Groucho Marxism

Questions and answers on socialism, Marxism, and related topics

  • Discrete calculus and optimization

    Mathematical optimization is the selection of a best element, with regard to some criterion, from some set of available alternatives. The criterion is specified using an objective function on a given domain and the aim is to find the variable that maximizes or minimizes this function within this domain. Mathematical optimization is generally divided into two sub-fields: continuous optimization and discrete optimization. In continuous optimization, the domain is a set of real numbers between which there are no gaps. Because of this no gap assumption, continuous optimization allows for the use of calculus techniques. In the simplest case, to find the maximum of minimum of a function f(), we simply set the derivative, f’(), to zero, and solve the resulting formula.

    For example, suppose we want to find the minimum of the objective function f(x) = x2-x+1 defined on the real numbers. First we take the derivative: f’(x) = 2x-1; then we set it to zero, which yields x = 1/2. So the objective function is maximized or minimized when x = 1/2. To know whether it is a maximum or minimum we need to take the second derivative: f’’(x) = 2. As this is positive, we know we have found a minimum, and therefore the minimum value of f() is given by f(1/2) = 1/4-1/2+1 = 3/4. Easy! Thus there is a fundamental and perhaps surprising link between calculus, the mathematical study of change, and mathematical optimization. I say surprising because calculus was invented for an entirely different purpose – to describe the motion of projectiles and other objects.

    In discrete optimization, on the other hand, the domain is a discrete (usually finite) set. In a previous blog post I outlined a discrete analogue of continuous calculus for functions defined on finite domains (see that blog post for more details). This raises the question of whether discrete calculus can be used for discrete optimization in the same way that continuous calculus can be used for continuous optimization. Consider a function f() defined on the finite domain X = {0,1,…,N}. The discrete forward derivative of a function f() defined on X is given by D+f(x) = f(x+1)-f(x), and the discrete backwards derivative is defined by D–f(x) = f(x)-f(x-1). Suppose again that we want to find the minimum of the function f(x) = x2-x+1 defined on X. Can we use discrete calculus to do this?

    Taking the forward derivative of the function f() gives: D+f(x) = f(x+1)-f(x) = (x+1)2-(x+1)+1-x2+x-1 = 2x; and setting this to zero gives x = 0. On the other hand, taking the backwards derivative of the function f() gives: D–f(x) = f(x)-f(x-1) = x2-x+1-(x-1)2+(x-1)-1 = 2x-2; and setting this to zero gives x = 1. Immediately we see a couple of problems: we get a different value depending on which derivative we use, and both values are different to the value we get using the continuous derivative! The latter problem shouldn’t concern us as the value we obtained using the continuous derivative is not in the domain X; but neither is the value we obtained using the discrete backwards derivative. Clearly, we cannot simply apply the same technique for discrete optimization as we used in the continuous case.

    We can, however, apply the same logic. If a minimum (maximum) exists at a point x in X then we would expect D+f(x) to be nonnegative (nonpositive) and D–f(x) to be nonpositive (nonnegative). Thus, to find the minimum  of the function f(x) = x2-x+1 we need to find a value x such that 2x ≥ 0 and 2x-2 ≤ 0, or x ≥ 0 and x ≤ 1. The only values of x in the set X that satisfies these inequalities are 0 and 1. Does these give us the minimum? The answer is yes, because f(0) = f(1) = 1, and this is indeed the minimum value of f(x) when x is constrained to lie in the set X. So we have successfully used discrete calculus to find the minimum of the function f(x) = x2-x+1 on the domain X. The question that naturally arises is: does this method work in general, or did we just get lucky?!

    Let us consider a more general problem of finding the minimum of the function f(x) = ax2+bx+c. Taking the forward derivative gives D+f(x) = f(x+1)-f(x) = a(x+1)2+b(x+1)+c-ax2-bx-c = a(2x+1)+b, and taking the backwards derivative gives D–f(x) = ax2+bx+c-a(x-1)2-b(x-1)-c = a(2x-1)+b. Setting the former to be nonnegative gives x ≥ -(1/2)-(b/2a), and setting the latter to be nonpositive gives x ≤ (1/2)-(b/2a). For both these inequalities to hold, x must lie in an interval of width 1 around the point -b/2a. In other words, x must equal -b/2a rounded to the nearest integer, which might be two integers if -b/2a lies exactly halfway between them (as with our example above). We know from continuous calculus that the function f(x) = ax2+bx+c defined on the reals is minimized when x = -b/2a, so this is the correct result.

    In fact it obvious when you think about it that D+f(x) ≥ 0, D–f(x) ≤ 0 are necessary conditions for x to be a minimum of the discrete function f(), and that D+f(x) ≤ 0, D–f(x) ≥ 0 are necessary for x to be a maximum. These are analogous to the conditions f’(x) = 0, f’’(x) > 0 and f’(x) = 0, f’’(x) < 0, respectively, for continuous functions.

  • What is the US doing in Venezuela?

    The US has recently launched a military build up in the Caribbean, the likes of which has not been seen in the region for decades. Just last week, a Venezuelan oil tanker was seized by the US in an act of imperial piracy. It is pretty clear that the US is after Venezuela’s oil reserves: Venezuela has 303 billion barrels of crude oil in reserve, 20% of the world’s total and more than any other nation. Trump’s claim that his motive is targeting drug traffickers is obviously a smokescreen. Along with the naval build up, in preparation for further action the military base on Puerto Rico, closed following mass protests in 2004, has been re-opened. Puerto Rico, the last remaining US colony that was seized in 1898, has historically been a crucial base and training ground for the US military.

