Category Archives: epistemolgy

The question of how mathematics could lay the foundation for a machine that sustains such a wide variety of practices is really quite well understood from the point of view of the mathematical theory of computation. From a humanities standpoint however, despite the number of texts commenting on the genius of key figures such as Gödel, Turing, Shannon, and Church, there is still a certain awkwardness when it comes to situating the key steps in mathematical reasoning that lead up to the birth of the computer in the larger context of mathematics itself. One of the questions I find really quite interesting is the role of the formalist stance in mathematics.

In the philosophy of mathematics, there are many different positions. The realist stance for example holds that mathematical objects exist. For the platonist, they exist in some kind of extra spatio-temporal realm of ideas. For the physicalist, they are intrinsically connected to material existence, even if that relationship is not necessarily simple. Then there is formalism and this is where things get interesting. In a tale we can read in many social sciences and humanities books on the computer, there is the young Kurt Gödel that smashes the coherent world of the “establishment” mathematician David Hilbert, inventing the metamathematical tools that will later prove essential for the practical realization of computing machinery in the process. What is most often overlooked in that story is that Hilbert’s formalist position is already an extremely important step in the preparation for what is to come. For Hilbert, the question of the ontological status of mathematical objects is already a no-go – truth is no longer defined via any kind of correspondence to an external system but as a function of the internal coherence of the symbolic system. As Bettina Heintz says, Hilbert’s work rendered mathematical concepts “self-sufficient” (autark) by liberating them from any kind of external benchmark and opening a purely mechanical world where symbolic machinery can be built at will, like in a game.

If we want to think about computing today, I think we should remember this break from an ontological concept of truth to a purely formalistic one (even if that mean Gödel put a pretty big crack in it lateron). Because in a way, programming is like a “game” with formulas and if the algorithm works, that means it is “true”. In this sense, Google’s PageRank algorithm is true. But without the reference to an external system, this “truth” is purely mechanical, internal. In a similar way, an algorithm’s claim to objectivity, impartiality, or neutrality should be seen as internal only. The moment we apply mathematics to the description of some external mechanism (gravity, for example), there is a second truth criterion that intervenes, which refers to the establishment of correspondence between the formal system and the external reality. In the same way, if an algorithm is applied to, let’s say the filtering of information, the formal world of the game is mapped onto another world. There is an important difference however. When mathematics are applied to physical phenomena, the gesture is descriptive and epistemological (verb: is). When an algorithms is applied to tasks such as information filtering, the gesture is prescriptive and political (verb: ought).

The fact than an automatic procedure works makes it true in a formal sense. The moment we apply it to a certain task, other criteria intervene. Hilbert’s formalism pulled mathematics from the empirical world and if we bring the two together again by writing software, the criteria by which we judge the quality of that action should be seen as political because there are no mathematical criteria to judge the mapping of on world onto the other. No Hilbert to hold our hand…




























When sites that involve any kind of ranking change their algorithm, there’ll probably be a spectacle worth watching. When Google made some changes to their search algorithms in 2005, the company was sued by (a search engine for kids, talk about irony) who went from PageRank riches to rags and lost 70% of their traffic in a day (the case was dismissed in 2007). When Digg finally gave in to a lot of criticism about organized front page hijacking and changed the way story promotion works to include a measure of “diversity”, the regulars were vocally hurt and unhappy. What I find fascinating about the latter case was the technical problem-solving approach that implied the programming of nothing less that diversity. It’s not that hard to understand how such a thing works (think “anti-recommendation system” or “un-collaborative filtering”), but still, one has to sit back and appreciate the idea. We are talking about social engineering done by software engineers. Social problem = design problem.

The very real-world effects of algorithms are quite baffling and since I started to read this book, I truly appreciate the ingenuity and complex simplicity that cannot be reduced to a pure “this is what I want to achieve and so I do it” narrative. There is a delta between the “want” and the “can” and the final system will be the result of a complex negotiation that will have changed both sides of the story in the end. Programming diversity means to give the elusive concept of diversity an analytical core, to formalize it and to turn it into a machine. The “politics” of a ranking algorithm is not only about the values and the project (make story promotion more diverse) but also a matter – to put it bluntly – of the state of knowledge in computer science. This means, in my opinion, that the politics of systems must be discussed in the larger context of an examination of computer science / engineering / design as in itself an already oriented project, based on yet another layer of “want” and “can”.

Thanks to Joris for pointing out that my blog was hacked. Damn you spammers.







  2. Read more Actor-Network Theory.









I have admired the work of Geoffrey Bowker and Susan Leigh Star for quite a while, especially their co-authored book Sorting Things Out is a major step towards understanding how systems of classification structure fields of perception and, consequently, action. The study of advanced technology is intrinsically related to information handling (in the largest sense, ranging from human cognition to information science): building categories, models, languages, and metaphors is a major part of designing information systems and with the ongoing infiltration of society by IT, the process of formalization (i.e. the construction of analytical categories that translate our messy world into manageable symbolic representations) has become a major difficulty in many software projects that concern human work settings. Ontology is ontology indeed but very often “reality as phenomenon” does resist being turned into “reality as model” – our social world is too complex and incoherent to fit into tidy data models. The incongruity between the two explains why there are so many competing classifications, models, and theories in the humanities and social sciences: no single explanation can claim to adequately cover even a small section of the cultural world. Our research is necessarily cumulative and tentative.

The categories and models used to build information systems are only propositions too, but they are certainly not (only) descriptive in nature. There is peculiar performativity to information structures that are part of software because they do not only affect people on the level of “ideas have impacts”. A scientific theory has to be understood, at least in part, in order to make a difference. When PageRank, which is basically a theory on the production of relevancy, became an implemented algorithm, there was no need for people to understand how it worked in order for it to become effective. Information technology relies on the reliable but brainless causality of the natural world to in-form the cultural world.

Why am I writing about this? The University of Vienna (my first alma mater) is organizing a workshop [german] on search engines before Google. And “before” should be read as “before digital technology” (think “library catalogue”). This is a very good idea because instead of obsessing about the “effects” that IT might have (or not) on “society” I believe we should take a step back and look at the categories, models, and theories that our information technologies are based on. And as a first step that means going back in time and researching the intellectual genealogy that is behind these nasty algorithms. The abstract I sent in (four days late, shame on me) proposes to look at early developments in bibliometrics that lead to the development of impact analysis, which is the main inspiration for PageRank.

The proposal is part of this project on mathematics and the humanities that I’m fantasizing about, but that’s a story for another day.