So, the long slope leading to the castle has come to be known as the Royal Mile. Steep staircases and narrow alleys (called closes or wynds) fan out from it, leading to hidden courts or down to the lowlands on either side. Labyrinthine, unpredictable, endlessly charming.

It gives the city a wonderful sense of texture, because each part has its own relationship with that geography and thus a miniature identity of its own. Like the low-lying Grassmarket, which is dominated by the castle and its imposing rockfaces.

And this geography is part of what gives Edinburgh its character, because it makes the city feel vertical. There are countless views that seem to defy gravity, with buildings apparently stacked on top of one another — concealing streets on different levels between.

Edinburgh is often called one of the world's most beautiful cities, but what makes it so special? Well, Edinburgh is built around an extinct volcano, and so it's a perfect example of how interesting geography leads to interesting architecture...