Over the past few days this image has been floating around on the internet.(It would seem that putting together complete sentences is also a struggle…)

While this meme is (or appears to be) rather innocent, worth a few laughs, it is also a blatant articulation of a troublesome attitude I have noticed amongst a variety of “Arts-Humanities” type people. This attitude roughly follows the subsequent progression:

- I am not good at and do not enjoy math.
- Because of this I want to spend as little time as possible doing anything mathematical.
- This is perfectly acceptable; I have no good use for math.
- Due to the fact that there is no good use for anything mathematical in my (very important) fields of interest/study it is probably a good thing that I am not good at math; in fact, it seems that math is responsible for a lot of bad things.
- Huzza for my poor mathematical skills! Now, where was that important book I was reading…

In essence, I have noticed that what may be a natural self mockery over a lack of math skills has turned into a celebration of this lack of ability. Put bluntly, this is problematic.

Like any other skill set, mathematics is not simply an innate ability; it is rather something that is learned and cultivated. It’s obvious that, again, as in all other skills, some come to math more easily than others, but that does not change the fact that math is something that is first and foremost learned. So, if you are one of those persons who “sucks at math,” you should recognize that this is primarily because of choices you have made; you have chosen not to pursue mathematics. Thus, whether explicitly or by implication, to go around proclaiming how much you “suck at math” is to declare that you do not find math stimulating or useful and are, at the very least, content with this state of affairs, with this chosen ignorance. In the process you minimize and ridicule the discipline of math. Now, I think that celebrating almost any kind of ignorance is unhealthy, and to ridicule a legitimate discipline simply because you don’t like it can’t really be described as anything other than an asshole move. But I have another worry, particularly when we minimize something as important and significant as math. There is no question (I hope) that we distort the world when we reduce it to the mathematical. However, it is equally foolish to deny that there are many different respects in which our world is deeply mathematical; math is inseparably a part of both the “natural” world and the world humans have created. I am convinced that we cannot do philosophy or theology well without paying attention to the world; whenever we are ignorant of different integral aspects of the world it is to our detriment as thinkers. To celebrate this is not just offensive to people who work with and love math; it should be insulting to everyone who values the discipline of rigorous thinking.

Some of you may think that I am reading too deeply into this meme. Isn’t it possible that it is a bit of self-deprecating humour and nothing more? Let’s change a few things around:

Every time I see poetry it looks like this: I have 10 ice cubes and you have 11 apples. How many pancakes will fit onto the roof? Purple because aliens don’t wear hats.

Every time people talk about politics, all I hear is this: If Harper has 10 ice cubes and another politician has 11 apples, how many pancakes will fit into congress? Answer: Purple because aliens don’t wear hats.

Every time somebody tries to tell me that nationalistic militarism is problematic all I hear is this: If foreign countries have 10 guns and you have 11 bombs, how many countries can we rip to shreds? Purple, because I’m an unpatriotic coward.

I could probably go on forever, but this should sufficiently demonstrate that this sort of humour amounts to a dismissal of whichever discipline it addresses and little more. This appears to be part of a wider trend (usually extending from math to the hard sciences and from there to other unimportant matters). It is no secret that the humanities are under attack – I know that I do not care to count the number of times I have defended the legitimacy of the humanities. Too often, however, our response has been to further close ourselves off from other disciplines, happily isolating ourselves in our small, stagnant worlds. But if the human sciences are truly to be the human sciences, then they must attend to the various and interwoven aspects of life.

I know three mathematicians. All have decided to engage broadly in other disciplines. My observation is that this has greatly enriched all aspects of their thinking, mathematical and otherwise. Further, while my own math skills are rather limited, my conversations with these mathematicians, often at the intersection of math and other disciplines, has been tremendously influential and beneficial for my own thinking; they have opened my eyes to new aspects of the world, providing me with more diverse fragments that my thinking can endlessly seek to rearrange.

If you want to make self-deprecating comments about your mathematical inabilities, fine; be aware, though, that even the least offensive of these jokes are growing rather tiresome. If this post has not inspired you to brush up on your math that too is fine; it is not possible to become fluent in every relevant discourse. It is time, however, for us to stop celebrating this ignorance, believing it to be irrelevant to the actually interesting work we intend to do. Our mathematical (and other) deficiencies should be acknowledged with regret, maybe even lament. Maybe then we will be open to new discourses and ideas and discover new interests and passions beyond our narrow worlds. That would certainly make things more interesting.

This reminds me of a post by Maddox from The Best Page In The Universe, an amusing(ly explicit) rant [EXPLICIT]: http://thebestpageintheuniverse.net/c.cgi?u=math

I actually read this post when Maddox first posted it. I had entirely forgotten about it, but now it’s rather obvious that it was informing this article through my subconscious. Thanks for the reminder; it’s always good to see how influential Maddox is for my thinking…I think…

This post reminded me of a conversation that I was having with a friend about the way in which we mix qualitative and quantitative distinctions. He is very disturbed by the fact that we distinguish between qualitative objects on quantitative grounds (there’s a name for this problem but I can’t remember it). So, the difference between a heap of sand and a non-heap-of-sand is based on the number of grains of sand present. It disturbs him because as soon as you translate the number-of-grains-present into qualitative categories it doesn’t make sense because you cannot have more or less heap-ness. You either have a heap or you don’t (it only changes in size, not in quality). So, what that means is that we’re working with two different understandings of truth – a binary is/is not kind, and a more/less kind. He doesn’t see how the two are commensurable.

