Groucho Marxism

Questions and answers on socialism, Marxism, and related topics

  • Techno-capitalism

    Neo-feudalism, or new feudalism, is a theorized contemporary rebirth of policies of governance, economy, and public life, reminiscent of those present in feudal societies. It refers to the idea that capitalism is evolving, or has already evolved, into a modern socio-economic system that bears similarities to the feudal social orders of ancient times, but with unique modern features. The term neo-feudalism has been popular since the early 2020s but the concept has been around much longer. The idea was first put forward by the German philosopher and social theories Jürgen Habermas, who used the term Refeudalisierung (‘refeudalization’) in his 1962 work The Structural Transformation of the Public Sphere to criticize the privatization of the forms of communication.

    Recently, the Greek economist and politician Yanis Varoufakis has proposed that capitalism has evolved into a new feudal-like structure of economies and societies which he refers to as ‘techno-feudalism’. Varoufakis explains that unlike under capitalism, feudal economies have the quality of being dominated by very small groups of people who predetermine the behaviour of markets as they see fit. He notes that massive online platforms such as Facebook and Amazon are primarily governed by the whims of single individuals and small teams, and thus are not truly capitalist markets of free trade, but rather feudal markets of stringent control. Varoufakis summarized the argument in his 2023 book Technofeudalism: What Killed Capitalism. But is he right?

    To answer that question we first need to define what we mean by ‘capitalism’ and ‘feudalism’. Or more specifically, we need to understand the key difference between the two. One distinction often made is that under feudalism, workers were tied to the land and owed labour to a lord; whereas under capitalism, workers are free to enter contracts for wages and can change employers or withdraw their labour if they wish to. I think this is a false distinction. In practice, most workers are no more free to withdraw their labour under capitalism than they were under feudalism. In both systems workers basically face a choice between working or starving. The only real difference is that under capitalism this stark choice gets masked behind the pretence of worker ‘freedom’.

    Another distinction often made concerns property relations. Under feudalism, land was held through loyalty (fiefs); whereas under capitalism, productive assets such as land are owned as private property. Again, though, this seems to be a distinction without a difference. Both systems involve non-democratic, private ownership of the means of production. The only real difference is that under capitalism the means of production includes machinery and not just land. Yet another distinction often made concerns social mobility. Feudalism had a rigid class structure based on birthright; whereas capitalism supposedly allows for upward mobility through success, merit, or capital accumulation. In practice, however, it is extremely rare for a worker to change class and become a capitalist.

    Both feudalism and capitalism are exploitative systems in which a small ruling class dictates economic decisions and a larger working class lives with the consequences. The thing that distinguishes them is the underlying economic logic. Feudalism was an agricultural system based on traditional obligation and consumption of surpluses by elites. It was essentially a static system that survived largely unchanged for centuries. Capitalism, on the other hand, is a dynamic system driven by competition, accumulation, and growth. This drives technological innovation and competitive efficiency but it also has tremendous downsides, particularly on the natural world. It is an unstable system that inevitably leads to war and crisis and is fundamentally unsustainable in the long-term.

    The accumulation drive of capitalism has not gone away; on the contrary, it is as powerful as ever. For that reason I cannot subscribe to Varoufakis’s techno-feudalism thesis. If anything, new technology is being marshalled to exploit workers further and drive accumulation to an even greater degree. Therefore I think ‘techno-capitalism’ would be a better term to describe the system under which we now live. The rise of AI will only turbocharge this process of worker exploitation and capitalist accumulation – unless we do something to fundamentally change the system and its underlying logic.

  • Measuring ED&I scientifically

    It is now generally accepted by most (although not all) people that promoting and delivering Equality, Diversity, and Inclusion (ED&I) is a good idea. But what exactly do we mean by ED&I? The usual definition given is something along the lines of: ‘equality’ means ensuring everyone has the same rights and opportunities, regardless of their personal characteristics; ‘diversity’ means recognizing, respecting, and valuing individual differences, including backgrounds, beliefs, skills, and identities; and ‘inclusion’ means creating an environment where all people feel welcomed, respected, and able to contribute fully. That’s all well and good; but how might we go about measuring these things? In this blog post I will attempt to answer that question using the concept of entropy.

    Consider a organization with members who are categorized into n groups based on personal characteristics (race, gender, sexual orientation, and so on). Let pi denote the proportion of people in the organization who belong to group i. To measure the ‘fairness’ of the organization scientifically we need to define a function Hn() which takes the proportions p1,…,pn and outputs a positive number, with the interpretation that that Hn(p1,…,pn) represents a quantitative measure of the organization’s fairness. What properties should this function have? First of all it should be continuous, so that changing the values of the proportions by a small amount only changes the fairness of the organization by a small amount.

    The function Hn() should be symmetric, so that the output remains the same if the proportions are reordered. This ensures that we are not applying preferential treatment to one particular group. It should attain its maximum when all proportions are equal. It should also increase with the number of outcomes when all proportions are equal; that is, Hn(1/n,…,1/n) < Hn+1(1/(n+1),…,1/(n+1)). The final property this function should have might be called ‘additivity’: if the organization is split into sub-organizations, then the fairness of the organization should be equal to a weighted sum of the fairness of the sub-organizations, where the weight is equal to the proportion of members belonging to that sub-organization.

    It turns out that the only function that satisfies these criteria is the so-called ‘entropy’ function: Hn(p1,…,pn) = -∑ipilog(pi). This gives us a basic measure of fairness. However it is not sufficient for most purposes. In the real world we usually want to compare these proportions against a baseline, which will usually be the corresponding proportions in the population as a whole. Let us now denote these baseline proportions by p1,…,pn and the corresponding proportions within the organization by q1,…,qn. Further, let X and Y be random variables which take the value i with probabilities pi and qi respectively. Then we can measure the fairness of the organization using the ‘relative entropy’ H(X|Y) = -∑ipilog(qi/pi), where I have suppressed the dependence on n for convenience.

    Note that a high value of H(X|Y) means that the organization is not representative of the population as a whole, whereas a value of zero means that it is perfectly representative of the population. Therefore, an organization would generally want to decrease the value of H(X|Y) as a high value represents a lack of diversity. This therefore gives us a measure of (lack of) diversity; but what about equality? Let us now suppose that the organization is stratified into a hierarchy with m levels. Let qij be the proportion of people in level i of the organization belonging to group j, and let Yi be a random variable which takes the value j with probability qij. Then the within-level entropy for level i is just the relative entropy H(X|Yi).

    How do we account for entropy across levels?Let rij be proportion of people in group j belonging to level i of the organization, and let Zj be a random variable which takes the value i with probability rij. Further, let ri be the overall proportion of people belonging to level i of the organization, and let and let Z be a random variable which takes the value i with probability ri. Then we may define the cross-level entropy for group j as the relative entropy H(Z|Zj). A high value of H(Z|Zj) means that members of group j are facing discrimination (either positive of negative). Therefore, an organization would generally want to decrease the value of H(Z|Zj) as a high value represents a lack of equality with respect to that particular group.

    The overall entropy H can then be defined as a weighted double sum: H = ∑i∑j[qijH(X|Yi)+rijH(Z|Zj)]. This gives a combined measure of both equality and diversity, which  can be considered as a measure of inclusion. Thus we have successfully defined measures of equality, diversity, and inclusion. The next step is to apply these measures to some real-world data; I will leave that for a future blog post.

