Groucho Marxism

Questions and answers on socialism, Marxism, and related topics

  • Our changeable brains

    The human brain is an incredibly complex organ. Nonetheless we usually imagine that our brains remain roughly static over time. A recent article in New Scientist argues that this view is incorrect. According to the conception outlined there, our brains our dynamic systems which transform continuously over the course of our lifetimes. In this blog post I will summarize some of the evidence put forward in this article. We begin by asking a seemingly innocuous question: When does adulthood begin? This question is notoriously difficult to answer scientifically. Legally of course, adulthood arrives at a specific time, typically at age 18 or 21 in most countries. But neurologically speaking things aren’t so straightforward as there isn’t an exact moment that the brain flips from a juvenile to adult state.

    Until around a decade ago, neuroscientists tended to assume that the brain fully develops around age 25 for most people. More recently, researchers have attempted to zero in on a more accurate number by looking at the development of brain structures. In childhood the brain has many neural connections which get pruned down during adolescence to make the brain more efficient. It should be possible in theory to pinpoint the moment when these structures top being pruned and define this as the point at which adulthood is reached. Unfortunately it is extremely difficult to do that in practice. Therefore, rather than asking when the brain starts looking like an adult’s, perhaps instead we should ask when it starts behaving like one.

    By analyzing the executive function of the brain – that is, the mental skills that allow us to plan, focus attention, remember instructions, and juggle multiple tasks successfully – researchers at the University of Minnesota have estimated that adulthood arrives much earlier than previously assumed, at around age 20. However given the complexity of the brain it may be misguided to fixate on this one particular function. Other researchers at the University of Cambridge have attempted to get a broader view by mapping brain development over the entire human lifespan. They found that the brain undergoes four major shifts, around ages 9, 32, 66, and 83. This suggests that the brain continues to refine itself far beyond the legal age of adulthood.

    Despite this lack of consensus, what is clear is that the brain is not fully developed at age 18, the legal age for adulthood in many countries. In particular, frontal lobe networks that are involved in impulse control tend to develop far later. This explains why younger people are less risk-averse than older people (they are far more likely to be involved in a driving accident, for example). The lack of consensus on when adulthood occurs makes clear that whereas legal, medical, and social systems need an exact definition of adulthood, neurology cannot provide one. The idea that there isn’t a clear point at which childhood ends and adulthood begins is something I think we all understand intuitively, even if we don’t always like to admit it.

    Another time of life when peoples’ brains go through a transformation is during pregnancy. At this time the brain remodels itself to allow a mother to more effectively to care for her baby. Scientific consensus around this has undergone a profound shift in the past decade, and it is now understood that the brain begins to change from the earliest stages of pregnancy. The most striking changes occur in the default mode network, a system involved in self-reflection, planning, and emotional and social cognition. These changes are what enable the mother to immediately bond with her child. Evidence indicates that parenthood alters fathers’ brains too. It is unclear how long these changes last, but what is clear is that the parental brain seems to come with durable improvements in cognition.

    The obvious explanation for this is that the challenges of parenting force the brain to work harder, thereby building up cognitive improvement. It is difficult to test this hypothesis scientifically due to the many confounding factors involved. Whatever the explanation, there are many studies which suggest that parenthood has a positive impact on the brain. Interestingly, the research points to a upside down U-shaped relationship between number of children and cognitive impact. Apparently having four or more children can actually increase the risk of degenerative neurological conditions such as Alzheimer’s. (Perhaps the brain just gives up at that point.) For better or worse, having children clearly leaves an indelible mark on us.

    In a previous blog post I argued that the ‘self’, as usually understood – a core identity which remains constant and does not change over time – is an illusion. This view is in line with eastern philosophies such as Buddhism, Hinduism, Taoism, and Confucianism, view the self as an illusion or a transient construct. The research outlined in the recent New Scientist article provides scientific evidence to back up this claim. It seems that modern science is finally beginning to cotton on to what eastern philosophers have already known for thousands of years.

  • Reclaim the game!

    We are currently around halfway through the 2026 World Cup. It is estimated that this event will generate almost $41 billion in revenue for the economies of the host nations: the US, Mexico, and Canada. It will also generate billions in revenue for economies across the world. But it is the big companies that will benefit, not the workers who serve the food, staff the hotels, make the replica shirts, and so on. This World Cup was mired in controversy several months before a ball was even kicked. Back in December last year, the draw witnessed the spectacle of FIFA President Gianni Infantino grovelling to President Trump and ludicrously awarding him a Peace Trophy. This set the tone for what would be the most corporatized World Cup in history.

    The most egregious evidence of this corporatization can be found in the exorbitant ticket prices. Although there are some ‘cheap’ tickets costing around $60, tickets for most games cost between $400 and $700, and tickets for the final are likely to cost $8,000 plus. These high ticket prices are effectively a tax the loyalty of fans who travel the World Cup, many of whom have been forced to take out loans or spend their life savings just to watch their country play. The inevitable result is that often it is only the financial elite who are able to attend games, with thousands of tickets being bought up by corporations and every match being attended by a gaggle of celebrities, most of whom have no connection to football whatsoever.

    Forms of football have been played throughout the world for thousands of years. Unruly ‘folk football’ was played in Britain between the 12th and 19th centuries, pitting village against village. In the 17th century this spilled over into political action when folk football was played to oppose the enclosure of land. Football was subsequently banned by the state but a form continued to be played in the universities and public schools. The rules of football were codified at a meeting in London in 1863, and the (English) Football League was founded in 1888. Whilst the rules of football were developed in England, the passing game – reflection of the discipline of workers – was developed in Scotland. The fusion of the English rules and the Scottish mode of play then swept the world.

    Football soon became part of the fabric of British society, as workers would leave their mills, factories, or shipyards at 2pm on a Saturday afternoon, head to the pub, then on to the match at 3pm. The Football League, initially a Northern and Midlands League, expended nationally as the development of the rail network made travel easier. Clubs such as Manchester United and Arsenal were formed by workers: rail workers at Manchester United (originally Newton Heath) and munitions workers at Arsenal (originally Woolwich Arsenal). These clubs naturally had a socialist ethos, but it wasn’t long before football became a money making enterprise. As crowds increased, grounds were enclosed and an admission price was introduced.

