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How dragons can fly: a mad science explanation

A recurring problem for fantasy/scifi writers is people pointing out what they consider to be factual errors. Now, with the help of illness-induced halucinations, our mad scientist will provide you with a scientific explanation of one of these:

How dragons can fly

Problem: Dragons are way too big to fly.
Solution: Blame pixies.

Like most appearant problems in a fantasy universe, this one too can be blamed on pixies. In this case, the mere existance of pixies in the universe makes it scientifically possible for a dragon to fly.

To explain this, one must only look at statistics. In statistics, an occurance is considered truely random if the population of possibilities is uniform. This means that if there are ten possible values, each of them has an equal chance of occuring (being 1 in 10).
Now, statistically speaking, if you take several such random values and add them together, the resulting value is not truely random anymore. Instead the population of posibilities forms a bell curve.
It is these statistics with which nearly all experimental data is analysed.

In a fantasy universe however, the existance of pixies excludes the existance of statistics. This is not merely because statistics are dull and boring, but has a more mathematical reason. After all, a pixie can generally be considered to be an aproximation of true randomness. However, if you add several pixies together, what you'll have is a sum that is MORE random, not less, thus invalidating all of statistics.

Since aerodynamics is at best a guessing game based on statistics anyway, it's clear that the laws of flight do not apply to a fantasy universe any more than the laws of gravity apply to a cartoon universe.

In the end, the science has to be redone to come to a set of aerodynamic laws that fit the universe. For this to be valid, the observation that dragons can fly would have to be an inherent part of the calculations. Therefore, it can be said that dragons can fly, because dragons can fly. This may seem silly, but when you dig deep enough you'll find that nearly all science in any universe boils down to similar statements.

To satisfy the cravings of those unable to wrap their minds around that, here's an alternate explanation.

The original statement was: Dragons are too big to fly using muscle power.
This statement would not even be correct in our (real) universe. After all, it presumes that volume = mass, which is not the case. Dragons are, after all, hot. They are fire based creatures. They breathe fire. They're hot.
Therefore dragon flight can be explained by looking at a dragon as a big hot air balloon with wings. Like a fish has an airsack to adjust its depth in the water, so do dragons have huge hot air sacks to provide extra lift.

Even so, it's not recommended to tell a dragon he's full of hot air.