Consciousness and causation

Few, if any, problems in philosophy seem as mystifying as the ‘hard’ problem of consciousness. How is that certain entities in the universe have this magical property of being able to perceive, think and experience? And where, in this picture, do we fit experience is ‘like’, how the taste of apple juice differs from dread of the unknown? The problem is not helped by the tendency to start introspectively. If we forget about the strangeness of our own experience for a moment, and examine instead how consciousness functions in the world, we might start to get a clearer picture. In particular, I think three points stand out.  The first is that consciousness is real, and it interacts with the world causally. The second is that our knowledge of consciousness is not simply drawn from introspection: we see evidence for consciousness in others in our everyday lives, all the time, and it plays a crucial role in our lives, both in explaining phenomena and setting accurate expectations. The third is that the causal function of consciousness is not independent from the qualitative properties of experience: what it’s like is intimately connected with what it does. 

The first point I want to make is a purely conceptual one. Perception presupposes that consciousness is causally embedded in the world. We can’t say we have seen something without believing that the thing we have seen has caused the perception of sight (in this instant reflected a light source into the retina). A similar sensation that is not brought about causally in this way we would call illusory (a mirage, a hallucination, a dream etc). For perception to be useful, this process itself has to be causal (it is conceptually possible that that perception is epiphenomenal, i.e not useful, but this seems improbable: more on this later). It has to have some impact on future actions or dispositions, if nothing else our memory. Every day experience seems to suggest this is the case, or at least it is very much part of our everyday descriptions of perception that it is (“I remember seeing the sunrise”, “I disagree with what you just said” etc etc). At the very least, it seems an inescapable part of life to live as ifcertain mental events, perceptual or otherwise, are causally significant. I cannot decide which train to take to work if I think that my thought process has no impact on events in the world. In the particular case of perception, what counts as perceiving something seems to be about the propriety of mental events to antecedent conditions, given the causal significance of the mental events. I perceive something if a particular mental experience associated with x occurs when x is the case, and that mental experience causes me to have the true belief that x, or respond in some useful way to x. 

We see evidence of the consciousness of others all the time. Our expectations and descriptions of their behaviour would make no sense if this were not the case. If you arrange to meet with a friend, they arrive at a particular place and time because they have decided to do so. Perhaps they are late because their clock displayed the wrong time, and they falsely  believed it was earlier that it was, or they misjudged how long it would take to walk from A to B. Examples like this are endless, and they are not easily replaced by accounts which do not allow for conscious agents. Imagine trying to predict the position of this friend purely by thinking about velocity, acceleration and displacement: even when such a description is possible (as it sometimes is), it could never hope to account for the fact that they have arrived at 11:04 near the bus stop, because 11:04 is ‘roughly 11:00’, and here is near enough to the bus stop for you to find me. 

As it happens, we actually have remarkably rich and accurate expectations of the behaviours of others as conscious agents. We are able to expect that people may be our friends, or partners, might be hostile to us, might be our boss at work, might give us parking fines if we park in the wrong place etc etc. All of these expectations seem to presuppose consciousness, in that they expect people to respond in a way that is situationally appropriate and specific in a way that often requires conscious perception.  Think of being arrested because a police officer believes you are behaving in a drunk and disorderly fashion. Or a shop that is particularly busy because there is a New Year’s sale. Or even taking a contrarian philosophical position and expecting angry disagreement. A huge part of the way we make sense of the world around involves thinking in terms of the expected behaviours of conscious agents.

This is even clearer when we think about emergent social phenomena, like money, schools and political institutions. A piece of paper with a picture of the Queen on it is money because people think it is. It has value because people take it to have value. Trump is the President of the United States because he is held to be, and millions of people putting crosses on pieces of paper (or pulling levers on machines) is part of a process called ‘voting in an election’. Between 1939 and 1945, the behaviour of tens of millions was part of some large social process called ‘being at war’. These phenomena are all quite comprehensible if we see them as emergent behaviours of large groups of agents.

Could these behaviours be equally possible for non-conscious agents? Perhaps, but for the time being, we could make no sense of them and would have no idea what to expect to happen in the world unless we were to say that things occurred ‘as if the Earth were inhabited by 7 billion conscious human beings’. And to think that the world might be so constituted that by extraordinary coincidence people behave in exactly the way they would if they were conscious, but in fact are not, through mechanisms that make no sense to us, while not logically impossible, would be a very strange belief to entertain indeed. 

