A new book on Loop Quantum Gravity

Amazon link

Some excitement about this book over at Backreaction. This from 'naivetheorist' in the comments.

".. a new book "Quantum Space" (available at Amazon UK now and at Amazon in a few weeks) is a really superb book on LQG. It is a 'pop science' book only in the sense of being equation-free. it traces the history of the development of LGQ (and string theory as well) and provides relevant biographical details on Rovelli and Smolin. it is by far the most impressive book on 'foundational physics' (as it is 'modestly' referred to by those who work on quantum gravity). I hope you will review this book with the usual incisiveness that you use in discussing arXiv manuscripts."

You can read my own thoughts here.

Three virtual posts

Amazon link

I was going to review Richard Morgan's latest tech-thriller "Thin Air" which I enjoyed a lot. But Steven Poole of The Guardian expressed my thoughts so much more clearly. Really, it's easier just to point you to his review.

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Like everyone else I had plenty of thoughts about the alleged Gatwick Airport drone incursion. The problem seems to be in two parts: first to identify the team launching/retrieving the drone; second to deal with the drone itself. The first part seems harder.

My idea was to run a real time video-acquisition platform (a satellite, police drones or arrays of ground-based CCTV) covering the operational radius of the hostile drone around the airport - I believe this is 2-3 miles. This would generate a great deal of video which would need to be searched very rapidly for hostile drone-team activity. Precisely what Project Maven was designed to address. Google may have gone pacifist but no reason for Qinetiq not to do the project.

But I read so many interesting ideas that it seemed pointless and redundant to add any more.

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I was going to write about this paper with the unpromising title: "Mapping morality with a compass: Testing the theory of ‘morality-as cooperation’ with a new questionnaire" by Oliver Scott Curry, Matthew Jones Chesters and Caspar J. Van Lissa.

What they've done is rethink Jonathan Haidt's Moral Foundations Theory on the basis of evolutionary plausibility. Instead of Haidt's five dimensions, they have seven and in their field trials it all seems to make sense. Here are their seven moral dimensions. Click on image to make readable.

This is what they say in their abstract.

"Morality-as-Cooperation (MAC) is the theory that morality is a collection of biological and cultural solutions to the problems of cooperation recurrent in human social life. MAC uses game theory to identify distinct types of cooperation, and predicts that each will be considered morally relevant, and each will give rise to a distinct moral domain.

Here we test MAC’s predictions by developing a new self-report measure of morality, the Morality-as-Cooperation Questionnaire (MAC-Q), and comparing its psychometric properties to those of the Moral Foundations Questionnaire (MFQ). Over four studies, the results support the MAC-Q’s seven-factor model of morality, but not the MFQ’s five-factor model.

Thus MAC emerges as the best available compass with which to explore the moral landscape."

I have been quite enthused here by Moral Foundations Theory, while being aware that it, like the five-factor model of personality theory, floats unanchored, crying out for a deeper evolutionary embedding. So this latest work is potentially quite exciting.

Unfortunately, the paper itself is dry and technical and does not excite. I hope the research community builds on it to progress Jonathan Haidt's work - particularly on the psychological/moral differences between liberals, conservatives and libertarians. Then I will feel motivated to comment.

Treed

Picture by Alex

APOE variants and Alzheimer's disease risk factors

From Wikipedia:

"Although 40–65% of Alzheimer's disease (AD) patients have at least one copy of the ε4 allele, ApoE4 is not a determinant of the disease – at least a third of patients with AD are ApoE4 negative and some ApoE4 homozygotes never develop the disease.

Yet those with two ε4 alleles have up to 20 times the risk of developing AD. There is also evidence that the ApoE2 allele may serve a protective role in AD. Thus, the genotype most at risk for Alzheimer's disease and at an earlier age is ApoE 4,4.

Using genotype ApoE 3,3 as a benchmark (with the persons who have this genotype regarded as having a risk level of 1.0), individuals with genotype ApoE 4,4 have an odds ratio of 14.9 of developing Alzheimer's disease.

Individuals with the ApoE 3,4 genotype face an odds ratio of 3.2, and people with a copy of the 2 allele and the 4 allele (ApoE 2,4), have an odds ratio of 2.6.

Persons with one copy each of the 2 allele and the 3 allele (ApoE 2,3) have an odds ratio of 0.6. Persons with two copies of the 2 allele (ApoE2,2) also have an odds ratio of 0.6."