    The US has wanted to overthrow of the Venezuelan government ever since the election of Hugo Chavez back in 1998. Unfortunately for the US, Chavez was popular with the Venezuelan people and won sweeping victories in election after election, making him difficult to depose. When Chavez died in 2013 and was replaced by Nicolas Maduro, the US smelled blood and imposed crippling sanctions and an economic blockade designed to strangle the economy and force regime change. As result, Venezuela has only managed to sell 4 of its 303 billion barrels of crude oil reserves, and the economy has gone into free-fall. Hyperinflation and shortages have all resulted in a devastating social collapse, resulting in country-wide opposition to Maduro’s regime.

    How much this social collapse is down to US sanctions, as opposed to the corrupt and authoritarian Maduro regime, is a difficult and perhaps even impossible question to answer. The US sanctions have clearly had a significant impact – they must have done, otherwise they wouldn’t have bothered implementing them – but Maduro and his regime must take a lot of the blame too. The problem for the people of Venezuela is that removing Maduro will not necessarily improve their situation. The right-wing opposition in Venezuela is a vicious Thatcherite coterie that will be ruthless in seeking revenge and enacting repressive anti-working class measures if it comes to power. This explains why the leader of this opposition, Maria Corina Machado, is so feted by the West.

    Machado is so adored by Western nations that she was awarded this year’s Nobel Peace Prize, apparently for “her tireless work promoting democratic rights for the people of Venezuela” and “her struggle to achieve a just and peaceful transition from dictatorship to democracy.” But what has Machado actually done? It’s difficult to find evidence of her doing anything other than protesting against Maduro in 2014 and leading the opposition to Maduro in the 2024 presidential election. Hardly seems worthy of a peace prize to me! Note also that there was a presidential election in 2024, as there was in 2018 and 2013. Frequent elections are not usually the sign of a dictatorship, although it should be noted that the 2024 election was mired in controversy and accusations of electoral fraud.

    The US is clearly is aiming at regime change in Venezuela. At this stage, the US has not amassed sufficient forces for a full ground invasion; this is unlikely, but cannot be ruled out entirely. It is important that we oppose this imperialist intervention in Venezuela, just as we must oppose imperialist intervention everywhere. The usual rejoinder that opposition to such intervention entails support for the Maduro regime is based on a fallacy. We must oppose imperialist intervention as a matter of principle, regardless of the nature of the regime that is being intervened with. At the same time, we must also condemn Maduro and his government for making such an intervention feasible through their corrupt mismanagement of the Venezuelan economy.

    The reasons the US is doing this now, as opposed to any other point in the 27 years since Chavez came to power, are twofold. First, the Venezuelan regime is weaker now than it has ever been during that 27-year period. And second, the Trump administration has decided to pivot away from starting wars elswhere in the world and towards starting wars in its own back yard. Trump has already intimated that Colombia might be next in the firing line, although that was probably an off-the-cuff idle threat. As already mentioned, the primary reason the US is attacking Venezuela is to take control of its vast oil reserves, which Colombia cannot match. No country can match Venezuela’s oil reserves, so it is really no surprise that the US has decided to attack it. The only surprising thing is that its taken them this long.

  • Marxism and MMT

    Just over a week ago there was an online spat between two high-profile left-wing bloggers, Grace Blakeley and Richard Murphy. The disagreement began after Blakeley left a comment on one of Murphy’s blog posts and centred on the relationship between Marxism and Modern Monetary Theory, or MMT. (I won’t explain what MMT is here – you can read my previous blog post on this for an intro.) In her comment, Blakeley, a Marxist, criticized MMT on the basis that it is naive and does not take into account the struggle between classes. Murphy, an MMT advocate, responded to Blakeley’s comment with two further blog posts, accusing her of making bad-faith arguments and attempting to undermine MMT. Blakeley then responded with a blog post of her own, doubling down on her position.

    So who is right, Blakeley or Murphy? The short answer is: both and neither. Both bloggers rightly accuse the other of attacking a straw man; but both are also wrong precisely because they are attacking a straw man! In this blog post I will attempt to pick apart their arguments and in so doing, argue that their disagreement is at best pointless and at worst actively harmful. Let’s start with Blakeley. In her original comment on Murphy’s blog, she wrote that proponents of MMT “… seem to argue that, *if only everyone else would just listen to them*, all the questions, debates and struggles around economic policy would simply disappear overnight”. This is our first example of straw man argument. I am not aware of any proponent of MMT ever making such a claim, or even implying it.

    She goes on: “If everyone woke up tomorrow suddenly accepting all of [Murphy’s] arguments, the structure of our society would not change…”. This is another straw man, as nobody is saying that it would (at least nobody I know). Henry Ford did once famously state that “If the American people only understood the corrupt nature of our money system, there would be a revolution before morning”. Ford was (presumably) being tongue-in-cheek, but there is more than a kernel of truth to his statement. MMT is obviously not going to fundamentally change society on it’s own; only a revolution will do that. However, a widespread understanding of MMT might lead people to start realizing that they are being lied to by the ruling class and their media-political lackeys, which would be helpful in raising class consciousness.

