Divergent problems in Schumacher's "Small is Beautiful"

[David Bibby]

Dear All,

I was prompted to borrow a copy Schumacher's "Small is Beautiful” from the library by John’s email on 9 January, and am impressed with some of his arguments.  I was particularly interested in his discussion on divergent problems.

"G.N.M. Tyrell has put forward the terms “divergent” and “convergent” to distinguish problems which cannot be solved by logical reasoning from those that can. Life is being kept going by divergent problems which have to be “lived” and are solved only in death.  Convergent problems on the other hand are man’s most useful invention; they do not, as such, exist in reality, but are created by a process of abstraction. When they have been solved, the solution can be written down and passed on to others, who can apply it without needing to reproduce the mental effort necessary to find it. If this were the case with human relations - in family life, economics, politics, education, and so forth - well, I am at a loss how to finish the sentence. There would be no more human relations but only mechanical reactions; life would be a living death. Divergent problems, as it were, force a man to strain himself to a level above himself; they demand, and thus provide the supply of, forces from a higher level, thus bringing love, beauty, goodness, and truth into our lives. It is only with the help of these higher forces that the opposites can be reconciled in the living situation.” (Small is Beautiful, chapter 6, The Greatest Resource - Education)

We may note the similarity between Schumacher’s convergent problems ("they do not, as such, exist in reality") and the abstract nature of Lonergan’s classical laws.

“There is no need to interpret classical laws concretely.  They can be statements of elements in abstract system where (1) the abstract system is constituted by implicitly defined relations and terms, (2) the abstract system is connected with data not directly but through the mediation of a complementary set of descriptive concepts, and (3) the laws of the abstract system are said to be verified inasmuch as they assign limits on which, other things being equal, vast varieties of data converge.” (Insight, chapter 4, section 3.4, 2008/159)

Schumacher then claims that physics and mathematics does not recognise divergent problems.

“The physical sciences and mathematics are concerned exclusively with convergent problems. That is why they can progress cumulatively, and each new generation can begin just where their forbears left off. The price however, is a heavy one. Dealing exclusively with convergent problems does not lead into life but away from it.” (Small is Beautiful, chapter 6, The Greatest Resource - Education)

I think it is a fair characterisation of mathematics and physical science to say it is concerned exclusively with convergent problems.  Although divergent series and uncertainty exists, the way both of these are handled is by reformulating the problem in such a way that it becomes convergent.  Probability is the convergent tool of physical scientists.  Finding proofs is the mathematical search for a convergent solution.  But this highlights the difference between economics and physical science, because economics cannot reformulate its divergent problems due to the social surd.  Acknowledging the existence of these divergent problems is essential in economics if it is not to lead away from life.

Where I disagree is that the focus on convergent problems is what allows cumulative progress.  It is not convergent problems, but knowledge handed on by belief that is responsible for the transmission of science to later generations.

“There is progress in knowledge from primitives to moderns only because successive generations began where their predecessors left off.  But successive generations could do so, only because they were ready to believe.  Without belief, solely relying on their own individual experience, their own insights, their own judgements, they would have ever been beginning afresh, and either the attainments of primitives would never be surpassed or, if they were, then the benefits would not be transmitted.” (MiT, chapter 2, section 5, 4th paragraph)

I think we can forgive Schumacher this oversight in 1973, but the distinction between convergent and divergent problems remains relevant.  The question is how to make profit from the distinction, and I think this may require developing the mathematics of insight, that definitively shows how to transpose the divergent problems of real life economics into convergent forms of knowledge. 

Kind regards,

David

[jaraymaker]

WOW, David, I just wrote warning against our shooting ourselves in our collective foot, but your posting below is just the opposite. I think we had a reference to Schumacher in our text, but I had taken it out since we do not want to overcomplexify, But the quote below and your insight into that has just changed my mind..... Like BL, Schumacher discerns how e. g. distinguish between convergent & divergent problems. Right up our alley. 

 

Thanks. I'll have to figure out how best use it.....

 

John

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[jaraymaker]

David,

 

below is a note on Schumacher that I just added (following the Bottzmann reference. Does it pass muster?

