rarity

As rarely are subjective things, events or substances when their share of a basic total amount less than about 1 percent is. This corresponds to a quantity ratio of 2 (decimal) orders of magnitude or more. Usually, rarities are spatially or temporally inhomogeneously distributed , which is rare in one place or at a given time, need not necessarily be rare in another place or at another time.

Rare objects or substances serve in human civilization - as long as they meet minimum requirements of transportability, harmlessness or convertibility - as value carriers that one seeks to increase. In human history, these include precious metals in particular .

Example: frequency of elements

Many distributions in nature follow the laws of scale . This also includes the frequency of the chemical elements . In the following semi-logarithmic representation you can see that the number of "rare" elements in the earth's crust is astonishingly high: The 9 most common elements make up more than 99% of the total material (arrow). Of the total of 85 elements considered, 76 make up less than one percent of the earth's crust - a percentage of 76/85 * 100, ie over 89%! So "rarity" is a relatively common phenomenon in this example. The same applies to the distribution of words in a text corpus according to Zipf's law .

The distribution roughly follows an exponential law of scale, with significant deviations from this for the highest and lowest-ranking elements. The data for the presentation come from UNI TERRA. The frequency f and rank r are roughly correlated here in the linear section of the rf relationship as:

${\ displaystyle \ log (f) \ approx 3.5890661-0.0675046r}$