    The development of the football industry has mirrored the development of capitalism and the industry now reflects the corporate neoliberal society that we live in, where the rich get richer and the poor struggle to survive. Big clubs are now owned by billionaires, or in some cases by petrostates. These corporate clubs are discussed in financial journals as much as in the back pages of the tabloids. Meanwhile, smaller clubs are facing financial meltdown. In 2019 Bury FC, one of the oldest football clubs in the world, went bust. Many smaller clubs have suffered a similar fate, often due to the actions of dodgy owners. Larger clubs appear to be exempt though: Manchester City, faced with 115 charges of financial irregularities, has so far not received any sanctions and continues to stack up trophies.

    Just as with any other multi-billion dollar corporate enterprise, football’s governing bodies are rotten to the core. But despite all the corruption football remains the peoples’ game. At every match in the World Cup we see people from all over the world sharing the joy of victory and misery of defeat. This shows that real solidarity naturally exists among people and is a refreshing counterpoint to the division fostered by capitalism and imperialism. It provides a glimpse of future human solidarity within a socialist society. We must link our fight against big business control of football to our fight against big business control of society more generally. It is time for us to wrest control of football from billionaire class, just as we must wrest control of society from the billionaire class.

  • A defence of MMT

    In recent years there has been a burst of interest in Modern Money Theory, or MMT. The essence of MMT is that sovereign currency-issuing governments, with flexible exchange rates and without foreign currency debt, are financially unconstrained and do not need collect taxes or borrow from financial markets to finance spending. This view, counter-intuitive as first seems, is nonetheless steadily accumulating adherents. MMT is not without its critics however. One particularly vocal opponent is the American economist Thomas Palley, who has recently devoted an entire series of academic articles to debunking MMT. In this blog post I will respond to some of the points made in Palley’s most recent article in this series, published in 2020.

    According to Palley, a sovereign currency-issuing government’s ability to create money to finance spending has “long been widely recognized by all economists” – including, presumably, Palley himself. Thus Palley does not object to the central claim of MMT, only to the idea that it is new. Personally, though, I don’t care whether the claim is new or not; I only care about whether it is true. The fact that a vehement critic of MMT such as Palley willingly accepts this claim can be taken as strong evidence that it is correct. Palley does however object to the claim made by proponents of MMT that the public cannot pay taxes until government has first spent it into existence, arguing that it is the central bank, not the government, that is the source of state money.

    Palley’s argument here rests on the independence of central banks. But are central banks really independent of government? The short answer is: no. Take for example the Bank of England, the central bank for the UK. Whilst nominally independent of government, the Bank of England is not really independent in any meaningful sense. Indeed, it has been wholly owned by the government since 1946. Although the government granted the Bank of England some operational independence in 1997, it kept a right of veto over everything it does: the Bank of England Act of 1998 provides a Chancellor with the option of overruling any decisions made by the bank. In practice, therefore, the Bank of England is independent of the government only as long as it does what the government wants.

    Palley argues that although in theory governments can create money at will to finance spending, in practice they are constrained by macroeconomic factors. In particular, he argues that any significant money-financed government spending without a concomitant increase in taxation will result in inflation, which in turn will cause long-term interest rates to rise. The reason for this is that lenders will only give out a loan if they think they can make money out of doing so. And they can only do that if the interest rate they receive on loan is higher than the rate at which the value of the loan depreciates in value, which is determined by the rate of inflation. Hence, higher inflation generally means higher long-term interest rates.

    There are a couple of ways to respond to this critique. One is to point out that MMT is a theory how government spending, taxation, and borrowing work in practice, rather than a theory of what governments should or shouldn’t do. MMT does not say that sovereign currency-issuing governments should run a money-financed budget deficit, just that there is nothing stopping them from doing that if they want to. You might wonder why a government would willingly choose to do something that will result in higher inflation and higher interest rates. But there might be case for doing that in situations where the alternative is worse – for example, if the economy requires a fiscal stimulus to avoid a recession.

    Another response is to point out that budget deficits do not necessarily lead to inflation (as I pointed out in a previous blog post). There is certainly a risk that running a persistent budget deficit will create inflation, which in turn will probably result in a rise in long-term interest rates. The risk of inflation alone might be enough to cause long-term interest rates to rise even if inflation does not actually occur in practice. But we cannot be sure that this will necessarily happen just because the government runs a budget deficit. There are many examples of countries running budget deficits for years without any significant increases in inflation (e.g. Japan). Inflation is a complex social phenomenon and assuming that ‘budget deficit = inflation’ is extremely reductive.

    Palley raises more points against MMT in his article, but I will leave responding to these to a future blog post.

  • Countering the far right

    Earlier this month the city of Belfast was rocked by racist violence. On 9 June, riots broke out across the city following a stabbing allegedly committed by a Sudanese man the previous evening. For the following two days gangs of youths roamed the streets of Belfast, spreading terror among migrant communities. Homes, businesses, and vehicles were set alight in scenes grimly reminiscent of the widespread sectarian violence of the past. There followed a courageous push-back by community groups with an anti-racist rally held on 12 June. The following day, thousands gathered outside Belfast City Hall to condemn the violence and targeting of ethnic minorities, in scenes that brought to mind historical protests against sectarian violence.

    Many are questioning the role of the police, particularly as a monitoring groups had been warning them for several months that far-right networks were circulating lists and addresses of immigrants. This highlights that immigrants cannot rely on the state to protect them from racist attacks. On the contrary, the state is largely responsible for these attacks. Successive governments have created the conditions for the emergence of the far right through starving working class communities of funding and essential services. The media and politicians have deliberately whipped up anti-immigration rhetoric to place the blame for the ills of society on a small minority. Clearly, the boast that the Good Friday Agreement would bring peace, stability, and prosperity to Northern Ireland has been exposed as a fraud.

