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While many people are aware of the increasing role of mathematical modeling in society in general, and science in particular, very few have dared to question this situation. The idea that mathematical models somehow reveal universal truths, in both business and science, has been successfully promoted, despite strong historical evidence to the contrary... [More...]
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I don't think we can put the blame on the mathematicians, though. I think the whole reason why the world turned to them in the first place is because of humanity's immense insecurity and fear of the Unknown. We'd rather create a fiction of understanding when we lack knowledge instead of coping with the uncertainty while we make the effort to understand.
At least on the Cosmological side of things, that is.
On the economic side, I think it's just basic human greed at work
"I have no fear to shout out my ignorance and let the Wise correct me, for every instance of such narrows the gulf between them and me." -- Michael A. Harrington
There are good mathemeticians out there, like Stephen J. Crothers, who keep their feet firmly on the ground, but there seem to be many more, in business and science right now, who are motivated by greed and egotism. Math should be our slave, not our master, as they say.
Accountants have their place in business, and mathematicians in science, but they shouldn't be handed the reigns of power. Just look at the mess that has resulted, in both business and science.
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'Mainstream' economists haven't got a clue what caused the current crisis exactly because they treat economics as an empirical science (or claim to do so in one or the other inconsitent way). It is not an empirical science. Economics is an a-prioristic deductive science whose propositions can be derived from contemplation. Economics is much like applied logic. Neither treating economics as a mathematical science with complex formula nor treating it as an empirical science in which the effects of creation of money ex nihilo must be empirically tested will yield a correct theory of economics. This is the reason why: economics deals with unpredictable human preferences that change over time. For this reason alone it is impossible to empirically establish economic laws. Physics assumes atoms will always behave the same in a given situation. Economics cannot do this for human prefences.
However, we can say that human action is always purposeful. Furthermore we can also say that someone who engages in an economic exchange expects to benefit from it in one way or another, otherwise he would not make the exchange. We know this is true and we do not need to test it with every exchange that takes place, just like we don't have to empirically test if every triangle has three corners or not. For this reason we can fully construct economic theory from a-priori axioms without ever needing to test our theory empirically.
Sadly, in over a century many schools of economic thought still have not understood this, causing governments worldwide to go unchallenged, or even supported by economists, in their blabant economic ignorance and outright destructive policies. (And this is where valid similarities with cosmology can be drawn, as many cosmologists still haven't learned about electricity.)
So while it might be a good idea to herald more empirical ways for cosmology, please don't do the same for economics.
(To those interested in more, I greatly recommend the work of Carl Menger, Ludwig von Mises, Murray Rothbard, Henry Hazlitt, Friedrich Hayek and other disciples of the Austrian school of economics thought. You should experience no difficulty in finding their books, most of which can be read or collected in pdf-format free of charge on the Ludwig von Mises Instutite (mises.org) website, including masterpieces as Human Action, Man, Economy & State, Economics in One Lesson and a great deal of other books. On epistemological and methodological issues, you'll specifically want to search for the keyword praxeology. You may also want to check their Baillout Reader which explains the origin of the crisis and why throwing money in bottomless baillout pits is a baaaaaad idea.)
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This is something the model builders constantly neglect. A model is a set of axioms that let you make hypotheses. This is the same as the mathematical system Godel described.
If the model builders are aware of Godel, they may assume that yes, it's not complete, but it works up to a certain accuracy.
However, chaos theory shows that that too is a fatal flaw, as the omission of small key facets of the real world can lead to wildly divergent results. Pi cannot be explained.
Experiments. Experiments are great, however, one must also remember that experiments are carried out in restricted circumstances...hence, they are often no more than a "model" of sorts.
The danger comes when the scientist then expands his results to a wider situations. Often the worst offenders are not the scientists themselves because real scientists focus on the smallest things, but the vast array of pop scientists who must forever tell us that because a polar bear is white, the current government policy to restrict mileage is justified or some such leap of logic.
To me, the best way to treat our math and science is not as overarching models -- but as sets of tools that serve very restricted and special purposes. It's ok to think about gravity and F=ma when considering an apple falling from a tree. It's not so good when trying to predict whether a fast ball will result in a strike or a home run.
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