Groucho Marxism

Questions and answers on socialism, Marxism, and related topics

  • Materialist physics

    In a previous blog post I suggested that some ideas in physics that seem strange when formulated in a continuous framework based on infinite sets make more sense in a discrete framework based on finite sets. In this blog post I will attempt to flesh this out in more detail. Consider a particle moving in discrete time and let x(t) denote the position of the particle at (discrete) time t. Let dt denote the increment between successive time steps. There are two ways to define velocity at time t: a ‘forward’ velocity u(t) = [x(t+dt)-x(t)]/dt, and a ‘backward’ velocity u(t) = [x(t)-x(t-dt)]/dt. We can already see therefore that it doesn’t make any sense to talk of ‘the’ velocity at time t. In a discrete context there is no notion of instantaneous velocity.

    Measure the position of the particle at time t, and you get x(t). Then measure the forward velocity of the particle, and you get [x(t+dt)-x(t)]/dt. Now measure position again, and you get x(t+dt) because the time has shifted to the next increment in order to allow the velocity measurement. In order to measure velocity, the position is necessarily shifted to its value at the next time step. In this sense, position and velocity measurements cannot commute in a discrete framework. Which is to say that the order you take these measurements in affects what measurements you get. This is the key idea that motivates our constructions. In a discrete time framework, position and velocity are not defined concurrently, as position is defined at a single point in time, whereas velocity is defined using two points in time.

    Suppose that we want to multiply together the position and forward velocity of the particle. If we measure position first we will get x(t)u(t), whereas if we measure velocity first we will get u(t)x(t+dt). Let us define the difference or commutator between the two as [x,u](t) = x(t)u(t)-u(t)x(t+dt). Then we have [x,u](t) = [x(t+dt)-x(t)]x(t)/dt-x(t+dt)[x(t+dt)-x(t)]/dt = [-x(t+dt)2+2x(t)x(t+dt)-x(t)2]/dt, and therefore [x,u](t) = -[x(t+dt)-x(t)]2/dt = -u2dt. Now suppose that our particle is undergoing a random walk, so that at each time step it moves a short distance dx to the left or right, each with probability p ≤ 1/2. Then u2 = dx2/dt2 with probability 2p, and u2 = 0 with probability 1-2p. Then using revised definition of the commutator [x,u](t) = E[x(t)u(t) – u(t)x(t+dt)] where E is the expectation operator, gives [x,u] = -2pdx2/dt.

    Let f(x,t) denote the probability that the particle will be in position x at time t. Then, using the fact that the particle stays in the same place with probability 1-2p, we can see immediately that the function f() satisifies the relation f(x,t+dt)=pf(x+dx,t)+(1-2p)f(x,t)+pf(x-dx,t). Analogously to the continuous case, we can define discrete partial derivatives as fx(x,t) = [f(x+dx,t)-f(x,t)]/dx and ft(x,t) = [f(x,t+dt)-f(x,t)]/dt. Then from our expression for f() above, we have ft(x,t) = p[f(x+dx,t)-2f(x,t)+f(x-dx,t)]/dt. Let us also define the second partial derivative of f() with respect to x as fxx(x,t) = [fx(x,t)-fx(x-dx,t)]/dx. Expanding this expression gives fxx(x,t) = [f(x+dx,t)-2f(x,t)+f(x-dx,t)]/dx2, and therefore ft = pfxxdx2/dt. In other words, the function f() satisfies a discrete version of the diffusion equation, with diffusion constant pdx2/dt.

    Now for the interesting bit. Let m denote the mass of the particle and set dx = ħ/mc, set dt = iħ/mc2, and set p = 1/2, where ħ is the reduced Planck constant, c is the speed of light, and i is the imaginary constant, so that i2 = -1. Then pdx2/dt = (ħ2/2m2c2)/(iħ/mc2) = ħ/2im = -iħ/2m, so [x,u] = iħ/m, or equivalently, [x,mu](t) = iħ, which is a discrete version of the canonical commutation relation between position and momentum. Furthermore, the function f() satisfies a discrete version of the Schrödinger equation: ft = -iħfxx/2m. We have just derived discrete versions of two of the most important relations in quantum mechanics using nothing but high-school algebra. Moreover, in deriving these results we may have uncovered some insights into why they hold, as we will now see.

    If m is the mass of the particle then ħ/mc is referred to as the particle’s Compton wavelength, defined as the wavelength of a photon whose energy is the same as the rest energy of that particle. Similarly, ħ/mc2 is referred to as the particle’s Compton time, which is simply the time of a step length of the Compton wavelength taken at the velocity of light. These are considered to be fundamental quantum mechanical properties of a particle. Now suppose that m is the Planck mass, the largest possible mass of a particle, so that m = √(ħc/G), where G is is Newton’s gravitational constant. Then ħ/mc is the Planck length, the smallest unit of length, and ħ/mc2 is the Planck time, the smallest unit of time. These amounts of mass, length, and time are constructed from the values of fundamental physical constants.

    Thus, our choice of units in the derivation above was far from arbitrary. What about the fact that we multiplied the Compton time by the imaginary constant i? This was not arbitrary either. The concept of ‘imaginary time’ is well established in physics, and was popularized by Stephen Hawking in his book The Universe in a Nutshell. It should be noted that the imaginary constant i is no more ‘imaginary’ than any other number; this unfortunate misnomer is only retained as it his become so well established in the mathematics world. I would argue that the imaginary constant i is more real than most ‘real’ numbers, as it can be constructed from the axioms of mathematics in a finite number of steps, whereas most ‘real’ numbers cannot.

