then you can make reasonable assumptions about what function is being computed. Someone who has never seen a calculator before might be able to figure out what it does by examining how it operates. However, that is because it is clear what the inputs and the outputs are. In the case of the rock rolling down the hill, it would not be at all clear what the inputs and outputs are, and without that information, no physical examination of the process could reveal what calculation is being performed.
Furthermore, even in the case of the calculator, what the inputs and the outputs are is a matter of convention much like meaning. The only reason anyone could figure it out is by inferring the intentions of the designer and assuming the designer would have designed the device following certain rules of design such as making it as simple as possible to perform the desired function, and that the desired function is rational. Without such assumptions--which depend entirely on the mind of the designer--no amount of physical examination could reveal what functions even a calculator computes.
Any reasonably complex physical system can be interpreted in many ways so that it computes a very large number of functions. All you have to do is assign various measurements to various inputs and outputs. For example, when the temperature of this tiny area is X, and the temperature of this tiny area is Y, then eventually the temperature of this tiny area becomes Z where Z is the average of X and Y.
So meaning, beauty, and computation are not properties of physical systems alone; they are properties that the mind imposes on physical systems.
Now, something similar can be said about any property of physical systems. Any measurable property of a physical system such as color, mass, velocity, temperature, etc. depends on our sensory capabilities and on conventions of units and measurement techniques. No amount of physical investigation of a physical object can tell you how many kilograms that object is unless you know the convention for kilograms. Measurements are like meaning, beauty, and computation in this sense.
However, the number of units is not the significant feature of the mass. What is significant is how the mass compares to the mass of other objects, and that is something that can be determined by any human or alien simply by examining the object psychically, with no knowledge of any human conventions. Such an examination can reveal how an object is going to interact in collisions with other objects, for example.
Therefore, physical properties like mass can enter into physical causality, because it is an encoding of an aspect of the physical world. But subjective properties like meaning, beauty, computation, and unit conventions cannot enter into physical causality because they are not aspects of the physical world itself, but aspects of a mind.