Groucho Marxism

Questions and answers on socialism, Marxism, and related topics

  • 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 M 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 M 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.

  • Capitalism and mental health

    I have suffered from depression for most of my life; and I am not alone. According to data from the Office for National Statistics, approximately 1 in 6 adults in the UK experience mental health problems like depression or anxiety in any given week. Furthermore, according to data from the NHS Business Services Authority, around 1 in 6 people in England were prescribed at least one antidepressant medication in 2023/24; and a 2023 BBC investigation found that over two million people in England have been taking antidepressants for five years or more. Moreover, usage of these medications has risen for six consecutive years. The UK is clearly experiencing a significant, growing mental health crisis. But what is causing this?

    Recently, some researchers have argued that the structure of a competitive, profit-driven society is fundamentally incompatible with human psychological needs, instead serving as a mental illness-generating system. One such researcher is British medic Dr. James Davis, who in 2021 published a book entitled Sedated: How Modern Capitalism Created our Mental Health Crisis. Using a wealth of studies, interviews with experts, and detailed analysis, Davies argues we have fundamentally mischaracterised the problem of mental ill-health. Rather than viewing mental distress as an understandable reaction to wider societal problems, we have embraced a medical model which situates the problem solely within the sufferer’s brain. In effect, we have resorted to blaming the victim.

    The standard medical explanation for depression is that it is caused by ‘chemical imbalances’ in the brain (whatever that means). Davis argues instead that mental illness is caused by a combination of modern environmental and economic stressors. There are several mechanisms through which this manifests. The pressure to secure basic needs such as housing and healthcare causes significant anxiety and depression, especially among lower-income groups. Growing income gaps also directly correlate to poor mental health outcomes. Modern work environments characterized by precarious employment, long hours, and high demands create a culture of burnout and mental fatigue. And the work that people do often lacks meaning, leading to feelings of alienation, inadequacy, and disempowerment.

    In his 2015 book The Burnout Society, the South Korean philosopher and cultural theorist Byung-Chul Han characterizes today’s society as a pathological landscape of conditions such as depression, attention deficit hyperactivity disorder, borderline personality disorder, and burnout. And in his 2017 book ‘Psychopolitics: Neoliberalism and New Technologies of Power, Han argues that modern capitalism has moved beyond the simple struggle between classes described by Marx: “When production is immaterial, everyone already owns the means of production, him- or herself. The neoliberal system is no longer a class system in the proper sense … This is what accounts for the system’s stability.”

    Han argues further that we have all effectively become self-exploiters: “Today, everyone is an auto-exploiting labourer in his or her own enterprise. People are now master and slave in one. Even class struggle has transformed into an inner struggle against oneself.” According to Han, this shift from class struggle to inner struggle is the primary cause of our current malaise. That’s not to say that the conflict between workers and capitalists no longer exists; clearly it does, and is as relevant as ever in understanding the workings of capitalism. Han’s point is that under modern neoliberal capitalism, us workers do not believe that we are exploited “subjects” but rather “projects” that are always “refashioning and reinventing ourselves.”

    Thus, according to Han, modern capitalism is as much state of mind as it is a socio-economic system. This idea has a lot in common with the ‘capitalist realism’ concept popularized by British philosopher Mark Fisher in his 2009 book Capitalist Realism: Is There No Alternative?. In this brilliant little book, Fisher defined capitalist realism as “the widespread sense that not only is capitalism the only viable political and economic system, but also that it is now impossible even to imagine a coherent alternative to it.” Elsewhere, Fisher wrote extensively about the link between capitalism and mental health, stating that “the pandemic of mental anguish that afflicts our time cannot be properly understood, or healed, if viewed as a private problem suffered by damaged individuals.”

    Fisher also wrote about his own struggles with depression. Tragically, these struggles eventually became too much for him and he committed suicide in 2017 at the age of 48. This is far from uncommon: around 7,000 people die by suicide in the UK every year. I myself have known two people who have committed suicide in the last 5 years. The work of researchers such as Davis, Han, and Fisher suggests that these deaths should be added to the list of people who are killed by capitalism and highlights once again what a dystopian system capitalism is.

  • Why are the US and Israel bombing Iran?