    The events in Belfast are not isolated but part of a broader trend. Within the past month far-right marches have occurred in Brighton, Edinburgh, Glasgow, Sheffield, and Southampton, with similar marches planned elsewhere. What’s notable is that those protesting never seem that bothered when a white person carries out a similar attack. It’s almost as if they are just using it as an excuse! However in both Brighton and Sheffield, the protestors were vastly outnumbered by anti-racist counter-protestors. In Brighton, an estimated 300 far-right protestors were met with at least 4,000 people as part of an organized counter-protest; and in Sheffield, an estimated 100 protestors were outnumbered by around 600 anti-racists

    These events are taking  place against a backdrop of political turmoil. Last week, Keir Starmer finally faced the inevitable and announced he would be stepping down as Prime Minister. It is of course hugely gratifying to see this vain, duplicitous man finally get his comeuppance. Watching him cry when giving his resignation speech felt like watching a toddler cry when their favourite toy is taken away. But to anyone who thinks replacing Starmer with Burnham will revive Labour’s fortunes: I have a bridge to sell you. Just like Starmer, Burnham is a man with zero political convictions who clearly has no idea how to solve the problems this country is facing. He has already chosen a pro-Israel corporate lobbyist as his chief of staff. In short, Burnham is Starmer with a northern accent.

    Despite being ushered in with a ‘landslide’ victory at the last general election, Starmer’s tenure as Prime Minister ultimately lasted less than two years. If there is a positive to take from his disastrous reign it’s that the British electorate was able to see through him quite quickly. People are not stupid. It’s just a shame that they didn’t see through him when those of us on the left did six years ago. Although we shouldn’t be too smug as after all it was the left that was largely responsible for electing him as leader of the Labour party. My prediction is that Labour will see a small bump in popularity after the new leader takes over, shortly followed by an even steeper decline in popularity once people realize the new leader was no better than the old one.

    All of this shows that we cannot rely on our politicians to combat racism, so we have to do it ourselves. The recent counter-protests in Brighton and Sheffield demonstrate that the vast majority of people in this country are not racist or anti-immigrant and should give us hope that the far right can be defeated. The way to do that is to unite the working class around common demands such as affordable social housing for all, a living wage, and better opportunities for young people. It may difficult to eliminate racism completely; it may even be impossible. There will always be a handful of idiots in any society. But we can and should fight for a world where people are not forced to live in fear. Such a world is surely possible.

  • Capital in the 21st century

    Capital in the 21st Century is a book written in 2013 by the French economist Thomas Piketty which focuses on wealth and income inequality in Europe and the United States since the 18th century. The bookwas an instant worldwide success, with over 2.5 million copies sold by the end of 2017. Piketty’s central thesis is that when the rate of return on capital, r, is greater than the rate of economic growth, g, over the long term, the result is concentration of wealth which causes social and economic instability. Thus, the fundamental force for divergence and greater wealth inequality can be summed up in the inequality r > g. Piketty argues further that inequality is not an accident but is a feature of capitalism that can only be reversed through state interventionism.

    The book argues that the  trend towards higher inequality was reversed between 1930 and 1975 due to the fact that the two world wars and the Great Depression destroyed much wealth, particularly that owned by the elite. Since then the world has returned towards a system of ‘patrimonial capitalism’, in which the economy is dominated by inherited wealth. As a solution Piketty proposes a progressive annual global wealth tax of up to 2%, combined with a progressive income tax reaching as high as 80%, although he says that such taxes “would be politically impossible.” Without such a tax adjustment, Piketty predicts a world of low economic growth and extreme inequality. He shows that over long periods of time, the average return on investment outpaces economic growth by a wide margin.

    The exceptional success of Capital in the 21st Century was widely attributed to “being about the right subject at the right time”, as The Economist put it. The book also received much praise from mainstream academic economists. However the work has also received a fair amount of criticism. One strand of critique faults Piketty for placing inequality at the centre of analysis without any reflection on why it matters. Another strand focuses on Piketty’s methodology, arguing that he relies too heavily on the mainstream ‘neoclassical’ formulation of economics in his theoretical work. Yet another strand focuses on Piketty’s definitions, arguing that he uses a narrow and misleading concepts of ‘capital’ and ‘wealth’. There have even been allegations of errors in Piketty’s data.

    In 2014 the Greek economist Yanis Varoufakis wrote a critical review of Capital in the 21st Century, arguing that the book’s “chief theoretical thesis requires several indefensible axioms to animate and mobilise three economic ‘laws’ of which the first is a tautology, the second is based on an heroic assumption, and the third is a triviality.” The three laws Varoufakis refers to are described as follows. Law 1 states that w = x/z, where w = W/Y is the share of wealth W in aggregate income Y, x = X/Y is the ratio of income accruing to wealth X to aggregate income Y, and z = X/W is the ratio of income accruing to wealth X to wealth W. It is self-evident that this ‘law’ is simply an identity and is therefore devoid of theoretical content.

    Law 3 states that the rate of growth of w – that is, w’/w where w’ denotes the time derivative of w – is proportional to i-e·d, where i = I/Y is the ratio of inheritance transfers I to aggregate income Y, e is the ratio of mean wealth owned by people at the time of their death to the mean wealth of people already alive, and d is the death rate. As Varoufakis points out, this ‘law’ is a simple codification of the inevitable feedback of wealth disparities when the rich bequeath their wealth to their offspring. Law 2 states that w rises if (and only if) r > g, where r = R/Y is the ratio of aggregate savings R to aggregate income Y, and g = Y’/Y is the growth rate of aggregate income Y. This ‘law’ is the theoretical workhorse that energises Piketty’s analysis, but it rests on a crucial assumption.

    This assumption is that aggregate net savings R feeds fully into aggregate wealth W, i.e. that W’ = R; and furthermore, there can be no new wealth unless there are positive net savings from which to materialize. Whilst this assumption seems plausible, the question is whether it is consistent with the particular definition of wealth Piketty uses in his analysis, which is the sum of the market value of all extent assets. Varoufakis argues not, pointing out that wealth can fall at the same time that net savings are increasing – if house prices collapse, for example. He also points out that under modern capitalism, wealth (as defined by Piketty) can effectively be created out of nothing through the creation of derivates and other financial instruments.

    Varoufakis is quite correct in his critique of Piketty’s analysis. But I think a more incisive critique of Capital in the 21st Century is to point out that it is unnecessary. Rather than reading this book, you can simply observe what is going on in the world around you. This is a world which now has its first trillionaire: Elon Musk. And there will surely be more to follow. It is obvious that wealth inequality tends to increase under capitalism, as anyone who has lived under capitalism since the mid-1970s should be able to tell you. Extreme wealth concentration is just a feature of the system. There is no reason read a 700-page book full of questionable data, unjustifiable assumptions, and dodgy neoclassical analysis in order to understand this.