    We have seen therefore that in a discrete framework, we can derive fundamental relations of quantum mechanics in a natural way without having to resort to the usual heavy-duty Hilbert space machinery. Furthermore, these derivations used parameters based on fundamental physical constants with a clear physical interpretation. Admittedly, we have only derived these relations in a special case, and more work would need to be done to see if these results could be generalized. There is no reason to think they couldn’t be though. In my view, a discrete framework is much more natural for quantum mechanics than a continuous framework. After all, quantum mechanics is fundamentally concerned with quanta – the smallest possible, and therefore indivisible, units of nature.

  • How old is human civilization?

    The standard account of human history runs as follows. First, modern humans evolved in Africa around 300,000 years ago. Then, for a long time nothing much happened, until about 11,000 years ago when somebody invented agriculture. After that, human civilization took off – and the rest, as they say, is history. There is a glaring problem with this story though: if modern humans evolved 300,000  years ago, why did it take us 290,000 years to invent agriculture? It’s not as though agriculture would be all that difficult to invent! In fact it’s now accepted that after agriculture was invented in the Middle East 11,000 years ago, it was invented again independently on at least four separate occasions. This makes the claim that we went 290,000 years without inventing it before that seem even more fishy.

    An alternative possibility is that we did invent agriculture before 11,000 years ago, perhaps many times, but then each time we subsequently forgot how to do it. This is rather implausible though, as if agriculture is relatively easy to invent, it is even easier keep doing it once it has been invented. Another possibility is that we invented agriculture before, but each time we invented it, for some reason civilization failed to develop. However, this also seems rather implausible, as almost every time agriculture has been invented in recent history, a civilization has subsequently followed. Agriculture was invented independently in the Middle East, China, Central America, and South America in the last 11,000 years, and in all these regions great civilizations then rose up.

    There is another possibility: we invented agriculture many times, and civilizations did follow, but then these civilizations subsequently fell into decline, leaving no trace. On the face of it this seems equally implausible. Surely any reasonably advanced civilization would have leave some sort of evidence for its existence that would have been discovered by now? Well, not necessarily. If our current civilization ended tomorrow, vegetation, storms, fires, frost, rust, earthquakes and burrowing animal activity would erase most of our visible traces within a thousand years. It is therefore quite possible that civilizations could have risen and fallen several times within the past 300,000 years and left no evidence behind – in fact, given the timescale involved, it seems more likely than not.

    Another reason that we may not have found any trace of previous civilizations is that the evidence may all be hidden underwater. Over the past 300,000 years, global sea levels have fluctuated significantly, with a rise of over 120 meters during inter-glacial cycles due to the growth and decay of ice sheets. If previous civilizations developed when sea levels were significantly lower then we wouldn’t have found any evidence for them, as it is very difficult to find archaeological evidence at the bottom of the ocean, and even more difficult to extract it! Perhaps flood-related myths like the city of Atlantis and Noah’s Ark aren’t myths at all, but are instead folk memories passed down through generations of events that actually occurred at some time in the distant past.

    The idea that human civilization might be much older than generally thought was recently brought to my attention by a YouTuber named Michael Button. I highly recommend that you check out his channel! Button’s thesis is very similar in spirit to the thesis put forward in a 2021 book by the anthropologist David Graeber and the archaeologist David Wengrow called The Dawn of Everything: A New History of Humanity. The book critiques traditional narratives of history’s linear development of civilization. Instead, The Dawn of Everything posits that humans lived in large, complex, but decentralized polities for millennia. According to Graeber and Wengrow, social emancipation can be found through this more accurate understanding of human history.

    In particular, Graeber and Wengrow argue that narratives of social development in which western civilization is self-appointed to be the highest point of achievement to date in a linear progression are largely myths. They suggest that our central question is how modern societies have lost the qualities of flexibility and political creativity that were once more common. Their argument is backed up by scientific evidence that has come to light only in the last few decades. Graeber and Wengrow’s thesis is a helpful antidote to ‘Capitalist Realism’, the widespread sense that not only is capitalism the only viable political and economic system, but also that it is impossible even to imagine a coherent alternative to it.

    Those who argue that capitalism is the only viable system are guilty of what might be called the ‘argument from personal incredulity’. This argument takes the form: ‘I can’t personally imagine how X could happen, therefore X couldn’t happen!’. The truth is that there are many possible alternatives to capitalism. Just because it is difficult to imagine what these alternatives might be doesn’t demonstrate that they don’t exist; all that demonstrates is a lack of imagination. The work of Button on one hand, and Graeber and Wengrow on the other, opens our eyes to the possibility that human civilizations existed in the past that were structured in entirely different ways to our modern society. This, in turn, should give us hope that capitalism can be defeated and replaced with something better.

  • Stand up to Zionism!

    The UK’s new left-wing party, provisionally called ‘Your Party’, still hasn’t officially launched yet, but already cracks are beginning to show. The bone of contention appears to be the question of the new party’s stance on Zionism. The dispute seems to have been sparked by Zara Sultana’s recent Twitter proclamation that she is anti-Zionist. This has led people to ask Jeremy Corbyn whether he is anti-Zionist too, to which he has so far failed to give a straight answer (in true politicians’ style). Many have concluded that his lack of a straight answer betrays that he is sympathetic to Zionism, or at least that the people advising him are. Some have even gone so far to argue that Corbyn is a Zionist himself. The issue has divided those supporting the party into two camps.