  • Word-initial velars in the IEW

    In a previous blog post I listed entries from the 1959 Indogermanisches Etymologisches Wörterbuch (IEW) with velars in different phonological environments. These data suggest that in palatalization of plain velars was blocked before *eiT, *o, and *r, and that labiovelars were delabialized after *s and before *H₂, *l, *m, and *u. In that blog post I only included entries with reflexes in at least two branches of both the centum and satem languages, where there is no uncertainty in the reconstruction, and where the velar only occurs in one phonological environment; and I excluded onomatopeic cases. Here I will investigate what happens if we relax the first condition and allow entries with reflexes in at least one branch of both the centum and satem languages. I will focus on velars in word-initial position.

    There are eighteen entries with a plain velar after *s and before *e: *sked- ‘split’, *skeH₂i- ‘bright’, *skeH₁t- ‘jump’, *skeH₁u- ‘cut’, *skei- ‘cut’, *skel- ‘bend’, *skel- ‘dry’, *skep- ‘cut’, *sker-  ‘cut’, *sker- ‘jump’, *sker- ‘wrinkle’, *skerbh- ‘turn’, *skerdh- ‘pitiful’, *skert- ‘across’, *skeu-  ‘get ready’, *skeu- ‘sneeze’, *skeud- ‘throw’, and *skeud- ‘unwilling’. There are seven entries with a plain velar after mobile *s and before *e: *(s)kel- ‘stab’, *(s)kel- ‘hit’, *(s)kel- ‘call’, *(s)kerd- ‘gird’, *(s)kert- ‘turn’, *(s)keu- ‘pay’, and *(s)keuHd- ‘shout’. There is one example with a labiovelar after *s, *skʷalos ‘fish’, where the *a vocalism points to a wanderwort. This suggests that labiovelars were delabialized after *s. I will therefore exclude these cases from now on.

    There are two entries with a plain velar before *eT, where T is any stop. The first, *ghed- ‘defecate’, should be reconstructed with a palatovelar; and the plain velar in the second, *ked- ‘smoke’, is reconstructed based on two Greek words that are probably unrelated to the other reflexes. There are four entries with a plain velar before *eiT: *geibh- ‘bend’, *geid- ‘stab’, *gheidh- ‘desire’, and *gheig̑h- ‘desire’. There is one entry with a palatovelar in this position, *g̑eid- ‘suck’, which is barely attested. There is one other entry with a plain velar before *ei, *keis- ‘arm’, where the plain velar is reconstructed based on three Dutch words that are probably unrelated to the other reflexes. This suggests that palatalization was blocked *eiT, but not before *eT or *ei when not followed by *T.

    There are five entries with a plain velar before *el. The Greek reflexes of the first, *ghelH₂d- ‘ice’, point to a zero grade *ghlH₂d-; whereas the third, *kelH₁- ‘drive’, and fourth, *kelH₁u- ‘wander’, are probably derived from the root *kelH₁- ~ *kleH₁- ‘call’. In all three cases the root may have contained a labiovelar which was delabialized by the *l. The second, *ghelou- ‘turtle’, and fifth, *kelg- ‘wind’, are barely attested. There is one entry with a plain velar before *em, *gem- ‘grasp’, where the Baltic reflexes point to an original labiovelar which was delabialized before *m in the zero grade. There is one entry with a plain velar before *en, *ken- ‘appear’, where the Slavic reflexes point to an *o-grade where palatalization could have been blocked by the *o.

    There are five entries with a plain velar before *er. The Baltic reflexes of the first, *ghers ‘weed’, third, *ker- ‘cherry’, and fifth, *kerm- ‘tire’, point to zero grade formations where palatalization would have been blocked by the *r. The second, *gherto- ‘milk’ could just as well be reconstructed with a labiovelar. The fourth, *kerd- ‘gird’, is probably derived from the root *(s)ker- ‘turn’, in which case it may have contained a labiovelar which was delabialized by the *s. There is one entry with a plain velar before *u, *gheubh- ‘bend’, where the Germanic reflexes point to a zero grade, so this may also have contained a labiovelar which was delabialized by the *u. There are no entries with a plain velar before *i. This suggests that plain velars were palatalized before *e and *i.

    There nine entries with a plain velar before *o: *gol- ‘bald’, *ghoilos- ‘froth’, *ghom- ‘stall’, *ghostis ‘stranger’, *ghouros ‘horrible’, *ghou- ‘pay’, *kob- ‘fit’, *koros ‘war’, and *koselo- ‘hazel’. There are three entries with a palatovelar in this position. The Indic reflexes of the first, *k̑onk- ‘doubt’, point to an *e-grade where the velar could have been palatalized by the *e. The second, *k̑ongho- ‘mussel’, is probably not reconstructable for PIE as the phonological correspondence between the Indic and Greek reflexes is irregular. The same cannot be said of the third, *k̑ormo- ‘torment’, but we also cannot rule out the possibility of a an *e-grade formation existing here too. This suggests that palatalization was blocked before *o.

    There are eighteen entries with a plain velar before *r: *grem- ‘damp’, *greus- ‘crumble’, *greus-  ‘burn’, *groHd- ‘hail’, *ghrebh- ‘scratch’, *ghredh- ‘stride’, *ghreib- ‘grip’, *ghrendh- ‘beam’, *ghreH₁u- ‘collapse’, *kred- ‘beams’, *kreH₁p- ‘strong’, *kreH₂u- ‘put’, *krei- ‘stroke’, *krep- ‘body’, *kret- ‘shake’, *kreuH₂- ‘blood’, *kreu- ‘thrust’, and *kreup- ‘scab’. There is one entry with a palatovelar in this position, *k̑rei- ‘shine’, which is barely attested and probably not reconstructable for PIE. This suggests that palatalization was blocked before *r. The blocking of palatalization before *r is well-known and is backed up by the gutturalwechsel (interchange between palatovelar and plain velar reflexes) in words such as *suekru- ~ *suekur- ‘in-law’.

    There thirteen entries with a plain velar before *H₂: *ghH₂eit- ‘hair’, *kH₂eilo- ‘whole’, *kH₂el- ‘beautiful’, *kH₂elni- ‘narrow’, *kH₂emp- ‘bend’, *kH₂ento- ‘corner’, *kH₂epro- ‘he-goat’, *kH₂eput ‘head’, *kH₂er- ‘revile’, *kH₂er- ‘hard’, *kH₂et- ‘plait’, *kH₂et- ‘bear’, and *kH₂eu- ‘humble’. There are three entries with a plain velar before *l: *klem- ‘slack’, *kleno- ‘maple’, and *klHuo- ‘bald’. There are five entries with a plain velar before *u: *gues- ‘twig’, *guosdho- ‘nail’, *kuers- ‘wood’, *kuet- ‘ferment’, and *kuoi- ‘wish’. In contrast, there are no entries with a labiovelars in any of these positions. This suggests that labiovelars were delabialized before *H₂, *l, and *u, as well as before *m, as was suggested above.

  • Can local authorities go bankrupt?

    Local elections are taking place across the UK on the 7th May. Where I live in Surrey these will be to elect councillors for two new ‘unitary authorities’: East Surrey and West Surrey. I live in the latter, which is an amalgamation of six previously separate borough councils in the western half of the county. All operations, services, and existing debts associated with these borough councils will be merged under this new unitary authority. The key challenge facing West Surrey is that it will start life with debts exceeding £4.5 billion (!). The debt was created in boroughs under the control of the Conservatives and Liberal Democrats – specifically Woking and Spelthorne – and equates to around £7,000 per resident. This will be the largest local authority debt per head of population in the country.

