So this is how a mathematician can be a public intellectual: Tim Gowers employed his characteristically lucid prose in the service of clarity in his cogent response in the Guardian to the Simon Jenkins column mentioned in my previous post. I agree with everything in Gowers’s answer to Jenkins, though his examples that show how mathematics can “be a tool for increasing one’s thinking power” are drawn from statistical reasoning; making the case for the value of learning the area of a circle or the quadratic formula is more challenging, and I don’t know that anyone has found the right way to counter the complaints of those who share the Jenkins worldview. (I suspect the solution must include the word “culture” but I’m not sure what other words need to be involved.)

A position on questions of education in mathematics or anything else rests implicitly on a theory of the good society. Jenkins must have such a theory but I couldn’t figure out what it is. Gowers makes his very clear:

…once you [understand some principles of statistics], you become better at making decisions. This is important for individuals – whether we like it or not, we all have to take major decisions based on statistical evidence – and it is even more important for people in positions of authority, whose decisions affect other people.

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Jon AwbreyRepresentation Theory

http://inquiryintoinquiry.com/2012/06/21/the-place-where-three-wars-meet/

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Jon AwbreyAgain, in a ship, if a man were at liberty to do what he chose, but were devoid of mind and excellence in navigation (αρετης κυβερνητικης), do you perceive what must happen to him and his fellow sailors? (Plato,

Alcibiades, 135A).Statistics were originally the data that a ship of state needed for stationkeeping and staying on course. The Founders of the United States (FOTUS, FOTI?), like the cybernauts of the enlightenment they were, engineered a ship of state with checks and ballasts and error-controlled feedbacks to achieve the bicameral purpose of representing both reality and the will of the people. And Max Weber understood that a state’s accounting systems were intended as representations of realities that its crew and passengers must observe or perish.

The question for today is —

What are the forces that distort our representations of what’s observed, what’s expected, and what’s intended?

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mathematicswithoutapologiesPost authorOften, for example in this instance, it’s easy to guess the answer.

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Jon AwbreyThe mark of a rhetorical question …

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John SidlesWhat are the forces that distort our representations?

Indeed it is

VERYeasy to guess the answer(s)!Alas, never in my memory have US politicians so outrageously embraced outright science-denial, as in the present election cycle. Is this trend comparably bad in the rest of the world?

Thanks for a well-merited encomium for Tim Gowers’ lucid essay.

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DRNOI think that the fact Gowers use “decision” as the field to apply math is quite representative of our new elite that is “MANAGERS”.

He could have said our society needs roads=>needs engineers=> needs mecanics of fluid=> needs partial differential equations=> needs distribution theory=>needs topology=>needs at least basic set theory, algebra…

and we can do it with electricity, hydrodynamics, all civil engineering, …

But of all exemple he choose people that are not “do-ers”.

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mathematicswithoutapologiesPost authorJenkins uses the word “society” once:

the curriculum systematically denies pupils what might be of real use to them and society. There is no “need” for more mathematicians. The nation needs, and therefore pays most for, more executives, accountants, salesmen, designers and creative thinkers.I find his slippage from “society” to “nation” unfortunate, and his neglect of engineers in his list of what the “nation needs,” in favor of “executives” and “salesmen” (!), is depressing. But at least he doesn’t agree with Thatcher, who famously said “There is no such thing as society.” I am convinced that it’s impossible to sort out the place of mathematics in education without clarity in the choice of words describing the structures of decision-making and the power relations underlying these structures.

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