    In one camp (the Corbyn camp) are those who believe that whether the new party calls itself anti-Zionist or not is irrelevant. These people argue that the important thing is that the new party stands up for the Palestinian people, regardless of the party’s explicit stance on Zionism. For these people, arguing about whether Corbyn is a Zionist or not is at best pointless and at worst risks derailing the project before it has even started. In the other camp (the Sultana camp) are those who believe it is crucial that the new party declares itself to be anti-Zionist from the outset. These people argue that it is not possible to stand up for Palestinians without taking an explicitly anti-Zionist stance. For these people, failure to take such a stance means that the party is doomed to repeat mistakes of the past, and will therefore fail.

    So who is right? In order to answer this question, we first need to define what we mean by ‘Zionism’. Contrary to what some might say, this term is actually quite easy to define. Zionism is the nationalist movement that emerged in late 19th-century Europe to establish and support a Jewish homeland through the colonization of Palestine. The stated aim of Zionism is to create a Jewish state in the Levant with as much land, as many Jews, and as few Palestinian Arabs as possible. Straight away we can see the problem with the idea that it is possible to stand up for the Palestinian people without taking an explicitly anti-Zionist stance: Zionism as a concept is fundamentally antithetical to the rights of Palestinians.

    Those in the Corbyn camp would probably argue that Corbyn is anti-Zionist but doesn’t want to state that explicitly, as making such statements has got him into trouble in the past. In particular, he may be wary of once again being smeared as an antisemite; and on a personal level, I can totally understand that. The psychological abuse this man has had to endure since he became leader of the Labour party nine years ago has been off the charts. Imagine devoting your entire life to fighting racism, only to then become the target of a vicious and coordinated smear campaign as a result of which most of the country now thinks you are racist! When put in that way, it’s amazing he’s still participating in British politics at all, and the fact that he is testament to his resilience and devotion to the cause.

    However, if that is the case, it suggests Corbyn and his supporters have failed to learn the lessons of the past nine years. The problem wasn’t that Corbyn was perceived as anti-Zionist; on the contrary, the problem was that under his leadership, Labour conceded too much ground to the Zionist lobby. This was exactly the point that Chris Williamson made in his speech at the Labour Party Conference, for which he was accused of antisemitism and thrown out of the party. There was nothing remotely antisemitic in what Williamson said – in fact the thrust of it was that he was proud to be a member of a party that had done more than any other to combat racism. His removal from the party was done solely to placate the Zionist lobby. Needless to say, it didn’t work, and the smear campaign simply continued as before.

    What about the claim that Corbyn is himself a Zionist? This claim seems absurd at first given Corbyn’s support for the Palestinian cause, but there is some evidence behind it. First, as Labour leader, he opposed any boycott of Israeli goods. Second, in 2018, he declared support for a two-state solution, which is incompatible with giving Palestinians the right to return to their homes. Third, in an article in The Guardian in August 2018, he wrote that it was it was wrong to say that Zionism is racism, despite the fact that it is, by definition, a racist ideology. Fourth, he drove acceptance of the Zionist IHRA definition of antisemitism, which conflates antisemitism with anti-Zionism, through the Labour Party. Taking all of this into account, the claim that Corbyn is a Zionist starts to seem a lot more plausible.

    It will probably be clear from the above that I sit squarely in the Sultana camp on this issue. Zionism is a poisonous, supremacist ideology which must be opposed. Appeasement of the Zionist lobby should not be countenanced – firstly on principle, and secondly because it has been proven not to work. In my view, taking a firmly anti-Zionist stance is imperative to making the new left party a success. We must learn the lessons of the past and stand up to Zionism. At the end of the day, those who belong to the Zionist lobby are bullies – and aren’t we always told we should stand up to bullies?

  • Why are energy prices going up, again?

    The energy regulator for Great Britain, Ofgem, has just announced that it will raise the energy price cap by 2% from October. But what exactly is the energy price cap? Actually there are four energy price caps: one in pence per kWh and one in pence per day, for both gas and electricity. These represent the maximum amounts that suppliers can charge you for each unit of energy you use, or for each day that you use energy. They are all going up by 2%, which means that suppliers will be able to charge you 2% more for your energy from October. This may not sound a big increase but it comes off the back of huge increases in energy prices over recent years: according to data published by the Department for Energy and Net Zero, domestic energy bills in the UK have increased by over 50% on average since 2020.

    So why has Ofgem done this? According to them, it is because of increased wholesale gas and electricity costs. And in fairness to Ofgem, these costs do seem to have gone up slightly in recent months. But this does raise the question of what the point of having a price cap is if it isn’t fixed but is instead tied to wholesale energy costs. Ostensibly the point is of course to prevent suppliers from charging too much for energy bills; but in making the price cap dependent on wholesale costs, Ofgem is effectively ensuring that whenever these costs go up, it is the public that has to foot the bill rather than the suppliers. Thus, although the cap is supposedly there to protect consumers, the way it is set means that it ends up protecting suppliers’ profit margins instead.

    In fact the very existence of the price cap is a tacit admission that a privatized energy system doesn’t make any sense. The unspoken implication is that if the price cap wasn’t there, energy suppliers would charge even more for the energy they supply by applying even bigger mark-ups to wholesale costs. But the whole justification for having a market-based system is that it will be better for consumers, as competition between suppliers will lead to increased efficiencies which will drive prices down! By this logic, there should be no need for the price cap, which is effectively a kind of price control; instead, we should simply be able to let supply and demand work its magic and reduce prices for the consumer. But as Ofgem and everyone else knows, in practice that just won’t happen.

