Mohs scale of mineral hardness

Mohs scale of mineral hardness was created by the German [Frederich Mohs]?. He based it on ten readily available minerals. The scale is not linear, for example corundum is twice as hard as topaz.

Hardness	Mineral	Absolute Hardness
1	Talc?	1
2	Gypsum?	3
3	Calcite?	9
4	Fluorite?	21
5	Apatite?	48
6	Orthoclase?	72
7	Quartz	100
8	Topaz?	200
9	Corundum	400
10	Diamond	1500

The table has been extended

Hardness	Mineral
1	Liquid
2	Gypsum
3	Calcite
4	Fluorite
5	Apatite
6	Orthoclase
7	Vitreous pure silica?
8	Quartz
9	Topaz
10	Garnet?
11	Fuzed zirconia?
12	Fuzed alumina?
13	Silicon carbide?
14	Boron carbide
15	Diamond

Question: if the scale isn't linear is there a linear scale that geologists prefer to use? And what exactly is 'absolute hardness'? How is hardness defined (we know what it is intuitively, but what is its physical definition?) Are there SI units for hardness? -- SJK

There is no absolute hardness scale. No units for hardness either. As for what "hardness" really is, I think that is an open question. It would certainly be related to [fracture toughness]?, but that defies analysis as well, relying on laboratory testing and depending on the geometry of the specimen.

Isn't part of the definition of hardness the scratch test (if you can scratch something with something else, that something else is the harder of the two)?

Thats the point of the Mohs scale. Frankly, the most useful materials for hardness testing in the field are fingernails (hardness 2-3) and pocket knives (hardness 5-6). Used in conjunction with luster, crystal habit and color, fingernails and pocket knives do a pretty good job.