Discovervented – the ultimate speculative fiction

piflagThis a belated American Pi Day post. I say ‘American Pi’ day not for an opportunity to make Don Mclean puns but because March 14 only looks pi-like if you do the month/date thing. Elsewhere it was 14/3, which could be 1.43 day or less-good-square-root-of-2 day (Feb 14 being better but Dec 14 being best). For the day/month people July 22 makes a better Pi day as it gives the classic rational approximation of 22/7.

I was asked where I stood on the issue of Pi being invented or discovered. I’m firmly in the discovervented camp.

The ‘discover’ camp tends towards Platonism – the idea that mathematics is not just real but really real. Indeed mathematics in Platonism is more real than reality, which is just a crappy shadow of truth, goodness and all things geometrical. Discovered feels right but if you follow the reasoning you end up having to swallow a very big metaphysical pill.

The ‘invented’ camp tends towards Formalism – the idea that mathematics is the logical outcomes of arbitrarily chosen rules. I’m much more inclined towards formalism but it can feel a bit arbitrary. After all we could make up all sorts of self-consistent logical schemes and prove empty theorems about them but we don’t. The ones we study in mathematics not only tend to be relevant ones but have had an uncanny knack of BECOMING relevant.

Aristotle pitched his tent just a little way away from Plato. From him mathematics was something embedded in the universe but maybe not as transcendental as Plato took it to be.
From Kant and modern notions of evolution and modern psychology and neuroscience we get an alternate notion of embedding – that mathematics is something kind of built into us and the way we make sense of the universe.

I’ll play pick and mix with all that. I do tend towards FICTIONALISM as a model of mathematical truth, which marries nicely with formalism. That is a mathematical truth like 2+3=5 is true in a similar sense as ‘Sherlock Holmes lived at 221b Baker Street’. Mathematics is a kind of fiction, a work of imagination but as any writer knows your imagination is constrained by your experience and by your contact with reality and by what makes sense and by what is self-consistent.

Mathematics is like that as well. We invent it to describe the world around us but in doing so we create a space which we explore within rules and then discover things. If we invent the abstract notion of a ‘circle’ based on our real world experiences of circles and a concept of ‘diameter’ and ‘circumference’ then we discover in our inventions a little pi, like an alchemic homunculus. Which is all well a good but then we find the same little fellow starting out at us in our other inventions and we begin to suspect Plato was right all along.

But if mathematics is fiction, what kind of fiction is it? Well in modern times we associate it with science but in the past it has played nicely with mystical and religious disciplines as well. Mathematics is like some strange kind of genre, a genre that can encompass imaginary realities, alternative sciences but also magic and fantastical worlds all within a broader notion of the weird and the speculative. Mathematics is the ultimate SF/F.



  1. Lurkertype

    Pi Day is so because it contains 3/14 1:59:26, the glorious Pi Second. And everyone eats pie in the middle of summer, but having an excuse to eat pie at the end of winter is swell. And also means you can get it into school lessons.

    Also, you foreigners don’t get to have Avogadro’s Day on 10/26. No guacaMOLE.

    Liked by 1 person

  2. greghullender

    I think it was Wittgenstein who said that mathematics was all that would survive of philosophy and science was all that would survive of theology. I can’t find it online (so maybe it’s not true), but you can definitely go a long way with the idea that math is philosophy refined to the point that at the end of the argument, everyone is in agreement.

    For example, consider the claim that (-1) x (-1) = +1. If everyone accepts the field axioms of real numbers, it’s easy to prove; it’s not something you take on faith. To wit:

    Everyone should agree that 1 – 1 = 0
    Which is the same as 1 + (-1) = 0
    And so we can multiply both sides by -1
    (-1) x 1 + (-1) x (-1) = 0
    -1 + (-1) x (-1) = 0
    And adding 1 to both sides gives
    (-1) x (-1) = 1



  3. Archbishop Laudanum

    Well, someone sure knows how to ask a good question! It would be more fun to discuss this in a Chevy by the levee where the conversation would never run dry.

    So many points of entry here (and in the comments). I think we can all stipulate the greatness of avocados so will leave that aside.