  • Constructing numbers from sets

    Most people assume that numbers are the basic building blocks of mathematics. But mathematicians take sets to be the basic building blocks and construct numbers from them. In this blog post I will explain how this is done. First we need to construct the natural numbers: 0, 1, 2, 3, and so on. There are several ways to do this; the standard method, due to the Hungarian mathematician Jon von Neumann, is to define 0 := {} (the empty set) then define a+1 := a∪{a} for each natural number a. Next we need to construct the integers: the natural numbers plus -1,-2, -3, and so on. This is done using ordered pairs (a,b) of natural numbers. Again there are several ways to define an ordered pair; the standard method, due to the Polish mathematician Kazimierz Kuratowski, is to define (a,b) := {{a},{a,b}}.

    We say two ordered pairs of natural numbers (a,b) and (c,d) are equivalent if a+d = b+c, and we write this as (a,b) ~ (c,d). The intuition is that (a,b) represents a-b, so (a,b) and (c,d) are equivalent if a-b = c-d. We can then define an integer to be an equivalence class of ordered pairs of natural numbers; so we define the integer a-b as the set [a,b] := {(c,d) : (a,b) ~ (c,d)}. Addition and multiplication of integers can be defined in terms of the equivalent operations on the natural numbers: [a,b]+[c,d] := [a+c,b+d]; [a,b]·[c,d] := [ac+bd,ad+bc]. The negation (or additive inverse) of an integer is obtained by reversing the order of the pair: -[a,b] := [b,a]. Hence subtraction can be defined as the addition of the additive inverse: [a,b]-[c,d] := [a+d,b+c]. The natural number a may be identified with the integer [a,0].

    Rational numbers are defined using ordered pairs (a,b) of integers where b ≠ 0. We say two ordered pairs of integers (a,b) and (c,d) are equivalent if ad = bc, and we write this as (a,b) ~ (c,d). The intuition is that (a,b) represents a/b, so (a,b) and (c,d) are equivalent if a/b = c/d. We can then define the rational number a/b as the set [[a,b]] := {(c,d) : (a,b) ~ (c,d)}. Addition and multiplication of rational numbers can be defined in terms of the equivalent operations on the integers: [[a,b]]+[[c,d]] := [a·d+b·c,b·d]; [[a,b]]·[[c,d]] := [a·c,b·d]. The multiplicative inverse of a rational number is obtained by reversing the order of the pair: 1/[[a,b]] := [[b,a]]. Hence division can be defined as multiplication by this inverse: [[a,b]]/[[c,d]] := [[a·d,b·c]]. The integer a may be identified with the rational number [[a,1]].

    In a previous blog post I sketched out a version of natural number arithmetic in which there is a largest natural number m with the following properties: m+a = a+m = m for any natural number a; m·0 = 0·m = 0; and m·a = a·m = m for any natural number a ≠ 0. We can identify m with the integer [m,0] and -m with the integer [0,m]. The integer -m is the smallest number. For any natural number a we have m-a = [m,a] and a-m = [a,m], and therefore m-m = [m,m] = 0. We can identify m with the rational number [[m,1]] and 1/m with the rational number [[1,m]]. The rational number 1/m is the smallest positive number. For any integer a we have m/a = [[m,a]] and a/m = [[a,m]], and therefore m/m = [[m,m]] = 1. We also have m·(1/m) = (1/m)·m = 1 and (1/m)·(1/m) = 1/m.

    Other well-known concepts in mathematics can also be constructed from sets. For example, a binary relation between two sets A and B can be defined as a set of ordered pairs (a,b) where a is an element of A and b is an element of b. The set of all such pairs is called the Cartesian product of A and B after the French mathematician René Descartes and is denoted by AxB or A·B. A function from A to B is defined as a binary relation f between A and B that satisfies the following conditions: (1) for all a in A there exists b in B such that (a,b) is in f; and (2) if (a,b) is in f and (a,c) is in f then b = c. The more usual terminology and notation can be derived from this formal definition by writing f(a) = b as shorthand for ‘(a,b) is an element of f.’

  • Young people are being screwed

    I often go and sell copies of The Socialist newspaper in my local town on a Saturday morning, as do many of my comrades in the Socialist Party. One of the things we have noticed recently is that more and more young people are approaching our stalls with concerns about education and employment. These people invariably seem to support the Party’s aims of nationalization, council house building, a £15 an hour minimum wage, and free education. They want better than what is being offered to them by capitalism – and frankly who can blame them? According to the Office for National Statistics, the numbers of young people not in employment, education, or training rose above one million in March 2026, the highest level in 12 years.

    For those in education the situation is also dire. They face a narrowed curriculum since the introduction of the EBacc in 2010 (focused on English, Maths, Science and the Humanities, at the expense of the arts), and a high stakes exams-focused curriculum which prioritises content and rote learning, all underpinned by competitive league tables. We should not be surprised by any of this. As the American sociologist Susan Ferguson points out in her book Children, Childhood and Capitalism, under capitalism schooling is fundamentally about disciplining children rather than educating them. We have seen this play out recently with the rise of ‘strict discipline-focused schools’ where compliance and control are prioritized above pupil wellbeing.

    As Ferguson outlines, schools disempower and repress children to force them to obtain the exam scores they need to be deemed ‘successful’. Any students who do not obtain the requisite grades are written off as failures. Children from poor backgrounds are hit particularly hard as they significantly underperform relative to their peers. According to the Education Endowment Foundation, in 2013 only around 30% of students receiving free school meals obtained five or more GCSEs at grade C or above, compared to around 60% for other students. Politicians talk of ‘closing the attainment gap’ but if anything the gap is getting bigger. Since 2019, the number of low-income, white British girls passing GCSE English and Maths has fallen by around six percentage points.

    Young people from poorer backgrounds are also more likely to be a ‘NEET’: not in employment, education, or training. The recent rise in NEETs has created some panic for those in the capitalist class – not because they care about the peoples’ wellbeing, but because the cost to the UK economy has been estimated to be around £125 billion per year. But there has been nothing done to alleviate the impact of poverty or the cost of living crisis on young people, especially the neurodivergent and vulnerable. According to the Milburn report, an independent review of the increase in the number of young people who are not in employment, education, or training, we have created “a generation that is functionally less able to engage with education and work.”