Two significant loci for APOE: SNP variants

Homozygous coding - as normally presented.

I'm 3,3 and Clare's 3,4.

Here's the incidence.

"Age is the most important risk factor for AD, with the prevalence rising substantially between the ages of 65 and 85 years.

The incidence of the disease doubles every five years after 65 years of age, with diagnosis of 1275 new cases per year per 100,000 persons older than 65 years, so that AD affects 30%–50% of all people by the age of 85 years.

Data on centenarians show that AD is not necessarily the outcome of aging, but the odds of receiving a diagnosis of AD after 85 years exceed one in three."

Capitalism incompatible with total automation/slavery

In the previous post, "Five questions on the last days of capitalism", I discussed the evolution and final fate of capitalism - which will be very different from the violent revolutionary end imagined by the Leninist left.

In this post I want to zero in on the exact mechanics of the final days of capitalism. Little of what follows is original, but it's seldom brought to prominence.

1. Start point: a model capitalist economy with competition

Our economy consists of a number of identical competitive companies serving an anonymous market. Each company spends per working period:

• £10 on constant capital c (= depreciation, raw materials, premises etc), 
• £4 on wages v (= 4 labourers at £1 each)

with a rate of surplus value s/v of 100%. This means that £4 of surplus value s is produced in the working period. So c = 10, v = 4, s = 4.

Revenue = c + v + s = 10 + 4 + 4= £18     -  4 labourers remember. Assume 18 objects are produced at £1 each.

Profit p = revenues - costs = £18 - (£10 + £4) = £4.

Rate of profit = profit/cost = p/(c + v) = 4/(10 + 4) = 2/7 = 29%.

2. The power of innovation

One of the companies buys some better machinery which bumps c up from 10 to 11 but which allows two workers to be eliminated. Their numbers look better:

c = 11, v = 2, s = 2 (same s/v) so c + v + s = £15.

Suppose that 18 objects are still produced in the working period. Initially the innovator can sell at the going market rate of £1 each - a total revenue of £18.

Revenue = £18. But his costs (c + v) = 11+2 = £13 are lower.

Profit = £18 - £13 = £5 .. and rate of profit = p/(c + v) = 5/13 = 38%.

This is far better than his business rivals (stuck at 29%).

3. Other companies follow the innovation

But all too soon other companies follow suit. Prices fall due to competition until each company finds that for itself:

New revenue = c + v + s =  £11 + £2 + £2 = £15

New profit = (c + v + s) - (c + v) = £15 - £13 = £2.

New rate of profit = p/(c + v) = 2/13 = 15%.

But the previous market equilibrium profit was 29%! Now each employer is worse off.

But the 18 objects now cost only £15, or 83p each. Consumers benefit from the wonders of competition and innovation driving productivity.

4. Robots now eliminate all labour

The robots are coming! A progressive innovator buys more automation which bumps c from 11 to 12 and which eliminates workers altogether.

c = 12, v = s = 0.

As before, 18 objects are produced in the working period and the going rate is still 83p each. Our innovator takes advantage of existing market pricing.

Revenue = £15 as before, but costs = £12 only (no wages).

Profit = £15 - £12 = £3 and the rate of profit = 3/12 = 25%.

An improvement over his competitors (who only see 15%) but again, they soon follow suit.

5. Everybody adopts total automation: no more wage bills

Competition drives prices down to costs (there is no surplus value s).

Revenue = 12 and cost = 12.

Profit = 0 and each object costs 12/18 = 66p. Except no-one is making any.

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Discussion

Slaves or robots: it makes no difference

I assert the above model holds whether the total automation is clever machinery, some humanoid AGI or a human slave.

Nonsense, you reply. A slave is just a worker where the employer is paying for food and shelter directly, rather than via wages.

Not so fast! The slave has to be bought as well as maintained - just like any other piece of capital equipment. What then is the cost of a slave in a competitive market?

The cost of a slave = expected-output-value - maintenance-costs (all discounted).

In one cycle above, assuming the slave is bought at price c and is as productive and exploited as a wage-worker (s/v = 1) then:

output-value produced by slave = (v + s) and maintenance-cost = v, so using the definition:

slave-cost = c = (v + s) - v = s                   - (values/costs here for one work cycle).

People (not slave-owners though) forget to include the initial cost of the slave, which already factors in the 'value' the slave will create.

