In science, simple solutions favour over more complicated ones. If a model in physics also explains evolution and other topics in other fields then it favours over other theories because it will simplify science.
In the math course I’m working on, it is explained that symmetries organize people’s viewpoints. Psychological phenomena such as confirmation bias are like inertia. They stop people from changing their minds every day. However, when people are encountered by new perspectives, their viewpoints are challenged. That is similar to a sinusoidal wave. Different opinions push one’s viewpoint up and down but psychological phenomena try to pull it back to where it was. This is a wave.
The same is true about evolution. Every new mutation generates a wave. Nature will then be about interacting waves. The subject of the field of evolution will be to discover those basic symmetries that produce those waves.
So the language of waves is not exclusive to the theory of probability. This will be used in many different areas.
UPDATE 1:
last year I submitted an idea to Campbridge’s startup scheme. It was about a programming language. New AI tools have changed programming. In some years programmers won’t write codes line by line at all anymore. It was suggested this new approach required a new programming language.
Very briefly, the programming language is based on common building blocks. To write a code some of those blocks will be linked to produce some functionality. So AI tools will not write codes from scratch every time. They search through a long list of all available blocks and connect them.
The same idea can be used for the wave language. Some months ago I wrote something that there should be some universal format for arguments and any type of expressions. Imagine instead of verbs and nouns, etc. a language consists of objects (as described in OOP). Then since objects are built by common building blocks, different objects may share common building blocks. Those shared elements can interact with each other (augment or diminish one another). However, each object is restricted by a symmetry which limits the amplitude of deviation from the equilibrium state (i.e. the state of no interaction).
Then probability expressions can also be expressed similarly by block-based wave languages.