    Blakeley rightly criticizes Murphy for stating that “The public most definitely does not want class war… They want… a competent government that delivers”. In a way Murphy is right, as I’m sure the public doesn’t want class war; but as Blakeley points out, they are in one whether they like it or not! This is just the nature of capitalism, as Marx realized over 150 years ago. Murphy clearly does not understand that – but he is not a Marxist, and doesn’t claim to be. In fact he seems quite scathing of Marxists in general, for reasons that are difficult to fathom (we are on your side Richard!). But this doesn’t mean he is wrong about the nature of government spending and taxation; on the contrary, he is generally spot on when it comes to these things.

    Much as Murphy’s disdain for Marxists is difficult to fathom, so is the disdain many Marxists seem to have for MMT. After all, MMT is just an accurate description of how government spending and taxation work in modern capitalist societies – and why should anyone have a problem with that? In my view, to criticize MMT on the basis that it includes nothing on class conflict is to miss the point entirely. It is not a theory about class conflict, nor is it meant to be. We don’t need a theory of class conflict in capitalist societies as Marx has already provided us with one which is perfectly adequate. What Marx didn’t do was provide a theory of fiat money – that is, money with a value that is not linked to the value of a commodity such as gold – which isn’t surprising as fiat money didn’t exist in Marx’s time.

    The antagonism between Marxists and Modern Monetary Theorists is unfortunate because the two theories complement each other. Marx provided a comprehensive account of capitalism which is still relevant to modern capitalist societies, with the exception that it doesn’t include anything on fiat money. If fiat money had existed at the time, I’m sure Marx would have written about it. MMT is a theory that neatly fills this gap. Not only that, I think there is clear crossover between the labour theory of value advocated by Marx and the tax-driven nature of the value of fiat money advocated by proponents of MMT. (Recall that Marx’s version of the labour theory of value says that the exchange value of commodities is proportional to the social necessary labour time required to produce them.)

    Fiat money is a unique commodity in that it has no use-value, only exchange value. The existence of fiat money seems to contradict the labour theory of value as it requires zero labour to produce, yet still has exchange value. But MMT explains that the value of a fiat currency is derived from taxes. Governments levy taxes on their citizens which are only redeemable in the currency they issue; and the only way most people can get hold of this currency is by selling their labour-power. Thus, combining the labour theory of value with the theory of tax-driven money provides us with a complete theory of why fiat money has value. This shows that the only way fiat money can have value is by forcing people to sell their labour-power in order to obtain it, which tells us something fundamental about the nature of money.

    There are other ways in which MMT can help reinforce Marxist ideas. MMT demonstrates that governments are far more powerful and have far fewer constraints on them than we are usually led to believe. A widespread understanding of  MMT will not bring about a revolution on its own, but it might help people to imagine a society existing beyond capitalism – and surely that can only be a good thing.

  • Indo-European word-initial velars

    In a recent blog post I argued, based on data collated by Lars Steensland in his 1973 PhD thesis, that his proposed word-initial delabialization before *o occurred separately in the western Indo-European languages rather than in Proto-Indo-European (see that post for more details). This supports the hypothesis that PIE only two types of velar consonant in this position: plain velars and labiovelars. In this blog post I will investigate whether the same can be said for other word-initial positions. Let us start with the position after *s. Steensland argued that only plain velars occur here, except before *i where only palatovelars occur. In a recent (2014) article, Robert Woodhouse criticized this view, claiming that only plain velars and labiovelars occur here. Either view supports the two-velar hypothesis.

    Steensland provides two examples of words with palatovelars occurring word-initially before *H₂ (or *a in his reconstructions): *g’hH₂ensiH₂ ‘goose’ and *k’H₂eueH₂ ‘owl’. As noted by Steensland, there is a clear case of ‘gutturalwechsel’ (velar interchange) in the root from which the first word is derived, *g’hH₂ens ~ *g’heH₂ns. There is also is a clear case of gutturalwechsel in the root from which the second word is derived, *k’H₂eu- ~ *k’eH₂u- ~ *k’H₂u- ~ *k’uH₂-. These can be explained by positing that these roots originally contained a plain velar which was blocked from palatalizing before *H₂. This, along with the fact that there are no other examples in Steensland’s data of palatovelars occurring before *H₂, supports the hypothesis that only plain velars and labiovelars occurred in this position in PIE.

    There are four examples of words with a plain velar word-initially before *l:*gloH₁imos ‘moist’, *gluH₁nos ‘knee’, *gloiH₁uos ‘sticky’, and *ghloumos ‘joke’.  The first two only have Albanian reflexes among the satem languages, whereas none of Steensland’s 17 examples of words with a palatovelar have Albanian reflexes, suggesting that palatalization was blocked before *l in Albanian. The latter two only have Balto-Slavic reflexes among the satem languages; but palatalization was not blocked before *l in Balto-Slavic as 11 of Steensland’s 17 examples of words with a palatovelar before *l have Balto-Slavic reflexes. However, in only two of these 11 words is the *l followed by *o, and in both cases palatalization could have been introduced analogically, suggesting that palatalization was blocked before *lo in Balto-Slavic.

    Steensland demonstrates that labiovelars do not occur word-initially before *u in PIE, but both palatovelars and plain velars do occur in this position. This is consistent with the two-velar hypothesis if we assume that plain velars were palatalized in this position in the satem languages and labiovelars delabialized in this position in the centum languages. Here we have one instance where it seems plausible to posit a parallel development occurring independently across several languages, as delabialization before *u is a very natural sound change that has been observed occurring many times in different languages. Indeed, there is independent evidence for this sound change occurring in the different centum languages long after the breakup of PIE.

