Currently there is a great debate about the use of algorithms in various areas, such as internet security, surveillance systems or customer segmentation.

Frequently, the problem centers on how algorithms should be used, avoiding a deep analysis of the different realities that shape these models – and which, in turn, they influence.

In this sense, a fundamental question that is often not even asked is: in what way are different actors, including the mathematical community, involved in the ethical questions surrounding the use of algorithms?

Among the most controversial algorithms are those for facial recognition, capable of identifying human faces and their characteristics.

These models have been used for very different purposes, from authenticating users to identifying people involved in illegal activities. In addition, they are used in user control systems, in theory to prevent potentially dangerous situations. At least, these are the justifications we are given.

These algorithms are based on mathematical concepts and, in some of their simplest versions, can be described in accessible terms.

The model is trained using a database of photographs of faces, and its objective is to infer the probability that a new image corresponds to one of the existing ones.

This, mathematically, corresponds to the problem of, given any point, determining its proximity to another in a pre-fixed set –those in the database–, in a space of many dimensions.

The photos are translated into mathematics in terms of vectors. An image is made up of pixels, or dots of color. For black and white photos, each pixel is encoded by a number between 0 and 255 that describes its intensity of gray, where 0 means “black” and 255 means “white”.

If the photos in question contain 250 * 150 pixels, then each image is represented by a vector of 250 * 150 = 22,500 numbers between 0 and 255.

Thus, the space of all faces is reinterpreted as a 22,500-dimensional vector space, the handling of which involves a serious computational difficulty.

If the initial photo file consists of 200 photos, then there are 200 vectors – or, equivalently, points – in a 22,500-dimensional space. But they are not interested in the images themselves, but in the variation –called covariance– between them.

These changes can be described – with algebraic arguments – within a subspace of a much smaller dimension and, therefore, much more manageable.

Thus, it is possible to reduce the problem to projecting the starting database to this subspace and, when a new photo appears, consider its projection and calculate the smallest distance between this point and the previous ones.

This closest face will be the one that the algorithm will give as possible recognition of the new face.

Although the algorithm is understandable from a theoretical point of view, when it is confronted with the real situations in which it is applied, its enormous limitations appear.

For example, the precision of the algorithm depends on how accurately the initial database represents the totality of human facial features.

Recent research shows that even the most cutting-edge facial recognition software can misidentify black women up to 35% of the time, while it works almost perfectly for white men.

This has extremely dangerous consequences, such as the false accusation and arrest of so-called suspects, and can contribute to the already high rates of violence.

But it’s not just about possible algorithmic errors. In fact, the following fundamental question arises: if models could be improved to 100% accuracy, would then be their use and circulation ethical?

Our position is that, even in this hypothetical situation, the answer is not automatically “yes”, but rather it is conditional on the algorithms not being used to create – or aggravate – situations of abuse of power, which is what ends up happening in almost all occasions.

Due to its central role in the design and implementation of these models, the mathematical community as a whole must make a deep analysis on these ethical questions and on which sectors are favored by the use of the different algorithms and which, on the contrary, are they see violated.

Right now, those who are favored are the ones who produce the programs and the ones who have the money to buy them. They hold the power. The rest of us simply go along for the ride.

There is not a situation in which, we, the people, benefit from surveillance and the use of algorithms for continues spying on a population that is composed in its great majority by law abiding citizens, while the criminals, the ones who buy surveillance technology, own the power to follow us everywhere we go.

Simply put, there is no ethical reason to use surveillance technology.