    It is often said that as a result of this £4.5 billion debt, West Surrey will start life effectively bankrupt. The claim is based on the fact that Woking Borough Council, which accounts for £2.6 billion of the £4.5 billion, supposedly declared bankruptcy in 2023 when it issued something called a Section 114 notice. This is a formal report issued by a UK local council’s Chief Financial Officer (under the Local Government Finance Act 1988) indicating that the authority cannot balance its budget and faces unlawful expenditure. Such notices are issued when expenditures are expected to exceed income. As a result, all new spending is banned, except for statutory services (e.g., social care, child protection) and essential safeguarding.

    However, this does not mean that Woking Council is bankrupt, contrary to popular belief. As I explained in a previous blog post, a council in Britain cannot go bust in the same way that an individual or private company can. Because only an act of parliament can dissolve a local authority, council services and the financing to provide them are implicitly underpinned by central government. To declare that a local authority is bankrupt is therefore to commit a category error. Actually the claim usually made is that Woking Council is ‘effectively’ bankrupt. Note the weasel word ‘effectively’. Those making the claim know that they cannot remove this word and simply say that Woking Council is bankrupt because this isn’t really true.

    The claim that Woking Council is bankrupt unravels further once you discover that the borough’s debt is owed almost entirely to central government. Originally the debt was to the Public Works Loan Board (PWLB), which provided funding to local authorities; in 2020, the PWLB was abolished as a statutory organisation and its functions were allocated to HM Treasury, which is presumably now who Woking Council owes the £2.6 billion to. The same goes for the rest of the £4.5 billion debt that West Surrey will inherit. This means that the entire debt could be written off by the UK government at the press of a button. In fact central government has already agreed to write off £500 million, which raises the question of why it doesn’t just write off the rest if it.

    This state of affairs seems even more ludicrous when you consider that one of the functions of central government is to provide funding for local authorities for necessary public services. Not only is the UK government not providing adequate funding; by refusing to write off the debt, it is effectively demanding that West Surrey provides money to the UK government! This is a crime against logic. The UK government is monetarily sovereign and can create money by fiat; it doesn’t need anyone to provide it money. The sensible thing to do would be to use the consolidation of the boroughs of West Surrey as an opportunity to write off the debt and begin again with a clean slate. But since when did common sense ever factor into decisions made by our political class?!

    The real reason the debt is being enforced has nothing to do with economics and everything to do with politics. The UK government knows that writing off the debt would create a precedent and encourage other local authorities to go into debt as well. They must therefore enforce the debt to ensure that other local authorities don’t step out of line and continue to pursue the austerity agenda. Viewed in that light, things seem rather bleak; but there is a more optimistic take on the situation. Woking Council has demonstrated that it is possible for a local authority to go into debt. Although it did that through speculative investments, there is no reason a local authority couldn’t go into debt for other reasons.

    In particular, there is nothing to stop a local authority going into debt to properly fund public services or build affordable housing. Indeed, this is precisely what Liverpool’s 1983-1987 socialist council did. As long as that debt is denominated in pound sterling – as almost all local authority spending is – it would be implicitly underpinned by central government, who would have the power to write off the debt at any time with the press of a button. The whole idea that a local authority can be in debt to central government is nonsense. It is a bourgeois conception to provide justification for policies designed to discipline the working class. The only thing preventing local authorities from properly funding public services is a lack of political will.

  • The colonization of Ireland

    Ireland was England’s first colony (Wales was the second but took a bit longer to conquer). The colonization began in 1169 when Anglo-Norman mercenaries were invited in by the deposed King of Leinster, the region covering most of eastern Ireland, to help regain his kingship. Dublin was originally a Viking city, having been founded by the Vikings in 841. But the Anglo-Normans claimed Dublin along with the rest of Ireland and were supported by a Papal Bull: a formal, authoritative decree issued by the Pope. The mercenaries swiftly seized control of areas like Dublin and Waterford and eventually gained control of around three-quarters of Ireland over the following decades, marking the beginning of centuries of English dominance.

    After the Protestant split away from the Catholic Church in the 16th Century, Ireland, unlike England, remained Catholic. This lead to English fears that Ireland would form an alliance with Catholic Spain and France. In response, Queen Elizabeth of England resorted to a classic divide-and-rule strategy. Protestants were planted in Ireland, mainly in the north east but also in Dublin. Meanwhile, Catholics were thrown off their land and brutally repressed. Laws were enacted which enforced Protestant conformity with heavy fines imposed for non-compliance, Catholic Masses were banned, and Catholic missionaries were executed as traitors. Around 200 Catholics were executed in Ireland during Elizabeth’s reign.

    The Irish Rebellion of 1641 brought much of Ireland under the control of the Irish Catholic Confederation, which engaged in a multi-sided war with Royalists, Parliamentarians, Scots Covenanters, and local Presbyterian militia. In 1649, Oliver Cromwell’s troops landed in Ireland, which by then was under the control of a coalition aligned with the Royalist cause. No quarter was given by Cromwell and his army. Once again there was massive repression of Catholics, including a massacre in Drogheda, and Cromwell’s men were given land at the expense of the native Catholic population. The Act for the Settlement of Ireland 1652 barred Catholics from most public offices and confiscated large amounts of their land. This period effectively saw the re-conquest of Ireland by England.

    The Orange Order, an anti-Catholic anti-independence organisation, was founded in 1794. This reactionary organisation drove thousands of Catholics out of the north of Ireland to Connaught in the west. The Order was named after Protestant William of Orange who won the decisive Battle of The Boyne in 1690, which ensured the continued Protestant ascendancy in Ireland. However in 1798 Protestant Wolf Tone, inspired by the American and French Revolutions, led his Society for United Irishmen in a fight for Irish independence. Ultimately though the United Irishmen were defeated and Ireland was forcibly brought into the Act of Union in 1801. Industry was suppressed in all but the north eastern counties, with the rest of Ireland remaining largely agrarian.

    The Great Famine took place between 1845 and 1852, during which over a third of the population either starved to death or were forced to emigrate. As a result the population fell from 8.2 million in 1841 to 4.7 million in 1891; the population of Ireland today is 7.2 million, still lower than its pre-famine peak. The famine was primarily caused by a water mold which destroyed potato crops across Europe. The blight caused catastrophic devastation in Ireland due to an extreme over-reliance on a single potato variety, combined with unjust land ownership systems, poverty, and inadequate, slow, or restrictive relief efforts by the British government. The famine was arguably an act of genocide by the British, who deliberately shipped food from Ireland during this period with the help of Anglo-Irish land owners.

    In the early 20th century James Connolly and Jim Larkin, Irishmen born in Edinburgh and Liverpool respectively, built a strong Trade Union movement across the whole of Ireland which organised strikes in Dublin, Belfast, and elsewhere. Connolly vociferously opposed the imperialist war of 1914-1918, unlike many other prominent socialist leaders (Lenin, Trotsky, and Rosa Luxembourg being notable exceptions). The Easter Rising, an armed insurrection launched by Irish republicans against British rule in Ireland, took place in 1916. Initially there was little support for Rising in Ireland. But the British murder of the leaders of the Rising, including James Connolly, changed the mood completely, and there were even reported mutinies of Irish soldiers.