    This leads to the question of why we have a privatized energy system at all. Even if you accept that energy bills need to be tied to wholesale energy prices, why should they also have an additional profit margin slapped on top of them? This wouldn’t be necessary if energy was provided by the state. As already noted, the usual justification that a market-based solution will drive down prices doesn’t hold here. In fact it doesn’t hold for any service that relies on fixed infrastructure, as fixed infrastructure creates what economists call a ‘natural monopoly’. This is why, for example, privatized air travel results in cheaper airline tickets, but privatized rail travel does not result in cheaper rail tickets (quite the opposite in fact).

    In reality, the reason we have a privatized energy system has nothing whatsoever to do with increasing efficiency, reducing costs, or any other of the phoney reasons usually put forward by neoliberal zealots. The reason, of course, is that it allows the ruling class to cream off additional profits at the expense of ordinary people, thereby providing another mechanism through which capitalists can exploit workers. In fact privatizing the energy system is particularly lucrative because, as any physicist will tell you, you can’t do anything without energy. As the economist Steve Keen puts it: labour without energy is a corpse. If energy prices go up then people basically have no choice but to pay the additional amount; it’s either that or freeze to death.

    The government would probably argue that even if it were to nationalize energy, prices would still need to be based on wholesale costs, which are set globally and are therefore not within the UK’s control. But this is only so because the UK is heavily reliant on imported gas to meet its energy needs, which in turn is a result of policy decisions made by this and previous governments. In fact in the UK we are in the bonkers situation where gas plants set the price for all electricity on the grid – even if that electricity is generated from renewable sources! This is due to our ’marginal cost pricing system’ where the price of electricity is set by the most expensive source needed to meet demand at any given time, which is typically gas-fired power plants.

    So under the existing framework, switching on mass to renewable energy sources would not result in price savings for the consumer, even if those renewable sources were entirely within the UK. This is particularly infuriating when you consider that it is now generally a lot cheaper to generate energy from renewable sources than it is to generate electricity from fossil fuels. Both wind and solar can now generate electricity at a cost of £40-£50 per MWh, whereas the  cost of gas-fired generation has increased to around £124 per MWh. Why don’t we simply get rid of the marginal cost pricing system then? Because it’s yet another profit-generating device. Until we remove the profit motive from our energy system, our energy prices will only continue to rise.

  • Why right-wingers are really protesting

    I recently returned from a long weekend visiting my family home in Devon. Driving back through the village where I grew up, I was surprised to see St. George’s Crosses painted on one of the village’s two zebra crossings. On the journey home through Somerset, Wiltshire, and Hampshire, seeing St. George’s Crosses and Union Flags flying everywhere, I started to wonder where this outpouring of patriotism was coming from. Was there a big sporting event on that I had failed to register? But the grim truth soon dawned on me. This was no outpouring of sporting patriotism: it was an outpouring of far-right nationalism. Suddenly the drive home started to seem much less enjoyable. This land I was driving through, which used to feel like home to me, now felt overtly hostile.

    It turns out that the proliferation of flags I was witnessing is the result of an orchestrated campaign run by a group called Operation Raise the Colours. The aims of this group are not entirely clear as they don’t seem to seem to have a website, or any other online presence for that matter. No doubt they would claim that they were simply being patriotic by encouraging people to fly their country’s flag; and under other circumstances, that would make perfect sense. In fact if the England men’s football team ever makes it to a World Cup final, I will be tempted to get the red paint out and start painting zebra crossings myself. But the circumstances we find ourselves in now are a lot darker. It seems clear, in fact, that this campaign is directly linked to a recent protest outside a hotel housing asylum seekers in Epping.

    Now protests outside hotels housing asylum seekers are nothing new. There have been many such protests at hotels all over the country, including at a hotel just down the road from where I live. But what makes the recent protest outside the Epping hotel particularly significant is that it succeeded in driving out the asylum seekers living there. Last week, a High Court judge granted a temporary injunction and said migrants at the site in Essex would need to be moved out by 12 September, and one of the reasons cited for this decision was disruption caused by the protests and concerns for the safety of the asylum seekers themselves. The message is clear: protesting outside hotels housing asylum seekers works. It’s no wonder the far-right felt emboldened to run its nationalistic flag campaign.

    What should the left do in response to all this? It is tempting to say we should do all we can raise the alarm about how this is the next step on our seemingly inexorable slide into fascism. And it certainly feels like we are heading that way. In my 40+ years living in the UK I have never known the far right to be so brazenly self-confident as they are at this moment. But I think making a big issue out of these events would play into the hands of those orchestrating them, who are obviously doing it at least in part to try and provoke exactly such a response. Instead, I think we need to take a more nuanced approach which begins with understanding the root causes. As ever, these root causes lie in the material conditions people find themselves in.

    I have often wondered why people bother giving up their spare time to protest about asylum seekers. You’d think they’d have better things to do! These protesters can’t all just be knuckle-dragging racists (although I’m sure some of them are). So I recently signed up to my local right-wing Facebook group to try and find out a bit more about what motivates them. What I found was quite revealing: far from being motivated by hatred of asylum seekers as people, these protesters mainly seem aggrieved by their perception that asylum seekers are getting a better deal than them and their fellow countrymen. Of course, that probably isn’t the case in reality, and I doubt many locals would willingly swap places with an asylum seeker given the chance; but still, this perception persists.

    What these people are really protesting about, I think, is the fact that their lives are hard and only ever seem to be getting harder. But they cannot articulate their grievance in this way as they have internalized the bogus right-wing narrative that we are all ultimately responsible for our own fate. Instead, having internalized this narrative, they take matters into their own hands in the only way they know how: by attacking those they perceive to be getting an unfairly easy ride. To be clear, I am not in any way condoning the actions of these protesters – far from it. There can be no excuse for the kind of behaviour we have seen recently in Epping and elsewhere. But only by understanding the root causes of social issues will we ever be able to adequately address them.

