Can physics now determine how many angels can dance on the head of a pin?

Philosophers used to seriously debate the question: How many angels could dance on the head of a pin?

Then science came along and said that was a silly question.

Science said that only questions that could be answered by objective observations should be considered REAL questions. Even if you can observe the head of pin, even if you can magnify it, you can’t observe angels, or their dancing feet, so it’s a silly – unanswerable – question.

And for a while science focused on questions that could be answered by objective observations, questions like: how many moons there are floating around Jupiter; or how many e-coli bugs are jigging around on the slide under the microscope; and then, how many are still jigging after a measured shot of penicillin.

But gradually, scientists started asking questions about very far off things, like the edge of the universe, or about very small things, like the smallest particle, or about the unknown future. Now, like the old philosophers, they’re asking questions about things they can’t observe, questions about shadows, about things they can’t see, but can only imagine. But unlike the old philosophers, scientists have access to a powerful new tool for dealing with things that can’t be seen, with “no-seeums”, with angels or ghosts, That tool is modern mathematics run on powerful computers.

Scientists use mathematics to map “reality”, to map the past, the present, and the future. That’s one massive space! They use mathematics to fill in the gaps between the relatively few observational check points they have established and the immense unexplored spaces they haven’t..

For example, they can plot the relationship between two variables, like the temperature of a rod and its expansion; or between measures of I.Q. and school grades. But they can’t afford to measure ALL rods at all temperatures, or ALL students, at different t times, in ALL countries. So on these particular maps of “reality” they have more empty spaces than they have observational dots, and of course they have no observational dots for the future. But scientists can, with a few big assumptions, use a mathematical formula to build imaginary bridges into the futrue, to help them predict what they probably would observe in the empty spaces if they actually did have the time, money, and technology to carry out the experiments to get hold of that enormous amount of missing observational data.

Of course the biggest empty space of all is the future. For example scientists try to predict the weather, or global warming, or number of present and future cases of West Nile virus, or the stock market, or the risks involved of cloning bugs or people, or when and where there will be lightning strikes, or hurricanes, or rolling truck tires, or epidemics, or heart attacks, or volcanoes, or Iraq’s weapons of mass destruction, or terrorist dirty tricks.

So gradually, the emphasis in science started shifting from making observations to doing fancier and fancier mathematics about what lay in the big gaps between actual observations and the unobservable future. This shift in emphasis from relying mainly on observations to increasingly relying on mathematical assumptions is understandable. Often the needed experiments are costly, messy, unethical, technically impossible, or take years to complete. Furthermore, it’s a lot easier – with the help of few presuppositions – to do mathematical calculations to predict where the observations would probably fall, if their assumptions are correct. And, of course, that’s a big if.

So the law of the conservation of energy predicts that scientists will shift their efforts from heavy, difficult and high cost observational and experimental work to doing the relatively lightweight symbol manipulations involved in mathematical modeling.

Additionally, mathematical models provide clear answers. Numbers don’t lie – do they? Of course you have to buy the underlying assumptions, most of which are not only unproven but improvable. We walk, shuffle, fly into the future, not on observational stepping-stones, but on assumptions. Scientists use mathematical models for predicting the unknown future, like the probability of what will happen if they add of pinch of this to a pinch of that; predicting the results of genetic engineering of bugs, crops, animals, and people. And if something can be tried, it will be tried – like atom bombs, thalidomide, hormone therapy, breast implants, and of course the perennial favorite – beating the market. We have to look no further than the sophisticated mathematical models of two Nobel Prize winning economists that led to stock market disaster.

But how does all this relate to angels dancing on pin heads? Well, it’s as if the philosophers of old used mathematics to solve the problem of how many angels could dance on the head of a pin.

What would happen if those ancient philosophers strung mathematical assumptions together the way modern scientists do. For example, mathematics makes the assumption that a point occupies no space. If you also assume that if angels, like ballerinas, used 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 – a mathematical assumption.

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 lightning strikes, power failures, computer errors, 9/11, 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.

But as the “reality” to be mapped becomes more complex, we can anticipate an increase in mathematically sophisticated analogies of how many angels can dance on the head of a pin. But with fewer and fewer pins (observational check points) and more and more mathematically choreographed angels (imaginary objects and events) 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 20 healthy years to our lives). Of course if even one of the assumptions is wrong we could get not A, but B. We could all live to be a hundred and ten but at ninety we’ll probably get cancers and grow green warts on our knees and foreheads.

But hey, nothing ventured, nothing gained!

*Sciencing*

Posted on January 30, 20110