    Elections in 1918 saw a majority for the pro-independence Sinn Féin party (Irish for ‘We Ourselves’), and over 70% voting for parties standing for independence, after Labour stood aside to back nationalist demands. Sinn Féin then established the Dáil Éireann (Assembly of Ireland) and boycotted Westminster. In response the British Secretary of State for War, one Winston Churchill, sent in the paramilitary Black and Tans to combat Irish revolutionaries. Whilst it is not clear that the Dáil ever intended to gain independence by military means, and war was not explicitly threatened in Sinn Féin’s 1918 manifesto, war broke out between Britain and Ireland the following year. Churchill made clear that Ireland would have to agree to partition or be reduced to rubble.

    Partition reinforced the divide and rule strategy that had been going on since the 16th century. Catholics were barred from jobs and gerrymandering ensured that Catholic areas were run by Protestant politicians. Catholic areas faced pogroms organised by the Orange Order and allowed – indeed, in some cases participated in – by the mainly Protestant police. In 1972 British Troops shot 26 and murdered 14 unarmed Catholic demonstrators in Derry in Northern Ireland, an event that became known as Bloody Sunday. This sparked off The Troubles, a 30 year war between the IRA on the one hand, and British forces and Loyalist paramilitaries on the other, which left over 3,000 dead. The IRA’s individualistic terrorism only further increased division.

    The Troubles eventually came to an end with the Good Friday agreement of 1998. More recently, however, Brexit has again highlighted underlying tensions between the Northern Ireland and the Republic. The population of Northern Ireland is now 51% Catholic and 49% and Protestant, whereas it was 66% Protestant at the time of Partition; this has led many to argue for a referendum on whether Northern Ireland should remain in the UK or join a united Ireland. But such a referendum would likely only heighten tensions once more. What is required is a class program to unite Catholics and Protestants in a common struggle against the misery of capitalist exploitation. Only then will Ireland finally throw off the shackles of English domination.

  • A spelling reform proposal

    In a previous blog post I set out the case for reforming English spelling and sketched out a proposal for such a reform. As that post received more likes than any other post on this blog (four likes!) I thought I should set out a more detailed reform proposal. The basic idea was to start with the Latin alphabet and to assign each letter a unique sound. This is straightforward for the letters a, b, d, e, f, g, i, k, l, m, n, o, p, r, s, t, v, w, and z, all of which have a clear default sound assigned to them under current English spelling which matches or closely matches the sound assigned in the International Phonetic Alphabet. On the other hand, the digraph th represents two different phonemes in English, one unvoiced and the other voiced; it makes sense to use th for the first and dh for the latter.

    Similarly the letter u represents two vowel phonemes, one rounded and the other unrounded. It makes sense to use u for the former, but not for the latter – the so-called ‘schwa’ sound – as that can be spelled using either o or u in stressed position, and any vowel letter in unstressed position. The only vowel letter left is y, so I suggest using this for the unrounded version. This would make English consistent with several other languages that use y for the schwa sound (such as Welsh). That gives us representations for all six short vowels: a as in trap, e as in dress, i as in kit, o as in lot, u as in foot (fut), and y as in strut (stryt). Of course this means we can’t use y to represent the semivowel at the start of yes, so I suggest using j for this instead, as in the International Phonetic Alphabet.

    Long vowels can be represented by a following h: ah as in palm (pahm), and oh as in thought (thoht). The h may be dropped if the long vowel is followed by an r which is not then followed by another vowel, as in start, force (fors), and nurse (nyrs). Closing diphthongs can be represented by a vowel plus a following j or w: aj as in price (prajs), aw as in mouth (mawth), ej as in face (fejs), ij as in fleece (flijs), oj as in oil (ojl), uw as in goose (guws), and yw as in goat (gywt). Conversely, opening diphthongs can be represented by a closing diphthong plus a following r: ajr as in hire (hajr), awr as in flour (flawr), ejr as in wear (wejr), ijr as in near (nijr), ojr as in coir (kojr), and uwr as in cure (kjuwr). The closing diphthong that would be represented by ywr has been replaced by ohr in most English accents.

    The fact that we are using j to represent the semivowel at the start of yes means that we can’t use it to represent the consonant at the start of jive, so I suggest using the digraph dj for this sound instead. For consistency I suggest also using sj and tj for the sounds currently transcribed as sh and ch, as in shy and China. These conventions potentially create an issue for accents that distinguish between dew and jew, or between dual and jewel. But nowadays most English speakers either pronounce these words the same way, in which case it there is no problem with spelling both as djuw; or, they pronounce the first as duw and the second as djuw, in which case there is again no problem as these speakers can simply use whichever spelling is appropriate.

    How might we mark stress in our proposed system? Stress is not marked at all in current English orthography, although it is phonemic in English. In fact there are usually considered to be two types of stress in English: primary and secondary stress. In our system only the vowels i, u, and y – what might be labelled the ‘high’ vowels – can be unstressed, whereas the vowels a, e, o  – what might be labelled the ‘low’ vowels – always carry either primary or secondary stress. This means that if a word contains only one low vowel and no other vowels, this vowel must carry the primary stress, as a word cannot have only secondary stress. If a word contains more than one vowel, primary stress will generally fall on the first syllable with a low vowel unless marked otherwise.

    If a word contains no low vowels, stress will generally fall on the (high) vowel which is followed by more than one consonant. If there is more than one such vowel, primary stress will generally fall on the first such vowel unless marked otherwise. If there is no such vowel then the word will generally be unstressed unless marked otherwise. These rules mean that in general it is not necessary to mark stress in our proposed orthography; if stress does need to be marked it can be done (for example) with an acute accent. Note that the digraphs dh, th, dj, sj, tj, zj, and ng count as single consonants for the purposes of these rules.

    Syw dhejr juw hav it. Y njúw ynd kymplíjt speling riform prypywzyl fyr dhij Ingglisj langwidj. Wot dy juw think?

  • What causes inflation?

    By bombing Iran and spreading carnage across the Middle East, the US and Israel have put the cost of living crisis back in the headlines. (Has there ever been a more dystopian phrase than ‘cost of living’?) When prices skyrocketed following Russia’s invasion of Ukraine in 2022 we were told it was a one-off; but we now know that this isn’t true. On the contrary, we appear to have entered a period of political instability characterized by high inflation. The standard explanation for inflation is that it occurs when demand for goods exceeds their supply. According to this explanation, the high inflation of recent years was caused by oil supply shocks, first by created by the war in Ukraine and now by the war in Iran. In this blog post I will examine this claim in detail.

    To fix ideas, let (A,L) be a Leontief economy where A ≥ 0 is the mxm commodity input matrix and L ≥ 0 is the 1xm labour input row vector. Given scalar profit and wage rates r,w ≥ 0, the equilibrium price vector is the 1xm row vector p* satisfying p* = (1+r)(p*A+wL). Converting this into a recursive equation gives us a model of price dynamics: p’ = (1+r)(pA+wL), where p and p’ denote the price vector at the current and next time step respectively. The solution to this equation is given by: p(t) = c[(1+r)A]t + (1+r)wL[I-(1+r)A], where p(t) is the 1xm price row vector at time step t and c is a constant 1xm row vector whose elements are determined by the initial conditions. We can say that inflation occurs if the sequence {p(t)} does not converge to the equilibrium price vector p*.

    According to a standard result from dynamical systems theory, the sequence {p(t)} defined by the equation above converges if and only all of the eigenvalues of the matrix (1+r)A are less than 1. (We say that the 1xm row vector v is an eigenvector of the mxm matrix M with eigenvalue e if vM = ev.) Thus, a necessary and sufficient condition for inflation to occur is that the matrix (1+r)A has at least one eigenvalue which is greater than 1. Note that this condition depends only on the commodity input matrix A and profit rate r, and not on the labour input row vector L or the wage rate w. Thus an increase in wages will increase equilibrium prices but will not result in a runaway increase in prices over time. This is one in the eye for those who wish to blame inflation on increased wages.