    There are two examples of words with a plain velar occurring before *n: *gnet ‘knead’ and *ghnid ‘nit’. As these only have reflexes in Germanic among the centum languages, we need only posit that labiovelars were delabialized before *n in Germanic to explain the plain velars in these words. In fact this is an example of a broader delabialization before consonants in the western languages – Germanic, Italic, and Celtic – which was first noted by Antoine Meillet back in 1894, and for which there is significant independent evidence. It is difficult determine the distribution of velars before *m or before syllabic resonants due to lack of data. Suffice it to say that there is no solid evidence against the two-velar hypothesis in these positions either.

    We thus arrive at the following picture. Proto-Indo-European had two types of velar in word-initial position: plain velars and labiovelars. In the satem languages, labiovelars were delabialized and plain velars were palatalized apart from after *s, and before *r, *s, and *H₂; palatalization was also blocked before *l in Albanian and *lo in Balto-Slavic. In the centum languages, labiovelars were delabialized before *u, and labiovelars were also delabialized before *o and before consonants in the western languages. This raises the question whether the two-velar hypothesis holds in word-medial position too; this is a more difficult question to answer, as there are more environments word-medially that need to be considered. I will therefore postpone attempting to answer this question to a future blog post.

  • Should we nationalize the economy?

    Former Labour MP Zarah Sultana caused a stir last week by suggesting that we should nationalize the entire economy. Put simply, nationalization is the process of transforming privately owned assets into public assets by bringing them under the public ownership of a national government or state. On the face of it this seems an entirely sensible thing to do and is in line with the usual socialist aim of abolishing private property. So it is somewhat surprising that Sultana’s suggestion has come in for a lot of criticism from people who claim to be on the left. The main objection seems to be that full nationalization, although a good idea in principle, has never been demonstrated to work in practice, and where it has been tried has only led to authoritarianism and destitution.

    Tempting as it is to dismiss such arguments, we have to be honest and admit that there is more than a kernel of truth to them. The 20th century is full of examples of socialist governments fully nationalizing their economies with often disastrous consequences: the Soviet Union, China, Vietnam, Cambodia, Cuba, North Korea, and so on. To be sure, things weren’t all bad in these countries. The Soviet Union went from a backwards agrarian society in 1917 to effectively winning the space race less than 50 years later, lifting millions out of poverty in the meantime. China followed a similar trajectory. Cuba was doing fine until the fall of the Soviet Union in the early 1990s. And there was even a time when it looked as though North Korea might turn out to be more successful than its southern neighbour.

    There are many on the left who venerate these achievements and play down the obvious downsides of these regimes; but I am not one of them. I think it is important that we on the left are honest about the true nature of these states if want to have any credibility. Anyone who lived in any of these countries during periods of full nationalization will tell you that life was hard and characterized by chronic shortages of basic goods. Apologists for these regimes will point to the fact that they often faced outside sabotage from capitalist countries, which of course is true. In my view, though, it was primarily the nature of the regimes in these countries which made peoples’ lives so hard. We see this playing out in socialist countries today – particularly North Korea, which is a failed state, and Cuba, which is well on its way to becoming one.

    So it’s true that full nationalization of an economy has never worked in practice. But that doesn’t necessarily mean it couldn’t work. The question is: what was it about the regimes mentioned above that meant that nationalization went so horribly wrong? The obvious answer is a lack of democracy. Here, I am going to break ranks and criticize both Marx and Lenin (gasp!). I think the issues stemmed to a large extent from Marx’s concept of the ‘dictatorship of the proletariat’, which describes a transitional phase between capitalism and socialism where the working class holds state power. Lenin interpreted ‘dictatorship’ as meaning ‘unlimited power, based on force and not restricted by law’, a concept that inevitably leads to authoritarian rule by a single party.

    Others, like the Austrian Marxist Karl Kautsky, argued that true ‘dictatorship of the proletariat’ should not be a rejection of democracy, but rather an expansion of democratic principles to include the working class. The problem is that for most people, the terms dictatorship and democracy represent polar opposites. Therefore I think we would be better off ridding ourselves of the ‘dictatorship of the proletariat’ concept altogether. In this respect I am more aligned with the 19th century Russian revolutionary anarchist Mikhail Bakunin, who advocated for the immediate abolition of all states, arguing that power inevitably corrupts and any new state would simply create a new ruling class. The events of the 20th century appear to have proven Bakunin correct.

    It is important to note that Marx and Bakunin were in agreement in advocating for a move to a stateless, classless society. Their difference of opinion lay in how they thought this should or could be achieved. Whereas Marx argued for the proletariat to organize as a political party to take over state power, Bakunin argued for the immediate establishment of decentralized, democratic federations of workers’ cooperatives, rejecting hierarchical and centralized power structures altogether. Of course I agree with Marx that it is necessary for the working class to organize to conquer the bourgeois state. But I also agree with Bakunin that once the bourgeois state has been conquered, a new state should not simply be established in its place.

    Returning to the original question, I think the controversy around Zarah Sultana’s suggestion that we should nationalize the economy stems from their being two different interpretations of the word ‘nationalize’. The first interpretation means creating a centralized workers’ state of the type advocated for by Marx and Lenin; whereas the second interpretation means establishing decentralized, democratic federations of workers’ cooperatives, as advocated for by Bakunin. People are rightly wary of the first interpretation, based on historical experience. But I think that the second interpretation represents exactly what most modern-day socialists envisage when they talk about ending capitalism and moving to a socialist society.

