Ian Wright


Has the background needed for doing model of Maksakovsky’s “Theory of the Capitalist Cycle”!

Hi! I’m a software engineer and scientist with overlapping interests in machine learning, economics and philosophy. I work as a data scientist at Semmle Inc. where I apply machine learning to software engineering data.
I hold a degree in Computer Science, from Durham University, and a PhD in Artificial Intelligence/Cognitive Science from Birmingham University. Outside my day job I continue to pursue academic interests, and publish in economics and philosophy. I also hold a degree in Mathematics, from the Open University, and was recently (2016) awarded a PhD in economics, also from the Open University.


Other research also looks very interesting:




Philosophy of Mind





The Law of Value:
A Contribution to the Classical Approach to Economic Analysis


Got all links above (except YouTube). Open Working Papers links broken:

http://fass.open.ac.uk/economics/research/discussion-papers (also got number 69 not listed)

Mathematica Model for thesis (machine readable cdf only – source code in thesis)

author = {Ian Wright},
publisher = {Harvard Dataverse},
title = {classical macrodynamic model 1},
year = {2014},
doi = {10.7910/DVN/27472},
url = {https://doi.org/10.7910/DVN/27472}


Blog post of talk on thesis (also check others) – “Karl Marx’s Invisible Hand”:


Handout summarizing model (with equations) from blog post talk:


Co-author of:

title = {Classical Econophysics (Routledge Advances in Experimental and Computable Economics)},
author = {Allin F. Cottrell, Paul Cockshott, Gregory John Michaelson, Ian P. Wright, Victor Yakovenko},
publisher = {Routledge},
isbn = {0415478480,9780415478489,0203877543,9780203877548},
year = {2009},
series = {Routledge Advances in Experimental and Computable Economics},
edition = {1},
volume = {},
url = {http://gen.lib.rus.ec/book/index.php?md5=1204640FA5C43650A11E2998B74DABFC}}

Michael Roberts has drawn attention to a blog post and paper:



Very interesting with lots of interesting references to follow up.

Lots more in google scholar eg:


Engels should get credit for first introducing statistical mechanics entropy concepts with his chemical analogy:

And to expect any other division of the products from the capitalist mode of production is the same as expecting the electrodes of a battery not to decompose acidulated water, not to liberate oxygen at the positive, hydrogen at the negative pole, so long as they are connected with the battery.

We have seen that the ever-increasing perfectibility of modern machinery is, by the anarchy of social production, turned into a compulsory law that forces the individual industrial capitalist always to improve his machinery, always to increase its productive force. The bare possibility of extending the field of production is transformed for him into a similarly compulsory law.


That “compulsory law” also translates into Marx’s:

Accumulate, accumulate! That is Moses and the prophets! “Industry furnishes the material which saving accumulates.” [23] Therefore, save, save, i.e., reconvert the greatest possible portion of surplus-value, or surplus-product into capital! Accumulation for accumulation’s sake, production for production’s sake: by this formula classical economy expressed the historical mission of the bourgeoisie, and did not for a single instant deceive itself over the birth-throes of wealth. [24] But what avails lamentation in the face of historical necessity? If to classical economy, the proletarian is but a machine for the production of surplus-value; on the other hand, the capitalist is in its eyes only a machine for the conversion of this surplus-value into additional capital.


Marx pointed to more than growing inequality. Concentration and centralization of capital results in ruin of most capitalists leaving only a tiny handful for workers to expropriate.

In 1928 socialist Frank Ramsey wrote first calculus of variations paper in economics, which described mechanics of concentration where rich can afford to save larger proportion of income while poorest savers find themselves consuming their capital until eventually split into two classes, which he sarcastically concludes by describing an “equilibrium” as follows:

…equilibrium would be obtained by a division of society into two classes, the thrifty enjoying Bliss and the improvident at subsistence level.


For Marx this process of concentration was closely linked to regular cyclical crises. During boom some expansion of capitalist class relying on credit. But crashes regularly bankrupt far more.

Marx did not have the mathematics to develop his theory of concentration, or indeed his theory of cycles (though when studying calculus he headed straight for Lagrange where duality prices in constrained resource allocation is found). But he did have in mind something along the lines of drive to accumulate to minimize long run probability of ruin as in Bernoullis “St Petersburg paradox”:


There is now an extensive financial literature on risk of ruin.


Important source is Myron Gordon who does give some acknowledgement to Marx in last chapter of his 1994 book.


  author={Myron J. Gordon},
  title={{Finance, Investment And Macroeconomics}},
  publisher={Edward Elgar Publishing},
  keywords={Economics and Finance},
  abstract={In Finance, Investment and Macroeconomics, Myron J. Gordon advances a theory of finance and investment under uncertainty and risk aversion which resolves problems left unsolved by Keynes in a manner consistent with his work.},




Following exchange with Ian Wright at Michael Roberts:


  • Arthur Says:

    Jack, Norman and mandm,

    Socially Necessary Labor time is not specific to capitalist production. It is much simpler as described in letter to Kugelmann:


    Marx explicitly points out that it is an obvious aspect of all social production, not just capitalism.

    If a tribe wants to do more hunting it has to do less gathering.