    We can take the input-output matrix A as fixed as in generally this will change only slowly over time. Therefore, to find the cause of inflation we must examine the profit rate r. Right-multiplying the price equation by an mx1 output vector q gives: p’q = (1+r)(pA+wL)q. Rearranging gives: r = P/(pAq+wLq), where P = p’q-(pA+wL)q is the total profit. In a previous blog post I explained how total profits are determined by the so-called Kalecki profit equation: P = C+I+N+G-T, where C is consumption out of profits, I is investment, N is net exports, G is government spending, and T is taxes on wages (I have assumed zero saving out of wages, as is customary). This demonstrates that profits are determined by decisions made by capitalists (C+I+N) and the government (G-T).

    From this we can deduce that inflation can be caused by an increase in consumption out of profits C, investment I, net exports N, or government spending G; or a decrease in taxes on wages T. It can also be caused by an decrease in any component of the output vector q or in the average wage w. Thus, not only will an increase in wages not result in inflation; it actually makes inflation less likely! To understand why, note that the equation r = P/(pAq+wLq) shows that there is an inverse relationship between the wage rate r and the profit rate w, so if the wage rate w goes up then all else being equal the profit rate r must go down. This is another one in the eye for those who wish to blame inflation on increased wages.

    As I mentioned in the introduction, the increased inflation of recent years is usually blamed on oil supply shocks, first by created by the war in Ukraine and now by the war in Iran. In our framework a supply shock can be modelled as a decrease in the ‘oil’ component of the commodity output vector q. The analysis above shows that a decrease in just one component of this vector will result in an increase in the profit rate r, which in turn can be enough to mean that the largest eigenvalue of the matrix (1+r)A switches from less that to greater than 1. This explains how a supply shock in a single commodity can push the entire global economy into an inflationary spiral. Moreover, the higher the dependency on this single commodity – as specified by the matrix A – the more likely this is to happen.

    The analysis above also explains why profits increase during times of crisis: namely, supply shocks automatically result in an increase in the profit rate r. This suggests that it is not (just) capitalist greed that results in increased profits during times of crisis; rather, this is something that is baked into the laws of capitalism itself. We have seen this play out in recent times with the capitalist class benefitting from the financial crisis and the COVID crisis, as well as from the wars in Ukraine and Iran. Of course, the fact that capitalists benefit from crises gives them an incentive to ensure that crises keep occurring. This demonstrates once again that we will never see true peace and stability in our world until we get rid of capitalism.

  • The impact of immigration on the UK

    Local elections are on the horizon here in the UK and immigration is likely to be one of the main issues on the agenda. So I decided to take a look at net migration figures to understand the scale of the issue, or whether it should even be considered an issue at all. Contrary to popular belief, the British government has a good handle on the number of people coming into and out of the country. The data are compiled and updated quarterly and are freely available on the website of the Office for National Statistics. These figures show that over the last 15 years or so, net migration to the UK has averaged around 350,000 people per year. That sounds like a lot, but 350,000 people represents just 0.5% of the UK’s total population.

    However, this means that over the last 15 years, 5 million or so people have been added to the UK population purely as a result of migration. That tallies with overall population statistics, which show that the population of the UK has increased from around 64 million to around 69 million over that same 15 year period. Furthermore, projections suggest that if current trends continue the population will grow further to around 80 million by 2050. It is clear therefore that the UK’s population has increased significantly in recent years due to migration and is likely to continue to do so for the foreseeable future. To deny that is to deny basic facts. The real question is: does it matter? This is a much more difficult question to answer.

    One way in which migration-driven population increase is claimed to have a negative impact is by putting pressure on public services. We should not be fooled by this argument, regardless of how superficially plausible it seems. It is true that our public services are under immense strain; but this is entirely down to a combination of privatization and a lack of proper funding. To those who ask where the money for increased funding would come from, we only need to point to the fact that the majority of immigrants that come into this country are of working age and therefore add to the government’s tax revenue. Or better still, we can point out that a sovereign currency-issuing government like the UK does not face any fiscal constraints when it comes to funding public services.

    Another way in which the migration-driven population increase is claimed to have a negative impact is through increased housing costs. House prices and rents have certainly risen sharply in recent decades; but this is mainly due to government policies designed to benefit the property-owning class. The vast majority of migrants coming into this country are poor, struggle to pay rent, and can only dream of getting on the housing ladder. They are victims of the housing crisis rather than perpetrators. The true explanation for the crisis lies in the fact that around 20% of households are in the UK – roughly 5 million households in total – are now in the private rented sector. (The comparable figure was around 10%, or 2.5 million households, in the early 2000s.)

    One way in which immigration does have a negative impact is by driving down wages. Studies have found that increased immigration often leads to reduced wages, particularly at the bottom end of the wage distribution. This explains why it is those on lower wages who tend to be most averse to immigration. Perhaps they aren’t just racist after all! This makes perfect sense in light of Marx’s concept of the ‘reserve army of labour’: the unemployed and underemployed segment of the population in a capitalist economy which suppresses wages and maintains a compliant workforce. It also explains why significant immigration is still allowed to occur, despite it being vehemently opposed by a large section of the British electorate.

    In short, immigration is allowed to continue because it benefits the capitalist class, by ensuring that wages remain low. Working people understand that immigration worsens their material conditions but tend to blame immigrants rather than the people they should blame: namely, capitalists. Better yet, they should blame the capitalist system which divides people into two mutually antagonistic groups – workers and capitalists. The fact that working people resort to blaming immigrants for their problems is a huge benefit to the capitalist class as it provides a convenient scapegoat for declining public services, unaffordable housing, and stagnating wages. It is a consequence of the deliberate diminution of working class consciousness that has being going on in this country for many decades.

  • The transformation problem

    In Marxian economics, the ‘transformation problem’ refers to the problem of finding a general rule by which to transform the values of commodities – based on their socially necessary labour content, according to Marx’s labour theory of value – into the prices of commodities seen in the marketplace. Here I will provide a mathematical treatment of the problem based on a 1974 paper by the Japanese Marxist economist Micho Miroshima. Let (A,L) be a Leontief economy where A ≥ 0 is the mxm commodity input matrix and L ≥ 0 is the 1xm labour input row vector. The labour value vector for such an economy is the 1xm row vector v satisfying v = vA+L. The ith component of this vector represents the socially necessary labour contained in 1 unit of commodity i.

    Given scalar profit and wage rates r,w ≥ 0, the equilibrium price vector is the 1xm row vector p* satisfying p* = (1+r)(p*A+wL). The ith component of this vector represents the equilibrium price of 1 unit of commodity i. It is assumed that wages are set at subsistence level, so that if the price vector 1xm price vector is p then w = pD for some mx1 column vector D ≥ 0. The ith component of this vector represents the quantity of commodity i required to keep one labourer working per unit time. The equilibrium price equation can then be written as p* = (1+r)p*(A+DL); setting M = A+DL, this can be written as p* = (1+r)p*M. Converting this into a recursive equation gives us a model of price dynamics: p’ = (1+r)pM, where p and p’ denote the price vector at the current and next time step respectively.

