Grammar - Scientific English (Physics) [duplicate]

I have a question about scientific English. I wonder when to use the article "the" when you refer to a physical quantity or to a formula. I promise that I have looked into so many manuals, but I am still terribly puzzled.

As I compared many textbooks and scientific articles, let's start from the cases I am sure about.

One always reads:

"the function f(x) is defined as ..."
"the functions f(x) and g(x) are defined as ..."

but, on the other hand, one (almost) always reads:

"Point A is defined as ..."

"Points A and B are defined as ..."

Now, both "point" and "function" are countable nouns and, moreover, by saying "f(x)" and "A" you refer to a specific function or point. So, why do I use "the" in one case and zero article in another?

Another puzzling case is uncountable nouns such as "conductance" or "energy". You, basically, can find whatever situation. I take the next examples from the same article written by native English-speakers (and supposedly corrected by a language polishing service):

"the values of conductance are..." "the dependence of the conductance at the neutrality point is..." "The conductance G(E) is determined in a standard way..." (notice the attribute G(E))

Can you help me to rationalize all this?

Finally, when you refer to a Figure/Table/Section/Equation/Chapter you always use zero article:

"As seen in equation 5 ..." "..., which was shown in Section 3 ..." etc.

Am I right?

Solution 1:

"The" is used with the description of a thing which is present already in the context of the discussion. Often there is no objective way of predicting whether "the" is appropriate, because it is used by a writer to convey what he thinks the context is like.

For instance, if you write "Being a metal, this substance has a conductance, and we measure the conductance thusly ...", it is evident why "the" was used before the second occurrence of "conductance" -- it refers back to the assumed conductance of this metal. But it would often be appropriate to omit the background assumption, since it would be known or at least deducible by the reader. So you might write just "We measure the conductance of this thusly ..."

Since it has this anaphoric function of referring to background assumptions, "the" can be used as an indirect way of conveying information about the background.

Solution 2:

This is a long question with many parts. I'll focus on one. You give the exemplar:

"Point A is defined as ..."

Now look at the following examples:

1.

"Examine this diagram. On it I have highlighted a particular point. The point, A, occurs at the junction of lines L and M."

This means

"Examine this diagram. On it I have highlighted a particular point. The point, which I shall call A, occurs at the junction of lines L and M."

You can see that 'point' is in lower case. This is because the word 'point' is an ordinary noun. It is not a proper noun. It has recently been mentioned so it requires the definite article.

2.

"Examine this diagram. I have labelled several points. Notice that Point A occurs at the junction of lines L and M."

In this case "Point A" is the name of the point. Therefore it requires a capital letter and no article.

You may be able to generalise from this to answer some of your other questions.

Solution 3:

The points in geometry have names, they are marked with capital letters. So when the text says "point A" it is exactly determined which point is meant and it is unnecessary to use the definite article.

As a general rule one can say English has a tendency to drop the definite article when it does not achieve much. One can regard this as a kind of shortening.

It is not possible to cover this tendency in clear-cut rules. The only thing to do is to observe the English language and see where the definite article can be dropped without loss of clearness.