Even if we accepted that consciousness was a real phenomenon, might we at some point in the future develop explanatory frameworks for human behaviour that make it redundant? Perhaps when it comes to certain behaviours (some things we think of as conscious decisions might turn out not to be, we are often deluded about how much about a situation we are really perceiving etc). But the difficulty remains that our behaviour is often circumstantially specific, where what counts as a given set of circumstances is itself reliant on the act of interpretation and on human volitions and expectations (I am annoyed because someone is ‘late’). As a practical matter, we could certainly never have the sufficient data to predict behaviour in everyday life. And then we must take into account the fact that conscious perception can be novel. Consciousness allows us to respond to an indefinitely large number of unique, never before described circumstances (and to describe them!) and for this to explain behaviour causally. We can be particularly moved by the sight of a star, and in doing so have our behaviour determined by a system thousands of light years away. We can think differently of a film because we missed the first scene. To do away with consciousness as explanatory would require a set of recursive rules which can account for a similar array of responses, all happening to coincide with conscious experience. 

And why would we have to do so anyway? The key motivation, I think, for attempting to do so, is the idea that seeing consciousness as part of causal chains makes us think that there should be some kind of intuitively satisfying explanation of how something immaterial like perception could arise and interact causally with the ‘material’ world. This is indeed an alluring assumption, and it is difficult not to see consciousness as somehow magical and mysterious. But this might be a misconception of what explanations should seek to do. There is no reason why the universe should be so constituted as to be describable in a way that allows for ‘intuitive’ mechanisms that would follow from how we visualise a problem. And even if we did, why would this make such an account more plausible? Our ability to derive satisfying metaphors that reduce causation to dominoes falling, or things pushing and bumping into one another does not make our descriptions more or less true. A complete causal explanation does not have to allow us to picture the process; being able to do so may be satisfying, and perhaps sometimes help us apply a concept, but it is not logically necessary. A more realistic ambition might be simply to have a description of consciousness that is theoretically comprehensible, i.e we can know what it predicts (in this case, the conditions under which consciousness occurs, how it behaves) and that does not violate other principles we know to be true of the natural world. 

On this last point, we might think that consciousness seems to violate other natural laws, as it seems to require spontaneous behaviour (i.e behaviour which is not determined by the laws of physics). But I think this is a mistake. Belief that consciousness is causally significant does not require consciousness to be random or spontaneous. It can be fully determined by antecedent conditions yet still causally necessary for subsequent events. We might say: a system would behave this way under these conditions, given that it is conscious, and it would be conscious, given what we know about the system, but it would not behave this way if it were not conscious. I think part of the problem might come from the a fallacy surrounding the transitive nature of causation. Typically it is the case that if A caused B and B caused C we can say (more or less usefully) that A caused C. But this does not imply that B did not cause C, that B’s causing of C was independent of A or that A’s causing of C was independent of B. If it rains on a cold night, the water freezes and the next day I slip on the ice, I may not have slipped were it not for the rain. But the rain only made me slip because it turned to ice.  And the slipperiness of the ice is not a property which exists independently from the arrangement of water particles in a crystalline structure at a certain temperature, but nor does a description of the latter get rid of the former. 

But how does consciousness ‘do work causally’? Or, put differently, how can the consciousness of an organism explain its behaviours? Certainly there is a lot we don’t know yet. One starting point might be that the phenomenal content (what experience is ‘like’) does not seem to be as separate to what an experience ‘does’ as some might suggest. It is not the case that what it is ‘like’ to experience pain is unrelated to how we behave when we are in pain. Pain, after all, is (generally!) something unpleasant we try to avoid. Perhaps we cannot describe the difference between the experience of seeing something blue to experiencing something red, but we can say that these are different experiences. That is, after all, what allows us to differentiate between the colours of different things (it can, correspondingly, be determined observationally that someone is colour blind, as they are unable to differentiate between colours). If, as earlier suggested, what makes something count as perception is the functional significance of the mental experience of perception, ie what it causes us to do, believe, remember etc, and whether this is appropriate to the antecedent conditions which brought this experience about, the question then seems to be: how does the phenomenal content of experience (what it is like) relate to its function (what it does). Might it be that certain types of experience, when brought about in the right conditions, are capable of generating useful responses, and others aren’t? And how does the function of a conscious experience affect what we might look for in the system from which it arises? If, for example, some consciousness is computational, we might look for a physical system capable of carrying out computations, or giving rise to a phenomenon capable of doing so.

