It’s unfortunate Marx was so bad at maths. Well, bad isn’t quite the right word, as he often expends a great deal of effort and creativity establishing the various mathematical conclusions he needs to establish, even when the conclusions are obvious. It’s rather wearing slogging through a whole chapter to finally get to the conclusion and realize what Marx has been trying to point out is the difference between the mean and the median. I do wonder what mathematical education was like in 19th century Prussia; Marx was an educated man, but seems to know less maths than you’ld expect from an 11 year old today.

Except, this mathematical inability turns out to reveal something important about Marx’s method. One of the most important aspects of skill in maths, I think, is a certain facility with abstraction, recognizing that the same thing can bear many different roles, and shuffling between these roles. The number 2, for example, can be a numerator or a denominator, or both, while still remaining the number 2. This kind of abstraction seems something Marx is incapable of. Perhaps the most obvious example is the way Marx doesn’t distinguish between a property and the way it is measured , and so rather than talking about, say, labor time and price as two different ways of representing the value of a commodity (in the way that, say, centigrade and and fahrenheit are two different ways of representing a temperature that exists separately from the representation), he discusses these as two separate things, which must be worked on to transform one to the other.

This resistance to a too-easy abstraction is, though, rather the point for Marx, because one of the things he wants to demonstrate in *Capital* is that capitalism is a system of real abstractions. Abstraction, that is, is not simply a mental process which leaves the world being abstracted unchanged. Instead, abstraction involves the production of social relations such that the abstraction can be acted on, and only then grasped by the mind. Abstract labor might be Marx’s best example of this, as he argues that the idea of work in general, as opposed to some particular type of work, depends on the whole process of primitive accumulation which brought about the existence of a class of wage laborers. It’s this idea that abstractions always arise from particular social relations which we can see at work in Marx’s laborious operations on the mathematics he discusses. Given the way that the abstractions of mathematical economics increasingly serve to evacuate any discussion of or resistance to social relations, Marx’s mathematics of suspicion, as we might call it, is salutory.

## ishi, 3:55 am, June 22, 2011

interesting post.

i’m not sure price and labor time are exactly identical (i tend to think quantum mechanically, so i’d say while classically they are, in ‘reality’ they are non-commutative operations, so there is a ‘fudge factor’ (in QM seen as plancks constant over 2 pi, in the uncertainty princple). Some in physics seem to argue this is the way abstractions turn into space-time-matter — without QM noncommutativity nonthing would exist or happen. ‘Perterb the vaccum’.

An example might be the whole discussion of ‘value theory’ and the ‘transformation problem’ amongst marxists, a bit like a snake eating its tail to survive. (i saw big copperhead snake the other day while picking berries).

## George, 1:04 pm, October 4, 2014

I know this is an old post but I came across a line from Capital that is tormenting the hell out of me. It’s this:

“.…the average work for the last 18 months has been at the very least 7 days, 5 hours, or 78 1/2 hours a week”

What on Earth does Marx mean by “7 days, 5 hours”? It can’t be an average for a week since it is clearly more than a week. Does he mean the 7 days and 5 hours to be the total time which would be equal to 173 hours? But he can’t mean a total of 173 hours for the entire 18 months. That would be a relaxing job! Does the figure refer to a monthly average? But that would come out at a little over 40 hours a week which would be just like a modern job.

Can anyone help?

## voyou, 1:26 am, October 5, 2014

I think “days” here refers to the “day’s work of 10½ hours”, which was the legal definition of a day’s work in the Factory Act of 1850 (which Marx refers to earlier in the chapter). So 7 (working) days plus 5 hours comes out as 78.5 hours.

I imagine Marx rather liked the fact that he was able to quote a capitalist blithely talking about making workers work over 7 days a week.

## George, 7:13 am, October 5, 2014

Thanks voyou. There was another couple of problems I had with Marx – this time re: The Grundrisse. I’ve already given these questions to another group and they admitted that Marx’s figures were sometimes dodgy although his basic arguments were usually sound. However – I thought I would ask you about these issues as well. I’ll just insert my earlier text:

I wonder if you can clear up a couple of problems I have with the Grundrisse.

Both appear just after the heading “Absolute and Relative Surplus Value”.

The first is this:

“If a half of a working day objectifies itself in one bushel of wheat, and if this is the worker’s price, then the surplus labour can only produce 2 bushels of wheat. Thus 2 bushels of wheat [is] the value of one working day,….”

One working day certainly produces two bushels but surely only ONE of those bushels counts as the product of surplus labour? (Otherwise ALL that the worker produces is the product of surplus labour!)

The second is this:

“Now, if the force of production were to double also in gold production, so that, if 13s. were the product of half a working day and this half a day were the necessary labour before; now 1/4 [working day] produces 52s. …”

If the force of production were to double and if previously half a working day produces 13s then, after the doubling, a quarter of a day would produce what a half day would previously produce i.e. 13s. But, seemingly, it produces 52s i.e. the production has increased by a factor of 8!

Would you explain how Marx arrives at these strange figures?

## Tornike, 11:03 pm, June 5, 2015

hey

check out this https://www.marxists.org/archive/marx/works/1881/mathematical-manuscripts/

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