    So I think we on the left need to find a way to explain to those protesting about asylum seekers the real reason why their lives are so difficult. And that reason, of course, has nothing to do with asylum seekers: it is because they are living under neoliberal capitalism. In fact these are the people most adversely effected by living under this draconian, exploitative system. If there is a positive to take from these recent events it’s that the working class in this country is genuinely angry and is willing to take their anger out onto the streets. If we can somehow redirect this anger away from asylum seekers and towards the real enemy – the ruling class – then who knows what we might achieve.

  • Reform or revolution

    Rosa Luxemburg led an interesting life. Born Rozalia Luksenburg in 1871 to a Jewish family in Russian-occupied Poland, Luxemburg became a German citizen in 1898. Her opposition to WWI led her to co-found the Spartacus League, an anti-war Marxist revolutionary movement, as a result of which she was imprisoned for most of the war. After her release, during the German Revolution, Luxemburg co-founded the Communist Party of Germany and was a central figure in the January 1919 Spartacist uprising in Berlin (mentioned in a previous blog post). When the revolt was crushed by the Freikorps, a government-sponsored paramilitary group, Luxemburg and the other leaders were captured and summarily executed, leading to her becoming revered as a martyr on the left.

    In 1899 Luxemburg published a short but highly influential book entitled Social Reform or Revolution? (German: Sozialreform oder Revolution?), in which she argues that trade unions, reformist political parties, and the expansion of social democracy, whilst important to the proletariat’s development of class consciousness, cannot by themselves create a socialist society. Instead, she argues that capitalism is intrinsically unsustainable and will eventually collapse, and that a revolution is necessary to transform capitalism into socialism. The book is written as a detailed critique of the thinking of Eduard Bernstein, another prominent socialist theorist of the time, who advocated for a gradual, parliamentary path to socialism.

    Reading Social Reform or Revolution? today, what’s particularly striking is how prescient it seems. For example, Luxemburg identifies the expansion of credit and the stock market as things that will exacerbate capitalism’s periodic crises – not, as Bernstein argued, measures that gradually remove the tendency towards crisis. Luxemburg was proved spectacularly right by the great depression of 1929 and again by the financial crisis of 2008; both of these events were caused by over-indebtedness of the private sector and were exacerbated by speculation in the stock markets. In highlighting these factors Luxemburg foreshadowed later 20th century economists such as Hyman Minsky, who argued that accumulation of debt (or credit) by the non-government sector pushes an economy towards crisis.

    In fact the 125-year period since the publication of Social Reform or Revolution? can be seen as one long vindication of the book’s central thesis. We had a period of social reform in the Western world in the 30 years following WWII, largely as a response to the threat of socialist revolution created by the existence of the Soviet Union and its socialist allies. But this did not lead to socialism as Bernstein predicted; instead, these reforms were rolled back as soon as the Soviet Union’s power started to wane and the possibility of revolution began to diminish. Conversely, where socialism has been implemented successfully in the last 125 years – e.g. in Russia, China, Vietnam, and Cuba – it has been as the result of a revolution.

    Another example of Luxemburg’s prescience is her insightful take on trade unions. The importance of trade unions, she argued, is not that they could end bourgeois ownership of capital; rather, they are the body through which workers come together and understand that they are part of a class. Trade unions will never bring down capitalism on their own – and in fact there are countless of examples of trade union bureaucracies acting as a brake on revolutionary movements. The best that can be hoped for is that by bargaining for higher wages, trade unions provide workers with a few more crumbs from the capitalists’ table. But bringing workers together is a necessary step in developing class consciousness, which in turn is a necessary step in bringing about a successful revolution.

    Capitalism is fundamentally unreformable, Luxemburg argues, because of features that are baked into it. For example, we will never be able to reform away unemployment as in order to function effectively, capitalism relies on permanently maintaining a class of unemployed people (referred to by Marx as the ‘reserve army of labour’). In other words, unemployment is a feature of capitalism, not a bug. Any reforms won by labour will therefore be relatively small and insignificant, and trying to reform capitalism from within will be like trying to sweeten the ocean with lemonade. In fact Luxemburg likens union struggles to the labour of Sisyphus, the mythical figure who was condemned to push a stone up a hill over and over again for all eternity.

    But rather than diminish the importance of the struggles by workers, Luxemburg argues that these struggles are central. Social Reform or Revolution? should therefore be read as a call to action. It would be great if capitalism could be gradually reformed from within, as then we could all just sit around reading poetry and let the social democrats get on with it, but it’s just not going to happen. Not only is capitalism unreformable; it will inevitably fall. The expansion of credit means that capitalism is structured as a giant Ponzi scheme, and like any Ponzi scheme, it will eventually collapse. The question is, what comes next? As Rosa Luxemburg herself said, there are two possibilities: socialism or barbarism. We have act now to make sure it’s the former and not the latter.

  • Why did Labour lose so badly in 2019?

    In 2019, the Labour party suffered a humiliating defeat in the UK general election, losing 59 seats, the second-highest loss by any opposition for a century. Many explanations have been put forward for this collapse, but the three most commonly touted are: 1) unpopularity of Jeremy Corbyn and, by extension, the party leadership; 2) the party’s overly ambitious manifesto; and 3) confusion over the party’s Brexit strategy. In this blog post, I will go through each of these reasons in turn and see which, if any, hold water. But before getting into the details, it’s worth pointing out that one of the reasons the defeat seemed so catastrophic is that it was compared to the 2017 election, where Labour performed above expectations. Therefore the question we need to ask is: what changed between 2017 and 2019?