    The product vD represents the socially necessary labour contained in, or value of, the column vector D. Fix an mx1 output row vector q. Then the scalar vAq is interpreted as the value of constant capital C and the scalar vDLq is interpreted as the value of variable capital V. Since the total value of output is given by vq, the surplus value is given by s = vq-C-V = vq-vAq-vDLq; substituting in the expression for the value vector v above gives S = (I-vD)Lq, where I is the mxm identity matrix. The rate of exploitation is therefore given by e = S/V = (I-vD)Lq/vDLq; and dividing through by Lq (a scalar) gives: e = (1-vD)/vD. Now let q* be the output vector corresponding to the equilibrium price vector p*, so that q* = (1+r)Mq*. Then it can be shown using a bit of algebra that r = evDLq*/vMq*.

    The formula r = evDLq*/vMq* transforms the vector of values, v, into a rate of profit, r. On the other hand, the formula p’ = (1+r)pM transforms the rate of profit, r, into a vector of prices, p’. These two formulae can therefore be seen as a solution to the transformation problem. Starting from an initial price vector, the second formula will generate a sequence of price vectors which, under certain conditions, will converge to the equilibrium price vector p*. However, this is incomplete as an algorithm as it assumes that the commodity vector q* is known. To get around this, Miroshima suggests replacing q* with the iteration q’ = vqMq/vMq, which he then demonstrates converges to q* under fairly weak assumptions.

    Miroshima proposes the following as a complete algorithm to get from values to prices: (1) calculate sequence of commodity vectors according to the recursion q’ = vqMq/vMq until a stationary solution q* is obtained; (2) calculate r = evDLq*/vMq*; (3) calculate the sequence of price vectors according to the recursion p’ = (1+r)pM until a stationary solution p* is obtained. He then proves that, provided the price sequence begins from the value vector v, the aggregate output in terms of prices p*q* is equal to the aggregate output in terms of values, vq*, and that the aggregate profit, P* = p*(I-M)q*, is equal to the aggregate surplus value, S* = v(I-M)q*. These conclusions are close to, although not identical with, conclusions Marx reached in Das Capital.

  • Velars in the IEW

    The Indogermanisches Etymologisches Wörterbuch (IEW) was published in 1959 by the Czech linguist Julius Pokorny and provides an overview of the lexical knowledge of Proto-Indo-European accumulated in the early 20th century. The IEW is now generally considered outdated, but it remains the only comprehensive Indo-European dictionary and as such it is still a useful resource. In this blog post I will list entries from the IEW with velars in different phonological environments. I have only included entries with reflexes in at least two separate branches in both the centum and satem languages; where there is no uncertainty in the reconstruction; and where the velar only occurs in one phonological environment. I have updated reconstructions where necessary and excluded onomatopoeic cases.

    There no entries with a palatovelar before *e(i)T, where T is any stop, but there are three entries with a plain velar in this position: *ghed- ‘defecate’, *geibh- ‘bend’, and *gheidh- ‘desire’. Similarly, there are no entries with a palatovelar before *o, but there are three entries with a plain velar in this position: *kH₂eiko- ‘one-eyed’, *koros ‘war’, and *spiko- ‘woodpecker’. Furthermore, there are no entries with a palatovelar before *r, but there are nine entries with a plain velar in this position: *grem- ‘damp’, *ghredh- ‘stride’, *ghrendh- ‘beam’, *ghreH₁u- ‘collapse’, *kreH₂u- ‘put’, *krep- ‘body’, *kreuH₂- ‘blood’, *kreuH- ‘thrust’, and *kreup- ‘scab’. This suggests that palatalization was blocked before *e(i)T, *o, and *r.

    There no entries with a labiovelar before *H, but there are seven entries with a plain velar in this position: *kH₂eiko- ‘one-eyed’, *kH₂eilo- ‘whole’, *kH₂emp- ‘bend’, *kH₂eput ‘head’, *kH₂er- ‘revile’, *kH₂er- ‘hard’, and *kH₂ers- ‘scratch’. Similarly, there no entries with labiovelars before *l or *n, but there are three entries with plain velars in these positions: *kleng- ‘bend’, *kleno- ‘maple’, and *knH₂ko- ‘golden’. There is one entry with a plain velar before *em, *gem- ‘grasp’, where the Baltic reflexes point to a zero grade *gʷm-. There is one entry with a labiovelar before *u, *perkʷus ‘oak’, with clear evidence of delabialization; and three entries with a plain velar in this position: *H₂erku-‘bent’, *gues- ‘twig’, and *kuH₂et- ‘ferment’. This suggests that labiovelars were delabialized before *H, *l, *m, *n, and *u.

    There are six entries with a plain velar before *e, aside from those already discussed. The first, *kelH- ‘drive’, is linked with another entry, *kelH₁- ~ *klH₁- ‘call’, which points to original root *kʷelH₁- where the labiovelar may have been delabialized in the zero grade *kʷlH₁-. The second, *kelg- ‘wind’, is sparsely attested and probably did not exist in PIE. The Slavic reflexes of the third, *ken- ‘appear’, point to an *o-grade where palatalization could have been blocked by the following *o, as do the Baltic reflexes of the fourth, *kenk- ‘burn’. The fifth, *kento- ‘rag’, is sparsely attested and probably did not exist in PIE. The final entry is *kerH₃- ‘burn’, where the Baltic reflexes point to an original labiovelar. There are no entries with plain velars before *i. This suggests that plain velars were regularly palatalized before *e and *i.

    There are no entries with a palatovelar after non-syllabic *n, but thirteen entries with a plain velar in this position: *dhengh- ‘press’, *dhengh- ‘reach’, *geng- ‘lump’, *g’hengh- ‘stride’, *H₁enk- ‘sigh’, *H₂enk- ‘bend’, *kenk- ‘burn’, *kleng- ‘bend’, *meng- ‘make’, *slenk- ‘wind’, *tengh- ‘pull’, *tenk- ‘pull’, *trenk-  ‘thrust’. There is one entry with a palatovelar after *m: *H₂emg’h- ‘narrow’; two entries with a palatovelar after syllabic *n: *bhng’hus ‘thick’, and *dng’huH₂ ‘tongue’; but no entries with plain velars in these positions. This suggests that palatalization was blocked after non-syllabic *n, but not after *m or syllabic *n.

    There no entries with a labiovelar after *H, but there are six entries with a plain velar in this position:  *bheH₂g- ‘apportion’, *ieH₂g- ‘venerate’, meH₂gh- ‘young’, *meH₂k- ‘skin’, *pleH₂k- ‘hit’, and *ueH₂g- ‘cry’. Similary, there are no entries with a labiovelar after *l, but there are four entries with a plan velar in this position: *melk- ‘wet’, *selk- ‘pull’, *spelg- ‘split’, and *uelk- ‘pull’. Furthermore, there are no entries with a labiovelar after *u, but there are ten entries with a plain velar in this position: *bheug- ‘bend’, *dheugh- ‘touch’, *dhreugh- ‘deceive’, *H₁euk- ‘accustom’, *ieug- ‘move’, *leuk- ‘shine’, *meug-  ‘slip’, *reug- ‘belch’, *sleug- ‘swallow’, and *smeuk- ‘smoke’. This suggests that labiovelars were delabialized after *H, *l, and *u.

