Mineralogy
"Hardness" is determined by comparison with other minerals. In the Mohs scale, a standard set of minerals are numbered in order of increasing hardness from 1 (talc) to 10 (diamond). A harder mineral will scratch a softer, so an unknown mineral can be placed in this scale by which minerals it scratches and which scratch it. A few minerals such as calcite and kyanite have a hardness that depends significantly on direction. Hardness can also be measured on an absolute scale using a sclerometer; compared to the absolute scale, the Mohs scale is nonlinear.
Blade
Typically blades are made from a material that is about as hard, though usually harder, than the material to be cut. Insufficiently hard blades will be unable to cut a material or will wear away quickly as hardness is related to a material's ability to resist abrasion. However, blades must also be tough enough to resist the dynamic load of impact and as a general rule the harder a blade the less tough (the more brittle) a material. For example, a steel axehead is much harder than the wood it is intended to cut and is sufficiently tough to resist the impact resulting when swung against a tree while a ceramic kitchen knife, harder than steel, is very brittle (has low toughness) and can easily shatter if dropped onto the floor or twisted while inside the food it is cutting or carelessly stored under other kitchen utensils. This creates a tension between the intended use of the blade, the material it is to be made from, and any manufacturing processes (such as heat treatment in the case of steel blades that will affect a blade's hardness and toughness). A balance must be found between the sharpness and how well it can last. Methods that can circumvent this include differential hardening. This method yields an edge that can hold its sharpness as well as a body that is tough.