I once watched someone lop a thick branch from a tree with a pair of branch cutters. They had one of the long handles in each hand and, to get the necessary leverage, they had their hands curled in like fists towards their ribs in the kind of pose a muscle man might adopt on stage. I could see the handles of the branch cutter bending under the exerted pressure as the blades bit slowly into the wood. I could also see what was coming: when the branch finally gave, the two handles and the two fists would attempt to meet somewhere around the spleen, via the temporarily resisting cage of the ribs.
I vividly remember thinking, “of course that won’t happen because, well… it’s so obvious that it will”. I understood very clearly the principles of leverage, stress, strain, reaction time and so on. I understood them in a physical, visceral way. Watching and waiting for the inevitable catastrophe to unfold, I could almost feel it.
When it happened, it was quite funny – this being how my low brand of humour works – and in the end, while the victim never quite saw the funny side, they eventually stopped hating me with that same initial pyrotechnic intensity. It stuck with me though, that moment, because it occurred to me then that some folks get it and some don’t. Some internalise a knowledge, an understanding of basic physics and others, though they could talk sensibly and at length about levers and stress and strain and do clever calculations of the same, nonetheless end up breaking their own ribsj.
Feynman told a storyi about how he amazed his classmates by pointing out that the bottom of a set of french curves was always flat. They knew, of course, that the gradient of a curve was zero at a minimum, but somehow they also didn’t know this. Something similar came up recentlya with mathematically competent people expressing amazement that 6% of 33 was the same as 33% of 6 as if the transitivity of multiplication wasn’t something they’d mastered decades before. By this, I don’t mean to say that they are fools. Clearly they are not. But it’s this: we don’t always know what we know. Even a simple shift can make us see something we thought we understood in a wholly new light.
The complement to this is that understanding can be like bad wifi. You have four bars and everything’s fine, then you shift your position just a little and suddenly there’s no signal at all. Or it’s like a rainbow – all the elements you need are there, but you can’t see it till you’re standing in just the right place. Something like that. Perhaps there’s a difference here though between understanding a principle and understanding its implications. Implications can take on a life of their own and necessitate whole new levels of understanding. Who could look at a water molecule and see snow?
The emergence of the complex from the simple puts limits on how far or how quickly understanding can take us. Undergraduate physics courses plough into topics at high speed only to get bogged down fast. Gravity’s great till you need to deal with three bodies. In quantum mechanics one just about manages hydrogen (whilst studiously ignoring the proton) but the rest of the periodic table, bar a few special cases, is left to the chemists. The simplest variation on a familiar situation can leave one building up an understanding again from scratch.
Taking a step sideways into statistics, Bayes’ Theorem is easy to prove but trying to intuit its implications in even the simplest of cases is tricky. Here one might take understanding to mean the ability to apply the theorem correctly, to understand what is meant by priors and posteriors and conditionals and so on and how these relate to things in the world (or to a problem set by the lecturer). Similarly, an understanding of Newton’s laws might mean the ability to code them up and run simulations. To be able to make predictions of how the world behaves and, as a sign of success, show that the world does indeed behave like that is a powerful thing. To reach the point where one can predict the behaviour of a system – like a set of branch cutters – without the need of laborious calculation might be one way to define understanding particularly if that skill of prediction can be extended to novel or unfamiliar situations.
Understanding as prediction has appealing aspects, for sure, but it is also somehow unsatisfying. When we think of understanding, we often think of the ability to explain why something is as it is or why something happened. An explanation has a number of elements: it breaks down a phenomenon into parts, it relates those parts to other things we already understand and it fits the facts. Almost any explanation that fits the facts will be satisfying and as story telling creatures we are very good at telling ourselves stories that do. Of course, one must be wary of explanations. It is nearly always easier to explain why something happened than to correctly predict that it would happen in the first place. Also, the satisfying truthiness of a neat story can trump the truthful messiness of the real world.