    It has been less than three weeks since the US and Israel effectively declared war on Iran but already thousands have been killed and no less than 14 countries have been bombed, including Israel itself. How long the war will continue is not clear. What is clear is that the US and Israel have massively underestimated Iran’s ability to fight back. It is also clear that the war will have impacts that go way beyond the Middle East. Already in Britain we have seen petrol prices begin to increase as firms aim to protect their profits from the oil supply shock caused by Iran blocking the Straight of Hormuz. Similar price rises are likely to happen across the world, including in the US. This raises the question of why the US and Israel have launched an offensive that is likely to impact so negatively on their own citizens.

    For the second time in less than a year, the US and Israel have taken military action against a another country at a time when a breakthrough in negotiations with that country was imminent. We saw this first with Venezuela and the kidnapping of president Maduro and we have seen the same thing happen now with the attack on Iran. The fact that this has happened twice in quick succession suggests that it is no mere coincidence. On both occasions, the US and Israel decided to take military action when they did precisely because they knew a deal was on the cards. Or more accurately, as Oman’s foreign minister pointed out last week, Israel persuaded the US to take military action because Israel knew a deal was on the cards.

    Israel patently has zero interest in diplomacy. Instead, it wants to turn Iran into a failed state as this will enable it to more easily pursue the ‘greater Israel’ agenda. Israel didn’t want negotiations between the US and Iran to succeed so it persuaded the US to bomb Iran instead. You might wonder how a relatively small country like Israel could convince a superpower like the US to do what it wants. The answer lies partly in the narcissistic character of the current US president. Trump is the perfect president from Israel’s point of view as his ego can be used to manipulate him. Netenyahu obviously managed to convince Trump that in perpetrating this conflict he would go down in history as the ‘big man’ who finally managed to defeat Iran.

    However, as already mentioned, Trump and Netenyahu massively underestimated Iran’s ability to fight back. The US also apparently did not foresee that Iran would block the Straight of Hormuz. Trump has responded by desperately trying to form a coalition of imperialist powers to provide warships to defend shipping in the straight – so far to no avail. The leaders of these countries understand how incredibly unpopular this war is with their respective electorates. Facing worldwide opposition to the war, the US and Israel have sought to justify their actions by highlighting the repressive and brutal character of the Iranian regime; but few are buying this argument. Israel’s genocide in Gaza has laid bare the hypocrisy of such moral justifications.

    The leaders of the US and other imperialist nations regularly tell us what a terrible country Iran is, but these same leaders have been shamefully silent on the Gaza massacre and are now silent on Israel’s invasion of southern Lebanon. Netanyahu regularly speaks of the ‘terrorist regime’ in Iran, but at other times seems to be quite fond of terrorism. Nearly 80 years ago, anti-Palestinian terrorist group Irgun blew up a hotel in Palestine, killing 96 people. Sixty years later, in 2006, Netenyahu attended the anniversary celebration of this attack. Netanyahu’s attendance was not a surprise as the leader of Irgun was one of the co-founders of the movement that in 1988 became his party, Likud. The hypocrisy is off the charts.

    Western leaders may not be joining in with the US-Israeli attacks on Iran but it is notable that few are calling for these attacks to stop. During last year’s US-Israeli attack on Iran, German chancellor Merz blurted out the truth that the bombing represented “the dirty work that Israel is doing for all of us”. Still, it seems unlikely that other Western countries will allow themselves to be dragged into this war any time soon. Many are still aggrieved about being hit by Trump’s tariffs and are therefore reluctant to come to his aid. Aside from that, Western leaders are wary about doing anything that might escalate the conflict as they know this will rebound negatively on them. If only Trump and Netanyahu had the same foresight.

  • The generalized FMT

    A central question of Marx’s Das Capital is: why is capitalism profitable and productive? Marx’s answer to this question boils down to: because capitalists exploit workers. But why does worker exploitation result in positive profits and positive growth? To tackle this problem scientifically, Marx had to go it alone as much of the mathematical apparatus economists use today had not yet been invented. He first used the classical labour theory of value to calculate the value or the labour-time directly or indirectly necessary to produce a unit of each commodity. He then divided the total supply of labour by a worker, T, into a paid part T* and an unpaid part T-T*, both measured in terms of labour time; and he defined the ‘rate of exploitation’ by (T-T*)/T*.

