Dany expresses his scepticism about this and argues maths is too complicated:
"I think that the average professional in the theoretical physics need at least five years to learn the math which I consider directly relevant to formulation of Relativistic QM (QFT). After that he needs to develop the necessary supplementary math on his own."
I explain that one can extract some knowledge from equations even without understanding the full context: First, there is the benefit of knowing how a system is quantified to begin with. But more importantly, there is some information that can be rather easily extracted, like what fields couple to which other fields, or how sources affect the field. General parameter dependence of solutions e.g. how the number of dimensions affects Newton's law. Questions of definition, like what is the cosmological constant, or what are the dimensionalities of quantities, scaling, and so on.
Let me call that 'reading maths', in contrast to 'speaking maths' in which you'd have to find a mathematical description for a system you want to investigate which is considerably harder. I think with a bit practice most people could learn to 'read' maths if they get used to it. If I open a newspaper I also wonder how many readers actually understand the details of the business part. But they are just used to the terms, and after a while they get some notion of what's going on. Using equations in the science part wouldn't be all that different.
Dany then argues that using equations and further references isn't nice for the reader because
"after first reading one remains with the feeling that it is interesting but only illusion of understanding and knowledge"
And yes, that's exactly the impression I want the reader to have. If you've had to argue with people who believe the Hawking effect is nonsense because in 'The Brief History of Time' it's written that it requires the existence of anti-gravitating particles, you'll understand what I mean. In fact, this was one of the aspects I meant to emphasize in that previous post: It has noticeable drawbacks to leave readers with the 'Illusion of Knowledge'. This drawback esp. in the science area is that readers come to believe it's all trivial and obvious and they don't even need to take a physics class to conclude that String Theory is nonsense, the LHC piles dogs, Special Relativity is wrong, and the tenth dimension is where the consciousness lives. After all, equations are unnecessary.
Example: I am still waiting for somebody to point out if you believe Lisa Randall's explanations for why mini-black holes at the LHC evaporate very fast: "just as a small drop of coffee evaporates more quickly than a big one" (Warped Passages, p.380, US Hardcover) then the temperature doesn't increase when black holes get smaller as is the case with Hawking's radiation. The problem isn't with the reader who just swallows this, but with the reader who takes such a metaphor literally and then tries to build upon it. I am not against using such verbal explanations, I would just wish the limitations of their usefulness would be made clear. (The actual mass-loss rate is the surface times the fourth power of the temperature, and the temperature grows with the inverse of the radius).
Dany further argues:
"I would not provide you any tools “to dig a bit deeper” since I honestly respect my reader"
If a book doesn't come with further references to dig into a topic this a) lowers the usefulness of a book dramatically, b) is an indication the author either doesn't know the literature well, or didn't take the time to scan it so limits his/her credibility and c) it's just unscientific. If you write about a topic without explaining all details you should at least provide a reference to look them up. If pop-sci books don't do that how can you expect millions of people on the internet to appropriately references their sources?
I agree with Andrew who mentions:
"You can have equations in a pop science book as long as you also include a written description so people can avoid the equations if they so wish. But people who want to dig a bit deeper could consider the maths. So it appeals to the widest audience. At the very least, they should have references to arXiv papers."
Yes, some references at least to arXiv papers or so are very useful - just that not every field (yet) has something like the arXiv. See, if I read a pop sci introduction into a field I don't know very well but I find interesting, I just want to have some recommendation for where to continue reading, preferably by somebody who has an overview on the literature and not by a Wikipedia article.
To add another aspect: when I was a kid I read several pop-sci books on Special and General Relativity. There is a huge abundance of literature that will tell you a lot about rockets and elevators and trains and twins and flying angels and signals and clocks and again the rockets, the rockets are everywhere. It's not that I totally didn't understand these explanations, I just didn't know what to make out of all the extra baggage. And some of these explanations are not very insightful.
I recall there was an explanation in a book which was a construction meant to 'proof' length contraction. Unfortunately, I assume now it was a construction done with the knowledge of what the outcome should be, but not meaningful in itself. So I went and 'proofed' it nonsense and showed it to my physics teacher hoping for some insight. All my teacher said was 'We know Special Relativity is correct'. Which didn't help me anything. However, today I can kind of understand his hesitation to take apart somebody's fancy construction of flying rockets and clocks and so on.
Special Relativity began to make sense to me the moment I learned what SO(3,1) is. No more rockets. What a relief. Okay, it is maybe a matter of taste but I found the maths underlying Special Relativity more insightful than all the thought experiments. It's not that I would want to throw verbal explanations out, just I'd prefer to use them as a motivation instead of a substitute. (And no, understanding what a orthonormal transformation is isn't all that hard and can nicely be explained with some pictures. The part with the Lorentzian signature is a bit more tricky. To the German readers I warmly recommend Ulrich Schröder's book on Special Relativity.)
I got a lot out of the magazine Spectrum (the German version of Scientific American) and Bild der Wissenschaft (which is a very similar German magazine), both of which usually provided at least one or the other equation and some references. (At this time however it was for me almost impossible to get a hand on the mentioned references. This would be considerably easier today.)
On the philosophical side it is quite interesting to which importance thought experiments (Gedankenexperimente) have grown since Einstein.
Anyway, what is your opinion on having equations in pop-sci books?
@ Dany: I didn't mean to pick around on your comments because they are so outrageous, they just made for a nice pro/con situation.