Well, not really a racecar, but rather because the title sounds catchy, and more importantly because “Formula One” is often abbreviated F1 – but what we really want is F_1.
I was once again taking another stab at perusing Karen Barad’s famous, at least made vaguely so, or perhaps infamous, given all the juvenile parodies that were thrown up, in the programming world, paper known as “Posthumanist Performativity”, trying once more to get some more ideas regarding just what these concepts actually attain. I have also looked into other things lately such as starting to examine the concept of “feminist Technoscience”, which seems like it would be the precise field which deals with what a “feminist programming language” might address.
But let’s go back to the Barad paper. I want to say I still have not fully digested the paper – but I nonetheless note a particular item of interest, which is that in several places it is mentioned how that in usual western philosophy, the notion that in order for relations to exist there must be some sort of “relata” to be related, that “things” exist which enter into “relations”, and Barad seeks to challenge this notion.
The reason I find this intriguing is because of a very interesting object in abstract mathematics I have looked into a little before known as F_1 – the “field with one element”.
Why is this interesting? To explain this, we have to dive into some basic abstract mathematics. One should be familiar with the real and possibly complex number systems from grade school, at least. Even if you did not fare so well in grade school mathematics, although if you’re a programmer I hope you’ve got at least some decent understanding of mathematics since it’s very important to programming, you should know that at least the real numbers have two operations defined on them, addition and multiplication, and two “derived” operations of subtraction and division, where “derived” means that the latter can be defined in terms of the former – for example, subtraction “undoes” addition. This structure of real numbers satisfies a number of rules, such as the commutative law which says that for any real numbers a and b, a + b = b + a, and ab = ba. These rules for addition, subtraction, multiplication, and division, taken together, are the foundation for study of abstract mathematical objects called “fields”, themselves studied as part of the branch of mathematics known as abstract algebra along with similarly defined structures such as groups, rings, monoids, and more. These fields, and indeed, most mathematical objects in general, are defined as a set of things together with some relations defined on them – in this case functional relations of addition and multiplication – that satisfy certain rules or axioms. Sound familiar – like what Barad was challenging? Well, it gets serious. In this usual conception of abstract algebra, a field can have only at least two elements – which are traditionally called “0” and “1”. That is, a set with fewer elements than these is not a field. In particular, there can be no field with only a single element. You can try and take a singleton set and then define addition, subtraction, multiplication, and division in the only way possible which is that they can only take in for both inputs the sole relatum in the set and for output that same sole relatum. But the structure so defined lacks many of the properties of a field, even though in some statings of the axioms for a field it should qualify. Thus it is usually excluded, with, e.g. an axiom that “0 != 1”, and is instead considered to be at home in the classification of rings, not fields. Yet there are a number of areas in which it seems as though an object that would behave in all ways like a field, but with one element should exist. Yet it cannot be accommodated in this traditional relations/relata schema, and some suggest therefore that a different foundation for abstract algebra is required. It is as though it is a rebel, “queer”, perhaps, if we want to look at the feminist terminology, or an “anomaly that threatens the system”, using pop culture terminology from the “Matrix” movies. Yet it is a profound one, with deep connections running through to possibly providing an avenue to a proof of the Riemann Hypothesis, one of the most celebrated unsolved problems in mathematics to date and a problem which, if you can solve it, you can get a $1 million prize from the Clay Mathematics Institute.
So the question would be: could philosophies like Barad’s, were they to be actually taken up seriously and looked into by the mathematical community, potentially have light to shed on problems like this, and perhaps so much more? Areas of inquiry where criticism of exactly these kinds of philosophical assumptions has a long history would certainly seem like something that any researcher in this field should consider deeply. What could be the result of such interdisciplinary collaboration and crossover study? What does this say about the pernicious effects of the kind of sexist dogmatism that led hundreds of websites across the Internet including programming sites to lampoon and lambast Schlesinger’s ideas and other, similar ones, have not just on women’s interest in and contribution to mathematics and science, itself a terrible shame, but also on the cherished “progress” that scientists seem to seek through their research in more direct ways? Furthermore, what does mathematical investigations into these issues suggest insofar as new insights into the feminist philosophy side of things? What could a fruitful collaboration between the two sides bring in terms of understanding, for both sides, so that not only perhaps could mathematical progress be advanced but also that new and surprising things be revealed within feminist philosophy itself, potentially providing great new insights into how we could build better societies and cultures? We really should have some feminist mathematicians!
Furthermore, what could be said about academe culture – in particular, its often full of rivalries and antagonisms between different fields and different departments, where each likes to dismiss the other (e.g. in Physics, one of the fields that I am currently getting my degree in, the other being Computer Science, and other “hard science” fields, there seems to be much antagonism against philosophy, thinking it’s “not hard enough”, while then the philosophers attack the “hard scientists” as being too concerned with only the results and not any further implications – or at least that’s what I remember, so it could be inaccurate.), instead of trying to find some common ground and get past the hostilities and see we are all in this one great knowledge-making enterprise together that, were it to be united and brought to its full potential would probably send humanity to the stars – figuratively and literally.
I invite the discussion to begin in earnest. As usual – keep it civil in the comments. Juvenile parodies of feminism of the “C+=” style will NOT be tolerated. I am going to see if I can advertise this post on a few sites to get some interest.
PS. GO ARIELLE!!!!! You should NEVER give up on your dream of Feminist Programming Languages, and neither should anyone else who seeks to explore that idea further.