Jenny: ” Ok. I get the general idea of the two camps. Both agree we have no direct access to out there ‘reality’. Both agree that we rely on trusted imaginary maps or bridges to make sense of our human experience, to carry us into the future. Hawking trusts mathematical bridges, he has faith that ‘reality’ behaves by mathematical rules. If there was a God he, she, it was a mathematician. But now that we’ve discovered mathematics, we’ve got access to the** rules** so we don’t need God. But we don’t have direct access to ‘reality’ to test the rules or mathematical predictions so we have to rely on our fallible observations – but some of those observations are pretty impressive. Einstein proposed the mathematical prediction that e=mc^{2 }– which, for instance, says that there’s a humungus amount of energy (e) in a rock (m). And … we finally get the impressive observation of the atom bomb – which results from releasing the energy in a rock of uranium. So count 1 score for Hawking.”

Peter: “But just because some mathematical maps or recipes produce impressive observations doesn’t mean that all mathematical formula’s or recipes work. For instance the recent global economic meltdown was triggered by relying on a mathematical model or formula of** risk** – which bankers trusted and it turned out to be a recipe for disaster, a recipe dreamed up by academic egg-heads who knew more about math than about people – a recipe that obviously left out some key ingredients – like greed! So we could do with a little more humbleness from Hawking and his mathematical nerds.”

Professor Wiggly: ” Right. Some mathematical bridges or maps have led to treasure and some to empty holes or disaster. So we shouldn’t make mathematicians, with their pet maps and models, our new Gods. Math models ‘work’ or help us make sense of some parts of our experience a lot better than for others. For instance math models seem to work better describing the behavior of **things** than the behavior of **people**e – the behavior of people is more complex, people don’t dance to current mathematical tunes the way billiard balls and iron filings do.”

Jenny: ” So if math models don’t work so well with human behavior, and we need models or theories to make decisions what kind of models do we rely on?”

Professor Wiggly: ” That’s where the other camp come in, for instance Kuhn and his paradigms or schools of thought. You’re familiar with political paradigms like Republicanism which relies on **emotionally anchored beliefs or biases **such as low taxes, less government and the right to carry arms. Whereas the Democratic paradigm is anchored on a larger roles for government, therefore more taxes, and more regulations on corporations and individuals (eg gun control).You don’t have to be a mathematician to use these two models or paradigms. The paradigm camp includes mathematics as one of many models used to map or construct our views of reality. We also rely on psychological, sociological, economic, religious, artistic, literary, agricultural, climate, etc. kinds of models, which may or not include some mathematical models in their paradigms. Some of our experiences lend themselves to mathematical mapping and other’s do not. Economics has relied increasingly on mathematical models resulting in some disastrous results – not all experience can be fitted into neat mathematical boxes or formulae.”

Penny: ” So each of these models or maps of reality – Hawking’s math models and Kuhn’s paradigms or schools of thought stand on Simon’s shoulders, on his mantra; **no conclusions without emotionally anchored assumptions.** Hawking’s emotionally anchored assumption is that ‘reality’ dances to mathematical rules and we’ve discovered some of them. Kuhn’s emotionally anchored assumption is that we need all kinds of models to map our experience – math models help us map some of our experience, but most of its models can’t be tested because we lack access to reliable observations – particularly about the future. So we rely mainly on a mixed bag of paradigms or schools of thought to make sense of our experience.”

Peter: ” Yeah, it’ll will be a while before I choose my friends, or wife, on the basis of a math model. Come to think of it I just lost a lot of money by trusting a mathematical model of the market.”

*Sciencing*

Posted on February 25, 20110