  • Proto-Indo-European velars

    In a previous blog post I explained how Proto-Indo-European (PIE) is usually reconstructed with three types of velar constant, which are referred to as palatovelars, plain velars, and labiovelars. I also mentioned that in 1973, Lars Steensland demonstrated a complimentary distribution between the three types of velar. Steensland first showed that in word-initial position, only plain velars occur after *s, except before *i where only palatovelars occur. He then showed that in word-initial position not following *s, palatovelars occur everywhere apart from before *r and *s; plain velars occur everywhere apart from before *e, *i, and what we would now call *h₁; and labiovelars only occur before *e, *i, *r, and what we would now call *H₁.

    Next, Steensland showed that in word-medial position, palatovelars occur everywhere apart from after non-syllabic *n; plain velars occur everywhere apart from after *e and syllabic *n; and labiovelars only occur after *e, *i, *o, and *n. Thus, in word-initial position, there isn’t a single environment where all three types of velar occur; and in word-medial position, all three types of velar only occur after *i and *o. Steensland also showed that only plain velars occur word-medially in words beginning with *(s)t, whereas only palatovelars and plain velars occur word occur word-medially in words beginning with *m. This includes all of his examples of words with a plain velar occurring after *i, and most of his examples of words with a plain velar occurring after *o.

    The obvious explanation for this distribution runs as follows. PIE originally had two types of velar: a palatovelar and a labiovelar. In the satem languages, plain velars became palatalized in word-initial position in all environments apart from (1) after *s, unless followed by *i; and (2) before *r and *s; and in word medial-position in all environments apart from (1) after non-syllabic *n, and (2) in words beginning with *(s)t. In the centum languages, labiovelars were delabialized in word-initial position in all environments apart from before *e, *i, *r, and *H₁; and in word-medial position in all environments apart from (1) after *e, *i, *o, and *n, except in words beginning with *m. There is a problem with the latter part of this explanation however.

    As I noted in my previous blog post, whereas the satem languages were geographically contiguous so could have undergone such changes together, the centum languages were not. The explanation above implies that the labiovelar developments described must have happened separately on seven separate occasions: in Anatolian, Tocharian, Greek, Germanic, Italic, and Celtic. This is implausible and removes one of the key arguments in favour of the two-velar reconstruction. However, a closer look at the data suggests we may not need to assume that all these developments occurred in all the centum languages. To see this, let us consider one environment where delabialization seems particularly common: word-initially before before *o.

    Steensland provides 20 examples of words with a plain velar occuring before *o in word-initial position, of which 11 only have reflexes in the western languages (Celtic, Germanic, and Italic). Of the remaining 9, three are derived from roots with a mobile *s, which accounts for the lack of palatalization in the satem reflexes. One of the remaining six, *kolH₂os ‘strike’, may be derived from a root *(s)kelH₂- ‘cut’, and another, *korios ‘army’, may be derived from a root *(s)ker- ‘cut’, both with a mobile *s. One of the remaining four, *ghordhis ‘garden’, is derived from a root *g’her- ‘garden’, which displays gutturalwechsel in the satem languages, suggesting that the word originally had a plain velar that was blocked from palatalizing in the zero grade *g’hr-.

    Another, *koH₂peH₂ ‘handle’, is derived from a root *keH₂p- ~ *kH₂ep- ‘grab’, where palatalization may have been blocked before *H₂. The plain velar in one of the remaining two words, *kom ‘with’, is based entirely on Albanian kë, which is now usually derived from the interrogative root *kʷ-. The final word, *kom, is a particle of unclear meaning and etymology which apparently only has reflexes in Anatolian among the centum languages, and even that isn’t certain, so we cannot be sure that this word contained a plain velar. Thus, to explain the data, we only need to posit that delabialization occurred before *o in the western languages – Germanic, Italic, and Celtic -rather than all of the centum languages. This seems a lot more plausible.

    One potential counterexample is *gʷous ‘cow’, which yields labial reflexes in Italic (Umbrian bum, Latin bōs)  and Celtic (Irish bó, Welsh  bu). One way around this is to posit a proto-form *gʷeH₃us and assume either that the delabialization before *o  occurred before the colouring of *e to *o in these languages. The problem with this is that the colouring of *e to *o is usually dated all the way back to PIE, or at least to a period very soon afterwards. Instead, we can simply assume that the change *gʷ > *b occurred in Osco-Umbrian and Celtic prior to the delabialization before *o in these languages (Latin bōs is known to be a borrowing from  Osco-Umbrian). This seems a better explanation as it does not create any issues from a chronological perspective.

  • Summarizing Das Kapital volume 1

    Das Kapital is the foundational theoretical text in Marxist philosophy, economics, and politics. It is one of the most influential works of social science ever written and represents the culmination of Karl Marx’s lifelong project to develop a comprehensive theory of capitalism. The central argument, which runs through all three volumes, is that capitalism necessarily involves the exploitation of workers. In putting forth this argument, Marx synthesized, critiqued, and built on three main intellectual traditions: the classical political economy of Smith and Ricardo; the dialectical philosophy of Hegel; and the utopian socialism of Fourier and Proudhon. Marx’s aim in writing Das Kapital was, in his own words, to ‘lay bare the economic law of motion of modern society’.