Is consciousness identical to neurological states, a property of a physiological system, or something separate which is ‘brought about’ by physiological systems? I’m not sure there’s as much difference between these descriptions as sometimes is made out. Consciousness  isn’t a separate entity (as John Searle once remarked “it’s not a juice squirted out by the brain”), and it’s not clear what it means to say it is spatially located, other than saying that its causal interactions are specially located. We can call it a property of a system if we like, so long as we remember that in doing so this property is taken to be something which is likely to explain the behaviour of the system (in the same way that liquid water behaves a certain way because it is fluid, ice because it is a solid etc). We can call it something ‘brought about by a system’, so long as we remember that this does not imply a separately existing spatial entity. 

Hopefully these few paragraphs might give some clarity to how we might think about this problem. At the very least, I hope they aren’t entirely trivial. I don’t wish to assert that these tentative answers are absolutely necessary. While perception may require consciousness to be brought about causally, how do we know we aren’t perceiving at all? And while reference to conscious agents might be important for making sense of the world, how do we know the world is structured in a predictable way, at all? These objections are of course all possible, but in the same way it is possible that the world is fundamentally incomprehensible, that the sun might not rise tomorrow, that we might all be brains in vats etc etc. We can still entertain doubt about the existence and nature of consciousness in the same way we can entertain radical scepticism about existence, in so far as we do not find answers to that scepticism satisfying. But we must not confuse this kind of radical scepticism with an observation specific to consciousness or the mind-body problem. And while the account outlined does not allow us to intuitively ‘get’ how this strange property could be true of physical systems, it does, at least, mean we do not have to doubt the every day phenomena that life does not allow us to seriously call into question. It is, perhaps, an attempt at answering a the following question: if, as may or may not be the case, our concepts of knowledge, perception and belief do roughly work, and if these concepts are at work in accounting for behaviour, how, in the abstract, do these experiences relate to the things they are supposed to refer to?


Dream Catchers

These days, most people tend to dismiss the Dream Catchers as a kind of sad cult.  Certainly, their rituals, strange terminology and mystical beliefs about the true self being unleashed only in sleep (that of 'perfect autonomous creation, uninhibited by the boundaries of physicality') are eerie, to say the least. But it's easy to forget that underlying the brief popularity of this movement was a sound argument. We spend a very large portion of our lives asleep, and a substantial portion of that in something akin to a conscious state, so why should this not be thought of as an equally valid and important part of lived experience?

Improving our dreams, so the idea goes, is as much an improvement of our lives as improving waking reality. You may have a great job, a happy family life etc etc but what good is any of that if you spend several hours a day being haunted by monsters, appearing naked at work in front of colleagues, or constantly losing and regaining your teeth? The 2010s saw a surge in interest in improving your sleep as a way of feeling better while awake, but it wasn’t until the next decade that interest grew in improving sleep for its own sake. A huge literature emerged on 'tips and techniques' to improve your dreams, there were endless talkshow debates, pages of magazines were filled, the British tabloids showing a particular interest in the subject. Most of this we of course now recognise as pseudoscientific junk, but it had tremendous purchase at the time. So much so that there was a crackdown by HMRC on dream therapists, once it was realised how much revenue was being lost to those who weren't paying their taxes properly. "Nobody dreams about VAT", a well known government minister once quipped. 

But for all the junk science and spurious, unregulated medical supplements, it's easy to see why so many were taken in by the idea that dreams mattered. In an age of increasing economic inequality, to many there was something emancipatory to this idea: perhaps there may be those with better careers, who own rather than rent, who have more fulfilling romantic encounters, but no waking money or good fortune can buy a pleasant dream. 

Some saw a sinister side to this early on. If, so the idea went, we gave equal weight to our waking and sleeping lives, might we simply lose focus on the present? Or was there something deeply regressive about this new interest in dreams? Might they come function in much the same way Nietzsche described Christianity, a system of morality where we focus not on the cruelties and injustices of the physical world, but instead take refuge in something else, something beyond? 