    Let’s start with the unpopularity of Jeremy Corbyn. There is no doubt that on the face of it at least, Corbyn was hugely unpopular with the British electorate. According to Ipsos Mori, Corbyn went into the campaign with the lowest net satisfaction ratings of any opposition leader since the late 1970s. There are reasons to be circumspect about statistics such as these though – the main one being that they don’t tell us anything about why Corbyn was so unpopular, and therefore only provide a partial explanation at best. It seems that for many people, antisemitism and the perceived absence of an apology was the key issue. If so, this largely exonerates Corbyn, as the Labour ‘antisemitism crisis’ has now been completely debunked.

    This suggests that it is not actually Jeremy Corbyn himself who was unpopular but the fabricated version of him that people came to know through the mainstream media. This fabricated person was either an antisemite himself, or on a slightly more sympathetic reading, was not necessarily an antisemite but was more than happy to lead a party full of antisemites into a general election. Of course, anyone who knows anything about Jeremy Corbyn knows that neither of these things is even remotely true, but that didn’t matter: what mattered was that enough people believed them. Clearly, though, it doesn’t make any sense to blame the election defeat on the personal characteristics of Jeremy Corbyn if the vast majority of the electorate didn’t know the first thing about these characteristics.

    So let’s move on to explanation number two: the party’s overly ambitious manifesto. We can dispense with this one pretty quickly. It’s true that there was a lot on offer in Labour’s 2019 manifesto: from free care for the elderly, free university tuition fees, reducing the voting age to 16 and payouts for Waspi women, the party attempted to speak to every sector of society. Apparently, this put people off voting for them. There are two things to say in response to this. First, nobody reads party manifestos. And second, it doesn’t make any sense to say that a party manifesto that appealed to all sectors of society would put people off voting for that party. In fact, the idea is plainly absurd. I honestly can’t understand how anyone can hold this up as a reason for Labour’s defeat and keep a straight face.

    Which brings us to explanation number three: confusion over the party’s Brexit strategy. It’s true that Corbyn and the party leadership equivocated over Brexit for a long time. However this explanation as it stands doesn’t make a lot of sense as by the time of the 2019 election, Labour’s Brexit strategy was clear: the party backed a second referendum. But perhaps it wasn’t confusion over the party’s Brexit strategy that was the issue; perhaps it was the Brexit strategy itself? This explanation is not popular with the liberal commentariat, most of whom voted remain, supported a second referendum, and agitated for the Labour party to do the same. Unfortunately for the liberal commentariat, however, this explanation is the one backed up by the most evidence.

    Labour announced it would back a second referendum in February 2019, as a last resort to stop a Tory no-deal Brexit. At that point, Labour were and the Tories were neck-and-neck on around 40% in the polls, as they had been since the 2017 election. From that point onwards, Labour’s vote share declined precipitously, reaching a low of around 20% in July 2019; and although it rallied slightly after that, it never fully recovered to it’s pre-February 2019 level. If that wasn’t incriminating enough, there is the fact that of the 54 seats Labour lost to the Tories, 52 were in leave-voting constituencies. Finally, there is the fact that between the 2017 and 2019 general elections, Labour lost around 3 million votes, whereas the number of people voting Tory remained roughly the same.

    Returning to the question posed earlier, we may therefore ask again: what changed between 2017 and 2019? The Labour party leadership and policy platform remained broadly the same during this period; the one thing that changed significantly was the party’s stance on Brexit. All the evidence points to this being the key reason for Labour’s catastrophic defeat. In fact, I don’t think the 2019 election would have happened at all had the Labour party not backed a second referendum. It doesn’t take a genius to work out why the Tories decided to hold an election when Labour was languishing at around 20% in the polls. The Tories understood what the liberal commentariat apparently didn’t, or at least pretended not to: in backing a second referendum, Labour had effectively committed electoral suicide.

  • Materialist mathematics

    An axiomatic system is a set of formal statements (axioms) used to logically derive other statements. Zermelo-Fraenkel set theory, henceforth ‘ZF’, is an axiomatic system proposed by mathematicians Ernst Zermelo and Abraham Fraenkel in the early twentieth century to formulate a theory of sets. Today, ZF is the standard form of axiomatic set theory and is considered to be the foundation of all mathematics. Most of the axioms in ZF are uncontroversial and coincide with our intuition about sets. For example, the ‘axiom of extensionality’ states that two sets are equal if they have the same elements; and the ‘axiom of pairing’ states that if x and y are sets then there exists a set which has x and y as elements. Axioms like these seem entirely reasonable.

    Another axiom in ZF which is usually considered uncontroversial is the ‘axiom of infinity’, which basically states that there exists a set containing infinitely many members. However, unlike the other axioms, which are rooted in our real-world experience of how sets work, this axiom cannot be justified in this way. Sets with infinitely many elements simply do not exist anywhere in the world, or anywhere in the universe for that matter. So why is this axiom not considered more controversial? The reason, I think, is that this axiom, in conjunction with the other axioms in ZF, allows mathematicians to have fun creating all sorts of weird and wonderful infinite sets. In fact it’s probably fair to say that 99% of modern mathematics would not be possible without it.

