Angels dancing on pin head #2

Posted on May 24, 2011

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Back to angels dancing on the head of a pin.

Well, its as if the philosophers of old used mathematics to solve the problem of how many angels could dance on the head of a pin. As Feynman says, use your mathematical imagination.

What would happen if those ancient philosophers strung mathematical assumptions together the way modern scientists do. For example, mathematics makes the assumption

Fig 1: Infinity

that a point occupies no space. If you also assume that angels, like ballerinas, use pointed toe slippers, their slippers would contact the head of a pin as points, therefore, since a point occupies no space (first assumptions), and angels use pointed shoes (second assumptions) therefore, an infinite number of angels can dance on the head of a pin.

So even though the philosophers couldn’t observe the angels, or their dancing feet, they could still solve the problem by relying on – by basing their whole case upon – iamginary assumptions.

That’s what mathematical models involve. They involve a string of assumptions: if A, and if B, and if C, etc., then probably X – ceteris paribus (i.e., assuming no surprises like lightening strikes, power failures, computer errors, 9/11, market meltdowns, etc., etc.)

Now I hear you say: “That business of angels dancing on pins is a silly, far fetched analogy.”

Is it? Both the Queen of the physical sciences, physics, and the self-appointed Queen of the social sciences, Economics, have “gone” mathematical. They rely less and less on objective observations, and more and more on mathematical models to map the unobserved, and unobservable, spaces of their respective domains. Super-string theory, the current hope for a unified physics, not only lacks strong observational anchors, but at present there are no conceivable ways of obtaining some of the necessary observations. Economics has become so theoretical that out of embarrassment from past failures, they dropped from their annual conventions sessions devoted to predicting future currency values.

In brief, as the problems they face become more complex – more experimentally costly or intractable – scientists are understandably devoting more and more time working with unobservables (mathematical ghosts) and trying to solve their problems in abstract, artificial space. If some of their assumptions – like some of Einstein’s – are sound, then we can expect more scientific breakthroughs.

Fig 2: warts

But as the “reality” to be mapped becomes more complex, we can anticipate an increase in mathematically sophisticated analogies. We can also expect a lot of “nonsense” but hopefully no major disasters from erroneous predictions. ASSUMING that IF I do this, and IF I then do that, and IF I add a pinch of this, and IF things I haven’t thought of don’t muck things up, then I’ll probably get A (add ten healthy years to our lives). Of course if even one of the assumptions is wrong we could get not A, but B. Yes we could all live to be a hundred but at eighty we all gets aids,  crippling arthritis and grow green warts all over our faces.

Fig 1: infinity:  Infinity – flickr.com/photos/inderanim/2903567265/

Fig 2: Green warts: .flickr.com/photos/36937723@N05/3403365894/

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Posted in: Sciencing