The irony of all of this was that it turned out that a good waking life was the only reliable predictor of a happy dreamer anyway. On this question all serious statistical studies were unanimous. The wealthier had better dreams and dramatically fewer nightmares, those who were worse off, particularly those in precarious work situations had a far worse night's sleep. As one columnist for the New Statesman put it: "inequalities in the afternoon reproduce themselves at midnight".

Certainly, only a small minority ever became fully fledged Dream Catchers, even at the zenith of public interest in the subject as a whole. Their asceticism, endless meditation and frankly bizarre ideas about sexuality were off putting to most. But it's easy to forget that their emergence was part of a quite widespread, if brief, fad for a novel kind of self improvement. 

Freedom and Social Democracy

A few months ago Chris Dillow, one of my favourite bloggers, wrote an interesting piece about the death of the idea of freedom on the right. This can be read here. The main points, are, I think, pretty good ones. Ending freedom of movement, the hostile environment for immigrants and regressive policies on criminal justice are all central projects of the British right, and all involve significant restrictions on individual freedom.  Anti-immigration policy is notable in particular, as its ostensive justifications (purported impacts on wages) tend to rely on the tacit assumption that labour markets don't function efficiently and immigrants simply impact the supply of labour, rather than create additional demand for it too (the lump of labour fallacy). Back in the 1980's, the dominant thinkers and politicians of the New Right used to think belief in freedom and belief in the power of the market went hand in had. Now, it seems, in large areas of social and economic policy the right believe in neither. Dillow suggests that the mantle of freedom might be taken up by the left, and concludes by arguing that this is well complimented by an understanding that unequal wealth and power can lead to forms of coercion. It was this understanding that was so central to the emancipatory themes of 19th century left wing thought.

I'd like to add a few thoughts as to why freedom might be an effective focal point for the left and centre left of British politics right now. The first point is it can be a good way of marrying the need to appeal to 'aspiration' with concern for social welfare. A functioning welfare state is not just about alleviating immediate poverty: by providing security and certainty people are more able to make choices about how they lead their lives. If, for example, you lose your job, meagre allowances and pressure from the DWP will likely force you to take the first thing on offer. You might well have better choices if a better level of support allows you to take the time to find something you are actually want to, or take the time to re-skill. The same is equally true for decent maternity and paternity allowances. A decent system of social support can, in a very real sense, be freedom enhancing, as can certain regulations aimed at providing greater job security. Free from insecurity, we can more confidently make better choices about our lives and have greater aspirations.

The second point here is that a focus on the value of the welfare state as freedom enhancing could help address one of the central problems Labour has had electorally under Corbyn. Many supporters of Corbyn have protested against what they see as the unfair depiction of their 2017 and 2019 manifestos as extreme. But this has not been helped by the fact that talking up the 'radicalism' of their platform has been a large part of the appeal of Corbyn amongst supporters. The rehabilitation of the word 'socialist' in particular as a self description is a notable part of this. The problem with the term as used today is for older generations it carries with it the baggage of the Cold War and a collectivist mindset, without even being a particularly useful description of a policy agenda (is anybody seriously advocating collective ownership of the means of production and distribution?) Moving away from this vocabulary and stressing social democratic policies as freedom enhancing might spare the left of these associations.

This focus finally offers a better opportunity for the kind of electoral alliance Labour, or any party of the centre left would need to win power. It could allow them to speak a language more recognisable to liberals, and have a common way of talking about the encroachments on traditional civil liberties and the erosion of constitutional norms resulting from Brexit and pushed by Johnson and the nativist right. It could, unlike Corbynism, effectively make this case, while simultaneously pushing the well evidenced proposition that more equal societies with greater levels of economic security are also freer and more politically stable ones, with a better functioning public sphere.

Abnormal Elections

The post mortem of the election results have, for the most part, focussed on different interpretations as to "why Labour lost", which tends to mean a list of things it did badly.  This is understandable, and not without merit. But there is another way of asking the same question, that while logically no different, tends to produce a different kind of answer. It is "why did Johnson win?". Or, more concretely, what aspects of his campaign may have contributed to his success? The answers to this, I think, are rather unedifying, but important if we value understanding our current predicament. 

