Difference vs. differential

Factual Questions
1

As a television sports viewer, I’ve noticed throughout the years that American sports always (in my view) misuses the word “differential”.
There are discussions of “run differentials” and “point differentials” and a “10 second differential between the shot clock and the game clock.”

Am I not mistaken, but shouldn’t the word in all of the above situations be “difference”? Isn’t that the proper term? I only took two quarters of calculus, but I learned what a differential was and it didn’t involve subtracting two numbers.

So, has “differential” caught on in other non-sports fields? (no pun intended) Do engineers now use “differential” in place of “difference”?

Or is there no difference between the two words now? (pun intended?

2

What an odd occurrence … the response to two sequential but unrelated threads can be almost the same.
This works for both :

Difference vs. Differential

and

Stupid Math Question
(although the math question’s already been answered, I thought I’d post this anyway)

Whatever has happened with usage of the word ‘differential’ outside of the technical fields[sup]*[/sup], the distinction between difference and differential is still quite meaningful in at least one mathematical sense. Difference equations are for discrete steps (differences), differential equations are for the continuous case (as you probably know, the differential works using infinitesimal differences).

As an example, consider compound interest : If you compound it at regular intervals – say r% a year, you wait until a year is up, then multiply by the rate and add to it to get the new amount.
This gives you the difference equation

V[sub]n+1[/sub] = V[sub]n[/sub] * ( 1 + r/100)

The solution to this difference equation for any V[sub]n[/sub] is :

V[sub]n[/sub] = V[sub]0[/sub] * (1 + r/100)[sup]n[/sup]

where V[sub]0[/sub] is the starting principal. This is the same formula that diamud posted.

But if instead of computing the interest after the period of time, you computed it continuously, you’d get the differential equation

v’ = r*v with v(0) = P, the starting principal,

and v’ denotes the time derivative of v. The solution to this equation is :

v = P**e*[sup]rt[/sup] (which was posted by Cabbage)

It all depends on how you compute the interest, although as you make the interval smaller in the discrete case, you of course come closer to the continuous case. Most credit card companies that I know of compound daily (check the fine print).

For more information, there’s a free (GNU copyleft) textbook titled “Difference Equations to Differential Equations” available in postscript and PDF formats at http://math.furman.edu/~dcs/book/
panama jack

[sup]*[/sup] Anyone who uses “American sports” as a singular conscious entity is pushing the language just a little bit, BobT. I don’t find these changes in language objectionable.

3

To be more precise, I was referring to sports broadcasters in the United States.

I believe that they are using the word “differential” instead of “difference” just because it sounds more intelligent even though it’s not the right word.

4

From Merriam-Webster:

Sorry, BobT but I think they are justified.

5

I’ll agree with douglips (and Merriam-Webster) that the word is correct, but I think you do have a point – sportscasters use words that they think will make themselves sound smarter, and this could be one.
It’s almost just a different way of speaking, though, since they seem to know that they’re speaking this way, but also know that they’re being understood. Often words with superfluous syllables are favored – thus differential, audibilizing, escapability, etc. The words themselves aren’t really wrong, it’s just that shorter words would convey the same meaning.

Sometimes there are outright errors – during the Raiders-Dolphins game last week, one of the commentators was talking about a Dolphins lineman (or maybe a back) and what the Raiders had done to prepare, and he said “The Raiders have nothing but platitudes for this guy. Even they admit he’s one of the best in the game.”
It’s possible he meant to say “plaudits”, but one can’t be sure.

6

Difference is either a noun or a transitive verb depending on how you use it.

Differential is either an adjective or a noun depending on how you use it.

What? That doesn’t answer your question?

When I used to teach electronics related math, I always used “difference” as a noun when performing a simple subtraction problem:

A mixer produces a difference *frequency when two unequal frequencies are input.

But I used “differential” when I needed an adjective to describe a circuit that performs algebraic addition:

A differential amplifier amplifies the difference between two input signals.

Differential can also be used when it is part of the proper name of something; a differential equation, a differential gear, but it still works as an adjective in these cases.

In several reference books I have checked, Difference is always listed as a noun first, verb second. Differential is always listed as an adjective first, noun second. And where Differential does appear as a noun, it’s always related to some highly technical or engineering field like differential gears, differential coupling or differential coefficient. They way your sportscasters are using it (a noun meaning the result of simple subtraction), it just doesn’t sound right.

“10 second differential between the shot clock and the game clock” makes about as much sense as “the differential between 9 and 12 is 3”. Sure I’d understand what you meant, but I’d also wonder who the hell you thought you were by saying it like that.

7

I think this must be a US/UK thing. When I read the tiebreaking procedures for soccer competitions, they always make reference to “Goal difference”.

But the NFL always talks about “Point differential”.

8

The use of longer words by sports broadcasters is one of the ways their jargon differs from ordinary speech. In everyday speech, we frequently develop clipped forms such as sync instead of synchronize or memo instead of memorandum. This makes conversation faster and easier.

Sports broadcastese goes the other way; they use words with extra syllables. The reason, as far as I can tell, is that they have a lot of dead time to fill. For example, I recently timed the last 3 game-clock minutes of a close basketball game at almost a half hour real time. There’s only so many beer and SUV commercials they can show, so they have to fill the rest of the time with idle chatter. The extra syllables on words helps do this.

9

I find that to be a very ineffective way to use up air time.

Strike that- it’s an ineffectual way to use up air time.