    The presentation of Das Kapital follows an ‘ascending path’, starting from the most abstract essence of capitalism and building up a theory from there. This is reminiscent of the axiomatic method in mathematics, which involves building a theory from a fixed set of axioms. Marx employs what he calls the ‘power of abstraction’ to analyse fundamental dynamics of capitalism. Das Kapital begins with a lengthy description of the commodity, which is a term used for anything produced by human labour that fulfills a human desire or want. The commodity may be considered the ‘elementary particle’ of capitalism. Hegel’s dialectic method is central to Marx’s approach in building up his theory; however, Marx adapts Hegel’s method by employing it in a materialist, scientific way.

    The writing of Das Kapital was a long and arduous process spanning several decades. Marx’s perfectionism and tendency to get sidetracked delayed completion, as did his fondness for alcohol. It is well-known that only volume 1 of Das Kapital was completed in Marx’s lifetime, with volumes 2 and 3 being completed posthumously by Friedrich Engels, Marx’s long-time collaborator. What is less well-known is that Marx originally planned to write six volumes! Perhaps we should be grateful that he only managed three, as reading just one volume involves a significant investment of time. I personally have only managed to read volume 1 (so far). In the remainder of this blog post I will attempt to provide a short synopsis.

    As mentioned above, volume 1 begins with a lengthy description of the commodity. There are two values associated with a commodity: a use-value, which is the value that arises from satisfying some human want or need; and an exchange-value, which may be defined as the proportion in which a commodity exchanges for other commodities. According to Marx, the ‘substance’ of exchange value is ‘human labour in the abstract’, and the magnitude of a commodity’s exchange value is determined by the ‘socially necessary labour time’ required to produce it. We now refer to this as the labour theory of value, although Marx himself never referred to it as such. This theory implies that exchange values are determined by social relations and are not properties of commodities themselves.

    Marx then goes on to discuss what he calls the transformation of money into capital. He first talks about the simple circulation of commodities, whereby commodities are produced, brought to market and sold for some amount of money which is then used to buy other commodities. This is usually how we think of markets working and may be characterized as ‘commodities-money-commodities’, or C-M-C for short. However, what actually happens under capitalism is that a capitalist first invests some money to produce commodities, which are then brought to market and sold for more money than was originally invested. This may be characterized as ‘money-commodities-money’, or M-C-M’, where M’ is greater than M. The difference M’-M is referred to as ‘surplus value’.

    A surplus cannot arise if equivalents are exchanged. So where does surplus value come from? The answer, according to Marx, is from workers – or more specifically from ’labour power’, the capacity to do work. Marx argues that in order for surplus value to arise, the value created by the labourer must be greater than the value of their own labour-power, which is what they receive in wages. Thus, the value that workers receive is lower than the value they provide, with the difference – the surplus value – being appropriated by capitalists. It is in this sense that workers are exploited under capitalism. This, I think, represents the key point of volume 1 and possibly even the whole of Das Kapital. The rate of exploitation is just the ratio of surplus value to wages, or ‘variable capital’ in Marx’s terminology.

    Marx then goes on to discuss two different types of surplus value, which he terms ‘absolute’ and ‘relative’. Absolute surplus value is created by capitalists prolonging working time for longer than is necessary for workers to produce what they actually need. Working time thereby becomes a locus of the struggle between capitalists and workers, with the former seeking to prolong it and the latter seeking to shorten it. In contrast, relative surplus value is created by capitalists shortening the socially necessary labour time required to produce a given commodity or commodities. They can do this through the concentration of many workers under the command of a single capitalist, the division of labour, the introduction of new technology, or a combination of the three.

    The final part of volume 1 concerns the process of capital accumulation. Under what Marx calls simple reproduction, the entire surplus is consumed by the capitalist. However, what usually happens under capitalism is that capitalists are driven to reinvest the surplus into further production; this is what is referred to as capital accumulation. Marx argues that capital accumulation relies on the constant maintenance of an ‘industrial reserve army’ of labourers – a permanent sub-class of unemployed workers. He then goes on to formulate what he calls the ‘law of capital accumulation’, which basically says that under capitalism, things only get worse for workers. Looking at how things are going at the moment, it is hard to disagree.

  • Should we be worried about AI?

    In the last few years there has been a rapid adoption of artificial intelligence across all sectors of society. This has been driven largely by the development if so-called ‘generative AI’ technology. Generative AI is a subfield of artificial intelligence that uses generative models to produce text, images, videos, audio, software code, and other forms of data. Unlike traditional AI that analyzes data to support decisions, generative AI produces novel outputs in response to user prompts, using models trained on vast datasets. Firms have been quick to jump on the generative AI bandwagon, mainly through fear of being left behind by their competitors. As exciting as this new technology seems, however, there are many potential downsides.

    The most obvious downside of the mass adoption of AI is often referred to euphemistically as ‘labour market disruption’, but is more accurately referred to as ‘mass unemployment’. This is something that inevitably occurs under capitalism with the widespread introduction of a labour-saving technology, and there are many historical case studies going back to the Luddites of the early 19th century and beyond. Usually, though, it is manual workers who are most at risk. What’s both interesting and novel about the current generative AI boom is that those most at risk of unemployment are high-skilled, white-collar professionals, such as writers, analysts, and legal assistants. I don’t think many people saw that one coming.

