## Del or Nabla?

I am today preoccupied with vector calculus so, following on from yesterday’s notational rant, I am wondering about the relative frequency of usage of names for this symbol, commonly used in math to represent the gradient of a function ∇f:

To write this in Tex or Latex you use “\nabla” which is, or so I am told, so called because the symbol looks like a harp and the Greek word for the Hebrew or Egyptian form of a harp is “nabla”:

When I was being taught vector calculus many moons ago, however, the name always used was “del”. That may be a British – or even a Cambridge – thing. Here is an example of that usage a century ago.

Anyway, I am interested to know the relative frequency of the usage of “nabla” and “del” so here’s a poll.

There may be other terms, of course. Please enlighten me through the comments box if you know of any…

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### 12 Responses to “Del or Nabla?”

1. John Peacock Says:

I blame Donald Knuth for this, calling it \nabla in TeX. Strangely, though, that symbol is a scalar and you have to work quite hard to make it come out in bold font, as is needed since del is a vector and a scalar del is wrong (except in 1D). However, this error is as nothing compared to what Knuth has done to the rationalised Planck’s constant, h/2pi. Every time I start a lecture course with any quantum in it, I ask for the name of that symbol. Depressingly, the reply is inevitably in accord with Knuth’s notation: “h-bar”. So I then have to go on a rant and explain that the proper name for the physicists’ Planck constant is “h-cross”. The name “h-bar” clearly refers to h with a bar above it, in analogy with “h-tilde”. To summarise, the TeX for h-cross is \hbar and the TeX for h-bar is \bar{h}. Donald, why did you do this?

• Wikipedia says, “TeX … is a typesetting system which was designed and written by Donald Knuth and first released in 1978.” But my undergraduate quantum mechanics course, in 1972, called it “hbar”, as probably did the earlier introductory chemistry and physics classes in 1970 and 1971.

• John Peacock Says:

Well, Knuth must have picked up the habit from somewhere. Where were these courses? I suspect it’s maybe a transatlantic thing, like the pronunciation of quark.

• telescoper Says:

We all have a cross to bar…

2. “I blame Donald Knuth for this, calling it \nabla in TeX”

I believe we can blame Edinburgh for nabla … because the term was certainly popularised (and perhaps originated) by Peter Guthre Tait.

In fact, I think Maxwell, Tait and Thomson all used nabla.

3. My lecturer in vector field theory in 1976 called it nabla. When I lectured the same course 13 years later (which was strange..) I hence also called it nabla. Think difference between calling it nabla and del is more a function of age than anything else – my lecturer was a senior middle-aged academic and presumably had been taught it as nabla. Now it appears to be mostly called del.

My UG quantum mechanics course called h/2pi hbar, and that was before the existence of TeX.

4. Peter has posted twice on notation in vector calculus. So maybe I can recommend the book

Crowe, “A History of Vector Analysis”, Dover

It sounds deadly dull — but it is absolutely superb reading.

The Vector Wars were at least as bitterly fought as the Hubble Wars.

It explains how we ended up with the notation of today (largely through the efforts of Heaviside & Gibbs).

It is almost the only English-language source on the sad life & contributions of Grassmann (who never had a University education in mathematics & was denied a University position, working on his own as a high school teacher).

5. During my time at Cardiff, I remember hearing both del and nabla in use! I can’t remember what you may have used Professor Peter?

6. Arttu Rajantie Says:

To avoid this issue, I just call it the gradient (or divergence or curl), rather than referring to the symbol itself.