One Line to Rule Them All
How a minor brain injury affected the way I understand mathematics and, well, everything else
I was one of those kids who came down with meningitis in college. The headaches had been bone rattling enough that I even trudged over to our campus clinic twice, but what can you actually tell a sleep-deprived twenty year old with a headache other than just to rest and try not to take things so seriously? The but it really hurts argument was met with a sometimes headaches really hurt takedown, and I could hardly argue with that.
In that spirit, I was slurping down pain meds on the floor of my supervisor’s dorm room with a group of other resident assistants when my days-long headache reached a new level so intense that for just a moment I thought I could actually hear it as a sound. It was massively jarring. In my memory, the pain was a wave of vibrations, starting deep in my lower neck, then washing up to the back of my eyes in a frenetic rush that made my stomach leap to action. I stood quickly, planning to bolt to the hallway bathroom in a ridiculous effort to avoid vomiting on my boss’s carpet, but one step into my launch, my body revolted and I fell. I was squinting, trying to understand why everything was so unbearably bright when I realized that something was stuck in my throat and I couldn’t swallow.
This next part is fascinating to me but I’m afraid it will make for a boring story, so I’ll cut to to the chase: there was indeed something stuck in my throat that made swallowing and speaking confusingly difficult but that thing was in reality nothing other than my own tongue. It turns out that I had temporarily lost the use and feeling of the entire left side of my body. My left leg and arm just became heavy lumps that might as well not have been connected to me at all. But my tongue was an entirely different matter, since half of my mouth could process and sense everything normally. Imagine what it would feel like if your tongue and half of your throat suddenly fell asleep and you’ll get the point.
It was uncomfortably weird and made my speech unintelligible, prompting my co-workers to heave-ho me down three flights of stairs and plop me in the back of my boss’s car for a sprint to the E.R. A lot of vomiting, a panic-filled CT scan and a totally-what-it-sounds-like lumbar puncture later, I learned that a blood vessel in my brain had thrown the equivalent of a hissy fit in response to a build up of inflammation.
It was just meningitis and although yes, it was scary, the doctors agreed that since the feeling was back in my limbs and face, I would be fine. It was just a little brain spasm.
I stayed in the hospital for a couple of days, feeling more and more like myself but exhausted in a way that felt almost spiritual. A walk across the room would set me back for hours. I took epic naps. It turns out even a little brain trauma takes a lot of time to heal, so I just decided to stick around and finish the semester where at least I could be close to my friends.
It was all going fairly well until I realized that I was consistently running into walls when I attempted to pass through open doorways. I would be walking, just like I had my whole life, towards a framed-out area and bam! I would hit my shoulder right on the edge. I was less worried about this than I was fascinated. Like, it was strange, but manageable. So, I learned to step over about 6 inches whenever I approached a doorway and voila! problem solved.
But the big kick in the pants came when I realized that there was definitely something wacky going on with the way I worked with numbers. Up until this point, I had a flirty relationship with math that never progressed to anything serious: I had taken calculus but since I had switched majors, the only math class I would still need in order to graduate was Intro to Statistics. I was hoping to take this nice and easy. But just a few lessons in, I realized that there was clearly something wrong.
When attempting to average a group of numbers, I found that I could not complete even the most basic math in my head. A task like adding together three one digit numbers and then dividing by three was suddenly impossible. I could not recall anything that related to this process. I mean, I remembered the idea of addition, but I had no memory of what numbers actually did when they interacted with each other.
Time would show that my little brain spasm had zapped my memory of even basic math facts. No multiplication tables. No ability to divide in my head. The best way that I can describe it is that the place inside of me where math had once resided was just suddenly empty. The tenant had left the building. My professor received a note from my neurologist (who had quipped Well at least you weren’t a math major when we put all this together) and granted me an accommodation for my final exam, which took me nearly five hours to complete. I passed the class with my tail between my legs and set out on a personal journey over how to solve the problem of rebuilding my math skills when nothing numerical now made any sense.