The sad truth is that this is an election that shows that disinformation and strongman rhetoric work. Let's think back for the last few months. Johnson tried to temporarily shut down parliament to circumvent his lacking a parliamentary majority. His election campaign included ramping up anti-immigrant rhetoric and pitting people against the institutions of liberal democracy (the 'people' vs parliament). His campaign used crude disinformation techniques, from fake 'fact checking' services to dubious Facebook groups like "Parents' Choice" set up in October to churn out party propaganda. 
This is all, of course, little more than a rehashing of the successful efforts of Vote Leave, whose 'genius' was the trio of promising greater levels of public expenditure on the NHS, clever disinformation campaigns and whipping up anger against outsider groups and those who support them. 

The problem is, on one level, simple to diagnose if difficult to treat. Strongman politics can be popular. The appeal of a strong leader who promises to 'end debate' and overcome the laws and institutions which appear to frustrate 'common sense' is a recurring sickness of modern democracy. Looking beyond the UK, we see it in Hungary, Russia, Turkey, Poland and the USA. Whatever inherent appeal this kind of politics has, it certainly seems to be made worse by periods of economic malaise. Financial crises in particular lend towards a conspiratorial mindset that seems crucial to these movements. Tentative treatments, unfortunately, require being in government. The best remedy may well have been larger fiscal stimuli in the UK and the USA and a more relaxed attitude towards inflation from the ECB. Out of government the conditions of this virulent strain of authoritarian politics cannot be addressed, and once it achieves power it tends to make life for the opposition much more difficult. In the UK this will likely mean compulsory voter ID and greater levels of intimidation from the tabloid press. 

In the UK, there has been a particular reluctance to recognise this for what it is. This is often ascribed to a peculiarly British complacency due to the longevity of its political system and the fact that it did not experience fascism during the second world war or interwar period. But I think part of this is about politics too. Parts of the Labour left were a little too keen to normalise the 2016 referendum as a valid exercise in democracy. You can see why. In part it was a defence of the leadership's absence from the campaign (if you frame explanations of the result in terms of popular opinion, you can downplay the role of the leadership). Part of this is due to the ambivalence of some close to the leadership on the EU. And part of this is just party politics: many in Labour, rightly or wrongly decided that being seen not to 'respect' the referendum result was politically toxic. As a result, those who criticised the leave campaign's conduct, and saw this as crucial to an explanation of the result,  were often dismissed as delusional, self indulgent or downright conspiratorial. This is encapsulated neatly by Owen Jones' remark that in 2018 that "the Remain cause is sabotaged by a small, vocal arrogant clique who treat the referendum result as just mass stupidity and delusion, won through cheating, without understanding the anger that brought it about."

I fear that something similar is going on now from those opposed to Corbyn's leadership, amongst whom I would be included. To be clear, the leadership was not just foolish, but at times ghastly. Its blindness and tolerance for antisemitism was an encapsulation of a greater tendency towards conspiratorial thinking and reducing the world into simplistic, antagonistic relationships that do no justice to the left's rich intellectual tradition. But it would be a great mistake to let that excuse and normalise the outrageous practices of Johnson and the Conservative Party. The effectiveness of their transgressive strategies, or at least, the fact that they do not seem to come with a price, may be part of the explanation too.

Misappropriating Institutional Credibility


The Conservatives have come under fire in the last couple of days over their Twitter debacle. For those fortunate enough not to have followed the events, during the televised debate between Corbyn and Johnson on ITV, CCHQ altered their Twitter profile so as to appear as if they were an independent fact checking organisation, called FactcheckUK. The Twitter 'blue tick' gave the impression that this was a real organisation, verified by Twitter. True, tweets also displayed the CCHQ handle, but this is much less prominent, and many users would not even know who CCHQ are. In any case, it is very difficult to imagine a motive for this change other than to deceive. What's more worrying is this isn't a one off event. It's a pattern of behaviour we are seeing increasingly often, and unless I am mistaken, it is all coming from broadly the same group of people with the same campaign strategists. Conservatives are using either fake institutions or falsely appropriating the credibility of real ones in order to disguise party propaganda as trustworthy independent analysis.