 

"It may be that just as Boltzmann built a bridge from our incomplete knowledge of a system to classical observations such as temperature and pressure,[1] so Lonergan built a bridge between economics and the deeper implications of intellectual, psychic, moral, and religious conversions[2] to which we add the implications and need of economic and environmental conversions. It is In view of this that we analyze and integrate Lonergan’s seminal, twin contributions in the fields of method and economics. Both of these contributions rely on and develop a twofold approach to ongoing transformations, be it in economics  or in GEM-FS healing-creating approaches. We aim to integrate so as reinforce the transformative properties needed to make this world more ethically responsible. 

 

      A note on E. F. Schumacher on Convergence and Divergence

 

As Boltzman and Lonergan have built bridges, so has Schumacher in his Small is Beautiful. He writes that G. N.M. Tyrell has put forward the terms “divergent” and “convergent” to distinguish problems which cannot be solved by logical reason. Schumacher argues that physics and mathematics do not recognize divergent problems:

 

The physical sciences and mathematics are concerned exclusively with convergent problems. That is why they can progress cumulatively, and each new generation can begin just where their forbears left off. The price however, is a heavy one. Dealing exclusively with convergent problems does not lead into life but away from it.[3]

 

For his part, Lonergan does deal with divergence. He writes:

 

There is no need to interpret classical laws concretely. They can be statements of elements in abstract system where (1) the abstract system is constituted by implicitly defined relations and terms, (2) the abstract system is connected with data not directly but through the mediation of a complementary set of descriptive concepts, and (3) the laws of the abstract system are said to be verified inasmuch as they assign limits on which, other things being equal, vast varieties of data converge.[4]

 

Note 1) the similarity between Schumacher’s convergent problems ("they do not,

as such, exist in reality") and the abstract nature of Lonergan’s classical laws. 2) Lonergan's different meaning attached to data converging.  

 

Lonergan’s Critical Realism Clarifies the Mistaken Presuppositions of Philosophers and Economists.......

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[1] The mathematician, David Bibby, advised us that it is likely that Maxwell-Boltzmann statistics requires both kinds of heuristic structure depending on the situation; scientists working in the field decide which is appropriate.

[2] To truly and fully understand Lonergan’s method one must advert to the spiritual, mystic, apophatic which are all integral components of a religious conversion. Our GEM-FS approach explicitly or implicitly integrates these components.

[3] Schumacher, Small is Beautiful, Chapter 6. We thank David Bibby for this reference.

[4] Insight, 159. Lonergan is here addressing the problem of indeterminism. He notes “Indeterminism is true as a negation of the old determinisms. But it cannot escape the necessity of methodological assumptions and precepts; it cannot prevent their conjunction in thought with laws and frequencies that are regarded as verified; and so it cannot succeed even in delaying the day when, from a new viewpoint, scientific anticipations once more will envisage a determinate to be known… I have offered a unified view that anticipates both the systematic and the non-systematic without excluding in particular cases insight into concrete non-schematic situations” such as the “subatomic order.” END quoting our text: John

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[David Bibby]

Dear John,

It is too good, and brings home to me the need to be more careful in what I write if you keep referring to me as a mathematician!

I don’t have any specific problems with the text, but I think we do still need to work out how best to use these references.  I was offering a mixture of observations and speculations.  To develop this idea, it might be helpful to offer some more examples, and ask some questions.  Schumacher gives this example:

“To have to grapple with divergent problems tends to be exhausting, worrying, and wearisome.  Hence people tend to avoid it and to run away from it.  A busy executive who has been dealing with divergent problems all day long will read a detective story or solve a crossword puzzle on his journey home.  He has been using his brain all day; why does he go on using it?  The answer is that the detective story and the crossword puzzle present convergent problems, and that is the relaxation...” (Small is Beautiful, chapter 6, The Greatest Resource - Education)

Some questions we might ask are:

• Can I identify any divergent problems in my life?  For example, juggling priorities, calculating risks, making decisions…
• What is it that enables us to handle divergent problems?  There is no clear solution, yet we are able to handle them with varying degrees of confidence and success...
• If I were to undergo one of Lonergan’s conversions, would that make me better able to handle divergent problems?  (The point is to get people to grasp the value of personal self-appropriation, to understand their own understanding).

I don’t know if these would work in your context, but I think we should start by looking for analogies and similarities, then figure out how best to incorporate it together.

Kind regards,

David

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