This is a good illustration both of how it’s really difficult to bring the sciences and humanities together because the two operate according to rather different logics sometimes, but also of the fact that we do it every day without really thinking about it. Anyway, if you’ve come across this problem in discussing the interface between math and humanities I’d be interested to hear your thoughts.

I’m not sure if I am entirely clear on the problem or disjunction you’re identifying here. As I see it, qualitative and quantitative forms of reasoning can and should intersect quite naturally. Precisely how many grains of sand are present is not irrelevant to whether or not those grains constitute a heap. At the same time, it would be foolish to reduce the definition of a heap to precisely how many grains are present; at some point, its status as a heap is dependent on the person or persons naming it as such; there is a certain amount of arbitrariness when it comes to whether or not these grains are a heap that depends on their named quality; but, again, the number of grains remains very much relevant to the quality of the heap.

Perhaps another example is helpful. There are a number of clear and definable standards with which we can measure music. These measurable standards, such as the musical complexity of a chord progression, are extremely important when determining whether or not a song classifies as a good song. And yet, it would be wrong to reduce the quality of a song to these measurements. These seemingly contradictory logics are both operative and are what allow us to have intelligible and stimulating conversations about the quality of certain music on the one hand and valid disagreements that have no hope of resolution through musical analysis on the other (which is not to say that I believe all or even most disagreements about music to be valid).

Is this helpful?…I suspect that I have perhaps not quite understood the problem.

As far as math is concerned, most contemporary fields are not really interested is quantification; this has particularly been the case over the last 70 years or so (this co-emergence with post-modern philosophy is not a coincidence, and we should keep in mind that many early post-modern philosophers (Wittgenstein, Heidegger) were also mathematicians). Gödel’s incompleteness theorem demonstrates the impossibility of axiomitization; math proves the impossibility of counting perfectly. Early quantum mechanics came up with the uncertainty principle; it is math that takes the world out of our controlling grasp. Chaos theory shows a living world in which everything is always and irreducibly interacting; math demonstrates the inadequacy of cause and effect causality.

I think that the connections with the humanities are apparent here. When Newton begins his theories by postulating the existence of pure planes and ideal environments he imagines the human as an autonomous thinking self and imagines that objects exist most purely as themselves when isolated from their surroundings. This informs modern philosophy as I’m sure modern philosophy informed Newton’s experiments. Contemporary mathematics, meanwhile, places humanity into the world and considers objects (and numbers!) to be irreducible, at least in the form they take there, from their environment.

I’m SUPER late to this party (only now found your blog). While you’re interpretation of the incompleteness theorems (there are 2) isn’t wrong it implies a futility to aspects of math. All fields of mathematics rely on axiomatization, in fact you could describe math accurately thus, as systems of axioms. It’s interesting to note that the incompleteness theorems have relatively little applications. While it’s philosophically important, it has little bearing on actual mathematics (it finds itself most useful in computer science). Also, the “counting perfectly” thing doesn’t make any sense. Godel doesn’t really apply to counting or number sets.

But, what I think I really want to get at here is the “most contemporary fields” business. These esoteric fields make up a tiny fraction of contemporary mathematics. The vast majority of pure mathematicians (who are a much smaller group than applied mathematicians) work in topology, analysis or algebra, in that order. Logicians are pretty rare in math depts. Much of mathematics is done without thinking of Godel or even non-axiom of choice systems. Though, they make much better conversation topics than C* algebras or Lie groups.

In physics and chemistry, the uncertainty principal also does not serve to show futility of any kind of explanation or promote any kind of idea of “mystery.” Rather it prompted scientists to treat electrons and their orbits as probability spaces. The same is true of Chaos theory, it’s just a new way to interpret previously impossible problems.

Thanks for the comment Eric. I guess the main thing I should take from this comment is that I would do well to learn more (about) math.

Seeing as I can’t really speak to your claims, I will accept them as true; and I’m sure that they are.

However, two things:

1. I never intended to suggest a sort of futility; what I meant to suggest was excitement.

2. You say Chaos theory is “just a new way to interpret previously impossible problems.” I’d like to seize on the term “just”. I’m sure that Chaos theory is a new way to interpret previously impossible problems, but why limit its significance to such a narrow sphere? Does/can it not tell us anything about the world? If it is a new way of interpreting problems (showing irreducible interaction) does that not also (at least potentially) have broader consequences for looking at the world? Put another way, why abstract these problems that we now look at differently into some sort of pure realm that has no relation or function to “reality”?

*Rubs forehead twice*