I recently finished my first set of classes toward a BS in data analytics. It’s not very useful advice now, I hope, but I wouldn’t necessarily recommend attempting this in the academic quarter containing the most critical election of your lifetime. That notwithstanding, this means I’ve spent the past several weeks immersed in discussions of deriving meaning from numbers.
As I was gearing up to start my term, a “debate” broke out on Twitter. I put the term in scare quotes, because what actually happened is that one group of offered reasoning and explanations and another group pointed to the first and had vapors about the end of Western civilization. The question at hand? “Does 2 + 2 = 4?” The answer some people found objectionable? “Sometimes. Not always.”
Surrounded as I’ve been this term with issues of data quality, making assumptions explicit, the limits of the most common statistical tests, and error terms, this “debate” has never been far from my mind. I saw an echo of it again today, and lo and behold, I finally have some time to write about it.
The boys who cry “Postmodernism!” without much understanding of the history of philosophy are all but background noise these days, so I mostly noted their existence once again and moved on. Funnily enough, though, this actually is a postmodernism question. This is all about deconstructing the meaning of the equation. Are we talking about some ideal of “2” and “4”, or are we communicating about something else, where “2” and “4” are abstractions of reality that may be more or less reflective of that reality?
Also, does anyone else laugh when someone claims that questioning the perfect, inherent two-ness of “2” will be the end of civilization as we know it?
No, what struck me about this particular debate was how wrong it is to claim that philosophy adds anything new to the practical math on this one. Engineering got there first.
Once upon a long time ago, when I was in high school, I took a bunch of physics. I enjoyed physics so much I majored in it when I went to college, and only when I was faced with the prospect of choosing a career in physics did I realize I didn’t want to work in physics. I just like doing math and logic puzzles. Mmm, word problems.
Anyway, one of the earliest things I remember from physics was learning about significant figures. Essentially, we were told that our calculators could produce a lot of digits after the decimal point, and most of them were garbage because our initial measurements weren’t that precise. This is, to put it lightly, not an unusual thing to be taught in the physical sciences.
Nor was it difficult to grasp. We measured things. We experienced doing estimation that was reasonable to our tools. We experimented and re-measured, and we saw how impossible it was to verify results more precise than our tools could measure directly.
If someone complaining about the postmodernism of 2 + 2 = 5 or 3 has taken a lab class that involved basic physical science, they have also done this. They know. Beyond that, they’ve almost certainly also experienced measuring 2 + 2 = 5 or 3 directly. We call those “rounding errors”, even though the problem isn’t in the rounding, which was executed correctly, but in the assumption that 2 + 2 = 4 is a universal truth.
If you’re having trouble visualizing this, picture a ruler where the smallest increment marked is centimeters. You measure one block and see the length falls closer to 2 centimeters than 3. If we had millimeters marked off, we would put the length at 2.3, but without that, we’d just be guessing. We note a length of 2. We do the same with another block of the same length.
Then we put them together and measure again. We note, entirely accurately, that the combined length is closer to 5 than 4. We note a length of 5. We’ve done everything correctly.
If you find yourself saying, “Oh, but the real length is 4.6!”, is it? If we were measuring in millimeters, we might be reading 2.33 as 2.3. Then the “real” length is 4.7 cm. Or 4.6667 cm, depending on where we hit the limit of our instruments.
This isn’t just some quibble, either. Losing track of the error in mathematics has real consequences. People who work in fields that depend on math know this, even if the perpetually or professionally incredulous on Twitter don’t.
The statement “2 + 2 = 4” is for people new to math. It’s a heuristic for teaching people who still need to see their examples laid out in blocks or pieces of fruit. There’s nothing wrong with that. Learning math isn’t automatic, and heuristics like these are the social conventions we’ve developed to teach it.
That, however, is precisely why it’s absurd to fall back on “2 + 2 = 4” as some kind of deep truth. That’s why it’s ridiculous to hyperventilate if someone points out that the equation is a social construct. And that’s why it’s childish to throw a tantrum if someone exposes you to a more complex idea. (Worse than childish, really. Part of growing up is supposed to be developing better communication skills than stamping your feet.)
Mathematics isn’t the only discipline that has to contend with this, of course. It’s just one of the simpler ones to debunk with basic examples. There are plenty of regressive groups that use this tactic.
There are creationists who ask, “If we’re descended from monkeys, why are there still monkeys?” We’re not. We’re descended from primates, and we have no living primate relatives who haven’t also evolved. “We’re descended from apes” is a heuristic we developed for children who aren’t ready to think about evolution more abstractly and completely.
There are transphobes who say, “Large gametes = female; small gametes = male. End of story.” It isn’t, of course. Even in nonhuman organisms, it’s the beginning of a story that also includes hormones, environmental and social influences, additional sexes, chimerism—and I’m leaving things out because I’m not a biologist. Then humans come along and add several societies worth of gender roles. “Large gametes = female; small gametes = male” is a heuristic developed from the practice of teaching people a subject by discussing the history of study on that subject.
There are racists who say, “We’re just recognizing human subspecies.” They aren’t. The question of how to define the boundaries of even a species is still being debated among taxonomists in biology. Subspecies as a concept is far from universally considered to be useful. And humans don’t genetically sort into subgroups that look anything like our conception of races. “These are the subspecies of humans” is a heuristic developed and maintained to justify colonization and enslavement.
The complaints about the complexity of science are a tactic. They are an industry. That doesn’t mean that science has everything right at any particular point in time, but people falling on their fainting couches exclaiming, “Can you believe someone said that?!” aren’t engaging in debate themselves, much less science.
This disingenuous froth is the work of people who understand the cultural cachet of science but aren’t fond of the results. They’re not standing up for mathematics or science. If they were, they’d be championing the methods that do a better job of describing reality as it really is. What they’re championing is their “right” to substitute rules—their rules—for the complexity that is reality. They’re championing their ability to be wrong.