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Could someone with an early edition of Men at Arms by Terry Pratchett, first published by Victor Gollancz Ltd in 1993, please answer with Detritus' equation?

In the scene where Detritus the troll is in the Pork Futures Warehouse, two equations are mentioned. The second equation ends with an equal sign and may have something to do with HHGTTG. I am interested in the first equation. The passage (near the middle of the book):

That meant he'd become stupid again, as sure as
equation here
Better make the most of it, then.

In my book (HarperTorch, 2000 Jul, page 194 of 377) the equation is:

from book one

This does not appear to me to be a proper equation, I suspect that it has been corrupted.

I think I understand why the equation might get corrupted. Fiction publishers do not normally print advanced mathematical equations. This publisher may not have been aware there was an equation in the data file for the book. And no one checked to see that the equation was printing correctly.

I found an online book with an equation that is a bit different (page 161 of 318):

from book two

This equation looks to me like it may be proper, but I am not certain. A collegue pointed out that N should be added to both sides to simplify the equation -- probably also corrupt.

I can imagine Pratchett flipping thru an advanced maths text book and picking an equation that looked interesting. Or he may have asked a mathematician associate, "hey Frank, I need a complicated equation for a super-cooled troll in a new book ... no, that's too long, about half that length ... that'll do! Thanks." I have not stumbled across anything about this equation while searching the Internet, if anyone knows something about it, please let us know.

I'm hoping that the correct equation is in an early Victor Gollancz Ltd edition, assuming that Pratchett would have inspected and corrected the galley proofs prior to first printing. If someone has an early edition, please answer with an image of the equation, the publisher, year of printing, the page number of the equation, and the page number of the story end. Consider cropping the image to just the passage mentioned.

On the copyright page, if there is another publisher in addition to or instead of Victor Gollancz Ltd, then I suspect the equation might be corrupted. It might be interesting to see other corrupted versions of the equation, one wonders just how bad the equation can get. Please include the requested information.

Once I have the (hopefully) correct equation, I will ask elsewhere (math or physics SX?) to actually identify what the equation represents.

==== update 2020 Dec 13

Trying to identify the equation at Identify equation in "Men at Arms" by Pratchett.

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    The only possible definition of "G" I can think of is Gauss' Constant (approx. 0.83) and I don't recall any expressions that use it as an exponent. Overall it looks like it's riffing on gravitational force ( G m_e m_o ) / r^2, which in SI is measured in Newtons ( N ), but it's most likely gibberish. – DavidW Nov 21 '20 at 4:24
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    The quantities M_e/M_p and α are the two important small quantities that up come up all the time in atomic physics, so the version with α is almost certainly closer to what the author intended. I may be able to figure out what it's supposed to be, and if I do, I can explain it without you having to ask again somewhere else. – Buzz Nov 21 '20 at 4:41
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    This audiobook, goldenaudiobooks.com/terry-pratchett-men-at-arms-audiobook (disk 5 at about 45:20), has yet another version, most notable for changing the Greek letter to an omega. – Buzz Nov 21 '20 at 5:19
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    Were I a betting man I would put my money on what @DavidW says: It's gibberish. I also note that I can remember seeing 10^-3 in an equation in any scientific paper I have read, divide by 1000 would be preferred, and it would also be very strange not to simplify the exponents of alpha and the expressions involving N. – Ian Bush Nov 21 '20 at 9:40
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    α⁶ is quite distinctive, and led me to this paper in European Physical Journal C. Equation 7 of that paper rearranges to give an expression (mₑ/(mₚα))⁶(c³/(ħG)) for the cosmological constant, where mₑ is the electron mass, mₚ is the Planck mass, α is the fine-structure constant, c is the speed of light in a vacuum, ħ is the reduced Planck's constant, and G is the universal gravitational constant. The paper says that its equation 7 has a provenance dating back to 1993, the same year Men at Arms was published.... – Daniel Hatton Dec 4 '20 at 1:01
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I have an early Victor Gollancz hardcover edition of Men At Arms, which appears to be from 1993. That's the only date on the copyright page (apart from the "right to be identified as author" date, 1988). That page also mentions Cassell, the immediate parent company of Gollancz.

The equation (on p. 150 / 288) looks almost identical to your HarperTorch version. Here's a LaTeX version of the equation. $$\mathrm{10^{-3}(M_e/M_p) \alpha^6\alpha^G-{}^{1/2}N\approx 10N}$$ which I used to generate the following image. (You can see a clearer preview of it by pasting the LaTex code into an answer box on Physics.SE or Math.SE, or any of the other sites that support MathJax).

Detritus equation

The equation is overall gibberish, but it does have some sensible elements, as mentioned in the comments. That superscript of ½ before N is pretty weird. Pre-superscripts do get used in isotope symbols, but they're always whole numbers.


I have to confess that I was a little annoyed by the gibberish equations in Pyramids and Men At Arms. Surely Pterry had access to scientists or mathematicians who could provide non-gibberish equations. Maybe he didn't have much close contact with such people until a few years later, when working on the Science Of Discworld books. Or maybe he knew full well what he was doing, and it amused him that those equations may annoy some scientific types. :)

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    Re: your last paragraphs. For a writer it would make perfect sense to include an equation that would appear to be gibberish, because he is trying to show that the level of advancement here is way above any current science we have. It is meant to be incomprehensible to anyone reading, including scientists. – Gnudiff Nov 21 '20 at 19:12
  • @Gnudiff That's a fair point. Advanced science & mathematics can certainly use notation beyond that used by current science (like that N with the pre-superscript). And G in that equation may be a pure number, not the gravitational constant. Generally, it doesn't make sense to add quantities with different units, or for exponents to have units. See physics.stackexchange.com/q/7668/123208 & en.wikipedia.org/wiki/Buckingham_%CF%80_theorem OTOH, also see physics.stackexchange.com/q/13060/123208 – PM 2Ring Nov 22 '20 at 3:25
  • Well, if you want to be pedantic about it, there is nothing that says in the book the notation has to have anything to do with the currently established algebraic one. – Gnudiff Nov 22 '20 at 7:19

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