Did von Neumann coin the eth or dyet for the inexact differential?

[nomadreid]

TL;DR

I was told that John von Neumann suggested the use of the lower-case dyet (D-with-stroke, crossed D) instead of the customary lower-case delta for the inexact differential.The related letter eth is used as a certain differential operator, so perhaps that is what my source meant. In any case, I have not been able to find any confirmation of a link to von Neumann. Did he ever suggest the dyet or the eth for the inexact differential or anything else? (And was the dyet ever used?)

Today the inexact differential is usually denoted with δ, but in a text by a Russian author I found a dyet (D-with stroke, crossed-D) instead:

In response to my question to the author about this deviation from normal usage, he stated that this was a suggestion from von Neumann. (Which of course does not justify its use in a modern text if it has not become standard, but that is another matter.) The closest I could find was a usage of the similar-looking eth

“The letter ð is sometimes used in mathematics and engineering textbooks as a symbol for a spin-weighted partial derivative.”
https://en.wikipedia.org/wiki/Spin-weighted_spherical_harmonics#Eth

Even if the author replaces the dyet by the eth, I am not sure that he is using it correctly, but that is not the point of my question. Historically, is there any connection between von Neumann and either the eth or the dyet?

(I apologize if this is not the right rubric -- since this is more the history of mathematics than of mathematics itself-- or whether a historical question even is allowed in this forum. If it is deleted or moved, then OK.)

 

[Haborix]

Wikipedia cites Carl Neumann as the source of the notation.

 

[nomadreid]

Thanks, Haborix. That would seem to clear it up partially. Wrong Neumann... However, I went to the source cited by Wikipedia, and what I found was that Carl Gottfried N. used a d with a bar above it

not a dyet. True, Carl didn't have a word processor, so I wonder if he was trying to just put a bar above a Latin d just as one might put a prime or an asterisk, or whether he was trying to imitate a dyet, or whether it started as a d-with-bar-above and morphed into a dyet. Wikipedia doesn't give any other source for its claim...

 

[atyy]

Thanks, Haborix. That would seem to clear it up partially. Wrong Neumann... However, I went to the source cited by Wikipedia, and what I found was that Carl Gottfried N. used a d with a bar above it
View attachment 269983
not a dyet.

In Neumann's book cited by Wikipedia, it looks to me like the bar is connected to the d (although it doesn't cross the d).

The notation I learned is d with a bar crossing the top. Mehran Kardar uses this in his notes and book.
https://ocw.mit.edu/courses/physics...chanics-of-particles-fall-2013/lecture-notes/
https://www.amazon.com/dp/0521873428/?tag=pfamazon01-20

 

[nomadreid]

Thanks, atty.

On the lecture notes link you gave, I presume you are referring to one of the lectures in thermodynamics, but even then there are four of them -- could you save me the trouble of going through them all by being a bit more specific in which lecture (and possibly even which page) Prof. Kardar introduces the notation?

I do not have ready access to the book, but thanks for the recommendation all the same.

In Neumann's book cited by Wikipedia, it looks to me like the bar is connected to the d (although it doesn't cross the d).

Yes, in the original it does look as if the bar is connected to the top of the d, but I suspect that this is just due to the limits of the typesetting at the time, and the fact that the vertical line of the d goes up to the top of the possible place for symbols on the line: for instance, it is possible that the same attempt to add a bar to an "a" would show the bar as not attached.

Another hint is that in that text, Neumann introduces two "marked" d's, one with a longer bar at the top, and one with a smaller bar at the top. This seems to speak for an "addition" to d rather than an alteration of the d.

Unfortunately Carl Neumann is no longer around to ask...

 

[atyy]

On the lecture notes link you gave, I presume you are referring to one of the lectures in thermodynamics, but even then there are four of them -- could you save me the trouble of going through them all by being a bit more specific in which lecture (and possibly even which page) Prof. Kardar introduces the notation?

https://ocw.mit.edu/courses/physics...-fall-2013/lecture-notes/MIT8_333F13_Lec1.pdf (Eq I.12, Eq I.13)

 

[nomadreid]

Super! Thanks, atyy. That helps!