The first examples of this were during the 2016 referendum campaign. Vote Leave, an organisation largely run by Conservative strategists, notably including Dominic Cummings, produced leaflets encouraging voters to support Brexit as a means of helping the NHS. They produced leaflets which used a (slightly changed) NHS logo, using a leaflet format  (font, colour scheme, layout etc) almost identical to those produced by the NHS. These appear to have been distributed in hospitals, with the words 'Help protect your local hospital' on the front. In doing so Vote Leave were misusing the institutional kudos of the NHS to add credibility their material. True, the leaflets also had the Vote Leave logo, and you might think that many people would realise what was going on. But some might not, which is why such deceptions can be effective. Indeed, Vote Leave were called out on this by the Treasury Select Committee during the campaign for this very reason, as can be viewed here:



Another, somewhat less egregious example of this behaviour during the campaign was this leaflet sent to households shown on the right here. The title page reads 'EU Referendum Facts', and the leaflet uses the independent sounding address www.eureferendumfacts.org, but the material was in fact produced by Vote Leave.


This strategy appears to have been repeated after the referendum, albeit with somewhat more organisational effort. In 2017, Conservative MEP and former Vote Leave committee member Daniel Hannan set up the pro-Brexit think tank IFT, whose launch event was attended by Boris Johnson. The organisation was initially called the Institute for Free Trade, but the organisation had to change its name. This is because the word 'Institute' is a protected title only given to reputable academic institutions publishing high quality research. The organisation managed to keep its acronym by changing their name to the Initiative for Free Trade. Once again, the effect of the exercise would have been to use misleading naming or presentation to pass of partisan material as that of a reputable, non partisan organisation.

There is a certain irony to all of this. Michael Gove famously said in 2016 that people had 'had enough of experts' from institutions 'with acronyms', and amongst many this remark has become symbolic of a particular style of politics. But in reality, those who practice that style seem to be fully aware of the power and kudos that can come with expert analysis backed up by trusted and respected institutions. This is why the strategy they seem to be pursuing is so dangerous.


Attitudes towards freedom of movement

A couple of days ago I spotted a rather surprising result on a YouGov poll: by an enormous margin, respondents said that they would like to maintain reciprocal rights of UK and EU citizens to live and work in each other's countries. Of those polled, 67% said such rights should be maintained, 15% said they shouldn't, and 19% said they did not know. In other words, what is generally believed to be the key motivation for Brexit, ending freedom of movement, is not wanted. These results got rather more attention on Twitter than I anticipated, and a number of people responded that they are merely a reflection of how the question is posed: if the question is framed in terms of 'control' of immigration, or simply in terms of support for "freedom of movement", the results would be quite different. I don't doubt that this is correct, but I wanted to briefly respond to this point, as I think it is an important one.

It is famously true that opinion polls can generate multiple answers to what is essentially the same question dependent on how it is framed. There are two possible responses to this. The first is simply to disregard the idea of popular opinion and see it purely as an ephemeral product of how questions are posed. Sometimes this may well be a reasonable assessment, and I think there is definitely such thing as a healthy skepticism around these issues.

But the second response is to say, OK, so what question is the most useful and informative? This of course depends a lot on what you are using the question for. If you are a political strategist, you might well find it very useful that questions which frame freedom of movement in terms of 'control' yield a negative reaction. But if you genuinely interested in trying to get an honest sense of public opinion as a means of guiding policy, the question has to be: "which way of describing freedom of movement is the most honest reflection of what the policy actually is?" No doubt this is itself contested, and there are occasions where the appropriate way of understanding a policy is genuinely a difficult question. But with freedom of movement, I don't see how framing the policy as a reciprocal right (the right for citizens to live and work in one another's countries) is not just the most simple, accurate, and thorough description. The alternatives either simply omit that reciprocity or present fictitious alternatives (one way rights for UK citizens, or systems of 'control' which imply much more effective and benevolent bureaucracies than actually ever exist).

For what it's worth, I don't think that public opinion on these questions should be the sole guide to policy. Stripping large numbers of people of acquired rights might well be wrong regardless of whether it is popular to do so. But it seems tragic for people to lose these rights on the basis of a popular support that does not even exist.

O Level and GCSE Maths Compared


When people of a certain age talk about GCSEs, the conversation may well quickly turn to the old ‘O Level’ qualification, and, more often than not, how much harder these were than anything 16 year olds are expected to do today. Part of the problem with these conversations is that few people are in a position to make a real comparison. Most people have only ever seen one type of exam, and if it is the O Levels, this was a long time ago. Perhaps for that reason, when I was a teenager (I was a weird teenager) the old exams had a certain mystique. As somebody who got a little too much of their sense of self through exam grades, I couldn’t help but wonder how I would have done at them.  While I’ll never know the answer to that question, thanks to the wonders of the internet, it’s certainly possible to compare the two exams, if you are geeky and obsessive enough to do so. What follows are the results of that endeavour with the old Maths O Level, and an attempt to answer that all important question: how much harder was it really?