    I’m fascinated by numbers and epistemology. I am not sure I agree with Camestros that a writer’s imagination is constrained by one’s experience, contact with reality, what makes sense and by what is self-consistent. I do though, appreciate the possible insight into what may be ontologically important to him (and, to be fair, most of us who strive to operate rationally on a material plane of existence).

    Consistency is a close cousin of harmony which is akin to symmetry which has been the measure of beauty which the west has deemed to be truth and thus eternal and ultimately godlike. The opposite of consistency presumably then would be chaos which is a liminal space that is hard to occupy for long so we have to tame it, put rules on it and control it. Thus, the claim to consistency is a search for control in an uncontrollable world. (At this point, CF may step in to tell me that chaos actually operates according to rules. I sip whiskey and rye and await).

    In this context, I make recourse to the dangerous idea of zero (which is one of my all-time favourite class lectures and the source of much enthusiasm when I talk about it!). It’s not unlike the concept of sin. Not every culture needed it or wanted it. We have created a world that is highly-enumerated and so we can’t un-know what it is like to live that way, try as we might. Same with the concept of sin. Aztecs, Maya, Inca, for example, had no analogous concept of sin before Christians brought it over (along with other cultural binaries: God/Devil, saint/sinner, man/woman, body/soul, divine/human, beginning/end etc). Their view of history was cyclical; ours is teleological heading toward some kind of salvation – formerly religious, now perhaps technological. They didn’t care about salvation at all. I am at a point in my life where I find that oddly comforting.

    There are Amazonian cultures that do not have words for numbers larger than 10, presumably because they are not needed. The Mayans operated on base 20 (so, 0-19) and believed 0=1. Zero for them was both infinity and nothingness at the same time. In Mayan mathematical cosmology, 7 is the glyph for man, 13 is the glyph for woman. 7+13= 20 (which they understood to be coming back around to the 0 in the one of their many calendar circles so it is both start and end). Curiously, 13 x 20 is 260, which is the number of days for human gestation. They have many of these sorts of human and divine equations all playing out across a complex series of calendar circles used in different ways at different times. That could not be more interesting !!!!!!!!!!

    We heirs of the Egyptians and Greeks probably can’t hold those ideas in our heads simultaneously because we have not trained ourselves that way. Lapsed Pythagorean or not, we still don’t like irrationality. On the other hand, the idea of knowledge as something acquired through training is not itself unproblematic. Like our modern existence without numbers or sins, it’s probably impossible for any of us to imagine operating wordlessly (emoji-speak may undercut my point there, I concede).

    But if any writers could transcend their reality, it might be the Latin American magical realists whose ideas definitely went beyond their own lived experiences. Or did they? I’ve been to places in Latin America and had encounters there that would mos def count as magical realist. Who knows? And perhaps more importantly, why do we seek to KNOW rather than feel or flow or “sit with” or something else.

    Perhaps all this is indeed what Camestros meant by saying that mathematics is a form of fiction. Sherlock Holmes’ address simultaneously exists and does not exist. I think that he’s surely right that numbers are embedded in our storytelling. Biblical numerology is littered with 3s, 7s, 13s, 40s etc.

    I better stop. I am descending into high school philosophy poseur-ness. I just like talking about this kind of stuff. If anyone is looking for me, I’ll be down by the river with Lenin reading a book on Marx singing dirges in the dark. Oh wait, that is high school history poseur-ness. Let me try again. I’ll be dancin’ in the gym, kicking off my shoes and diggin’ those rhythm and blues. Much better.

    Coda: I just pulled a book off my shelf that has an appendix which uses logic and syllogisms to prove that Winston Churchill is a carrot. Most enjoyable.


  4. supplanter

    @Greg Hullender: The problem is that mathematics and science don’t remotely exhaust the interesting questions. So the chance that they consume philosophy and theology respectively seems minute, or smaller.


    • camestrosfelapton

      I find that philosophy and theology always take me back to the philosophy of mathematics and from there to the mechanics of mathematics. Maybe it is just that Plato infected Western thought with a Pythagorean memetic virus way back when…