> Your claim that "math is a tool" is demonstrably false.

> Mathematics is an artifact of the human mind which has

> given rise to a significant number of provably mathematically

> correct but demonstrably physically false theorems in the

> real world.

Mathematics does not attempt to prove things in the real

world. It can be used to model things in the real world,

and it gives helps us build things like airplanes, TVs, and

computers. Thus, it is a tool. The fact that models are

never perfect, or that humans can apply models incorrectly

doesn't change this.

> The most obvious example of this is the Banach-Tarski

> Theorem.

The theorem is correct. The paradox came about when somebody

forgot that it assumes matter is infinitely divisible. Real

matter is not infinitely divisible. Yet, the theorem has

useful application in areas such as cryptography.

> However, the most vivid recent example is the economic work

> leading to the Nobel Prize awarded Merton and Scholes for their

> Balck-Merton-Scholes options pricing equation.

I'm not familiar with this, but it sounds like the model they

were using didn't take into account that pricing is an

iterative process involving feedback, as you say.

> Math is not a tool. It is a fabrication of the human mind,

> as Cohen's 1964 proof of the invalidity of hte Zermelo-Fraenkel

> theorem under certain conditions showed so clearly.

It is a fabrication of the human mind, and it can be a tool.

As a tool, it can be used correctly or incorrectly.

> Math is as useless in explaining music as it is useless in

> trying to explain or predict the hemlines of women's dresses, or

> the hot new form of pop music in 5 years.

Math itself will never explain anything. It doesn't attempt to.

> just study the dizzying spiral into incoherence followed

> by Milton Babbitt and Pierre Boulez and their pseudo-scientific

> epigones,

I long ago concluded that both of these guys were spouting useless

nonsense.

-Carl