The End is the Beginning (Strange Loops)

There come moments where, despite travelling further and further from a starting point, one is surprised to find oneself back at the beginning.

School improvement is one such strange loop. There is a sense of making progress: each challenge that presents itself is tackled with degrees of success; matters are resolved; there is a sense that things are generally better than they were before. And yet, you find yourself back at the place you set out from.

The feeling is akin to deja vu. It is mildly disconcerting. You catch the moment and think, ‘huh, so I’m here again’.

If you have never had this feeling, perhaps you’ve not stuck around long enough to do so.

It happened to me this September, 10 years into headship. Throughout this period, I have a recollection of forward momentum, but as I stepped into my 11th year it felt familiar, as if I had entered via the door I had left by a decade before, having been on a wild journey.

I wasn’t sure what to make of this feeling. Was the sensation an illusion, or was my belief in progress the illusion? Surely one must be the case? If the latter, then what purpose would another 10 years of effort serve, to only end up once again where I had begun?

I looked for answers. I found more strange loops.

The stonecutter

According to Japanese legend, there was a poor stone-cutter who longed to be something more. First, he wished that he were rich. The spirit of the mountain granted this wish. Then he wished he were a prince. Again his wish was granted.

Not satisfied with riches and power, the stone-cutter wished to be immune from the heat of the day, so became the Sun, then wished to be the clouds which could block out the sun’s rays. With each wish, he desired to become greater than his former self. Then he saw the mountain’s longevity and how it withstands the wind, the rain and the sun. The mountain spirit granted his wish to become the mountain.

But a stone-cutter arrived and began chipping away at the mountain. With one final wish, he took back his form as a man and came to terms with his place in life as a humble stone-cutter.

This parable appears in many cultures. Morally, it is a ‘the grass isn’t always greener’ tale. But it speaks to an altogether deeper phenomenon of the strange loop.

This statement is false

Strange loops appear across many disciplines: mathematics, logic, linguistics, philosophy, music, networks, and cognitive science to name a few. The underlying paradox is that, whilst moving up or down a hierarchical structure, one finds oneself back where one started.

The concept was famously depicted as the Penrose Staircase (above) and can be heard in infinite ascending melodies. But strange loops are more than just optical or auditory illusions.

In ‘I Am a Strange Loop’, Douglas Hofstadter (2007) defines the concept as follows:

not a physical circuit but an abstract loop in which… there is a shift from one level of abstraction (or structure) to another, which feels like an upwards movement in an hierarchy, and yet somehow the successive “upward” shifts turn out to give rise to a closed cycle. That is, despite one’s sense of departing even further from one’s origin, one winds up, to one’s shock, exactly where one has started out.

Hofstadter’s ‘upward movement’ resonated with my sense of how our school had ‘improved’. There are always enough indicators that things are getting better to allow yourself to generalise that they probably are. And then you find yourself beginning a new school year with the realisation that the same problems you set out to tackle present themselves again, maybe not in the state you left them but definitely in a state that leaves you feeling that there is work to be done. It is not merely that standards have slipped back, although there are always reversions to the mean that do occur. It is, as Hofstadter suggests, when you move to another level of abstraction that a sense of beginning again returns.

The stone-cutter parable perhaps provides some insight. In schools, we form and reform, endlessly striving for ‘better’, while the parameters of ‘better’ constantly shift – scissor cuts paper, paper wraps stone, stone blunts scissors. Improvement is heterarchical, a tangled hierarchy that loops back on itself. We might set out to improve punctuality, but once this is secured we want the students’ presence to be purposeful, and once we are assured of this we desire to prove it, but the act of proving it places stresses on the system, which causes teachers and leaders to look elsewhere, an in doing so some of that which has been secured becomes untethered, which is drawn to our attention causing us to wonder why we ever turned our attention elsewhere.

But this analogy did not satisfy me completely. What, I wondered, made this ‘upward movement’ feel like progress?

What came before defines what comes after

Turning to the temporal, I reflected that our sense of things getting better is fed by our cognitive biases.

Firstly, we have an anchoring bias whereby our decisions about the future are tied to the point from which we begin and where we have come from. When we decide to improve an aspect of the school we are anchored by an assumption that what exists is not good enough. The realisation that things must change creates a hinge-point bias; an exaggerated importance regarding the moment when we change direction. This hinge point colours our perception of what went before and what comes after.

Tied to the above, there is a causation bias, which is the notion that the past has somehow brought us to where we are now. In other words, we fixate on noticeable features of past events to which we causally attribute the present circumstances which displease us. If only we hadn’t done that, we wouldn’t be where we are now, we tell ourselves. Therefore, our solutions must be in opposition to past actions, leading to swings in policy and acceptable beliefs.

This sense of the past as a mistake is fed by hindsight bias. The negative consequences of past decisions appear obvious in hindsight, therefore we assume incompetence in those who made these decisions under the less optimal conditions of having to rely on foresight!

Lastly, we suffer from superiority bias in relation to the future. We are hard-wired to expect the future to be an improvement on the past: reality two point zero. This is due to a misconstrued over-confidence in our own agency and impact and a belief that we see the world more clearly than those who have come before us, or even than our past selves.

Our temporal cognitive biases mean that change is more likely to feel like progress. In the story of us, this moment is a turning point; what comes next is so much better than what came before. It is the illusion that keeps us moving forward against the odds.

How do our minds make sense of the paradox created by our bias towards believing that things are getting better, whilst being confronted with the reality that we are back where we started? Perhaps we are driven to avoid this cognitive discomfort by moving on before we are forced to reconcile the evidence of our senses against the narrative of our success we have created.

The end of the beginning

Do schools improve? Of course they do. We can achieve tangible improvements in real things. We can measure these things.

But I think two other things are also true. First, that there are strange loops in school improvement that mean, despite every sign we are moving forwards, we end up where we began. Second, that our sense of progress may itself be subject to an illusion, to a bias towards the superiority of the future over the past.

I have a feeling that I’ll be here again. But next time I’ll be expecting it.