Question regarding the use of "function of"

The phrase “function of” means “a relation such that one thing is dependent on another”.
Yet the following use of it (below) conveys the meaning (to me at least): “as a result of”.

I would like to know if the use of “function of” has another meaning besides “dependent on” or am I misreading the use of it below?

“violent crashes that punctuated the Gilded Age—a function, in part, of the era’s rampant financial chicanery”.

I look forward to your feedback.
Here in full:

“Toil as he may, the steelworker’s chances of advancement seemed vanishingly small. Meanwhile, the violent crashes that punctuated the Gilded Age—a function, in part, of the era’s rampant financial chicanery—consigned plenty of industrious, abstemious men to poverty.”

“A function of” usually means “was influenced by.” It’s not usually used to denote a full cause/effect relationship, but rather suggest that one thing merely played a strong role in something else. It seems normal here to me.

Thanks Jragon. I was going by this definition I found online: “a relation such that one thing is dependent on another”. Is it wrong?
“influenced by” does make better sense.
What about the following usage, though, from the the same article
“If success was a function of a man’s good character, then failure must be evidence that his character was weak.”
Would you say “influenced by” or “dependent on” as a substitute for “function of” makes more sense?

It is often used loosely, and more or less metaphorically.

So what would be a good workable definition in your opinion njtt?

This particular sense of the word comes orginally from maths, where “function” means “a variable quantity regarded in its relation to one or more other variables in terms of which it may be expressed, or on the value of which its own value depends”. (We owe the mathematical sense of “function” to Leibniz, apparently.) In this sense we can say that the circumference of a circle is a function of its radius.

The word is used in a similar sense in scientific disciplines. So we can say, for example, in physics that the momentum of a body is a function of its mass and its velocity.

It gets used by analogy in non-mathematical and non-scientific contexts to point to a relationship, even if the relationship can’t be expressed as an inflexible rule. The quote in the OP is suggesting that there is a relationship between a climate of rampant financial chicanery and regular economic crashes.

Thanks UDS. I do understand that the phrase “a function of” is used to signify a relationship, but because of the vagueness of the term, I was prompted to ask the question. I was trying to narrow down some comparable phrases that might work and make more sense, such as “dependent on” or as jragon suggested “influenced by”. I believe the examples I’ve listed highlight the confusion (at least for me) that the phrase “function of” can generate.

Replace “function” with “effect”, because the meaning I get is
“violent crashes that punctuated the Gilded Age—an EFFECT, in part, of the era’s rampant financial chicanery”.
A function is usually attached to some entity or thing… like a Reserve Bank ,or a thing like a transformer, or a mathematical equation of course.
The sentence quoted attaches function to “chicanery” which seems wrong… “Chinanery” is only a thing in that its a collection… its the name of a category of actions (so to expand the list, one would put a list of verbs… )
Yes the intention of the chicanery is to allow buying low and selling high, but there’s no specific entity or thing to have the function… Nuances like a function being government or good or something may also come into , but gets complicated… do you let villians have a function ? probably not.

Yes Isilder. “Effect” sounds reasonable for no. 1. (All three examples are from the same article.) 2. “influenced by” or “dependent on”(?)could replace “function of” 3. ? dependent on?

  1. Meanwhile, the violent crashes that punctuated the Gilded Age—a function, in part, of the era’s rampant financial chicanery—consigned plenty of industrious, abstemious men to poverty.
    2.If success was a function of a man’s good character, then failure must be evidence that his character was weak.
  2. But Lawrence wasn’t merely a living exemplar of Poor Richard’s maxims. His popularity among antebellum success writers was also a function of his religious rectitude.

It is intentionally vague. As UDS says, it signifies that there is a relationship between X and Y, but it is a way of saying that without committing yourself to anything as definite as whether X is a cause or an effect of Y, or whether the relationship is just one of covariance or of influence rather than direct cause, and, if it is influence, it still leaves open whether X is influenced by Y or is an influence upon Y (or perhaps each influences the other).

If as you say it signifies a non-committal relationship between X and Y, in which cause and effect remain vague, as does the question of who influences whom, my question then has to be

Why be vague? Why not be explicit?
The author of the article seems very comfortable with the phrase. He uses it three times, and in each case it seems to convey something different. He must have a specific idea of the meaning he’s trying to convey with the phrase. By simply leaving it at “a vague X/Y relationship”, I don’t see how anyone can get comfortable using it.
What I’m really trying to get is a working definition that would satisfy any use of it. Any suggestions?

A function is a relation (that is, a set of ordered pairs), no two of which have the same abscissa.

There. Perfectly clear.

Because you do not know, or are not sure, exactly what the relationship is.

With historical relationships, such as the one in your example, this will be often be the case, although it is probably fair to say that if someone overuses deliberately vague expressions like this (especially the same one, over and over) they are probably a bad writer, or a wooly thinker, or both.

Thanks Senegoid and njtt. Good answers. Thank you all.

I couldn’t resist… The function of villains is to keep the police occupied.

Nicely done, except it doesn’t cover multivariate functions. Would replacing “pairs” with “n-tuples” work?

Regarding the OP’s question, a something can be a function of x AND other variables, so there is no implication that x is the only variable that determines the resulting value.

Also, in common language, “function of” is often used when there might be multiple abscissas, and most of us wouldn’t object. I.e., “if x is A, we get alpha. But if x is B, we could get beta or gamma or both.” Nonmathematical types might use the word “function” here even though it’s not mathematically applicable. (And yeah, there are ways to force it into a function returning sets, but I won’t go there.)

I think all these references to the mathematical sense of “function” are probably less than helpful, and may be actively misleading. In the example given in the OP, the word is certainly not being used in its mathematical sense. Its use, there (and in similar contexts), may, perhaps, be a metaphor derived from the mathematical sense of the word, but that is far from being a given. The word “function” in English (quite apart from its French and Latin roots) goes back to the 1530s, whereas its mathematical sense probably does not go back before Leibnitz introduced it in 1692.

I would go so far as to say that I think it is very probable that for the majority of words that have both a mathematical sense and one or more non-mathematical senses, the mathematical sense appears later than, and derives metaphorically from, at least one of the non-mathematical senses. (Despite their vaunted precision, most mathematical terms are, ultimately, metaphors.)