    Perhaps surprisingly, an estimated one in ten NEETs are also graduates. For many such graduates this has meant having to take out a ‘plan 2’ student loan. A recent inquiry suggests that around 30,000 of those who have taken out these loans did not understand the terms and conditions before they took them out. Many of these students were promised that a university degree would mean a guaranteed career; but this is not the case with an increasingly harsh jobs market. We have all heard horror stories of young people applying for hundreds of jobs without success or even contact from a human. Defenders of capitalism have offered various explanation for this ‘lost generation’, from a culture of disability and benefits to inadequate preparation in schools. But these are a smokescreen.

    The problem is not that young people are lazy or unwilling to work, as many right-wing commentators would have us believe. The problem is that they are being screwed over by neoliberalism capitalism. Just look at what the current ‘Labour’ government has done since coming into power: hiking tuition fees whilst making cuts to schools and other public services used primarily by young people. A functioning society requires investing in the future of young people. We could start by making education free and wiping off all student debt. The reason the government won’t do this is not because of a lack of money but because it goes against the neoliberal austerity agenda. This agenda exists to create artificial scarcity and discipline the working class.

    Anyone who thinks that young people can continued to be screwed over this way indefinitely is in for a surprise. There is only so far that people can be pushed. Young people are increasingly turning to socialism as they understand that is the only way out from the doom loop they find themselves in – as the heightened engagement with our socialist stalls demonstrates. Perhaps the revolution might not be too far off after all. And when it comes, we can be sure that young people will be the ones leading it.

  • What if there is a largest number?

    When children first start learning about numbers, a question they often ask is: what is the biggest number? At which point we adults usually explain that there is no biggest number as whatever number you can think of, you can always add 1 to make an even bigger number. But what if that wasn’t actually true? What if there was a number that you can’t add 1 to make an even bigger number? At first this idea strikes us as absurd. However we must bear in mind that numbers are a human invention and we are therefore free to define them, and operations on them, as we please. There is nothing to prevent us defining our number system in such a way that, instead of numbers going on forever, at some point they simply stop.

    The natural numbers – 0,1,2,3, and so on – and the operations on them are defined formally using something called the Peano axioms, named after the 19th century Italian mathematician Giuseppe Peano. The first axiom asserts the existence of at least one natural number; the next four are general statements about equality of natural numbers; the next three are statements about natural numbers expressing the fundamental properties of the ‘successor operation’; and the final axiom is a statement of the principle of ‘mathematical induction’ over the natural numbers. The successor operation is codified using a function S() which maps the set of all natural numbers to itself, with the interpretation that S(n) = n+1.

    These axioms were chosen because they best represent our intuitive understanding of how natural numbers work. But there is nothing to prevent us from changing any of these axioms and seeing what happens when we do. So let’s do that. One of the Peano axioms says that for all natural numbers m and n, S(m) = S(n) if and only if m = n; in words, the successor function always takes different output values given different input values. What if we replaced this axiom with its negation? The negation of this axiom says that there exist natural numbers m and n such that m ≠ n and S(m) = S(n); in words, there are (at least) two distinct numbers which yield the same result when the successor function is applied to them.

    Intuitively, we may take one of these numbers – say m – to be the largest number, and the other – say n  – to be the largest number minus 1. We can also stipulate that S(m) = S(n) = m – in words, adding 1 to m yields m – and that m is the only natural number with this property. As in standard Peano arithmetic, we may define addition of natural numbers using the successor function by a+0 = a and a+S(b) = S(a+b). Then m+0 = m; m+1 = m+S(0) = S(m+0) = S(m) = m; m+2 = m+S(1) = S(m+1) = S(m) = m; and so on. Therefore m+a = m for any natural number a. Similarly, we have 0+m = 0+S(m) = S(0+m), so 0+m = m; 1+m = 1+S(m) = S(1+m), so 1+m = m; 2+m = 2+S(m) = S(2+m), so 2+m = m; and so on. Therefore a+m = m for any natural number a.

    Again, as in standard Peano arithmetic, we may define multiplication recursively using the successor function by a·0 = 0 and a·S(b) = a+a·b. Then m·0 = 0; m·1 = m+m·0 = m+0 = m; m·2 = m+m·1 = m+m = m; and so on. Therefore m·a = m for any natural number a ≠ 0. We have 0·m = 0·S(m) = 0+0·m, which doesn’t tell us anything about 0·m, so we can stipulate that 0·m = m·0 = 0. For any natural number a ≠ 0 we have a·m = a+a·m, so a·m = m. Thus addition and multiplication with respect to the largest number m work as follows: m+a = a+m = m for any natural number a; m·0 = 0·m = 0; and m·a = a·m = m for any natural number a ≠ 0. These are identical to the rules usually used when applying addition and operation to infinity: ∞+a = a+∞ = ∞; ∞·0 = 0·∞ = 0; and ∞·a = a·∞ = ∞ for a ≠ 0.

    The Peano axioms can be derived from set theoretic constructions of the natural numbers and axioms of set theory. The standard construction of the naturals, due to the Hungarian mathematician John von Neumann, starts from a definition of 0 as the empty set, ∅, and defines the successor function S() by: S(a) = a∪{a}. Under this definition, a = {0,1,2,…,a-1} for each natural number a. In standard set theory the so-called axiom of infinity ensures that the set of natural numbers is infinite – i.e. that numbers go on forever. In a previous blog post I suggested that to better root mathematics in the material world we should replace the axiom of infinity with its negation, which in turn would mean that numbers do not go on forever. So perhaps the idea that there is a largest number is not so absurd after all.

  • The 2008 financial crisis

    As most people know, a major global financial crisis took place in 2008. The context for the crisis was the neoliberal boom of the late 90s and early 2000s, during which western governments claimed to have ended boom-and-bust. However a surface-level analysis is enough to make clear that ending boom-and-bust completely is not possible under capitalism. Even a naive ‘household’ theory of government spending demonstrates that you cannot grow an economy on money borrowed from the future for any significant period of time. This was made abundantly clear in 2008 when the celebrated boom, which had been going on over a decade by then, was ended by the deepest crisis of capitalism since the great depression.