    There are no entries with a labiovelar after *s, but there are thirteen entries with a plain velar in this position: *mosgo- ‘marrow’, *resg- ‘weave’, *skeH₂i- ‘bright’, *sked- ‘split’, *skei- ‘cut’, *skel- ‘bend’, *skep- ‘cut’, *sker-  ‘jump’, *sker-  ‘cut’, *skerbh- ‘turn’, *skeH₁u- ‘cut’, *skeud-  ‘throw’, and *skH₂ebh- ‘support’.  Furthermore, there no entries with a labiovelar after mobile *s, but nine entries with a plain velar in this position: *(s)kH₂el- ‘hard’, *(s)kH₂end- ‘shine’, *(s)kel- ‘stab’, *(s)kel- ‘hit’ *(s)kel- ‘call’, *(s)kreH₁p-  ‘leather’, *(s)kert- ‘turn’, *(s)keu- ‘pay’, and *(s)keuHd- ‘shout’. There are also three entries with palatovelars in these positions: *sk’eH₂i- ‘shimmer’, *(s)k’em- ‘hornless’, and *sk’erd- ‘defecate’. This suggests that labiovelars were delabialized after *s and *(s).

    There are no entries with a palatovelar in roots beginning with *(s)t, but five with a plain velar in this position, aside from those already discussed: *steigh- ‘stride’, *streig- ‘stop’, *(s)treg- ‘strengthen’, *tek- ‘stretch’, and *tek- ‘weave’. Similarly, there are no entries with a labiovelar in roots beginning with *H₂, but three with a plain velar in this position, again aside from those already discussed: *H₂eig- ‘move’, *H₂lek- ‘close’, and *H₂rek- ‘protect’. Furthermore, there are no entries with a labiovelar in roots beginning with *(H,s)m, but four with a plain velar in this position, aside from those already discussed: *H₃meigh- ‘flicker’, *mek- ‘bleat’, *merk- ‘rot’, and *smek- ‘chin’. This suggests that palatalization was blocked in roots beginning with *(s)t, and that labiovelars were delabialized in roots beginning with *H₂ and *(H,s)m.

    There is one root with plain velars after *e, aside from those already discussed: *rek- ‘arrange’. This root is sparsely attested probably did not exist in PIE. There are four entries with a plain velar after *i, aside from those already discussed. The first, *dhrigh- ‘hair’ is sparsely attested and probably did not exist in PIE. The Greek reflexes of the second, *H₃leig- ‘needy’, point to a formation *H₃loigos, and the Slavic reflexes of the third, *ueik-‘force’, point to a formation *uoikos; in both cases, palatalization could have been blocked by the following *o. The same cannot be said of *leig- ‘hop’, but equally we cannot rule out the possibility of a similar formation existing here too. This suggests that plain velars were palatalized after *e and *i unless followed by *o.

    There are three entries with a plain velar after *r, aside from those already discussed. The first, *H₁ergh- ‘shake’ is sparsely attested and probably did not exist in PIE; and the Slavic reflexes of the second, *suergh- ‘care’ point to a formation *suorghos where palatalization could have been blocked by the following *o. This suggests that plain velars were palatalized after*r unless followed by *o.

  • What is a quantum computer?

    Quantum computers are advanced computing systems that harness  quantum mechanics—specifically superposition and entanglement—to solve complex problems beyond the reach of classical computers. Unlike classical computers that use binary bits (0 or 1), quantum computers use quantum bits (qubits), allowing them to process vast amounts of data simultaneously. Qubits can exist in multiple states at once, allowing exponential increases in processing power compared to classical bits. Furthermore, entanglement of qubits, a quantum phenomenon where qubits become linked, allows for high-speed, complex calculations. Whilst still in development, this technology is accelerating towards practical applications in simulation, optimization, and security.

    The simplest model of computation is something called a ‘finite state machine’. This is defined by a finite set of states, X; a finite input alphabet, A; and a transition function f() from XA to X. This is quite an abstract definition so let’s illustrate it with a simple example: a turnstile. This has two states, locked and unlocked, so we can take X = {0,1}, where 0 corresponds to ‘locked’ and 1 corresponds to ‘unlocked’. There are two possible inputs that affect its state: putting a coin in the slot, and pushing the arm. We can therefore take A = {0,1}, where 0 corresponds to putting a coin in the slot and 1 corresponds to pushing the arm. If a coin is put in the slot it becomes unlocked, and if the arm is pushed it becomes locked; the transition function is therefore given by f(0,0) = f(1,0) = 1, and f(0,1) = f(1,1) = 0.

    A quantum computer may be modelled using something called a ‘quantum finite state machine’. As with an ordinary finite state machine, this is defined by a set of states, X; an input alphabet, A; and a transition function f() from XA to X. However, the set of states X is not longer finite but is instead assumed to be finite-dimensional a complex vector space. The transition function is represented by a collection of a ‘unitary matrices’, one for each element of the input alphabet A, which as before is assumed to be finite. A complex square matrix U is said to be unitary if its matrix inverse U-1 equals its conjugate transpose U*; that is, if U*U = UU* = I, where I is the identity matrix. The conjugate transpose of U, in turn, is the matrix obtained by transposing U and applying complex conjugation to each entry.

    Given an input letter a from the input alphabet A, the unitary matrix U(a) determines the transition of the machine from its current state x to its next state y, as follows: y = U(a)x. Thus, the transition function f() for the quantum finite state machine is given by f(x,a) = U(a)x. Again, this is quite an abstract definition so let’s illustrate it with a simple example: a quantum turnstile. This is a (theoretical!) quantum version of the turnstile described above. As there are just two underlying states, locked and unlocked, we can take the state space X to be the set of complex vectors of the form x = c0x0+c1x1, where x0 = (1,0)’ corresponds to the locked state, x1 = (0,1)’ corresponds to the unlocked state, and c0,c1 are complex numbers which are normalized so that c*c = 1, where c = (c0,c1)’.

    The unitary transition matrices are given by: Ujk(0) = 1 if j = 0, Ujk(0)= 0 if j = 1; and Ujk(1) = 1 if j = 1, Ujk(1) = 0 if j = 0. The transition function is given by f(x,a) = U(a)x, thus: f(x0,0) = U(0)x0 = (0,1)’ = x1; f(x1,0) = U(0)x1 = (0,1)’ = x1; f(x1,0) = U(0)x1 = (1,0)’ = x0; and f(x1,1) = U(1)x1 = (1,0)’ = x0. Therefore in the case where x is a pure state (so x = x0 or x = x1), the result of running the machine will be exactly identical to the classical deterministic finite state machine described above. The non-classical case occurs if both c0 and c1 are nonzero, which captures the notion of a ‘qubit’. In this case, the probability of the machine being in state x0 is given by |c0|2 and the probability of it being in state x1 is given by |c1|2, where for a complex number a+bi we have |a+bi|2 = a2+b2.

    If c0 = a0+b0i and c1 = a1+b1i, the probability of being in state x0 is given by|c0|2 = a02+b02 and the probability of being in state x1 is given by |c1|2 = a12+b12. We also have c* = (c0*, c1*) = (a0-b0i, a1-b1i), and therefore c*c = (a0-b0i, a1-b1i)(a0+b0i, a1+b1i)’ = a02+b02+a12+b12. Since c*c = 1 by assumption, the probabilities of being in states x0 and x1 must sum to one. This can all be easily generalised to the case where the underlying machine has arbitrarily many states, as long as the number of states remains finite. Therefore, given any classical finite state machine, a corresponding quantum version can be defined. At the time of writing, most quantum computers are implementations of quantum finite state machines, which suggests that this model captures the essence of quantum computation.

