The gag is on

Walking down to Waitrose this morning - and dragging the new sholley, my weight-training-induced sore forearms still haven't gone away and it's 'no more Mr Heavy-Shopping-Bags' - I ventured this thought to Clare.

"Shall I tell you the new thing I've learned today?"

Grudging acquiescence.

"You know I'm continually fascinated by the way AI and robotics are going to transform capitalism, and how exactly that transformation's going to work ..."

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The new thing was from Part 2 of Michael Roberts' insightful series, 'Robots and AI: utopia or dystopia?' ..

"The question often posed at this point is: who are the owners of the robots and their products and services going to sell to make a profit?  If workers are not working and receiving no income, then surely there is massive overproduction and underconsumption?  So, in the last analysis, it is the underconsumption of the masses that brings capitalism down?

"Again, I think this is a misunderstanding.  Such a robot economy is not capitalist any more; it is more like a slave economy.  The owners of the means of production (robots) now have a super-abundant economy of things and services at zero cost (robots making robots making robots).  The owners can just consume.  They don’t need to make ‘a profit’, just as the aristocrat slave owners in Rome just consumed and did not run businesses to make a profit.

"This does not deliver an overproduction crisis in the capitalist sense (relative to profit) nor ‘underconsumption’ (lack of purchasing power or effective demand for goods on a market), except in the physical sense of poverty. ..."

Roberts here puts his finger on the key mode of production change required by total automation: production of exchange-values collapses and all production is of use-values, just like in slave-owning antiquity.

The issue is, who gets to be the recipient of such wonders of production, the owners of the robots .. or everyone? It seems contentious.

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Where to start? The only place was the labour theory of value.

"So Marx said that the capitalist pays the worker the value of his labour-power - what it costs to maintain the worker as an effective employee - and sets him to work. But the value the worker actually creates in his day's labour is more than this, and that value belongs to the capitalist, creating his profit once realised in the exchange process.

"But if the worker is replaced by a robot ..."

But Clare was having none of this.

"That can't be right. If the worker is paid less than what he produces, then the employer won't be able to sell all his products. No, Marx was quite wrong."

I hesitatingly began to talk about Marx's simple and expanded reproduction equations, Departments I and II .. but the audience had switched off.

In truth, I don't think the objection can be addressed in ordinary conversation, the sources of demand being manyfold: in addition to the needs of proletarians you will find capitalists' spending on themselves, the market for reproduction and expansion of the means of production .. .

No less a luminary than Rosa Luxemburg got it wrong.

In fact I explained quite clearly both simple reproduction and expanded reproduction within capitalism on this blog, but if you review the two posts you will see the analysis is not wholly trivial.

This afternoon I considered going through the spreadsheets with her - and decided against having my arm bitten off.

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You may have heard over the last couple of days: Mathematicians Measure Infinities and Find They’re Equal.

It relates to whether there are cardinal numbers between the infinity representing the size of the natural numbers and the larger infinity capturing the size of the real numbers. The continuum hypothesis says no, but that can't be proven using the normal axioms of set theory.

The work of Malliaris and Shelah has some bearing on the matter although not all is completely clear (is the cardinality of p = t the same as the continuum?).

I said to Clare, "Did you know there are different sizes of infinity?"

She snorted, "That kind of nonsense is just what gives mathematics a bad name."

I advanced on her with paper and pen; she sat back on the couch, closed her eyes, put her hands over her ears and started to hum.