An algorithm is a method of calculation. The word “algorithm” was already in use in this sense in the early17thcentury, or more generally in the sense of the art of calculation. An algorithm has a purpose: for example, the multiplication algorithm we learn in elementary school is intended to… multiply two numbers.
An algorithm performs mechanical operations that do not require the intuition or intelligence of the person performing the calculation. Several algorithms can achieve the same goal, but they may require more or fewer operations and more or less memory space. Of course, in the absence of other factors to consider, we try to minimize the required computation time and memory space.
For example, there are much faster methods than the algorithm we learned in elementary school when multiplying numbers with many digits. This may seem surprising, given how familiar we are with that algorithm and how it doesn’t seem to involve any unnecessary work! The great Soviet mathematician Andrei Kolmogorov had conjectured in 1956 that no fundamentally faster multiplication algorithm existed, and was very surprised when, in 1960, a young student attending his seminar, Anatoly Karatsouba, proposed one to him. Karatsouba’s ideas opened up a fruitful line of research (the Toom–Cook algorithm, etc.), which in particular enabled the use of efficient cryptographic encryption, used daily today for accessing websites, banking transactions, and more.
The field of study that designs and analyzes algorithms is called algorithmics; it is a branch of computer science. A problem as seemingly simple as sorting data or searching for a specific piece of data in a table has inspired the writing of lengthy scholarly works!
How did the term “black box” come to be widely used?
How did we go from this scientific and precise meaning to the concept of a “black box” with unpredictable and poorly understood results? I see several factors at play.
The first is that computer science is relatively little known. Admittedly, we are no longer in the days when people were surprised that one could earn a Ph.D. in this discipline, but it is less widely recognized than, for example, history or physics. In fact, when certain computer science researchers are featured in the media, they are described as working “in computer science and mathematics,” perhaps because the word “computer scientist” conjures up other images (a technician installing hardware, a hacker in a hoodie sitting in the dark in front of a green screen where cryptic symbols scroll by…).
In 2021, an article in *Libération* stated: “Some researchers believe this is a mistake: by focusing too much on the effects of algorithms, we forget to study the algorithms themselves. It’s as if they were ‘black boxes’ that are impossible to open, virtually autonomous—as evidenced by the fact that there are still debates over how to define what an algorithm is.”
Thus, a major newspaper appears to deny the existence of a scientific field—computer science—that designs and analyzes rather precisely defined objects: algorithms…
The second factor is that a human does not interact with an algorithm, but with software—or even a system that is far more complex. When you search for directions in a GPS navigation app, it is certainly an algorithm for finding the shortest path in a graph that responds, but this algorithm is based on a cartographic model, which may be incorrect or inaccurate… The map is not the territory! Just as in physics, the devil is in the details of how we’ve modeled the world using mathematical quantities—the only ones suitable for an algorithmic process. Furthermore, the algorithm will attempt to optimize a certain quantity—which might be an estimate of time (assuming what driving style?) or an estimate of fuel consumption—based on parameters not necessarily within the user’s control.
Similarly, the ParcourSup system, which is used in France to manage admissions to higher education, consists not only of a few very simple algorithms for selecting candidates—which are directly derived from regulatory texts—but also of online applications with room for improvement in terms of usability, and of human ranking committees, each of which applies different criteria. The much-feared “algorithm” is thus a metonymy for this entire system, whose decisions are sometimes difficult to understand.
A "black box" can be partially analyzed
Furthermore, for most consumer software, the source code—that is, the description of how it works internally—is not public. It is therefore impossible, even for an expert in the field, to know exactly what these programs do—although it is often possible to make an educated guess: even a “black box” can be partially analyzed. It is therefore wise to be cautious!
Finally, one last factor: the widespread deployment in recent years of applications that utilize machine learning, a form of “artificial intelligence.” These types of approaches were developed to address problems that could not be effectively tackled using traditional algorithms, since traditional algorithms require modeling the world until a well-defined problem is obtained.
However, it is not easy to come up with, for example, a mathematical definition of how to distinguish a cat from a dog based on the pixel values in a photo of an animal. We therefore proceed by having the system “learn” the correct answers from databases, which in practical terms means that an algorithm adjusts parameters—sometimes billions of them—so that the system responds correctly not only to the examples provided but also to others, through a form of analogy.
The quality of such a system therefore depends on the database used for training—which may contain errors and coverage biases—as well as on the care designers have taken to identify various potential flaws. Above all, such a system produces results without explaining them—explainable artificial intelligence is a topic of research. We can therefore refer to it as a “black box,” even though we can understand certain aspects of it.
Confusion between algorithms, decision support, software, and artificial intelligence is rampant. For example, the MonMaster website—which helps students apply to master’s programs at French universities—is described as “algorithm-free, ” even though the simple act of displaying a sorted list of options or allowing users to search for a submitted application involves algorithms!
What can be done? In many public debates or television programs on computer science, the guests invited are almost exclusively advocates or critics of a particular technology. Yet governments—and France in particular—pay people whose job is precisely to analyze algorithms and their limitations: computer science researchers and faculty members. Perhaps we should invite them more often and listen to what they have to say?