And this led to an observation of something that had been siting just in the periphery of my consciousness. In all this thinking about numbers, I suddenly noticed something that had always been with me but that I had never paid any attention to at all: I could see numbers in my head.
The more dug into this, I realized that I had a whole visual line of numbers that mentally appeared whenever someone said or referenced a specific number. Sometimes they were colorful, sometimes they weren’t but always, the numbers appeared in the same spacial place, just quietly hanging out in my mind. This discovery was new to me, for certain, but the sobering part was that when I thought back over my life, this number line was always there, immersed in my memories, automatically working whether I consciously realized it or not. In a way, it was like suddenly noticing that I was breathing and had indeed been breathing for my entire life.
I just hadn’t been paying attention.
Could this quirk be the key to getting my use of numbers back? These mental images were static, like paintings hanging on a wall and I wanted them to be mobile and fluent, so I made it my mission to get them into action. But the problem was, the more I focused in on that mental picture of what numbers actually looked like in my mind, the weirder it all became.
So, first off: do you see numbers in your head? Like, if I were to say what does the number 18 look like to you? does that question even make sense? Here’s what I’ve learned about that. For some people it does, and for some it definitely doesn’t. You either see them or you don’t. When I asked my college friends if this happened to them, most returned blank stares and shrugs. A couple said yes. I had no idea what to do with this. And let me clarify here that there is absolutely no indication that people who do are special or smart or clever or really anything at all, as far as I can tell, except for being visually situated to see numbers and maybe other stuff in their mental map. You either just do or you just don’t.
So, for me, the number 18 is pink and larger than both of its neighbors, 17 (black) and 19 (black), and it sits on a curved line that approaches 20, where the number line makes a sharp turn and heads in the opposite direction. The line squiggles a lot. I believe, although I can’t be sure, that 18 always looks like this in my mind’s eye, except for the color which changes. These numbers have been this way in my head for as long as I can remember. I don’t visualize zero and most of the pictures stop completely when you get to a million.
Why does this happen? The earliest descriptions I have found in modern psychology came from Francis Galton’s 1880 publication in Nature titled Visualized Numerals. Unfortunately, Galton’s horrific views on race seeped even into this paper, so that’s a bust. But, interestingly, the appendix included several drawings that the subjects had sketched detailing their own visualized number lines. Most of them just seemed foreign to me — but then I saw one drawing that looked strikingly similar to my own unwieldy little line. It was almost identical except that it branched off in the opposite direction.
Apparently this was indeed a thing.
A more recent paper published in the Journal of the History of the Neurosciences describes something similar to this visualization as a form of synesthesia:
Synesthesia is an unusual form of experiencing the world in which music may elicit colors, numbers may be visualized as a line running through space, and words might have tastes. These many different variants of synesthesia today have different names (e.g., experiencing colors from letters or numbers is called grapheme-color synesthesia), but all today fall under the broad umbrella term of synesthesia. The experiences tend to be automatic and consistent over time. The developmental form is present from early childhood, runs in families, and has a prevalence of around 4% (for a review, see Simner and Hubbard 2013; Ward 2013). The condition is linked to structural and functional differences in the brain (Rouw, Scholte, and Colizoli 2011), but is not considered pathological.
From The “Golden Age” of Synesthesia Inquiry in the Late Nineteenth Century (1876–1895) Jörg Jewanskia,b, Julia Simnerc , Sean A. Dayd , Nicolas Rothene and Jamie Ward, JOURNAL OF THE HISTORY OF THE NEUROSCIENCES 2020, VOL. 29, NO. 2, 175–202
Not considered pathological. Huh. Hadn’t even considered that one.
I should disclose here that I have never pursued whether or not I actually have synesthesia and it’s not a priority for me to find out. The idea behind the concept is what resonated with me and eventually changed my life. Once I become conscious of the fact that I visualized numbers, I became Inception-level obsessed with the idea that if I could find a way to manipulate those images more efficiently, it might then be easier for my still-wonky brain to relearn mathematics.
