The Importance of Distance in Cluster Analysis

We can think about cluster analysis in two broad types. There's hierarchical and there's non-hierarchical. Both of them are fundamentally driven by this notion of distance. So if I start with everything having only one characteristic, right, like all your hot sauces having only whatever their scoville rating is based on how hot they are, I could line up all the hot sauces along that continuum. But now imagine I have two characteristics. One is how spicy it is and the other is the thickness of that sauce. Some are more runny and some are really, really thick,. Well those are really different variables, aren't they?