## onsdag 19 oktober 2011

### Mathematics of Financial Crisis, and Climate Crisis

In Climate Crisis vs Financial Crisis I identified a common root of a (i) global financial crisis and (ii) global climate crisis as an instability from a two-way flow of (i) money between banks and loan takers and (ii) heat energy between atmosphere and Earth.

In the case (i) this is illustrated by an entrepreneur with an idea (e.g. solar panels) but no money (=0) who gets a loan X when signing a debt contract of X, according to the equation
• 0 = X - X
with the loan X exactly balanced by a corresponding debt X. This gives the entrepreneur the possibility to start a company for production of solar panels. If the interest rate is close to zero (as in Japan and the US) and there are no restrictions on the size of the loan, then the entrepreneur will be able to realize the idea on any scale.

But some ideas are not so good and the company will go bankrupt (e.g. Solyndra) leaving the contradictory equation 0 = - X , which will ask for new even bigger loans, et cet. This is how the financial crisis is now escalating with central banks feeding fresh X into the market without limit on X, and - X going to minus infinity, like in Greece right now.

In the case (ii) of climate crisis X is about 350 W/m2 according to the Kiel-Trenberth energy budget, about the same as the total insolation from the Sun.

The equation 0 = X - X has a special property, which underlies the instability, namely that X is arbitrary. If there is no interest are no restrictions the loan X can be take any size, and if X is large then instability results: If X is large then a loss of even a small portion of X may be large and a financial crisis will result.

The Kiehl-Trenberth energy budget has the same property: X = 350 W/m2 is supposedly being motivated by a Stefan-Boltzmann law, but the motivation is weak being based on a False-SB:
The exchange X in the Kiehl-Trenberth is fictitious and could be anything, and if it is chosen to be large (= total insolation), then climate crisis results: With X = 350 W/m2 an alarming climate sensitivity of 3 C is claimed by CO2 alarmists.

Conclusion: The financial crisis is real because the equation 0 = X - X with large X is real and unstable, while the climate crisis is fictitious because the equation 0 = X - X in climate science with X large is unreal, in fact only valid for X = 0 and then not unstable.

If you are unsure of the meaning of the equation 0 = X - X, assume that you have no money (=0)
and then as compensation you go to the bank and borrow X = \$1 billion. Would you then say that you suddenly have become a billionaire?