    Using this definition, Marx established a theorem to the effect that the equilibrium profit rate and the equilibrium growth rate are positive if and only if the rate of exploitation is positive. It is important to note that his proof relied on the labour theory of value. As soon as durable capital goods, joint production, and choice of techniques are admitted, we must discard the labour theory of value, at least in the way Marx formulated it. This raises the question of whether Marx’s theorem still holds in under these more general assumptions. In 1974, the Japanese Marxist economist Michio Miroshima tackled this question and found the answer to be ‘yes’ in the case where we allow joint production, whereby several outputs from a single activity can emerge together.

    Consider an economy which produces m types of commodities using n processes, where in general m is not equal to n. Assume that the economy employs N workers, where each workers works on average T hours per day and is paid wages at a subsistence level. Let us denote the mx1 subsistence-consumption column vector (per worker) by C, so that N units of C are required to keep the N workers alive for one day. We can then define the ‘necessary labour time’ for the economy as the minimum labour time necessary to produce consumption goods, CN, and the ‘surplus labour’ as the total labour time per day, TN, minus the necessary labour time. This definition of necessary labour was introduced by Miroshima in his 1974 paper.

    In each process j, quantities Aij ≥ 0 are used up and quantities Bij ≥ 0 are produced of commodity type i, and a quantity Lj of labour time is also used. Let A and B denote the mxn matrices with elements Aij and Bij, and let L denote the 1xn row vector with elements Lj. Each commodity i will have an associated price pi, and each process j will be used with an ‘intensity’ qj. Given a 1xm price vector p = (pi), the vector pA represents the total cost of operating the different processes and the vector pB represents the total revenue obtained from the different processes. Similarly, given an nx1 intensity vector q = (qj), the vector Aq represents the total commodities of different types used up, the vector Bq represents the total commodities of different types produced, and the scalar Lq represents the total labour time used.

    Under Miroshima’s definition, the necessary labour time required to produce consumption goods C is given by the minimum value of Lq subject to the constraints q ≥ 0 and Bq ≥ Aq+ CN. This is referred to as a ‘linear programming’ problem, as it involves minimizing a linear function subject to linear constraints. Let q* be a solution to this problem, so that the necessary labour time is given by Lq*. Then the surplus labour is given by TN-Lq* and the rate of exploitation by (TN-Lq*)/Lq*. Next, consider the ‘dual’ linear programming problem of finding the maximum of pCN subject to the constraints p ≥ 0 and pB ≤ pA+L. Let p* be a solution to this problem. Then by the so-called ‘duality theorem’ of linear programming, we have p*CN = Lq*, and the rate of exploitation is therefore given by (T-p*C)/p*C.

    Let w ≥ 0 be the wage rate. As wages are assumed to be set at subsistence level, we have wT = pC, therefore w = pD where D = C/T. Let rj be the rate of profit for process j. The 1xm price vector p satisfies (pB)j = (1+rj)p(A+DL)j for each j. Letting r* = max rj, we must then have pB ≤ (1+r*)p(A+DL). This inequality says that the revenue at the next time step – i.e. pB – cannot be more than was spent at the previous time step multiplied by 1 + the maximum profit rate – i.e. (1+r*)p(A+DL). Now let gi be the growth rate of commodities of type i. The nx1 intensity vector satisfies (Bq)i = (1+gi)(Aq+DL)i for each i. Letting g* = min gi, we must then have Bq ≥ (1+g*)(pA+DL). This inequality says that what the economy to consumes at the next time step – i.e. (1+g*)(pA+DL) – cannot be more than was produced at the previous time step – i.e. Bq.

    The profit rate that is guaranteed in this economy is given by the minimum value of r* satisfying the inequality pB ≤ (1+r*)p(A+DL) for some p > 0. We may refer to this minimum value as the ‘warranted profit rate’. Similarly, the growth rate that is guaranteed by this economy is the maximum value of g* satisfying the inequality Bq ≥ (1+g*)(pA+DL) for some q > 0. We may refer to this minimum value as the ‘warranted growth rate’. Miroshima proved that under some relatively weak assumptions, the following statements are equivalent: (1) the warranted profit and warranted growth rate are greater than zero; (2) the rate of exploitation is greater than zero. This result is referred to as the ‘generalized fundamental Marxian theorem’.

    The theorem states that the propositions (1) the economy is profitable and productive, and (2) capitalists exploit workers, are equivalent. It demonstrates that Marx’s key insight in Das Capital – that capitalism is profitable and productive because capitalists exploit workers – holds in more general economies with joint production.