    Now, we are free to choose the axioms of mathematics however we like. We could therefore choose to replace the axiom of infinity with its negation – i.e., assume that there are no sets containing infinitely many members. In fact it can be shown that ZF implies neither the axiom of infinity nor its negation and is therefore compatible with either. As noted already, the reason mathematicians are unwilling to do this is not that the axiom of infinity makes intuitive sense; it’s because replacing the axiom of infinity with its negation would deprive them of the opportunity to work with infinite sets. This seems to run counter to the way the axiomatic method is supposed to work. It is choosing the axioms to fit the mathematics, rather than fixing the axioms then seeing what mathematics be derived from them.

    If we want to root mathematics in the material world, it would make much more sense to assume the negation of the axiom of infinity (or equivalently, assume an ‘axiom of finiteness’). This raises a philosophical question about what mathematics is actually for. Is it a way of describing the world, or is it just a fun game that mathematicians play? Opinion seems to be divided on this matter. If it’s the latter than there is no problem with using the axiom of infinity. And to be clear, I have no problem with mathematicians treating mathematics as a fun game if that’s what they want to do. The problem arises when mathematicians try to justify what they do based on its real-world applications. This makes little sense when mathematics is based on an assumption that simply doesn’t apply in the material world.

    At this point mathematicians will probably point out that the whole of physics is based on mathematics which uses infinite sets. For example, differential calculus, the cornerstone of Newtonion mechanics, is defined using infinite limits. And quantum mechanics is defined mathematically using infinite-dimensional Hilbert spaces. The mathematics of general relativity also relies heavily on infinite sets. Wouldn’t the replacement of the axiom of infinity with its negation deprive us of the ability to do physics? I don’t think so. All of the theories mentioned above were developed intuitively before they were developed rigorously using infinite sets, and the reason they were developed rigorously in this way was simply that this was the prevailing mathematical paradigm of the time.

    It may actually be the case that many ideas in physics that seem strange when formulated using infinite sets make perfect sense in a finite framework. For example, the Heisenberg Uncertainty Principle states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. This seems counter-intuitive if we assume that time can be divided up into infinitely many segments. But if we assume time can only be divided up into finitely many segments, it seems a lot more intuitive. Position is then measured at one time point, whereas momentum is measured at two separate time points, so it makes sense that both cannot be known simultaneously.

    In my view, mathematics took a wrong turn over 100 years ago with the widespread acceptance of the axiom of infinity. In adopting this axiom, mathematicians unwittingly committed themselves to working within a Platonic or Idealist framework entirely detached from the material world. This wrong turn highlights the importance of getting your philosophical underpinnings correct. To put mathematics back on a firm materialist footing, we should replace the axiom of infinity with its negation. Only then will we be able to say that mathematics can truly describe the material universe in which we live.

  • What is the labour theory of value?

    Labour plays a central role in Marxian economics. In this context, ‘labour’ refers specifically to the physical act of working by human beings – but, crucially, not by animals or machines. Almost all other concepts in Marxian economics are derived from this basic concept. For example, ‘labour time’ is defined as the period of time that a person spends doing labour; and a ‘commodity’ is defined as a good or service produced by (human) labour and offered as a product for general sale. We can also define the ‘socially necessary labour time’ (SNLT) associated with a commodity as the average labour time required under current prevailing conditions to produce it. This is also referred to as the labour value, or simply the value, of a commodity.

    Labour value is just one attribute of a commodity, the other four being use value, exchange value, production price, and market price. ‘Use value’ refers to the tangible features of a commodity which can satisfy some human requirement; ‘exchange value’ refers to the proportion at which a commodity can be exchanged for other commodities; ‘production price’ refers to the cost of producing a commodity multiplied by a factor of 1 + the average profit rate under current prevailing conditions; and market price refers to the actual prices paid for a commodity on the market. The ‘labour theory of value’ (LTV), also known as the law of value, posits that the exchange value of a commodity is proportional to its labour value (or equivalently, to its SNLT).

    Production prices can be thought of as exchange vales expressed in monetary terms. Marxian economists argue two things about such prices. The first is that they act as ‘centres of gravity’ for market prices; and the second is that they are proportional to labour Values (i.e. the LTV holds). To make rigorous the second of these propositions, consider an economy with n sectors that specialize in the production of one commodity type. The economy is determined by an n × n input-output matrix of inter-sector coefficients A = [aij], where aij ≥ 0 is the quantity of commodity i directly required to produce one unit of commodity j; and a 1 × n vector of direct labour coefficients L = [Li], where Li > 0 is the quantity of labour directly required to output 1 unit of commodity i.

    For such an economy, labour values v are usually defined by the equation v = vA + L, and prices of production p by the equation p = (pA + Lw)(1 + r), where w,r ≥ 0 are the average wage and average profit rate respectively. Rearranging these equations gives v = (I – A)-1L and p = (I – A(1 + r))-1Lw(1 + r). If the average profit rate r = 0 then p = vw and the LTV holds; but in general, r > 0, and the LTV doesn’t hold. However if instead we define Labour Values by the equation v = (vA + L)(1 + r), we have v = (I – A(1 + r))-1L(1 + r) and therefore p = vw for all values of r. Therefore we can easily define labour Values such that they are proportional to Production Prices and the LTV holds. Moreover, defining Labour Values in this way is arguably closer in spirit to the socially necessary labour time concept first introduced by Marx.

    Thus, it is possible to define labour values and production prices in such a way that the LTV holds trivially by definition. What about the claim that production prices act as a centre of gravity for Market Prices? This proposition must be tested empirically. Many studies have attempted to do this and have claimed to demonstrate a correlation between production prices and market prices. However, these studies have been rightly criticized on the grounds that they use aggregate prices of entire sectors of the economy rather than using prices of individual commodities. A correlation at sector level does not imply a correlation at commodity level, as it could be caused by the number of commodities in each sector correlating with itself.

