Something I found interesting: The Mpemba Effect.

It is an observed phenomenon that under certain circumstances warmer water freezes quicker than cooler water. Its historical documentation goes all the way back to Aristotle; thinkers in the Middle Ages and the Renaissance (Francis Bacon, Descartes for example) also observed it. After the "advance" of thermodynamics in the 19th century, this observation is relegated to the status of urban legend: for it is just "unreasonable" that something warmer can cool down faster than something cooler.

The classical gedanken experiment goes something like this

Say I have water at temperature T₀, which I know takes 10 minutes to chill to the freezing point (roughly 273K) of water, and it takes another 5 minutes to freeze after that. Say I now have the water at temperature T₁ > T₀, and I know that it takes 3 minutes for the water to chill from temperature T₁ to T₀, then it should take 10 minutes to chill to the freezing point, and 5 more minutes to freeze, and so should take, over all, 3 more minutes to freeze.

What a lot of "intellectuals" don't realize is that sometimes simplifying assumptions are just presumptions. This is best summed up in the joke:

A dairy farm owner wants to increase his daily output of milk, yet he doesn't feel comfortable with purchasing more cows. So he hired a psychologist, an engineer, a bio-chemist, and a mathematician to see what he can improve on his farm. After one week, he gets into a meeting with the four of them.

The psychologist starts excitedly about this new research he read in PubMed about Mozart making people smarter, and how he spent the week with his allowance of 2 cows and found out through experimentation that Beethoven's Pastoral Symphony can increase milk output by about 3 percent.

The engineer scoffed at such an unsound idea and presented his invention: a machine to forceably suck milk out of the udders.

The bio-chemist, aghast at the engineer's lack of respect for lifeforms, interjected with his compilicated analysis of the lower intestinal germ culture in his allowance of 2 cows and explains his desire to spend more time finding out how to make a medicine to change the balance just right so more milk would be stimulated.

The owner turns to the mathematician, and asks, "How'bout you, any simple answer that I can understand?"

"Sure, suppose we start with a spherical cow..."

The "spherical cow" in the thought experiment is the assumption that water is completely characterized by its temperature. In reality, water is a complex system: it has interplay between thermodynamics (measured by temperature, pressure, and volume) fluid dynamics (affected by the shape of the container, pressure, and viscosity) and chemistry (changed by the amount of impurities and their characters, which can be in the form of both solvents [gasseous, liquid, or solid] or suspended particles). Considering just temperature is over simplifying.

The Mpemba effect is one that is still not well understood. The number of variables that could effect the observation (yes, I used the word "effect" correctly) is very large and the underlying physical theories rather incomplete. But at least by experiments several explanations can be ruled out (for example, since the observation persists when water is placed inside a closed container, evaporative mass loss on the warmer sample is ruled out as a viable explanation).