  • How to waste money

    The ‘Astute’ class is the latest class of nuclear-powered fleet submarines in service with the Royal Navy. The Astute program began in 1986 when the UK’s Ministry of Defence (MoD) launched several studies to determine requirements for replacement of its existing submarines. These studies were conducted during the Cold War, when the Royal Navy maintained a strong emphasis on anti-submarine warfare to counter increasingly capable Soviet submarines. However, by 1990 the Cold War had come to an end. The project was promptly cancelled and a new set of design studies were started, this time with cost control as a key objective. As we will see, to say that this objective was not met is something of an understatement.

    A joint design by GEC-Marconi and British Maritime Technology was favoured both cost and capability grounds. With the signing of the contract in 1997, GEC-Marconi started work on developing a complete and comprehensive design for the Astute program. In 1999, British Aerospace purchased GEC-Marconi and created BAE Systems. By 2002 both BAE and the MoD recognized they had underestimated the technical challenges and costs of the program, as much rework was needed once the detailed designs were complete. In 2009, a House of Commons Defence Select Committee found that delays due to technical issues brought the Astute program to a position of being 57 months late and £1.3 billion (53%) over budget, with a forecast cost of £3.9 billion for the first three boats.

    In 2015, the National Audit Office (NAO) forecast that the total cost of producing seven boats would be £9.6 billion, £1.4 billion (17%) over budget. In 2024, the Infrastructure and Projects Authority reported the total cost of the Astute programme had risen to £11.3 billion, explained by “inflation and delivery cadence within the shipyard”. And in 2025, the MoD reported that the Astute program will cost £12.2 billion. This £12.2 billion figure is almost three times the initial £4.3 billion forecast made by the NAO back in 2001. Some of the £7.9 billion discrepancy is attributable to inflation, which has been higher than predicted since 2022. But the vast majority is due to a combination factors that could have been avoided.

    These factors included design failures, a shortage of technical expertise, poor contract management, a lack of quality control, and a declining industrial base. The project was initially viewed as “low-risk” but turned into a 70% new design. In 2001, it had been nearly 17 years since the UK had built a first-of-class submarine, resulting in a shortage of skilled workers. Early contractual agreements were counterproductive, with engineering work having to be ripped out and redone. Early ships in the class suffered from problems with subcontractors providing sub-standard materials, leading to costly repairs and extensive testing. And the supply chain for specialized submarine components had declined significantly by 2001.

    These issues led to long delays, which meant the program required more labor hours than estimated, with additional costs also stemming from the need to manage complex, shifting technical requirements. To put the £7.9 billion overspend figure into perspective, with this money the government could have built around 20 new hospitals, 100 new schools, or 40,000 new council houses. And that’s just the overspend. The £12.2 billion spent on the project as a whole would have paid for around 30 new hospitals, 150 new schools, or 60,000 new council houses. As eye watering as these figures seem, however, they pale into insignificance when compared to the costs of another submarine program known as Dreadnought.

    The UK maintains a stockpile of around 215 nuclear warheads, with around 120 active (usable). Since 1998 the British nuclear arsenal has been wholly submarine-based. Dreadnought is name of the program to replace the four Vanguard class submarines, which have provided the ‘continuous at-sea defence’ since 1992, with four new submarines that will be built in the UK. The four new submarines will be introduced, on current plans, from the 2030s onwards and will have a lifespan of at least 30 years. The Dreadnought submarines will carry the Trident Missile System. In 2011, the UK government approved the initial assessment phase for the new submarines and authorized the purchase of long lead-time items.

    When the project was approved in 2011, manufacturing the four submarines was forecast to cost £25 billion in total. In 2015, this figure was updated to £31 billion. These costs do not include the related Trident missile renewal, new infrastructure projects at the re-nationalized Atomic Weapons Establishment, or new nuclear fuel production facilities at Rolls-Royce. Annual in-service costs are expected to be approximately 6% of the defence budget (around £3 billion). The Nuclear Information Service and the Campaign for Nuclear Disarmament estimate a lifetime cost in the region of £200 billion. With this money the government could build around 500 new hospitals, 2,500 new schools, or 1 million new council houses.

    Meanwhile, politicians tell us there is no money to properly fund public services! They must think we are stupid.