    Despite the hubris of the pre-crash era, on some level the capitalist class must have understood they were being confronted by the largest fundamental problem of capitalism – namely, that growth cannot continue indefinitely. Having exhausted new areas of exploitation for the capitalist machine, the capitalist class convinced their friends in government to relax lending regulations. So loan eligibility regulations were eased to keep the money flowing. Banks understood that many of these loans would not be repaid, so they packaged them up with other, higher-rated debt into what became known as collateralized debt obligations or CDOs. Competition between credit rating agencies created a race to the bottom whereby many of these CDOs were given the highest AAA rating.

    Banks would then proceed to sell these AAA-rated CDOs to other banks in the market. But the banks buying these CDOs were well aware of what was going on as they were engaged in exactly the same dodgy practices themselves, so demanded an insurance policy against non-payment of these loans. This insurance policy took the form of a financial instrument called a credit default swap or CDS. These CDS instruments then started being traded on the market themselves, with further insurance – this time called re-insurance – taken out for any resulting losses. Inevitably the whole house of cards came crashing down when the underlying loans were not repaid. Looking back now it seems remarkable that any of this was allowed to happen.

    The capitalist media used the word ‘contagion’ to describe knock-on effect the crisis had on the wider economy, as if it was caused by some kind of outside invading force rather than an inherent problem with capitalism itself. The collapse of the financial services industry hit the UK particularly hard as Margaret Thatcher and her government had dismantled our primary secondary industries in the 1980s and re-organized the economy around the financial sector. Instead of bailing out workers, who had trusted banks with their money, states prioritized preventing banks from going bankrupt by guaranteeing liabilities and injecting liquidity: the US government issued $426 billion in bailouts to the banking sector, and the UK government £137 billion.

    These bailouts resulted in the crisis being transferred from the private to the public sector. The debts generated by speculative finance were effectively socialized – that is, paid for by ordinary people. Private financial excess was transformed into public debt and then repackaged politically a crisis of state overspending, which was then used to justify the austerity programs that followed. The UK coalition government that came to power in 2010 wasted little time in dismantling public services and farming out those that remained to the private sector. The impact on working people was devastating. Dependency on food banks increased dramatically and the UK saw are return of diseases not seen for over 100 years such as scurvy and rickets.

    Just as the boom causes the crises, usually the crisis also causes the next boom, as failing business are sold off cheaply to new capitalists who are then more easily able to extract a profit from them. However in this case there was no such recovery. Since 2008 capitalism has entered a zombified state with austerity and anemic growth the norm. You might wonder why governments are still inflicting austerity on us nearly 20 years after the crash occurred – particularly as the argument for austerity, which rests heavily on the government-as-household analogy, has now been completely discredited. The short answer is that capitalism relies on scarcity in order to function effectively. As we move to a post-scarcity society, scarcity must be imposed artificially through austerity.

    The 2008 crash was not simply a crisis of irresponsible lending, greedy bankers, or a few bad financial products.  It was a crisis rooted in the contradictions of capitalism. Faced with declining opportunities for profitable investment, capital increasingly turned towards financialization, debt expansion, and speculation to maintain growth. The inevitable collapse that resulted was paid for by working people through austerity, privatization, falling living standards, and the dismantling of public services. One thing is clear: the claim that capitalism can operate without boom-and-bust cycles has been well and truly debunked. The question is not whether capitalism will produce another crisis but whether the working class is organized to respond politically when the next one arrives.

  • A theory of justice

    A Theory of Justice is a 1971 work of political philosophy and ethics by the American philosopher John Rawls, in which the author attempts to provide a moral theory which is an alternative to utilitarianism and addresses the problem of distributive justice: the socially just distribution of goods in a society. In A Theory of Justice, Rawls argues for a principled reconciliation of liberty and equality that is meant to apply to the basic structure of a well-ordered society. The book is written in the social contract tradition, which assumes the legitimacy of the authority of the state over the individual. Rawls develops principles of justice through the use of an artificial device or thought experiment he calls the ‘original position’ whereby everyone decides principles of justice from behind a ‘veil of ignorance’.

    This ‘veil’ is one that essentially blinds people to all facts about themselves so they cannot tailor principles to their own advantage. Rawls claims that those in the original position would adopt a maximin strategy which would maximize the prospects of the least well-off. This idea is referred as a ‘thin theory of the good’; a ‘full theory of the good’ follows after we derive principles from the original position. Rawls then sets about doing just that. After some 45 chapters (!) of argumentation he finally arrives at two principles of justice. The first principle states that each person is to have an equal right to the most extensive total system of equal basic liberties compatible with a similar system of liberty for all. This is referred to as the ‘liberty principle’.

    The second principle states that social and economic inequalities are to be arranged so that they are both: (a) to the greatest benefit of the least advantaged; and (b) attached to offices and positions open to all under conditions of fair equality of opportunity. Part (a) of the second principle is referred to as the ‘difference principle’ and part (b) is referred to as the ‘equal opportunity principle’; the second principle as a whole may be referred to as the ‘equality principle’. The principles are ordered such that the greatest equal liberty principle takes priority, followed by the equal opportunity principle, and finally the difference principle. (Why Rawls decided to label the equal opportunity principle as (b) and the difference principle as (a), rather than label them the other way around, I’m not too sure.)

    In 2001 Rawls published Justice as Fairness: A Restatement as a revision of A Theory of Justice. In thisupdated work, Rawls list five types of political systems: (1) laissez-faire capitalism; (2) welfare-state capitalism; (3) state socialism with a command economy; (4) property-owning democracy; and (5) liberal democratic socialism. He then argues that the first three “[violate] the two principles of justice in at least one way” thus leaving property-owning democracy and liberal socialism as the “ideal descriptions” that include “arrangements designed to satisfy the two principles of justice.” Laissez-faire capitalism and welfare-state capitalism violate the second principle (equality) whereas state socialism violates the first (liberty).