  • Justifying the labour theory of value

    The labour theory of value (LTV) posits that the exchange value of a commodity is proportional to the socially necessary labour time required to produce it. Marx was the greatest champion of the LTV but many Marxists have since abandoned it, raising the question of whether the LTV is a necessary component of Marxism or whether it can be discarded. In this blog post I will attempt to answer this question. To fix ideas, consider an economy which produces m commodities. For such an economy we can define a commodity vector as an mx1 column vector with positive elements. The economy is defined by an activity set, with the interpretation that an element (X,u,Y) of this set represents a possible configuration of commodity inputs X, labour inputs u, and commodity outputs Y.

    According to Japanese Marxist economist Michio Morishima, the socially necessary labour time associated with the commodity vector K may be defined as the minimum value of u subject to the constraint that there exists commodity vectors X and Y such that (X,u,Y) is an element of the activity set and Y-X is greater than or equal to K. This is quite a technical definition so let us try to unpack it a bit. Minimizing u can then be thought of as giving us the ‘socially necessary’ part of socially necessary abstract labour. The constraint in the minimization is there to ensure that the commodity vector K can be produced by the economy; to see this, note that Y-X represents the net output of the production process defined by the triple (X,u,Y).

    Thus, under this definition, to find the socially necessary labour time associated with the commodity vector K we must find the minimum value of u subject to the constraints that (X,u,Y) is in the activity set and Y-X ≥ K. Let u* be a solution to this problem, so that u* is the socially necessary labour time for K. Then given another labour input u that satisfies these constraints, the surplus labour time is given by u-u* and the rate of exploitation is given by (u-u*)/u. The ‘dual’ problem involves finding the maximum value of pK subject to the constraints that (X,u,Y) is in the activity set and p(Y-X) ≤ u. Let p* be a solution to this problem, so that p* represents the profit-maximizing price for M subject to these constraints. Then we would expect that p*K = u*.

    As firms maximize profits, we would therefore expect that the exchange value of a commodity vector is equal to the socially necessary labour time associated with this commodity vector. This provides an intuitive justification for why the LTV should hold. This can be made rigorous in the case where we have X = Aq, u = Lq, and Y = Bq for some fixed mxn matrices A ≥ 0 and B ≥ 0, some fixed 1xn row vector L ≥ 0, and some variable nx1 ‘intensity’ vector q ≥ 0; such an economy is referred to as a von Neumann economy, after the Hungarian mathematician and physicist Jon von Neumann. Then the primal problem is to minimize Lq subject to (B-A)q ≥ K and the dual problem is to maximize pK subject to p(B-A) ≤ L, and if q* and p* are solutions to these problems it can be shown that p*K = Lq*.

    This result can be restated succinctly as follows. Let (A,B,L) be a von Neumann economy, where A ≥ 0 is the mxn commodity input matrix, B ≥ 0 is the mxn commodity output matrix, and L ≥ 0 is the 1xn row vector of labour inputs. Then we may define the socially necessary labour time associated with the mx1 commodity vector K ≥ 0 as the minimum of Lq subject to (B-A)q ≥ K, and the exchange value of the commodity vector K as the maximum of pK subject to the constraint p(B-A) ≤ L. If q* and p* are solutions to these problems then, by the duality theorem of linear programming, we have p*K = Lq*. The exchange value of K is therefore equal to the socially necessary labour time associated with it. This provides a logical justification for why the LTV should hold.

  • The decline of the petrodollar

    In a previous blog post I suggested that Israel convinced the US to bomb Iran because Israel wants to turn Iran into a failed state. That’s not to suggest that the US doesn’t also want to attack Iran. On the contrary, the US has wanted to attack Iran ever since the Iranian revolution of 1979. This revolution culminated in the overthrow of the Pahlavi dynasty, essentially a puppet government of the US. The pertinent question is not ‘why the US bombing Iran?’ but ‘why it has taken it so long?’. The answer is that previous US administrations all understood that attacking Iran would be a disaster and therefore refused to be drawn into such a conflict. And for a time it seemed the current administration would do the same.

    Trump himself has said many times that he would not bomb Iran, despite pressure from hawkish Republicans. So what changed? This is where Israel comes in. Netanyahu and his administration knew full well that they were pushing at an open door in encouraging the US to attack Iran. They understood that now is the time to do that when Trump is punch drunk following the relative ease with which the US was able to kidnap Venezuelan President Nicolas Máduro. Netanyahu probably appealed to Trump’s ego and convinced him he is the ‘big man’ who could succeed where previous presidents had failed. It may also be that Israel has compromat on Trump and others high up in US politics and can blackmail them by threatening to release this material to the general public.

    Whatever the explanation, Israel was able to put its finger on the scales to convince Trump and his administration that the benefits of attacking Iran would outweigh the costs. But what exactly are these benefits? Let us first dispense with the bogus explanations that have been put forward in defence of this war. This is not about spreading freedom and democracy to Iran, despite the fact that it obviously has a huge deficit in these areas. This is also not about preventing Iran from having nuclear weapons as there is no evidence whatsoever that Iran was developing such weapons. Trump himself claimed last year that the US had completely destroyed Iran’s nuclear facilities, yet now apparently expects us to believe that they have managed to build them up again in the space of six months!

    The obvious explanation as to why the US is so desperate to attack Iran is that it wants Iran’s oil. But is attacking a country really the best way to get hold of its oil reserves? The US seems to think so, but there are other ways. China, for example, is able to get hold of oil from Iran through diplomatic means. Indeed, China buys more than 80% of Iran’s exported oil, with oil from Iran accounting for around 15% of China’s total oil imports. Of course China is able to do this because it is allied with Iran whereas the US is not. This points to the real reason that the US has launched its attack. Since the 1970s, all oil on the global market has been priced in US dollars. This arrangement, referred to the ‘petrodollar’ system, has afforded the US exorbitant power, but this power is now beginning to wane.

    The petrodollar system is unravelling due to shifting geopolitical alliances and the green energy transition. The expansion of the BRICS bloc, which now includes Iran and Saudi Arabia along with Brazil Russia, India, China, and South Africa, has encouraged trading oil and other goods in non-dollar currencies. Saudi Arabia has shown willingness to trade oil in other currencies following the expiration of the original 50-year U.S.-Saudi pact in 2024. Other Middle Eastern oil producers are shifting focus to Asian markets, with China pushing for more oil to be invoiced in yuan. The declining demand for dollars could lead to higher inflation in the US, as demand for currency is what gives it value, which could lead to political instability.

    However this is not the reason that the US is so desperate to prop up the petrodollar. The reason is that the petrodollar significantly enhances the ability of the US to implement and enforce economic sanctions. By ensuring that the vast majority of global oil trade is denominated in USD, the petrodollar system forces nations to maintain access to US financial markets, which the US can then restrict to impose sanctions. Furthermore, the US can freeze foreign assets held in dollars, crippling the ability of targeted nations to conduct international trade. The US can also impose secondary sanctions on foreign companies, threatening to cut them off from the US banking system if they do business with sanctioned entities.

    Thus, the reason the US is attacking Iran is not so much about getting hold of Iran’s oil as it is about trying to ensure that the US can continue to wield enormous power on the global stage. We have seen this power exercised in Cuba recently when the US cut off oil imports to the country, leaving the island in darkness. If oil was priced in another currency it would have been a lot more difficult for the US to do this. Whether the US will succeed in propping up the petrodollar system by attacking Iran remains to be seen. Personally, I find it unlikely. According to a recent report by Deutsche Bank, the war on Iran could actually usher in the end of the petrodollar. Once again we seem to be witnessing the American empire collapsing in real time.