Are filtering algorithms Turing-complete?

Of course not, but still, the exact nature of our interaction with the algorithms that try to profile us and personalize the world according to those profiles deserves many intellectual probes (a la McLuhan) like this.
There is hardly a moment in our lives when we are absent from the unaverted gaze of algorithms that observe certain aspects of our behavior, collect data on us, and organize that data in our digital profiles. Our observed actions in turn affect the functionality and behavior of those very systems that observe us: as they learn about us they adjust the search results and news items we see, they hide and show friends and their activities, offer different bits of information, etc.
By our behavior we program these systems. Though we hardly feed information (or misinformation) into these systems consciously and strategically, still, we are able to affect the output of the system by changing the inputs.
We assume, that we are not able to adjust how the input is processed, that we have no influence over the program itself, the algorithm that produces the output. But that does not need to be true, and there is plenty of evidence that we are already part of a giant feedback loop, that adjusts the profiling and filtering algorithms by some success or fitness measure applied to the output, or to be more exact, to our satisfaction with the output algorithms produce.
We may have only an implicit understanding of the inputs we provide. We may have no information whatsoever on the workings of the profiling, filtering and recommendation algorithms that observe and serve us. We may never fully understand what logics lead to the search results and news feeds we consume every day, but our satisfaction with those output can certainly be measured, dissected, formalized, operationalized, because all of us have some hazy impression whether the figure that appears in the mirror of the personalized world is an appropriate representation of us or not.
Since that satisfaction with the algorithmic representation of the self and of the world is one of the factors that is being observed, and since the output of that observation is directly on the algorithm, rather than on the output of the algorithm, I believe that by strategically using this input channel, we are able to program the algorithms itself.
We may not know anything about that programming language, but it is certainly there, and we are using it every day.