## Thursday, August 20, 2009

### Drop in World Temperatures?

Robert S. Boyd of McClatchy newspapers writes:
Official government measurements show that the world's temperature has cooled a bit since reaching its most recent peak in 1998.
Can we mathematically prove this amazing result? Let's try.

THEOREM: The world's temperature will always cool after reaching its most recent peak.

PROOF: Let X be a series {X1, X2, ..., Xn}. Let Xmax be the largest element in X. The "peak" of the set X is defined as that Xi for which Xi > Xj for all i not equal to j. Therefore Xmax > Xi for all elements in X not equal to Xmax. Therefore Xi < Xmax for all i not equal to max, by the principle of trichotomy.
Now, Let Ti be a time series of temperatures. By the lemma above, all temperatures other then Tmax are less than the maximum tempertature, i.e. "cooler" than the maximum temptrature (the peak). Thus all temperatures are cooler than the most recent peak. Q.E.D.

EXAMPLE: Consider the set of average mean tropospheric temperature anomalies as determined by the University of Alabama: June 2009: +0.01°C July 2009: +0.42°C
Clearly, Tjuly > Tjune, so by the theorem above and the principle of trichotomy Tjune < Tjuly. That is, the world is on a warming trajectory, at a rate of 492 degrees per century.