Often people will say that if you can’t explain your work to someone then you don’t understand it. Extra layers are added to this challenge by the insistence that you explain it to someone like a layperson or a child, or an angry swarm of bees. Someone with whom a common framework of understanding and assumptions cannot be assumed. While you must be able to understand something to explain it correctly, I don’t think, in general, a failure to explain something to a child or layperson implies a lack of understanding. Communication is difficult at the best of times and the ability to put something in terms familiar to another person requires – on the part of both parties to the explanation – characteristics like patience, good will, empathy, and at least some common grounds. It also suggests that once explained, the child understands it which in turn implies they ought to be able to explain it to a member of the royal family or three dogs dressed in an overcoat. As a test of understanding, this approach has drawbacks, but it implies that there are perhaps levels of understanding.
One can probe the number of levels in this multi-story carpark of understanding by asking “why” a few times. It rarely takes more than a few “whys” to hit bottom or to find that, somewhat disconcertingly, everything we think we understand – the whole edifice of comprehension – appears to have no bottom level. At least none that can be articulated. In other cases, the “whys” propagate endlessly or go round in circles. Weather and climate are rife with explanations like this. Understanding is never complete and in so far as we may be wrong about some important things, provisional.
Sometimes words simply fail us. There is no particular reason why understanding need be put into words or indeed limited to those things that can be expressed in words. If I’d never heard of levers and fulcrums, the practical experience of using branch cutters (and other tools) would have given me what I needed to know. Part of the understanding wasn’t relatable in words anyway. I could try and relate the fact that when the blades start to cut, they go fast; that it is harder to react quickly when all your force is applied at the limits of your strength; and so on, but words run out. How to say other than in the most general terms that I could feel the rubber grips twisting against my palms, the slight flex in the long handles of the cutter, the bite of blade in wood? That some part of me could feel all this even though it wasn’t my hands on those handlesb.
Some folks have a kind of genius for explanation, for choosing words that can transmit their understanding to others. YouTube has given these people a phenomenal reach across a wide range of topics, that cover almost the full spectrum of legal human activity. It has also given people with a talent for transmitting completely erroneous understanding a huge platform too, so we should perhaps be qualified in our praise. Words are excellent for transmitting information, but the visual aspect is equally important. I watch videos on glass engraving and embroidery and there is no real substitute for seeing. Part of the skill in explanation is directing the attention of the viewer at the critical moment, but the words are only a pointer towards a skilful act of embodied understanding. Indeed the very best embroideryd videos I’ve seen are silent. The necessary understanding being transmitted with the point of the needle as a pointer and by artful exaggeration of the movements. These movements reveal an understanding of not just what it takes to perform a particular task, but also where a novice might find that task harder or easier.
This understanding of misunderstanding is, in part, transmitted and evolved over time, in some cases independent of whether the person passing it on has any understanding of what they do. Oftentimes, someone who it teaching you, or guiding you through a new skill will tell you to do something. Not because they have given it much thought, but because that is how they were taught. Even if they know why, there is another level beneath that understanding, some substrate of comprehension that they take for granted. Eventually, it all gets down to clever cells and their connections. The internet allows – at least in principle – for good practice to spread. In doing so, other people will take those methods for transmitting understanding and pass them on, with their own twists, slowly honing and evolving better methods
There is a particular satisfaction in watching someone skilled in a particular art or craft simply exercising their skill. When I was a kid, my friend came back from a trip to York. He told me excitedly about the glass blower who blew his glass in front of a crowd who crammed themselves into his workshop to see. I could picture them, squished together, breathing each other’s air, and staring mesmerised as the glowing cherry blob of glass span and inflated, cooling to transparency as it did. Tony Hart filled minutes of my childhood air time simply by drawing and painting. He said things, but what he said scarcely mattered. In our evolutionary history, we must have learned first by watching and copying before we could put anything into words. I think perhaps there is something in us that makes that an inherently pleasurable experienceh.
