Annotated Bibliography

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WR Ashby

Design for a brain 1960. (Ed. 2 has significant improvements.) A cybernetic classic. Ashby notes the correspondence to game theory (and thus to Whitehead). In simpler case Cybernetic language is considerably more accessible than Whitehead.

With Conant: Every Good Regulator of a System must be a Model of that System, 1970. It claims that:

“The theorem has the interesting corollary that the living brain, so far as it is to be successful and efficient as a regulator for survival, must proceed, in learning, by the formation of a model (or models) of its environment.” [My italics.]

The notion of a regulator is an objective mechanism which is required to maintain pre-defined objective criteria: i.e., keep some output within a ‘good’ domain. It may also have other functions, e.g. optimising something. The theory shows that in so far as a system to be regulated conforms to some model, it will need – in effect – to be modelled to be regulated effectively. It does not explicitly consider feed-back from output to input. Where this is present on could apply the theory to short-term regulation, within the delay of the feed-back. Alternatively one could apply it at the level of strategy rather than base events and activities. In this case one needs to model ‘the game’, including the ‘board’, the players and their motivations.

JM Keynes

Keynes was a mathematician student of Whitehead, employed by the treasury during the war, who worked with JC Smuts on the transition to peace. The Prime Minister (Lloyd George) supported Keynes in producing the first two references as ‘lessons identified’ from the war.

Treatise on Probability 1919. Keynes’ critique of ‘standard’ (numeric) probability theory, together with some useful generalisations. Refers to Whitehead (Keynes’ tutor). Underpins subsequent work.

The Economic Consequences of the Peace 1919. Keynes shows that although depressions are impossible according to the then classical economics, based on standard probability, ‘animal spirits’ introduced the greater uncertainties, of the kind described in his treatise, made a crash and a sustained impression virtually certain. Thus whereas the conventional view was that economies were inherently buoyant, so that recessions could occur as a result of ‘exogenous events’, such as war, a depression could actually occur endogenously – due to ‘market failures’.

The General Theory of Employment, Interest and Money 1935. The master work on economics. It explains how crises such as those of 1929 and 2007/8 occur, and suggests some remedies. Underpinned by the treatise on probability, but this is not widely appreciated. ‘Keynesian’ economics means the application of stock remedies whatever the cause. In this sense, Keynes was not a Keynesian. Rather he developed a theory as a way of looking at economies. His approach was to follow where theory led, taking account of residual uncertainties.

JC Smuts

Smuts worked with Keynes on economics.

Holism and evolution 1927. Smuts’ notoriously inaccessible theory of evolution, building on and show-casing Keynes’ notion of uncertainty. Although Smuts and Whitehead worked independently, they recognized that their theories were equivalent.

The Scientific World-Picture of Today, in ‘British Association for the Advancement of Science, Report of the Centenary Meeting’. London: Office of the BAAS, 1932. Smuts’ presidential address, outlining the new ideas in ‘Holism and evolution’ and their import.

I Stewart

Ian has done more than most to explore, develop and explain the most important parts of qualitative mathematics.

Life’s Other Secret: The new mathematics of the living world, 1998. This updates D’Arcy Thompson’s classic On growth and form, ending with a manifesto for a ‘new’ mathematics, and a good explanation of the relationship between mathematics and scientific ‘knowledge’. Like most post-80s writings, it’s main failing is that it sees science as having achieved some great new insights in the 80s, ignoring the work of Whitehead et al, as explained by Smuts, for example. 

M Tse-Tung

Chairman Mao.

On Contradiction 1937. Possibly the most popular account of Whitehead’s ideas.

AN Whitehead

Whitehead was Russell and Keynes’ tutor.

Process and Reality 1929. Notoriously hard going, it refers to Keynes’ work on uncertainty.

W Whitman

American civil-war thinker and poet. Part of the inspiration for the Beat movement.

Leaves of Grass 1855. Part of Smuts’ inspiration.

See also

ABACI – a consultancy who offer to tailor solutions.

Dave Marsay

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

8 Responses to Annotated Bibliography

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