How to express in physics if some value depends on a variable? Dependence, or dependency? And what about the plural? [duplicate]

In physics, people very often measure some values which depend on some variable, say the air temperature as a function of time. I think the verb depend is used correctly, since dictionaries define "dependent variables" and "independent variables". The resulting data (mostly shown in graphs) reflect something which mathematicians use to call a function (which would have a rigorous definition), but since the measurement involves often numerous parameters, physicists commonly call the result a dependence.

Is this correct? I have not found any dictionary definition of "dependence" which would express this relation between the imposed variable and the result.

The plural seems even more problematic. One may measure the air temperature and humidity in parallel. Is it then correct to say that the given graph contains these two dependences? Dictionaries say "dependence" is a mass noun, so there would be no plural. The plural can be found in Wiktionary, but without any explanation. Or should we use the word dependencies? For "dependencies" I can not find a suitable dictionary definition either.

• Not really; my question was only aiming at the usage concerning the data shown in graphs. Mar 24, 2021 at 13:37

This Science Direct article contains typical statements:

• Temperature dependence of the resistivity in a U3As4 single crystal was measured as shown in Figure 2 ....

• Temperature dependence of the elastic moduli Bij is another important anharmonic effect. This temperature dependence in quasiharmonic approximation results from ...

• The temperature dependence of viscosity of several melts is illustrated in Figure 7 ...'.

The non-count usage is certainly used in the first two examples above; I'd argue that the third example is indeterminate. The distributive singular is often used ([speaking to an adult male audience] "When you get home, tell your wife you love her").

The plural usage can also be found in academic articles, such as

• Temperature dependences of fluorescence lifetimes in Cr3+-doped insulating crystals.
• Electron and gas temperature dependences of the dissociative recombination coefficient of molecular ions with electrons

{ie DRC = f(Te) and DRC = g(Tg)}

...................

In everyday English, dependence is often found in the noncount usage:

Another possible solution for minimising a person's dependence on family and friends outside the household is to recruit a relative to join the household.

[Cambridge English Corpus; Cambridge Dictionary] ('dependences' would be rare here)

and as CD says, 'dependency' is a spelling variant here.

• I know that many scientific papers contain these examples of usage. But many of these papers are written by non-native English users, so I am cautious - the editorial teams may not correct all mistakes before publication. These doubts of mine are supported by the absence of an appropriate dictionary definition, and strengthened by the fact than spell checkers, as a rule, do not accept the spelling "dependences". That is why I thought a native English speaker could give an answer more trustful than examples in scientific papers. Mar 22, 2021 at 12:35
• My two degrees are in chemistry, and I taught maths beyond A-Level. These are typical and authoritative usages. Dictionaries don't usually get as far as 'stipulating definitions' and technical usages (though CD has some relevant examples). Spell checkers are unreliable even for some everyday English. Mar 22, 2021 at 12:52
• Perfect. Thank you for your answers and for pointing out these imperfections of the dictionaries. For me as a non-native English speaker, it is not easy to put the dictionaries in doubt without additional strong arguments. Mar 22, 2021 at 13:25
• You can check more technical usages on Mathematics.SE; they have a 'terminology' tag. // The most problematic areas are, as with this case, usage/s in everyday language have different meanings and/or behave differently grammatically from those (stipulating definitions) used in the sciences or law or business etc. Mar 22, 2021 at 17:41