Suppose c_R represents the cost of the raw materials the slave works with and other non-slave constant capital costs. In a work cycle or period:

revenue = c_R + value-added-by-the-slave = c_R + (v + s)

costs = c_R + slave-cost + slave-subsistence = c_R + s + v.

Profit = revenue - cost = [c_R + (v + s)] - [c_R + s + v] = 0.

There have been capitalist economies with slave sectors of the economy

You say, there have been slave-owning sectors of capitalist economies, the antebellum south, and I remind you that this is well-trodden territory on the left.

Read more at this post: "Total automation under capitalism?" - the topic area is the theory of equalisation of the rate of profit between sectors with differing levels of automation and the concept of prices of production.

It's perfectly possible for sectors of a capitalist economy to transition to total automation (point 4 above). The automated sectors extract value produced by workers in other sectors through profit equalisation. But it's not possible for the whole economy to 'lose its workers'.

8. What kind of an economy can you have with total automation?

What does work, you ask. Absent complete overproduction capability ('abundance') of everything, there will be a need for exchange between different production units: commodity exchange at value via simple (or petty) commodity production. Like in the Roman empire, or during feudalism. In this mode of production, exchange is driven by the need for use-values. The dynamic is not profit maximisation.

One can only hope that innovation and dynamism in such an utterly-transformed society of the future is not stifled. Perhaps the AIs will have some objectives of their own? Not everything that is wonderful and creative in human affairs is driven by capital valorisation.

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You will have observed that the cost equation for a slave already incorporates elements of rent. Yet the treatment here is not definitive. As Poulantzas reminds us (Classes in Contemporary Capitalism, chapter 1), 'capital is not a thing'. In arithmetical examples social relationships are reified.

So I'm thinking that the 'expected value of future output' term in the value of a slave is similar to the way we value a share. Marx called this fictitious capital. Compare with the labour involved in delivering the slave as a market-commodity (reproduction, transport and transaction costs) which is how we normally value constant capital. Not sure how to bring these two paradigms together. On this rather opaque thought I must leave it.

Update: Reading Poulantzas (Classes in Contemporary Capitalism, Productive and Unproductive Labour: 2) I am reminded that slaves are not produced in factories.

Slave traders are engaged in non-productive labour and the commodity price form of the slave, like that of the bond or share, is not derived from some quantity of abstract social labour incorporated in it.

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My further posts on Marxist theory.

Five questions on the last days of capitalism

1. Isn't it absurd, in this day and age, to talk about the last days of capitalism?

The prospect certainly isn't imminent. For a century and a half the hard left has talked about the transition to post-capitalism. Yet despite world wars, economic convulsions in the 1930s and 2000s, and major social conflicts in the 1970-80s, capitalism today as an international system is richer and stronger than ever.

2. Why no communist revolutions in the West?

For a century, a dwindling band of revolutionary Marxists have anticipated a violent overthrow of capitalism by the massed proletariat led by a Leninist revolutionary party. That prospect was never realistic.The working class en masse never aligned around a credible anti-capitalist programme. That's because the alternative to capitalist production in an epoch of scarcity can only be a planned economy. And that doesn't work.

3. What will the end of capitalism really look like?

Marx wrote that "no social order ever perishes before all the productive forces for which there is room in it have developed; and new, higher relations of production never appear before the material conditions of their existence have matured in the womb of the old society itself".

Capitalism continues to grow, indeed it has to. Without profits, investment stalls and the economy implodes.

Michael Roberts has argued persuasively that the long stagnation of the last decade or so was caused precisely by the heroic efforts of governments back in 2008/9 to minimise the effects of the crisis. Consequently there was no clear-out of inefficient firms, no devaluation of capital and few opportunities for industrial reorganisation. Zombie firms and debt overhang have stifled profitability and as a result the recovery has been anaemic. Still feels like it.

The underlying trends of capitalism persist through peaks and troughs though. The tendency to revolutionise production through automation, the replacement of workers by machines. So far - at least during an expansionary phase - the economy produces more roles for people displaced than it eliminates.

Cognitive and robotic automation changes that.

The 'safe' jobs right now seem to be those where manual skills are at a premium (care homes) and those where intelligence and interpersonal skills are required (senior executives, politicians, designers). But eventually over the next century or two those will also succumb to cheap automation.

What happens then? People get displaced from the labour force and don't get rehired.

This imposes additional welfare costs on the economy. Meanwhile the active workforce tends to zero. Fewer workers in a highly-automated economy means surplus value (which translates to profit) decreases. And don't forget all those transfer payments to the unproductive unemployed.