    Demand for meat and fruit will obviously affect how much work is done for each but socially necessary labor time to acquire a tonne of the meat or of fruit will approximately determine how much time spent on getting fruit and therefore how much fruit has to be reduced to spend more time on getting another tonne of meat.

    That’s all.

    Classical economics already got the basics and already understood that without knowing in advance how much SNLT is required, approximate ratios MUST emerge from fluctuations in demand and supply since there IS only so much working time available and it DOES have to be switched from doing one thing to doing another.

    This was not understood as much earlier because both feudal and slave society did not conceive of labour as something common to humans. (The class that had leisure to think did not do much work and did not see much in common between different sorts of work). In fact even in Marx’s time it was better understood in America than in Europe because Americans switched occupations more readily.

    Mainstream Micro 101 describes it as “opportunity costs” and “trade offs”. Convex analysis and duality theory describes such “trade offs” mathematically and Marx went into very detailed and far reaching consequences that were not and are not understood by others. But the “mystification” and obscurantism about this is from Marxians and other opponents of Marx, not from Marx.

    There is no exact predetermined proportion and nothing “embodied” or “crystallized” except metaphorically.

    This objective necessity is expressed in the form of exchange value when production is organized through commodity exchange which exists long before capitalism and even feudalism but becomes fully dominant only when wage labour and other inputs are themselves commodities – consequently with (fluctuating) prices as both inputs and outputs. The fluctuations necessarily express both changing SNL time with changing technology etc and disproportions in demand and supply.

  • Ian Wright Says:


    Very nice! Indeed, a key passage is the Letter to Kugelmann, perhaps the most important paragraph in the history of economics.

    Both SNLT and exchange-value are not specific to capitalism. E.g., law of value, exchange-value, money etc. all existed and operated in feudal times, wherever extent of market, and competition, was sufficient.

    Yes, a lot of obscurantism around on this issue. A mode of production is defined by the dominant mechanism of pumping out surplus-labour. In capitalism, that’s the wage system.

    One question/clarification: I agree that SNLT can also change in response to fluctuations in supply and demand, but only through the latter’s affect on productivity (e.g., greater demand may induce less productive techniques). The important point is that SNLT is a market-independent property of an economy.

    Best wishes.

  • Arthur Says:

    Thanks Ian!

    I would rank it as one of the most important paragraphs. I regard the “fragment on machines” which I fully quoted above in this thread as just as important and with even more contemporary resonance (technically two paragraphs but the very long first para covers it). Also the explanation of Marx’s “general conclusion” in preface to 1859 “Contribution” (technically historical materialism rather than economics but arguably so is letter to klugmann). Also many of the paras in Introduction to the Grundrisse. This guy wrote too many important paras and they were too long. No wonder he is widely misunderstood!

    Re question/clarification, I did say (fluctuating) “prices”. Did not say fluctuating SNL time nor fluctuating exchange values. Don’t want to get into fine distinctions between market prices, market values, regulating prices and values etc etc.

    Do agree important aspect is market independent but many qualifications. Merchant capital trading margins, interest and capitalization of rent and interest with “production prices” based on average rate of profit could also be regarded as merely development/modification of SNLT. But domination of supply costs depends on fact that supply is generally more elastic than demand (can switch to meet demand easier than relative requirements adjust to costs). But demand side works primarily through budget constraints which depend on incomes which depend on state of market.

    As you mention, choice of technology is itself dependent on market conditions eg switches to higher organic composition after cyclical crash as explained by Maksakovsky (and excess demand in boom puts mothballed higher cost plant into use).

    But also it is hard to avoid directly considering demand and supply with joint products. Exchange values of “main” and “waste” products produced in fixed ratios, like different cuts of meat tend on average to be sold at a TOTAL price of production that depends on SNLT. But relative prices of different joint products entirely dependent on demand. This is not a minor qualification since pretty well everything is in fact a joint product (though with less fixed ratios than for cuts of meat). So the actual averages around which prices fluctuate do depend on demand as well as on SNL time.

    Particularly important these days with so much being a joint product of urban infrastructure, heavy investment in advertizing and segmentation of markets to capture “consumer surplus”. All these can only be properly understood after first grasping the fundamental as outlined to Kugelmann so must be treated as secondary for later development. But ignoring them completely would concede too much to the vulgar economists.

    Anyway thanks again!

    PS. Flattery will get you everywhere. I just took a look at your blog and am very interested. Will have to get back to it later. Downloaded and skimmed your paper on “The General Theory of Value”.

    Quick skim left me with impression that your production matrix A is square i.e. with no choice of technology (as well as no joint production). But you specifically indicated above that you are aware of choice of techniques being affected by price structure and you took a step towards actual prices by introducing stocks and flow of money.

    Please take a look at references on this page of my (unopened) blog:

    Hopefully you will find it of interest and will follow up on helping to do models for Maksakovsky (links on my home page).

    PPS I am curious about apparant inconsistency of first post at your blog re “theft” and enthusiasm for Marx’s account of “equal exchange” (which is not theft). Does that reflect shift since you started blog?

Lots more with others in that thread. Will put under “Jack Rasmus“.


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