    The problem is that testing directly for a correlation at commodity level is almost impossible as it requires estimating an input-output matrix A at commodity level (i.e. one row and column for each commodity type in the economy), and the data required to estimate such a matrix just doesn’t exist. However, there is an alternative: we can look at how firms set prices. Do firms set prices based on supply and demand, or do they set prices by applying a fixed mark-up to their costs? If it’s the former, there is no reason that there should be a correlation between production prices and market prices; if it’s the latter, the two must be correlated. This empirical work has in fact already been done, and the results are clear: firms almost exclusively apply a fixed mark-up to their costs when setting prices.

    Therefore, we have clear evidence that production prices will act as a centre of gravity for market prices. Furthermore, we can define Labour Values in a sensible way such that the LTV holds, from which it follows that Labour Values will also act as a centre of gravity for market prices. It seems odd therefore that this idea is often considered controversial. The only step in the chain that can really be argued with is the definition of labour values; but any other measure of ‘value’ will not, in general, correlate with Market Prices. As Marx realized over 150 years ago, the only measure of value that can explain Market Prices is one based on accumulated labour time. It is for this reason that the LTV is and will always remain cornerstone of Marxian economics.

  • Lessons from the German revolution

    We are currently seeing a rise of right-wing population across the Western world. In the UK, Reform, an openly racist party, is leading in the opinion polls; and in the US, populist president Donald Trump seems to be attempting to act like a medieval king. It’s not all bad news though. In the UK, the announcement of a new left-wing party has created a wave of optimism and the party has already attracted over 700,000 members despite not yet having a name. And in France and Germany, young people are increasingly turning to Melanchon and Die Linke respectively. This bifurcation in political views has clear parallels with the situation in Europe around a century ago, which raises the question of what we can learn from looking back at that period. In this blog post I will focus on lessons from the failed German revolution of 1918-1923.

    Germany was unified as a nation relatively recently, in 1871. After unification, German industrial production grew enormously and a mighty industrial proletariat was created, with Germany soon rivaling Great Britain as an industrial power. However, as imperial Britain and France carved up the world, Germany was offered crumbs from the table. This led to tensions between Germany on the one hand and Britain and France on the other which eventually lead to the breakout of war in 1914. WWI was a capitalist war driven by profit, and as such was generally opposed by the left. However, the left-wing German Social Democratic Party (SPD), which had an official position opposing imperialism, sided with the capitalist parties in the German parliament and supported the war.

    In response, anti-militarist socialists convened a conference in Zimmerwald in 1915, where the majority of delegates called for peace. However, a certain Vladimir Lenin was at the conference, and he and other left-wing delegates called for turning the capitalist war into a class war to take power from the bourgeoisie and end capitalism. This eventually led to the Russian Revolution of 1917, which had an enormous effect on German workers and troops. By that point the war was going very badly for Germany: hundreds of thousands had been killed with no obvious path to victory in sight. Dissatisfaction with the war and awareness of what was happening in Russia led to increasing calls for a socialist revolution in Germany.

    The SPD, still officially a Marxist party, used its authority to try to strangle the developing revolution, even going as far as murdering revolutionaries. But the German workers could not be crushed. The Bolsheviks in Russia saw a revolution in Germany as key both to breaking the isolation of the Russian revolution and to fermenting a wave of further revolutions across Europe, and lent their support to the German proletariat. In September 1918, there was an uprising of sailors in Kiel, Hamburg, and other cities, who refused to fight against the superior British fleet. Officers of the German navy had wanted a last sortie against the British even though the war was all but over, but the sailors took control of the fleet and flew red flags from the ships. Revolution was in the air!

    The sailors’ revolt sparked mass uprisings across Germany. In fact the German revolutionary movement was arguably stronger in 1918 than the Russian movement had been in 1917. Workers’ councils (soviets) were set up and cities were controlled by revolutionaries. This led to several opportunities for workers to seize overall control of the German state between 1918 and 1923. In 1919, for example, there was an uprising in the capital, Berlin, during which 500,000 came out on strike. Ultimately, though, none of the opportunities were taken. If any of them had been, Germany could have linked up with the otherwise isolated Russia to create a Europe-wide revolution. Instead, the failure of the German revolution led to civil war and famine in Russia, and ultimately to the consolidation of bureaucracy around Stalin.

    So why didn’t the revolution succeed in Germany as it had done in Russia? One obvious reason was the malign influence of the SPD. Trade unions were controlled by the SPD and union leaders acted as a reactionary brake on revolution. Another reason was the lack of a centralized revolutionary party with a program to take power. Although a centralized communist party was formed in 1920, this came only after a series of defeats and was a case of too little too late. It wasn’t all bad: the capitalist class, fearing revolution, granted an 8 hour working day, women’s suffrage, and release of political prisoners. But in the final reckoning, the German revolution must go down as a failure which ultimately led to the rise of Nazism and to WWII.

    There are many lessons we can learn from this failure. One lesson is to be wary of established left-wing organisations that often act against the interests of the people they purport to represent. Another lesson is to make sure a centralized revolutionary party is in place well before a revolution is likely to occur. A third lesson is that although a failed revolution may bring concessions from the capitalist class, a revolution needs to succeed fully in order to bring about the necessary transformation of society. A fourth lesson is that a successful revolution must take place across and not just within countries. And the final and probably most important lesson is that unless there is a successful international revolution, we are likely to again slide into fascism and war – and who knows what horrors that might unleash.