    At this point it is worth reminding ourselves of why unemployment is a problem in the first place. Unemployment being a bad thing is usually taken as axiomatic – that is, something that does not require any explanation. But if you think about it, it’s bizarre that our first reaction whenever a new labour-saving technology is introduced is to worry that it might mean us humans have less work to do! Shouldn’t that be a good thing?! The reason it isn’t a good thing is that we live under a system which requires 99% of people to sell their labour-power in order to survive. Under capitalism, if you are unable to sell your labour-power, you are in deep trouble. Labour-saving technology is seen as bad as it inevitably results in less opportunities for us to do this.

    This isn’t the fault of the technology though; it is the fault of the system we live under. What makes this even more perverse is that under capitalism, a lot of people have jobs where the main objective is to devise ways to reduce human labour! We should not be surprised by this though; it is just one of the many contradictions of capitalism, and these contradictions have existed for as long as capitalism has. However, the rise of generative AI has brought this contradiction into sharp focus. In the past, we’ve always been able to invent new jobs for people to do – even if a lot of them are ‘bullshit jobs’, in the memorable phrase of the late, great American anthropologist David Graeber. But the proliferation of AI is going make it increasingly difficult for us to invent jobs that can’t be done by a machine.

    There are other downsides to generative AI too. As these models are trained on vast datasets, they often perpetuate existing societal biases and stereotypes, leading to discriminatory outcomes in areas like recruitment. The ability to easily generate convincing, but false, information (hallucinations) and malicious content like deep fakes poses a threat to information reliability and security. We are not quite at the point where AI-generated content is indistinguishable from the genuine article, but we aren’t far off. Another major downside is that training and running large AI models require substantial energy and water consumption, which will inevitably exacerbate the climate crisis. Then there is the problem of over-reliance on AI leading to the erosion of essential human skills such as critical thinking.

    We would do well to remember that for all its supposed intelligence, generative AI is just compiling information originally created by human beings. This information is often obtained from specialist online forums. In future, generative AI might make such forums obsolete, so the information will no longer be created – and what happens then? Presumably, AI will start creating content based on information it has previously collated, effectively turning itself into a self-replicating feedback loop. It might be tempting to speculate that AI might then start to evolve and even become sentient, as self-replication is the key mechanism behind evolution by natural selection. Indeed, many people are worried about exactly such a scenario occurring.

    Personally, though, I think these fears are overblown. Evolution by natural selection requires more than just replication; it also requires a constant stream of new information. This is essential for the ‘selection’ part of the process to work effectively. As we have seen, new information would not be present under the scenario just described. A more likely outcome under this scenario is that generative AI ends up becoming irrelevant and simply stops being used. Given all the downsides of this technology, that might not be such a bad thing.

  • Do we need pronouns at all?

    A debate is currently being waged over the use of gender-neutral pronouns such as ‘they’ and ‘them’, especially when they are used to refer to individuals who identify outside the traditional gender binary. This is part of the wider debate on trans rights, which for reasons that are difficult to fathom seems to have some people foaming at the mouth with rage – particularly, although not exclusively, those on the right of the political spectrum. The contentiousness of the debate over pronouns seems bizarre, as pronouns are just a part of speech. Before this debate kicked off I suspect most of those people who are now vehemently opposed to the use of gender-neutral pronouns were barely even aware of what a pronoun is.

    So, what is a pronoun? Put simply, a pronoun is just a word or a group of words that one may substitute for a noun or noun phrase. The reason we have pronouns is to avoid multiple repetitions of a noun or noun phrase within a sentence, which can sound a bit clunky. Pronouns are interesting from a historical linguistics perspective because they can often be traced back many thousands of years to reconstructed proto-languages. For this reason they are sometimes referred to as the ‘Devonian rocks’ of historical linguistics. For example, the first-person singular subjective pronoun ‘I’ can be traced all the way back to Proto-Indo-European, and other pronouns such as the now obsolete second-person singular pronoun ‘thou’ can likely be traced back even further.

    Pronouns are very familiar to us as languages that descend from Proto-Indo-European, which includes most of the languages of Europe, Iran, and Northern India, have them in abundance. However, there are languages that make far less use of pronouns. Speakers of east Asian languages, such as Mandarin Chinese, Japanese, and Korean, frequently omit pronouns and rely on context to fill in the gaps. Even speakers of some Indo-European languages, such as Spanish, Italian, and Hindi, often drop the subject pronoun because the verb conjugation indicates the subject. There are languages with no gendered third-person pronouns, such as Turkish, Hungarian, and Finnish. There are even languages that apparently have little to no personal pronouns at all, such as the Arhuaco language of South America.

    This raises the question of whether it is possible for a language to have no pronouns whatsoever. Some linguists speculate that the South American language Pirahã may have once lacked pronouns. The fact that the pronoun system of Pirahã is incredibly simple and has a very low functional load suggests that the language may not have had pronouns at all at an earlier stage. Still, I am not aware of any attested language that lacks pronouns completely. But that doesn’t mean that such a language could not exist. How would a language work without pronouns? The obvious way would be to simply substitute back the relevant noun or noun phrase; but as noted above, this can make a language sound quite clunky, and is also inefficient.

