### Physics can 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?
Fig 1: Dancing angel
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 dancingf feet, so its 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.
Fig 2: Einstein & math
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 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 cant be seen, with “no-seeums”, with angels or ghosts. That tool is modern mathematics run on powerful computers. Enstein’s famous formula e=mc ^{2 }is an example.
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 predict what they probably would observe in the empty spaces, and in the future, 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 lightening 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.
Fig 3: Imaginary bridge
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. Much of modern science now travels on imaginary bridges supported by mathematical formula. 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, or have the computer do them for you, 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 increasingly shift their efforts from heavy, difficult and high cost observational and experimental work to doing the relatively lightweight symbol manipulations involved in mathematical modeling.
Fig 4: The Future?
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 many are 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 – if it 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 the sophisticated mathematical models of risk provided by Nobel Prize winner’s to Wall Street that led to stock market disasters.
But how does all this relate to angels dancing on pin heads?
Fig 1: angels: flickr.com/photos/bollywoodnewss/4333994149/
Fig 2: flickr.com/photos/jeffmyles/4194307248
Fig 4: Future flickr.com/photos/93779577@N00/4922010209/sizes/s/in/ |

Posted on May 22, 20110