Understanding precedes words. Everyone has struggled for the words to express something. On the other hand, putting something into words can reveal that ones understanding was lacking, incomplete, or unnecessary. Words can therefore help to shape understanding. Whether this is due to something particular about words, or whether having to choose particular words tests understanding as would any other specific application, I don’t know.
But why am I rambling on about all this? I admit that I do not know that either. If you’ve got this far, maybe you understand better than I do. Making sense of the world, is notionally what scientists dof and part of that is making sense of how we make sense of the world. However, one can be a scientist without musing in such ways. Understanding is also much in the news. How we come to understand topics like climate change and COVID that affect the way we live at a profound level is part of those stories and inseparable from them. As we grapple – usually wordily – with what Large Language Models, like those on which Chat-GPT are based, can and cannot do and how that relates to what we can and cannot do, I feel like we pass close to these ideas. Does Chat-GPT understand what it writes? How is what I do different from that, if it is? All of these things, perhaps, and more.
Anyway, I once watched someone lop a thick branch from a tree…
a and keeps coming up.
b I have similar problems when trying to explain how I climbed a particular boulder problemg. Sometimes, you see the holds, the crystals and minute variations in the angle and roughness of the rock and just know that if you put a foot just there, and twist the heel out, then reaching over with your left hand will… if you put it into words, you can never grasp the full bodied, embodied understanding that occurs to you in that moment. Of course, oftentimes you are wrong and twisting the heel outwards shifts your centre of balance outside of the axis between your other foot and your right hand, causing you to swing away from the rock like a badly hung barndoorc.
c It’s actually called barndooring. Sometimes words nail it.
d Embroidery is an interesting one because words fail almost completelye. I can imagine what a text describing even the most basic of stitches would be like and I wouldn’t want to learn from it. Static diagrams are better, but for anything moderately complex, forgetaboutit. I don’t think there’s any substitute for seeing it happen.
e And then there’s the case of risotto. I have never had a risotto that was made by someone who knows what real risotto is. I have only ever made it for myself from cookery books. I like the risotto I make and it’s probably similar to the real thing. It’s like that weird philosophical mind game where someone is bought up knowing everything about the colour blue but has never seen the colour blue, except, it might be that I see blue all the time (as it were, keep up) and all I’m missing is for someone to say, “yup, that’s blue alright” or “um, no, are you a monster?”
f though some would argue that what scientists do is make the world less comprehensible. I suppose one could say they are exposing the incomprehensibility of the world, but it’s not always the case. Sometimes we make things incomprehensible by accident, sometimes just for the hell of it.
g a boulder problem is a very short climb. Some people enjoy bouldering because it separates the technical difficulties of climbing from everything else. Some people like it because it’s safer, though as for that, it’s still very, very easy to hurt yourself. Sometimes, having chosen to climb the smallest rocks in the valley, a boulderer (as that is what they are called) will try to get the most climbing out of their chosen boulder problem by starting from a sitting position, sliding as far as possible underneath the rock they are scaling, or by going sideways. It’s a strange past time.
h It was suggested to me recently that there might be interest in recording the process of creating a climate data set, which stemmed from the same consideration – we had been watching a video of a master craftsman making a violin. Is science a craft in the same way? Whether it is or not, about 80% of the video of my working pattern would be me tapping the combination for strong black coffee into the office coffee machine.
i Characteristically flattering to his own intelligence and insight, much like my branch anecdotej.
j I once sawed off a branch I was sitting on, an act which is comic shorthand for gross stupidity. In a similar vein: once, in a rush to leave the house for an interview, I noticed that the shirt I was wearing was creased. I plugged in the iron, cranked it all the way up to 3 dots, waited for the little click and chuffing hiss of steam which told me it was at maximum heat and proceeded to iron out the crease. This would not be a story worth relating if I had taken the shirt off first. Sometimes, we’re in the group who get it, sometimes, we’re in the other group.