This paradox was invented by Zeno of Elea (c.490-430 BC). Zeno was one of the earliest Greek philosophers, active before the time of Socrates. He is mainly known to the world through Plato's depiction of him in the Parmenides. See below for a funny re-telling of the paradox of Achilles and the tortoise.
Napoleon's invasion of Russia was based upon a fundamental underestimation of the sheer size of the country. He assumed that his strike against the second capital, Moscow, would paralyse the entire empire; instead, Russia absorbed the blow and continued to function. The normal rules of surrender would have involved the Russians handing over Moscow formally and helping Napoleon find billets for his troops, but the Russians simply abandoned the city without comment, forcing the French to fend for themselves in the devastated city. The half-inadvertent Russian policy of avoiding engagement meant that even after the Battle of Borodino, and after the invasion of Moscow, Napoleon had still failed to deliver the knockout blow that would force Russia to her knees. Napoleon had not planned, nor could he afford, a long-drawn-out war in Russia; Spain was proving difficult enough in this respect.
The fire of Moscow destroyed the supplies the Grand Army needed in order to continue fighting, but Napoleon stayed in Moscow despite this seemingly because he couldn't make up his mind about what to do next. Three possibilities were open to him: to press on to St Petersburg and attack Tsar Alexander; to stay in Moscow until the spring, then try again; to retreat back the way he had come. He didn't have the necessary resources to pursue either of the former options, so retreat became the only answer. Napoleon's unwillingness to accept this led to the dangerous delay in Moscow that pushed the retreat into winter.
Saragossa was besieged twice during the Peninsula War, in 1808 and 1809. During the first 61-day siege the Spanish forces successfully withstood attack by the French under General Jean-Antoine Verdier, although the town's defences were largely destroyed. The Spanish Captain-General Palafox became a national hero. However, the following year, the French Marshal Moncey approached the city once more. Palafox quickly started to repair the city's defences, and another long siege ensued. After Saragossa's defences were breached, fighting continued from house to house; the French were even forced to storm the town's convents and monasteries. Eventually the Spanish were defeated with the loss of around 54,000 lives. This siege is now known as one of the most deadly and vicious battles in the Napoleonic Wars.
Unsurprisingly, given the climate, the oven was at the heart of any Russian peasant's home. The traditional peasant cottage (izba) would be made out of logs, with a huge brick oven in the centre, often with two hearths: one for cooking and one for warming the house. Russian ovens are extremely efficient wood burners that use a complex chimney system to heat the bricks, ensuring that they have an extremely long cooling down period. A well-made oven would require fuel two or three times a day at the most. The structures are so large that during the Great Patriotic War (the Second World War) men used to hide from Nazi soldiers within their ovens. In the winter, people would sleep on shelves on top of the oven to keep warm.
Columbus's egg refers to the apocryphal story of Christopher Columbus's response to criticism. According to Girolamo Benzoni's History of the New World, Columbus was told that his discovery of America was nothing to be proud of, as it showed no special intellectual talent: anyone with his resources could have done the same thing. Columbus responded with a challenge, asking his accusers if they could stand an egg on its end. No one could. Columbus then took the egg, bashed one end slightly against the table to flatten it, and stood it on this end. His message was that just as in this trick, the voyage to America only appears easy after it has been achieved. The expression 'Columbus's egg' is now used to describe a solution that seems obvious after the fact.