Specifically, since numbers showed up in my mind on all sorts of curves on a very long, connected line, I became hyper focused on what could happen if I could train my brain to realign those numbers into a visual system that made use of base-ten patterns. I reasoned that would be a more efficient system and it also might help me understand mathematical concepts even better than before, since I had learned math mostly from memorization as a child.
The goal was simple: I would try to rearrange my mental numbers into cubes consisting of faces with ten rows and ten columns. If I could accomplish that, then I should be able to speed through mental calculations! (This is how Montessori math was later taught to my kids but through the use of tactile cubes). So, I repeatedly tried to reposition the numbers on my mental number line.
Over the years, I got as far as being able to see the new cubes, with numbers on them, but I could never get my brain to automatically recall these images without prompting. In other words, 18 stayed exactly where 18 has always been in my visual number line, no matter how many times I tried to move it onto a straight line positioned in the eighth slot of row 2 in a plane with ten rows of ten.
So, nothing changed. At least visually.
I think that what happened here, or failed to happen, was that I made a fundamental mistake in thinking about the whole issue from the jump. I had assumed that the place in my brain that saw mental pictures of numbers was the same place in my brain that calculates those numbers. And then, I reasoned that if I could willfully change that visual representation, then I could also learn to rethink mathematics in general.
It turned out that I could fix one but not the other and that ultimately, the two things appear to be completely unrelated, at least for me.
So, what improved? Although I never permanently altered my mental number line (it’s as wily as ever), I did finally relearn my basic math skills. And it had nothing directly to do with my deep dive into synesthesia. But indirectly, that curiosity encouraged me to take other small steps towards trying new strategies that actually worked. Time showed that moving through this little trauma came down to a recipe of practice and patience, mixed with a human-sized helping of humility.
I started small and back at square one, working my way through Singapore Math books written for elementary students. I became more curious about the mind and how it worked. I found myself housing less fear of math and my limitations. I slowly became more confident. Years passed.
I also let myself read books I was interested in, even if I knew I would not completely understand them. I nibbled on books about quantum mechanics by Richard Feynman, Robert Gilmore and Stephen Hawking, as my family often entered into dreamy, sometimes heated discussions about holograms, repeating decimals and the golden ratio. We weren’t a family of mathematicians or physicists. We just liked to discuss big ideas and these books let me back in on the action.
I could honestly admit that the complexity of numbers still escaped me, but I was coming around to the concepts. I finally understood what a derivative really was! To be clear, I still was unable to do much of this math, but I started to allow myself the pleasure of just being around it. I went down a rabbit hole reading all I could about quantum entanglement. Those books opened me up to the vastness of the universe in a way that never would have happened if I had remained afraid of a little injury to the part of my brain that just happened to be central to mathematical calculations.
I guess the takeaway here is that I had a wild idea years ago that maybe I could fix myself by trying to change a fundamental aspect of how I’m wired. I failed at that, but that failure led to a whole other world of discovery.
So today, if you randomly blurt out the number 247, I’ll unwillingly still see a visual picture of the number, right where it’s always been in my mind (up high, over to the left on a downward squiggle). Today it’s green. I cannot manipulate that image in any way, nor do calculations with it or anything useful at all.
But, what I can do is imagine a scenario that somewhere, sometime, someone might chance to run a simulation detecting 247 electrons serially progressing through a double-slit experiment. Although I don’t know how to predict the outcome of this experiment, I am fairly certain of one thing: that the very act of observing those 247 electrons will actually change the outcome of the experiment. A different future. Just because we paid attention.
And that’s when things get really interesting.
Well speaking of numbers, I'm a little surprised. Where are the vast amounts of 'likes' and comments?
Life is FULL of mystery and seemingly sometimes only seen in the "mirror,..."
I personally was pulled in simply with the word 'periphery'.
Yours is quite a story. I hope you continue writing more.