With fewer workers and an increasing proportion of the population on welfare, demand for consumer goods (produced by Department 2) declines and as a consequence the market for increased automation products goes into reverse (which hits Department 1). This is not a linear process - nothing in a capitalist economy is linear - but it is tendential. It feels much like the current stagnant economy but with mass unemployment and few job prospects going forwards.

4 What will replace capitalism in the end?

The process I just described results in the economy - in fits and starts - breaking down. There are no good investments. There will always be demand - the unemployed gotta eat, and the capitalists who own the means of production still need their luxuries - but the economic dynamism has gone. Without profit there is no incentive to address that demand and the factories stay shut.

Capitalism has finally completed its work.

I doubt the mass of people will tolerate this state of affairs and the capitalists will not see a way forward as there is none. At this point we have to imagine a world where the environment has become heavily optimised to provide everything a person wants (the result of all those decades of relentless consumer-oriented automation - smarter and smarter AI systems and more efficient robotic systems) yet it can't be put to good use via capitalist processes.

The resulting political transition might be something like the collapse of the Soviet Union rather than a Leninist insurrection. But after that, who knows? We're into science-fiction.

5. What do we do in the meantime?

What has the left done during the last century? Capitalism wasn't abolished, not even close. The workers' movement fought to secure its own existence and social reproduction in material and cultural terms. It didn't do a great job on the latter front, seemingly bewitched by the smug fairy-tales of neoliberal social-liberalism.

But that won't last forever - it's gotten silly now.

I'm in favour of continuing all the processes of increased automation. They're a net good. Within capitalism they will be used of course to buttress and reinforce the reproduction of capitalist relations of production (AI and robots are great for repression).

But in the end it will be self-defeating because capitalism is incompatible with the elimination of the workforce. That truth preempts even the Draka solution .. even if that's the form automation eventually takes. Slaves are equipment, not proletarians.*

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* Part two of this post: "Capitalism incompatible with total automation/slavery".

Reading Poulantzas and McDonnell

Classes in Contemporary Capitalism

Amazon link

From the preface:

"The book starts with a general theoretical essay that for the first time seriously explores the distinction between the “agents” and “positions” of capitalist relations of production, and seeks to avoid the typical errors of either functionalism or historicism. It also provides a polemical reconsideration of the problem of the “nation state” as a political unit today, and its relationship to the internationalization of capital.

Finally, and most originally, Poulantzas develops a long and powerful analysis of the much-abused concept of the “petty-bourgeoisie.” In this, he scrupulously distinguishes between the “traditional” categories of petty-bourgeoisie—shopkeepers, artisans, small peasants—and the “new” categories of clerical workers, supervisors, and salaried personnel in modern industry and commerce. At the same time he demonstrates the reasons why a unitary conceptualization of their class position is possible. The difficult question of the definition of “productive” and “unproductive” labor within Marx’s own account of the capitalist mode of production is subjected to a novel and radical reinterpretation. The political oscillations peculiar to each form of petty-bourgeoisie and especially their characteristic reactions to the industrial proletariat, are cogently assessed.

Poulantzas ends his work with a reminder that the actions and options of the petty-bourgeoisie are critical to any successful struggle by the working class, which must secure the alliance of important sections of the petty-bourgeoisie if the fateful experience of Chile is not to recur elsewhere tomorrow."

These are really critical issues when trying to understand the kind of class dynamics underlying the recent events in France, the left and right populist movements everywhere and specifically the SJW phenomenon. It's also relevant to any incoming Labour government here in the UK.

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State, Power, Socialism

Amazon link

This is Poulantzas's great exposition of the anatomy and dynamics of the various forms of the capitalist state, and the implications for the transition to socialism. I already read "The State and the Transition to Socialism" (Chapter 14 "The Poulantzas Reader" - PDF) where Nicos Poulantzas debates with the (at that time) Trotskyist Henri Weber (of the LCR) as to whether the Leninist model of a proletarian revolution/state based on federated soviets is really viable in modern Western Europe.

Poulantzas further questions whether the power of the bourgeois state can really only be overthrown by dual-power soviet structures as in the Bolshevik revolution (that was Trotskyist orthodoxy at the time of the interview, 1977). A kind of head-on assault.

My sympathies align with Poulantzas here, insofar as he at least thought about the nature of the state unlike the FI which had not moved beyond "The State and Revolution".

