As I pointed out in my reply to Luke, knowledge of that fact constitutes "understanding of relativity" to the same extent that knowledge of the fact that you can get hurt by sticking your fingers into electrical installations constitutes understanding of electromagnetic theory. It's just a single fact you know in complete isolation, not a fact that is a part of some broader framework for understanding the world.
We aren't talking about the memorization of a simple fact about pings. We are talking about all the understanding you can have about relativity without having memorized a mathematical equation. This can be used to make the prediction that ping times will never be lower than the aforementioned limit.
You asked for examples of predictions about the world that can be made based on understanding physics minus the math. It would be disingenuous in the extreme to then dismiss all examples of predictions about the world given because they are, in fact, mere predictions about the world and therefore could have been memorized without real understanding.
To build on this particular example, some things like shadows, reflections, etc., can indeed move faster than light. Or, if you just spin on an office chair, in your rest frame the celestial objects are spinning around you way faster than c. Unless you can explain why such motions are consistent with the "no faster than c" principle, you have nothing more than a literally memorized fact that if it might be useful if something could move faster than c, it can't happen. It's a true fact, to be sure, and even a potentially useful one, but still.
My first prediction: If you (who I believe professed understanding of at least this much understanding of math) and lukeprog were locked in rooms disconnected from the outside world and given the task of answering this question not only would Luke be able to give an explanation, his explanation would be better than yours. You both know enough about physics to answer and Luke is better at explaining things.
My second prediction: There are many students who, in their physics exams, get all the questions that require mathematics correct and who, when encountering a question like this one, can't give an answer. Because not only is knowing the math not strictly necessary to answer this question, it isn't even sufficient.
Additional claim: It has been too long since I studied physics for me to remember all of the mathematics of special relativity. Yet when I did the aforementioned study I also gained a solid grasp of the fundamental principles. With that understanding I could recreate the interesting mathematics from first principles. I am confident of this because I've done it before, just for kicks. Because memorizing the math wasn't enough for me and I wanted to really grasp the science in depth. The way you do that is by knowing the concepts well enough that you could work out the equations for yourself. Because just memorizing them is detail work. (I haven't got a chance in hell of doing this with GR.)
In the various responses you have been given your claim that you can't have any understanding of physics without math has been overwhelmingly refuted. All you are left with is "But that understanding isn't true understanding, true understanding means you remember the math!" To that I reply "No, not all Scotsmen like haggis. You can only tell a true Scotsman by the kilt they are wearing!"
It is time to retreat from a complete rejection of all non-mathematical understanding so that you can express an actually tenable position regarding the limits of how much you can know about physics sans math. Because there really are such limits and I would love to be able to support you in declaring them. But right now you've gone overboard and tried to reject even that understanding which can exist. And that brings you to the realm of the absurd and I just can't support a position which is just obviously factually incorrect.
My second prediction: There are many students who, in their physics exams, get all the questions that require mathematics correct and who, when encountering a question like this one, can't give an answer. Because not only is knowing the math not strictly necessary to answer this question, it isn't even sufficient.
No one else is arguing that it is sufficient, but they are arguing that it is necessary. In this context, I'm going to make a counter prediction: if one did give a test on SR to physics students just learning about it, the ones who answer the c...
Richard Dawkins
My private school taught biology from the infamous creationist textbook Biology for Christian Schools, so my early understanding of evolution was a bit... confused. Lacking the curiosity to, say, check Altavista for a biologist’s explanation (faith is a virtue, don’t ya know), I remained confused about evolution for years.
Eventually I stumbled across an eloquent explanation of the fact that natural selection follows necessarily from heritability, variation, and selection.
Click. I got it.
Explaining is hard. Explainers need to pierce shields of misinformation (creationism), bridge vast inferential distances (probability theory), and cause readers to feel the truth of foreign concepts (quantum entanglement) in their bones. That isn’t easy. Those who do it well are rare and valuable.
Textbook writers are often skilled at explaining complex fields. That’s why I called on my fellow Less Wrongers to name their favorite textbooks (if they had read at least two other textbooks on those subjects). The Best Textbooks on Every Subject now gives 22 textbook recommendations, for fields as diverse as scientific self-help and representation theory.
Now I want to jump down a few levels in granularity. Let’s pool our knowledge to find great explanations for each important idea (in math, science, philosophy, etc.), whether or not there is equal value in the rest of the book or article in which each explanation is found.
Great explanations, in my meaning, have four traits:
A great explanation does more than report facts; it uses analogy and rhetoric and other tools to make readers feel the target idea in their bones.
A great explanation is not a single analogy nor a giant book. It is, roughly, between 2 and 100 pages in length.
A great explanation is comprehensible at best to a young teenager, or at least to a 75th percentile college graduate. (There may be no way to seriously explain string theory to an average 13-year-old.)
A great explanation is exciting to read.
By sharing great explanations we can more often experience that magical click.
List of Great Explanations
I’ve barely begun to assemble the list below. Please comment with your own additions!
(The list below is exclusive to written explanations, but feel free to share your favorite explanations from other media. My favorite explanation of BASIC programming is a piece of software from Interplay called Learn to Program BASIC, and of course many people love Khan Academy’s videos and The Teaching Company’s audio courses.)
Epistemology
Aumann’s agreement theorem: Landsburg, The Big Questions, chapter 8.
Occam’s razor: Yudkowsky, Occam’s razor.
Math and Logic
Physics
Special relativity: Wolfson, Simply Einstein, chapters 2–12.
General relativity: Hawking, The Universe in a Nutshell, chapters 1–2.
Infinite, flat universe: Greene, The Hidden Reality, chapters 1–3.
Timeless reality / block universe: Greene, The Fabric of Reality, chapter 5.
Inflationary cosmology: Greene, The Hidden Reality, chapter 3.
Rainbows: Dawkins, The Magic of Reality, chapter 7.
Biology
Psychology
Anchoring: Kahneman, Thinking, Fast and Slow, chapter 11.
Availability heuristic: Kahneman, Thinking, Fast and Slow, chapters 12–13.
Prospect theory: Kahneman, Thinking, Fast and Slow, chapters 25–26.
Modularity of mind: Kurzban, Why Everyone (Else) is a Hypocrite, chapters 1–4.
Economics