The first thing to mention is that the O Levels (at least the exams from the ’50s and ‘60s) feel in many ways like very dated exams. They are densely printed, long, and in terms of structure feel a lot more like university exams. They have two sections, one of short questions and one of longer questions of which you choose a few (GCSE Maths papers don’t involve any choice).



Some of the material is very much from a time when people didn’t have calculators. There are lots of questions which are clearly testing your ability to use logarithmic and trigonometric tables and others which ask you to approximate π as 22/7 (at GCSE you’d either just put it in a calculator and round, or give your answer as a multiple of π, but it's still a nice approximation to use for rough calculations). There are then arithmetic problems which require some numerical manipulation to solve, often better thought of first as algebraic expressions to simplify, such as these ones here:


You can see why there would have been a greater focus on numerical skills before calculators, but I think it’s a bit of a shame this kind of numerical manipulation isn't taught as much anymore, as it can help children with algebra.  Part iii) of this question is also a reminder of another pesky feature of these exams: old, imperial units and pre-decimal currency (I couldn't answer part iii without looking up how many shillings there were in a pound!)  

That said, there is a lot about the exams that hasn’t changed at all. The algebra is pretty much the same, both in terms of content and level of difficulty (if we are comparing the O Level to the Higher Tier GCSE, after Gove’s reforms. The Foundation is dramatically less challenging, and prior to Gove’s reforms the GCSEs were considerably less difficult). This question, for example, taken from a 1962 O Level exam could have come straight out the GCSE were it not for the font: 
 



There are a few algebra questions in the O Levels which do seem a little more inventive in terms of what is asked. Question 4 (ii) below, for example, requires students not to solve for a single unknown but a quotient of two. That said, how difficult this kind of problem is very much depends on whether you have been taught to do it before or seen it for the first time, and I haven’t seen enough papers to know if this was a standard problem.


The section B algebra problems also seem to have required a little more in terms of initiative and personal input to solve. This one here, for example, I could only solve easily by introducing two unknowns of my own (I used n for the initial number of items sold and N for the total) which you could then get rid of by rearranging. 

The GCSE does require algebraic proof and introducing an unknown to solve numerical problems, but not introducing several unknowns to derive a purely algebraic expression which does not contain the variables you’ve introduced. An example of the type of problem tested at GCSE is here, which you solve by forming a quadratic (e.g by setting the number of green pens as x and blue as x+ 3). 



One way in which the O Level was definitely more challenging was the geometry. GCSE geometry questions tend to provide diagrams, the O Levels required you to figure out yourself what they would look like based only on worded descriptions. This question here, for example, could easily be a GCSE question, but there is no way they would ask you to do it without a diagram provided.


The proof questions were stylistically different, but don’t seem all that much more challenging. The main difference is volume: the O Level papers seem to have a lot of geometric proof involved, whereas on the GCSE there will only be a couple of questions. Below, for comparison, are two geometric proof questions, first a 1968 O Level and below that a 2017 GCSE question.





Content wise, the other main difference is that the O Level was in some ways a narrower exam. In the 1950’s and 60’s papers I didn’t find any statistics, data handling or probability questions, and very little on volumes, number properties, primes factor decomposition or surds. Algebra, geometry and doing long calculations with tables and slide rules seemed to be the greater focus. That said, the O Level did require knowing some basic calculus, and apart from the Edexcel IGCSE this isn’t taught until A Level (and even with the IGCSE there is no integration). And one exam I found from 1957 also had a rather charming third paper on the history of mathematics. I don’t know if this was a common part of the curriculum or not, but there is certainly something wonderfully quaint about it.



So, all in all, was the O Level Maths exam more difficult than the GCSE? Compared to the exams I sat, pre Michael Gove, I regret to say the answer is certainly yes. Compared to the exams students sit now, I’m less certain. There are certainly fewer gift questions (even the higher tier GCSE still has a some very easy questions at the start of the exam, the O Level seemed to have fewer, and they were less easy). On balance, I would still conclude that the O Levels were a little more challenging, if nothing else because they required more personal input and initiative to do start the questions (introducing your own variables, working out what a geometry problem looks like based on a description). But they aren’t a million miles away from one another.