    Rawls was undoubtedly one of the twentieth century’s preeminent philosophers. His ambition was to develop a theory of justice which appealed to basic moral intuitions as well as rational self-interest, thereby creating a ‘sense of justice’ that placed divisive conflicts within the context of agreed-upon principles. He rejected utilitarianism, correctly observing that it is often invoked so as to supersede fundamental rights and liberties. However for some, particularly those on the left, Rawls’ theory was insufficient as a critique of injustice. By holding the liberty principle prior to the equality principle, he effectively placed the right to property above distributional claims. Many saw this as a tacit defence of capitalism.

    When Rawls wrote A Theory of Justice – after the legislative achievements of the Civil Rights Movement and toward the tail end of the post-war boom – he was hopeful that liberal democracy was progressing on a just, egalitarian path. By the time he wrote Justice as Fairness: A Restatement, he had become deeply troubled by how private funding of elections allowed organized wealth to dominate the political process. Rawls understood that if the wealthy dominate the political system, the result is class domination rather than popular sovereignty. Whether that made him a socialist or not is open to debate (personally I think he wasn’t). But in the end it doesn’t really matter as Rawls’ intention was not settle arguments about justice but to enable us to better frame them.

  • Addiction and free will

    Some 10 years ago I witnessed a clash on BBC Newsnight between the British commentator Peter Hitchens and the American-Canadian actor Matthew Perry on the subject of addiction. Hitchens put forward the view that addiction does not really exist and is instead used as an excuse for hedonistic behaviour. Perry, who had claimed to have struggled from drug and alcohol addiction for many years, naturally disagreed. The sad death of Perry in 2023, later revealed to have occurred due to the effects of ketamine, once again put the issue of addiction at centre stage. It is tempting to dismiss Hitchens as a crank; but there are many who subscribe to his view on addiction. In this blog post I will attempt to debunk his arguments.

    Hitchens summarized his views on the subject in a 2017 article entitled ‘The Fantasy of Addiction.’ The crux of his argument is outlined in the following paragraph: “The chief difficulty with the word “addiction” is the idea that it describes a power greater than the will. If it exists in the way we use it and in the way our legal and medical systems assume it exists, then free will has been abolished. I know there are people who think and argue this is so. But this is not one of those things that can be demonstrated by falsifiable experiment. In the end, the idea that humans do not really have free will is a contentious opinion, not an objective fact.” However this last sentence is demonstrably false. As I explained in a previous blog post, the idea that human beings have free will is an illusion.

    Hitchens would probably respond to my claim by asking me to back it up experimentally. Unfortunately for him, there is a lot of experimental evidence which reinforces the idea that free will does not exist. A pioneering experiment in this field was conducted by the American neuroscientist Benjamin Libet in the 1980s, in which he asked each subject to choose a random moment to flick their wrist while he measured the associated activity in their brain. Libet found that the unconscious brain activity leading up to the conscious decision by the subject to flick their wrist began approximately half a second before the subject consciously felt that they had decided to move. Libet’s findings suggest that decisions are first made on an unconscious level and only afterward are translated into a ‘conscious decision.’

    There are dozens of other studies with similar findings that I won’t go into here. Suffice it to say that Hitchens’ second-to-last sentence above – “… this is not one of those things that can be demonstrated by falsifiable experiment” – is also false. However there is a better riposte that does require any experimental evidence at all, which involves pointing out that the concept of free will, as usually understood (and as understood by Hitchens), is incoherent. It implies that we can think a thought before we have thought it. In the memorable phrase of the Austrian-Swiss physicist Wolfgang Pauli, it’s “not even wrong.” There is no need to falsify the concept free will with experimental evidence as logic alone is enough to tell us that it cannot possibly exist.

    Hitchens goes on to argue that by using the word ‘addiction’ we are giving the addict “permission to carry on as before.” This is patently untrue. By using the word ‘addiction’ we are recognizing that the addict is suffering from an illness and needs to seek professional help. Hitchens laments the widespread use of the words ‘addiction’ and ‘addict’, arguing that addiction cannot be real because many ‘addicts’ cease to become ‘addicted’. I find it difficult to argue with this as I’m not really sure what point he’s trying to make. He seems to be getting bogged down in semantics here. Or perhaps he has difficulty understanding that someone can be addicted to something and some point in time, then not addicted to it at a later point in time.

    One (slightly) better argument Hitchens makes is that the burden of proof lies with those who posit that there is such a thing as addiction. This is quite correct; but what Hitchens hasn’t noticed is that the evidence that addiction is a real phenomenon is all around us. Millions of people around the world from all walks of life can be observed engaging in self-destructive, compulsive behaviour. There are two possible explanations: either these people are wilfully ruining their lives for the sake of a few minutes or hours of short-term pleasure, or they are suffering from an affliction which is making them act in ways in they wouldn’t dream of acting in otherwise. Hitchens apparently thinks the first explanation is more likely to be correct than the second. Most thinking people would disagree.

  • What is Palantir?

    The US tech giant Palantir Technologies recently won a contract with Coventry City Council to process data for its children’s services. This is one of many public contracts Palantir has secured in Britain recently, which include contracts with the NHS, Ministry of Defence, and police forces. Palantir also does work for the Israeli military, as well as with Immigration and Customs Enforcement (ICE) in the US. Donald Trump is apparently a big fan, as he wrote on his social media site, Truth Social: “Palantir Technologies (PLTR) has proven to have great war-fighting capabilities and equipment. Just ask our enemies!.” Thanks to its contract with the NHS, Palantir now has access to personal data of millions of UK citizens. But what is exactly is this company that nobody had even heard of until a few years ago?

    Palantir Technologies is an American software company that specializes in big data analytics, intelligence gathering, and artificial intelligence integration. Founded in 2003 with early funding from the CIA, it provides operating systems for defence, healthcare, and commercial enterprises to consolidate fragmented datasets and uncover complex patterns. Palantir offers three flagship software products: Palantir Gotham was built for the military and allows users to connect disparate information to manage operations; Palantir Foundry functions as a central data operating system for large commercial and public enterprises; and Palantir AIP (Artificial Intelligence Platform) allows organizations to securely activate and control artificial intelligence algorithms on their own private networks.

