The Voldemort Derivative

Patrick Reany

22 January 2024

With apologies, Potter couldn't make it here to present this, so I will in his place.

If you were given the function G(x,y,z(x,y)), and told that its derivative is

\partial_x G + \partial_z G \partial_x z,

you might ask yourself, as I did way back in 1982, what actual derivative has been taken on G?
What does it look like and what do we call it? I call this the Voldemort derivative, as the
mathmatical community can't seem to bring itself to give it a name and a symbol. It's taboo
for some reason. My explanation for this is that the mathematical community thinks of it as
a generalized derivative (that is, a generalization of the d/dx derivative), but calls it a
'partial derivative'. This schizoid way of looking at it must induce some form of
cognitive dissonance.

My solution was effected in the notational system I call Structured Differentiation (SD),
in which I boldly proclaim the Voltemort Derivative for what it really is,

(1)      \delta_x G = \partial_x G + \copartial_x G = \partial_x G + \partial_z G \partial_x z.

A mathematician replied to my post on sci.math about my SD (1999). We then had a back and
forth for eight posts. In the posts below, I gave him the alias Defender. In various
places throughout the posts, Defender begrudgingly conceded four points (at least
that's how it looks to me):

1. One need not duplicate a function symbol with its own variable symbol, or vice versa.
2. There is an inconsistency with applying a 'partial' derivative to a function that is not in
   primitive form, as the partial derivative is usually defined on primitive functions only.
3. The formalism used in SD is advantageous for some calculations.
4. To avoid confusion when taking a total derivative and then splitting it, one really needs
   separate symbols for both the total and explicit derivatives, as in Eq. (1) above.

The following are pdf versions of those exchanges, prefaced by a series introduction
of recent writing:

0. Series Introduction

1, Patrick's first response (15 Nov)

2. Defender's response (17 Nov)

3. Patrick's response (17 Nov)

4. Defender's response (18 Nov)

5. Patrick's response (18 Nov)

6. Defender's response (19 Nov)

7. Patrick's response (19 Nov)

8. Defender's response (22 Nov)