    A better approach would be to restructure language so that pronouns are not needed. For example, instead of saying ‘I am tired’ or ‘he is tired’ we could say something equivalent to ‘tiredness is occurring here’ or ‘tiredness is occurring there’. Such constructions sound ridiculous to our ear, but that’s only because we are not used to them. Restructuring language like this would have several advantages. It would help rid us of the illusions of self, ego, and free will, which pronouns subconsciously reinforce – particularly first-person pronouns such as ‘I’ and ‘me’. It would also help rid us of the subject-object distinction: the erroneous feeling we all have of separation of the observer (the subject) from the thing being observed (the object).

    Realistically, such a drastic restructure of language is unlikely to happen. Removing gendered pronouns seems a much more achievable goal, particularly as several languages function perfectly well without them (as noted above). This would also have several advantages. Using gender-neutral language affirms a person’s identity, which is a form of basic courtesy and respect. It acknowledges and includes individuals who do not identify in a binary way as male or female, making them feel seen and valued. Avoiding assumptions about a person’s gender helps to break down rigid expectations about roles and occupations. Gender-neutral pronouns help shift the focus from gender to an individual’s qualities, skills, and contributions.

    The fact that moving to gender-neutral pronouns would have such advantages raises the question of why some people are so opposed to the idea. One theory is that people use opposition to this as a way of expressing their transphobia without explicitly expressing it. There is definitely some truth to this, but I also think there is more to it. From an early age we are conditioned into thinking that all human beings can be neatly divided into one of two genders, to the extent that this becomes ingrained in our psyche. Suggesting that we don’t need to categorize people in this way feels jarring to many as it involves shattering a core belief. This, I think, explains why many people act with such irrational anger about moving to gender-neutral pronouns, despite the obvious benefits that would result.

  • What’s going on in Sudan?

    Since April 2023 there has been an active civil war in Sudan between two rival factions of the country’s military government: the internationally recognized government controlled by the Sudanese Armed Forces (SAF), led by General Abdel Fattah al-Burhan; and the paramilitary Rapid Support Forces (RSF), led by General Hemedti, who leads the broader Janjaweed coalition. Fighting has been largely concentrated in the capital, Khartoum, where the conflict began, and in the Darfur region in the west of the country. Such conflicts are not exactly rare in Sudan. Since gaining independence in 1956, Sudan has endured chronic instability marked by 20 coup attempts, prolonged military rule, two devastating civil wars, and a genocide in Darfur.

    The conflicts that have occurred in Sudan since 1956 have largely been between the relatively wealthy, Muslim north and the less developed, predominantly Christian or animist south. These culminated with the southern part of the country breaking away and becoming a separate country, South Sudan, in 2011. But anyone who thought that the secession of South Sudan would put an end to the conflicts would have been sorely mistaken. Along with tensions between the north and south of the country there are also longstanding tensions between the western Darfur region and the east of the country. The fault line in this case is not religion, but ethnicity. The east is populated mainly by Arabs or Arabized Africans, whereas Darfur is populated by indigenous Fur, Zaghawa, and Masalit ethnic groups.

    These tensions came to a head with the war in Darfur, which lasted for 17 years from 2003 to 2020. One side of the conflict was mainly composed of the Sudanese armed forces, police, and the Janjaweed coalition, whose members are mostly recruited among Arabized Africans. The other side was made up of rebel groups, notably the Sudan Liberation Movement and the Justice and Equality Movement, recruited primarily from the non-Arab indigenous ethnic groups in the region. The origins of this conflict go back to the 11th century, when Arab migrations into the Nile valley resulted in the people there becoming heavily Arabized, whilst the people of Darfur remained more faithful to native Sudanese cultures. The war in Darfur led to a genocide of the indigenous population by Janjaweed militias.

    Against this backdrop it may be tempting to write Sudan off as a failed state that will always be mired in conflict as a result of its internal ethno-religious tensions. However, there is a lot more to it than that. The current war is tied to global financial interests, with sponsors of opposing parties profiting from the chaos. Sudan has effectively become the stage for one of the world’s most devastating proxy wars. At the heart of the crisis lies the struggle for profit, power, and influence. The UAE has been deliberately working to destabilize Sudan for the sake of resource extraction, by sponsoring the RSF rebels. The UAE’s dominance in the illicit gold trade is a key feature of its influence in Africa, and the RSF’s control of gold mining operations in Sudan makes it a valuable proxy.

    Israel also has role in the conflict, which revolves around advancing normalization agreements and limiting Hamas’s influence. Whilst the UAE has focused on the RSF, Israel has cultivated ties with the SAF. Under the SAF, Sudan has become an ally of Israel and has agreed to join the Abraham Accords, and has also frozen Hamas assets within the country. It may seem strange that the UAE and Israel are supporting different sides in the conflict, particularly as the UAE is also a signatory of the Abraham Accords. But both countries seek a weakened Sudanese state with limited sovereignty, and as such it makes sense for them to back opposing sides. As far as Israel and the UAE are concerned, the longer the conflict goes on, the better.

    As ever, it is ordinary people who are suffering most from this game of international power politics. The humanitarian impact of the war is difficult to overstate. A senior official from the United Nations World Food Program warned in April this year that Sudan is facing the world’s worst humanitarian crisis, with nearly 25 million people experiencing extreme hunger, over 12 million displaced, and at least 20,000 confirmed dead. Ultimately, the cause of all this needless suffering is the global capitalist system under which we are all forced to live, which prioritizes profit, power, and influence over human life. Proxy wars such as the one currently going on in Sudan will continue to occur until we get rid of capitalism and replace it with a system that prioritizes human well-being.