    Palantir has expanded significantly beyond its initial counter-terrorism and intelligence roots into several other sectors, particularly defence and healthcare. This has raised concerns from many observers. Human rights organizations and privacy advocates have voiced concerns over the company’s work with immigration enforcement and its technology being used in foreign military conflicts. Palantir has been criticized for its role in expanding government surveillance using artificial intelligence and facial recognition software. Critics have also questioned the ethics of integrating private tech platforms into sensitive national infrastructure like healthcare and defence. According to a former employee, the government can use Gotham to “centralize everything an agency knows about a person in one place.”

    Concerns about Palantir can be broadly categorized into four types. First, there are concerns around data privacy, as both Gotham and Foundry are designed to ingest and synthesize massive, disparate databases, raising fears of ’Big Brother’ levels of surveillance. Second, there are concerns around the company’s involvement in controversial operations such as US ICE deportations, predictive policing initiatives, and targeted military operations. Third, there are concerns around state dependency, with the UK government’s heavy reliance on a US corporation to manage highly sensitive public sectors, such as the NHS and police forces. And fourth, there are concerns around the ideological stances of Palantir’s leadership, with co-founder Peter Thiel and CEO Alex Karp frequently promoting right-wing views.

    The Israeli government began using Palantir software in 2014 and significantly scaled up its partnership during its genocide on Gaza. CEO Alex Karp has said: “I am proud that we are supporting Israel in every way we can.” The Israeli military has also used Palantir to plan further attacks in Lebanon and Gaza. Taking all of this into account, it is no exaggeration to say that Palantir is the most dangerous company in the world right now. It uses artificial intelligence to weaponize our data against us and to facilitate genocide. Palantir is a weapons company disguised as a software start-up; and it is everywhere. It is used by militaries, police forces, banks, hospitals, and even your local pharmacy or favourite fast-food place. This is truly dystopian stuff.

    So how can Palantir be stopped? Trade unions have a crucial role to play here. By coming together and organizing, unions can force the NHS, councils, and other public bodies to scrap their contracts with Palantir. Pro-capitalist commentators argue that we need tech giants like Palantir to ‘modernize’ the state; but this is nonsense. There is nothing to stop the government from hiring teams of skilled tech workers to develop the technology in-house. The technology could then be publically owned and put under constant democratic scrutiny. Unfortunately, when it comes to private companies profiting from the NHS and other public services, Palantir is just the tip of the iceberg. That is why our public services must be nationalized and placed under democratic, public control.

  • Marxian value theory

    The so-called Fundamental Marxian Theorem (FMT) was first proven by the Japanese economist Nubuo Okishio in 1963 and was developed further by the Japanese economist Michio Morishima in 1973 and 1974. The theorem asserts that, in Miroshima’s words, “the exploitation of labourers by capitalists is necessary and sufficient for the existence of a price-wage set yielding positive profits or, in other words, for the possibility of conserving the capitalist economy.” On the other hand, the ‘New Interpretation’ of Marx, put forward by the French economist Gérard Duménil 1980 and developed further by the American economist Duncan Foley in 1982, approaches Marxian value theory from another perspective, emphasizing the direct link between labour time and price.

    More recently, the issue of Marxian value theory was raised again by the development of the so-called ‘Temporal Single-System Interpretation’, first put forward by the American economist Andrew Kliman in 1999. There appears to be some controversy around which interpretation is the ‘correct’ one. In this blog post I will investigate these different interpretations of Marx. I’ve already devoted two blog posts to the original formulation of the FMT so I won’t go over that again here (see those blog posts for more info). In contrast to the original formulation, both the New Interpretation and Temporal Single-System Interpreration aim to connect price and labour time directly through the concept of the ‘monetary expression of labour time’, or MELT.

    Let (A,L) be a Leontief economy, where A ≥ 0 is the nxn commodity input matrix, and L ≥ 0 is the 1xn row vector of labour inputs. Then the MELT associated with the 1xn price vector p and nx1 commodity output vector q is defined by m = p(I-A)q/Lq, where I is the nxn identity matrix. Further, the value of labour power is defined by v = w/m = wLq/p(I-A)q. The total surplus value is then given by the equation S = Lq(1-v) = p(I-A-L)q/m = P/m, where P is the total profit. The FMT says that S > 0 if and only if P > 0, so a necessary condition for the FMT hold is that m > 0. From the definition of m, this is equivalent to p(I-A)q > 0, as Lq > 0. This is a different condition than was used in the original formulation of the FMT.

    Under the Temporal Single-System Interpretation, the value of labour power at the next time step, v’, is determined by the 1xn price vector at the previous time step, p, by v’ = pA+L; and the 1xn price vector at the next time step, p’, is given by p’ = pA+L+g, where g a 1xn vector with the property that gq = 0, where q is the nx1 commodity output vector. The real profit associated with the 1xn price vector p is defined by by P = p’q/(1+i)-C-V, where i is the rate of inflation, C = pAq is constant capital, and V = wLq is variable capital. Further, the rate of inflation is defined by i = (m’-m)/m, where m and m’ are the MELT at the current and next time step respectively. These are different to the definition of the MELT used in the New Interpretation and are instead defined recursively by m’ = mp’q/(pA+mL)q.

    According to the Temporal Single-System Interpretation, the total value added by labour, Lq, must be equal to p’q/m’-C/m. Multiplying both quantities by m gives mLq = mp’q/m’-C, and substituting in the expression for i above and rearranging gives p’q/(1+i) = C+mLq. Substituting this into the formula for real profit above gives P = mLq-V, and therefore P = mS, where S = Lq(1-w/m) is surplus value. The possibility of a negative m disappears provided the initial value in the recursion m’ = mp’q/(pA+mL)q is positive, in which case the FMT holds automatically. However, this result is only possible due to the change in definition of the MELT, from a static definition to a recursive one. This redefinition is considered somewhat controversial and is not accepted by all Marxist economists.

    Each of the three interpretations of Marxian value theory outlined in this blog posts starts with some assumption then shows that the FMT holds under this assumption. In the conventional interpretation, the FMT is proved under an assumption of ‘reproducibility’; in the New Interpretation, the FMT proved under the assumption of a positive MELT; and in the Temporal Single-System Interpretation, the FMT is proved under the assumption that the MELT satisfies a recursive equation. Which interpretation is considered to be ‘correct’ boils down to which assumption is most defensible. This is a question that can only be answered empirically, by looking at which assumption holds in actual capitalist economies.