Weber is right against Poulantzas that the state is too strong and - in extremis - too focused to be subverted/reused from within. But they are both wrong to think that modern capitalism is vulnerable to the revolutionary imposition of a post-capitalist mode of production led by the massed ranks of the industrial proletariat.

That isn't the failure mode.

Update 23rd February 2019:

I've just read Ellen Meiksins Wood's book, "The Retreat From Class", where she devotes a chapter to Poulantzas. She takes him to task for assigning white-collar workers to the 'new petty-bourgeoisie'  (rather than the working class) and also for assuming this category is equivalent to the Marxist (technical) distinction between productive and unproductive workers (productive of surplus value, that is).

Poulantzas was undoubtedly wrong about this, and Wood has him nailed.

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Economics for the Many

Amazon link

I'm expecting this book to be a bunch of left-Keynesians arguing that an incoming Labour government should put more demand into the economy through deficit spending and increased transfer payments in order to stimulate investment and productivity.

I'm completely with Michael Roberts here: good luck with that.

Still, no sense in prejudging. Let's listen to what Mr McDonnell's favourite economists have to say.

My mother in DNA.LAND

My mother, Beryl Seel, died on the 3rd of December 2015 aged 92. In August the previous year I had persuaded her to spit into the 23andMe sample collection tube and get sequenced.

"Now we can bring you back," I murmured, but she didn't seem keen.

I understand 23andMe pussyfooting around, not wishing to fall foul of the US regulators yet again. This means DNA.LAND if you want to play with polygenic scores. I uploaded her genome subset (the 23andMe downloaded text file) and here are some of the results.

As usual, click on an image to make it large enough to read.

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This is the top-level screen showing some of the traits they can begin to predict

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Educational attainment

My mother was predicted to have 14.7 years of schooling (two years at university). In fact she had 9, leaving school in 1937 as a 14 year old.

My prediction from DNA.LAND is also 14.7 years but in fact I had 19 years equivalent full-time education. Clare was predicted to have 14.4 years yet she is a graduate with an additional teacher-training qualification.

Heritability of EA is low and the small numbers of relevant SNPs available to DNA.LAND makes even the genetic component estimate a very noisy measure. See the discussion below.

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Intelligence and IQ

This is marked as 'very preliminary' which - as they are quoting only 16 SNPs - seems about right.

Heritability of IQ is of the order of 80% but given this few genetic markers the signal will be swamped by the effects of all the other relevant SNPs which are unknown and whose contributions are therefore unmeasured.

About all you can say in favour of the exercise is that correlations between IQ-enhancing alleles based on an underlying soft sweep probably gives this slightly more predictive power than one might naively expect.

Note also we don't get a central IQ estimate with error bars. The normal distribution curve above is referenced to the DNA.LAND sign-up population, with unknown IQ parameters.

Anyway, FWIW, my mother seems to be one IQ point above the DNA.LAND average based on a super-noisy regression line.

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Neuroticism

Neuroticism (emotionalism, anxiety) is one of the 'five factor' personality traits and is the opposite to emotional stability, calmness on this dimension. There are strong gender differences in this factor, women scoring as more emotional.

I have memories of a fair degree of maternal emotionalism, but perhaps that was par for the course.

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Height

My DNA.LAND polygenic score was 182 cm, which is exactly right. My mother's (above) equates to 5' 7". That is taller than I remember, perhaps by an inch. I recall that growing up in the 1930s was not a picnic. My father was just under six foot.

My parents on their engagement: is she taller than average?

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Discussion

How seriously should we take all this? Not very, at this point (except for height, where PGS scores are accurate predictors of genomic potential - although DNA.LAND aren't using the latest estimators).

Example regression line for scatter plot with correlation 0.38

The correlations between the small numbers of SNPs currently being used by DNA.LAND and the physical/cognitive variables they're trying to predict are very low. Educational attainment was discussed on their website as follows:

"Overall, educational attainment is estimated to have a heritability of around 20%. This means that in a population of individuals with varying years of education, 20% of that variation can be explained by variants in the individuals' genomes."

So the polygenic score will give the phenotype value on the regression line, but the true value could be a long way up or down depending on life events. My mother, a working class girl, left school at 14 for example. Nobody does that today.

Thousands of SNPs are implicated in complex polygenic traits like those listed above, yet relatively few are currently known (except for height) .. and DNA.LAND uses only those publicly available (a tiny subset). So their regression lines will be pretty inaccurate.

