In a math-type science one normally does not assume that the models are 100% correct. They are provisional and subject to improvement. And they have limited ranges of applicability---they stop giving meaningful numbers if you push them too far.
General Relativity (GR) is a good example. It was formulated in 1915 and as I recall by around 1920 Einstein had already explained why it must fail if applied to very small phenomena. Sorry I don't have an historical source for that. But this isn't special to GR! It's widely known that generally speaking ANY mathematical theory of the physical world fails if you try to go beyond the bounds of that theory's applicability--we live with that, and it's one of the motivations for constantly improving theory so it fits nature better and covers more extreme circumstances.
A competent science writer or lecturer will normally have some ritual reservations and qualifications that they slip in like:
"According to Einstein's General Relativity the whole of the observable universe at one time occupied a space no bigger than the nucleus of an hydrogen atom."
This does not mean that the statement is correct, it is simply a mathematical consequence of GR (which we know has limited applicability). GR does not apply in very high density situations.
Also it does not say that the whole universe at one time occupied some finite volume. The observable universe is not the same as the whole place. There is a huge difference. In the most commonly used model the volume is infinite now and also back then. It is only a finite piece of the universe that is said to have been small---the observable portion, basically the stuff we have already gotten light from and therefore can say we see. A lazy listener may not realize that it is the observable chunk of the universe that is being talked about, not the whole thing.
Also the quoted statement does not say that the whole of the observable universe at one time occupied a point. A point has no volume. The nucleus of a hydrogen atom is, after all, not a point :-D
Now what's the topic here? What I've been hearing recently is sounding more and more like WHINING and destructive bickering. A tendency to argue (uselessly I think) about WHO IS TO BLAME for public misunderstanding.
Do we badmouth God for making the physical universe too hard for ordinary folks to understand? Heh heh.
Do we badmouth the Lazy Lecturer who failed to emphasize the limitations of the models he was describing?
Do we badmouth the Lazy Listener who did not HEAR the reservations, like "according to GR, the observable..."
And there are even Fundie websites which may intentionally misrepresent the message professional scientists are trying to get across, which quote scientists out of context omitting qualifiers, which have a hostile agenda: namely to convince people that the scientific picture of the world is absurd, incomprehensible, cannot make sense to ordinary folks. These sources may have a positive interest in promoting mistaken conceptions. Discourage seekers and bring them back to Genesis.
============================
And then you can say why don't we just stop the pissing contest about who is to blame and experiment to see what constructive steps could be taken to REMEDY the situation. For some of us this is an interesting hypothetical problem---I don't write books or give public lectures. I've taught some but am retired now. So I'd basically like to know how the problem MIGHT be remedied. Others of us might teach or write books and give public lectures. So basically they are in the front line facing this problem of public misconceptions and it's interesting to watch them coping. Communicators must constantly adapt. I think I learn something from watching this process of adaptation.
============================
And then there's the problem of GOOD FAITH. When someone comes and starts asking questions and engaging in discussion, I find myself trying to be sensitive to their "temperature". Does this person have real curiosity. Do they really want to learn? Or are they just trying to tear down the research community, impute absurdity incomprehensibility, misrepresent findings, etc. Is this a warm receptive seeking mind, or is it a cold opinionated possibly hostile mind? And I find myself constantly revising my perceptions of people. But that's more of a subjective personal footnote, not something I want to discuss in this thread.
=============================
What I'd like to do in this thread, if anybody else is interested and wants to comment/discuss, is try to arrive at a NO-FAULT description of the problem from the average person's perspective. Where have scientists failed most miserably to communicate, and the public most miserably suffered from a lack of attention? What, if anything, can be done to remedy?
Mathematical sciences are a special case because understanding IS NOT VERBAL. So every verbal popularization has to be using analogies and graphic illustrations to "translate" understanding. Often the math is ridiculously simple (like the Friedmann equation used in cosmology) or I guess beautifully simple would be a better way to say it. And yet one can trip on ones own shoelaces and make it seem bewildering when one tries to explain. You know the "expansion of the universe" business---that's the equation Alex Friedmann devised in 1925.
Should the preface of every verbal interpretation book carry a WARNING LABEL that says mathematical models can be beautifully accurate to like 6 decimals where they apply and still go haywire if pushed beyond their applicable range?
That's the working conditions, and anybody who rejects math models because they are provisional with limited range, anyone who want the complete ANSWER right away and can't live with "I don't know". Well the person is a lost cause and should just leave the lecture hall or shut the book. Approximation, reservation, and uncertainty is what we live with.
That's one idea of a "remedy"---the warning label remedy. Maybe you can think of other kinds of remedies. Presumably if the problem can be solved it will be by a whole spectrum of remedies.
Also my statement of the problem may be wrong! I'd like to hear other people's description of the science communication glitch, if there is one.