Monday, February 17, 2014

The mathematics of welfare



In its heyday, New Zealand Railways was the Wired magazine of its time. What had started as a publication for the Railways Department’s 18,000 staff and its principal suppliers and customers was able to morph into a whole-of-culture, broad-ranging popular publication because it was wedded to a technology that signified social and economic progress in the same way that computing does today.

Even in early 1934, as the country struggled out of the worst of the Depression, an ad in the magazine could proclaim ‘Railways for Happy Days Again.’ In the same issue, we were introduced to the Railway Department’s section of the industrial procession known as ‘Wellington’s Drive for the Restoration of National Confidence.’ Good times were ‘overdue’, and the train would lead the country to them. Witness the bright sun of tomorrow filling the horizon at the end of the straight railway track on the cover.


By mid 1938, confidence had been restored, and the magazine could print ads such as this one:


But faith in technology and rational progress could not be bound to a means of transportation alone, however shaping of the nation and its mindset. So in the June 1938 we find an extended piece by O. N. Gillespie entitled: The Marvels of Mathematics – “The Mirror of Civilization” – The Coming Of An Arithmetic Of Social Welfare. The bulk of its content is devoted to showing how the ancient Greeks and Romans never mastered basic mathematical concepts such as division and the zero, which set hard limits on their ability to progress not only technologically but also culturally, as civilisations. The last suggestion of that long-winded title – that social welfare can be reduced to a mathematical problem, thereby solved – receives a somewhat shorter and more elliptical treatment. But it’s intriguing nonetheless.

At the outset, Gillespie declares his admiration for ‘the great Professor Hogben’ , meaning Lancelot Hogben , the author of the 700-page best-seller Mathematics for the Million, an extraordinary work of popular science that is still in print to this day. Being an admirer of Hogben myself (I’ll get around to writing a post on my copy of Science for the Citizen sooner or later), I’m not unsympathetic to the argument that a more widespread mastery of numbers might lead to a more critical and engaged citizenry. But Gillespie takes it further. He writes:
When the common men of the world have universally a command of the grammar of mathematics, there will arise from them greater men still, more profound thinkers, who will conduct the impeachment of the evils that infest our world.
And:
The language of mathematics represents an emancipating force, freeing intellects and setting free influences which pass over national barriers. From the study of its eternal truths, from the appreciation of its beneficence of discovery, its inescapable exactness of conclusion, will come the ultimate realisation of happiness for all mankind.

Nowadays you might find pronouncements such as the last one above – centred on the idea that knowledge is humanity’s prime and inexhaustible resource – precisely in magazines such as Wired. Outside of the fevered dreams of the technologists, however, this age of austerity and brutal economic upheavals offers too many reminders that a science of numbers capable of guaranteeing the people’s well-being has yet to be discovered. Gillespie’s ‘vision of comfort and glory’ has found more takers among right-wing radicals economic theorists operating out of think-thanks and universities than in the highly numerate polis that he foreshadowed.

Fittingly, the desire to foster a literate, intelligent popular readership is what we mostly remember about New Zealand Railways Magazine, but there wasn’t a safe arithmetic to ensure that admirable goal either. The publication that just a few years earlier had cheerfully offered the prospect of ‘happy days again’ abruptly ceased to operate in 1940, and didn’t reopen after the war.

5 comments:

Peter Bradburn said...

Of note; http://en.wikipedia.org/wiki/Transport_Licensing_Act_1931

Ben Wilson said...

>Gillespie’s ‘vision of comfort and glory’ has found more takers among right-wing radicals economic theorists operating out of think-thanks and universities than in the highly numerate polis that he foreshadowed.

Wasn't he suggesting that individuals would emerge from the polis, though, rather than saying the polis itself was going to do great maths?

But yes, the most dedicated maths nuts in economics do tend to buy into the mainstream. I'm not surprised, either - coming to the end of a degree in Maths myself, I'm amazed at how highly mathematical minds seem to approach economics. Because maths itself is always "standing on the shoulders of giants", there is always only progression, very seldom questioning of the applicability. That's almost an irrelevant question in pure maths. Each theorem builds on the last, with very high levels of certainty.

For instance, we spend an entire lecture on discussing the way to linearly solve a supply/demand problem, noting as the only flaw that linear is an approximation to non-linear. The idea of questioning supply/demand laws themselves, no way. The idea of actually looking at whether anyone ever sets their prices in the way they outline, so that the efficacy could perhaps be tested, is of no consequence at all. What matters is the cleverness of the mathematics.

Obviously many economists do actually tackle the fundamentals. But you can tell that to anyone highly trained in economics, that's like challenging Pythagoras' theorem. Possibly interesting, but hard for them to see how useful it could really be. When someone has progressed on to the calculating partial derivatives of price movements, they don't really want to concern themselves about whether the basic addition is being done right.

This is the barrier that the non-mainstream people face - they don't get to stand on giants and so what they achieve looks puny by comparison, even if it is actually better.

James Robb said...

For all his admiration for the great professor Hogben, Gillespie seems to have missed Hogben's main point, which was that mathematics was a creation of human beings and arose to serve real-world human problems, not as a set of 'eternal truths'. The outstanding characteristic of Mathematics for the Million is that, unlike almost the entire literature of mathematics, it takes this materialist starting point. From memory, I think that the expression 'the mathematics of human welfare' was the title of Hogben's chapter on Statistics. Statistics is unlike the rest of mathematics in that from the start it was very much grounded in the real world - hence the tendency for Statistics to separate itself out as a distinct field of study at universities, schools etc.

Giovanni Tiso said...

"From memory, I think that the expression 'the mathematics of human welfare' was the title of Hogben's chapter on Statistics."

To be fair to Gillespie, he does wax lyrical the Littledene, suggesting that he sees analysis of the material conditions of communities and the larger society as one of the key tasks of mathematics. But he doesn't really connect that idea to his larger vision.

Giovanni Tiso said...

"Wasn't he suggesting that individuals would emerge from the polis, though, rather than saying the polis itself was going to do great maths?"

Yes and no. You could train bright individuals in an elitist education system - what he insists on (and indeed was one of Hogben's driving ideas) was that progress would arise from people equally sharing in that knowledge.

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