Finally, note that my mother is positioned with respect to DNA.LAND's user population which is self-selected. We don't know how the norms for this group compare to the general population.

It will get better, even if we're a way from the option of bringing her back.

Scale discrepancies

In the summer of 1977 I decided to leave teaching. I had spent a couple of years at Ormonde High School (now Maghull High School), an ex-secondary modern in Maghull, Liverpool teaching maths to the 11-16 year olds. I think it would be fair to say that my students were at the lower end of the ability range. I was burnt out and exhausted.

At that time computers were entering practical use in industry and there was an increasing need for programmers. The Government set up the so-called TOPS courses (Training Opportunities Scheme), which subsidised people changing career. I passed the tests and started a 20 week course to learn COBOL programming with KBS Computer Services in Dale Street, Liverpool. The class was told the course would be really intensive, seven day working , evenings thrown in, partners expected to be abandoned for the duration.

I was in competition with a guy named Paul. He was intuitive, writing code festooned with GOTO statements. I was more organised, knew that GOTO was considered harmful and taught myself structured programming. We were both taken on by KBS at the end of the course.

One module was IBM S/360 assembly programming. I recall working on a program with maybe a hundred or so instructions - load this register, add packed, and so on. I thought: 'It's taking me an hour or more to get this code right, yet when it executes it will take 100 microseconds'.

I found that scale discrepancy rather disquieting. It's true of every program but in assembler it's somehow more visceral.

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We ran our programs on punch cards through the IBM 360 owned by the Merseyside Docks and Harbour Company. The machine was on the top floor of the Liver Building at Liverpool Pier Head, and we'd go in the evening when the machine was not in regular use.

Access was easy. It wouldn't work today. I once took Clare (who I was 'going out with' at the time) to see the unimpressive sight of those big blue cabinets and the dinner plate sized removable disk drives (20 Megabytes). She does not recall an epiphany.

Modelling total automation under capitalism (a progress report)

What actually happens to a capitalist economy as automation increases, employees are laid off and the budget for workers' wages tends to zero? It's possible to explore this in a spreadsheet using Marx's equations for expanded capitalist reproduction (which I wrote about here).

You divide the economy into Department 1, which makes machines (capital goods) and Department 2 which makes consumables (wage goods and luxuries). Then you iterate through cycles in which you try to make both Departments more capital-intensive while aggressively laying off workers.

There are some constraints: Department 1 sells Department 2 its machines; Department 2 supplies the consumption needs of workers and capitalists in Department 1. The following quantities need to stay non-negative:

1. Constant capital (machines, factories, raw materials) - c
2. Variable capital (wages) - v
3. Capitalist personal remuneration (dividends) - a
4. Overall sector profits - s  (or p, when adjusted to equalize the rate of profit between Departments).

Additionally the rate of surplus value s/v can't go through the roof. You can't have one worker alone in an enormous factory who works ten minutes to produce the value of their own wage, and then eight hours plus to provide the surplus value which pays for dividends and the next round of automation investment (s/v = ~50). They really wouldn't buy-in to that.

Click on the figures to make the spreadsheets large enough to read. You are not meant to understand what's going on - just to get an impression. More detailed stuff later.

Department 1: s/v tends to infinity while production is anaemic

The problem is this: as automation increases and the number of workers declines in Department 1, those few left have to (unrealistically) produce far more value than their wages to keep the edifice afloat.

Meanwhile the collapse in the number of workers overall leads to a chronic decrease in demand for Department 2's consumer goods. No new machines are being bought: instead there's accelerated depreciation - which destroys surplus value, hitting profits there.

Department 2: this sector begins to collapse

To reiterate: with decreasing demand for wage-goods, Department 2 finds itself losing the value invested in its machines, not buying more. Depreciation hits surplus value making Department 2 increasingly unprofitable.

So far I've been unable to find a combination of parameters which allows capitalism to eliminate all its workers. I'll keep trying ... .

More: Five questions on the last days of capitalism.

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You ask, why use the framework of Marxist economics? Because orthodox (ie bourgeois) economics has no interest or explanation as to where profit comes from:

"Rent, wages, interest, and profit are the four factor incomes that land, labor, capital, and enterprise provide respectively."

Roughly the idea that if you put some money into 'enterprise' then by some magic it can become larger (profit). Magic is not a good analytic framework for edge cases of capitalist reproduction.