Matt Strassler : “In particular, I did not want to make compromises that would require me to lie. Sure, some amount of compromise is necessary when explaining a difficult concept to someone who’s never seen anything like it. But that shouldn’t go as far as telling someone something they will later have to un-learn, or that will confuse them because it is actually false.”
Your article is truly a great report of personal experience. But, I am a bit surprised that you still need to make compromises (even to the edge of lying) sometimes. I fully agree with John Duffield’s quote, ” … Einstein saying ‘You do not really understand something unless you can explain it to your grandmother’”. In addition to simply agree with Einstein 100%, I would like to give it a theoretical support with the following points.
A. Whatever the “foundation” of this universe is, this universe evolves via the self-similarity transformation from that foundation. However complicated a “physics law” is, it is always only a higher tier manifestations of that “foundation”. That is, the essence of that physics law is expressed in every piece of the higher tier “expression”. If we cannot use a “story” which is easily understood by the old grandmother, we did not truly understand that complicated physics law, period. Absolutely no compromise is needed. Furthermore, if a physics law can be told with two different folklores, the old grandmother will and can be the “judge” to decide which one is a good story while the other is a hallucination.
B. In general, people view the linguistics as languages. I will define the linguistics universe with three parts.
a. A meta-space — it encompasses the events and objects in the physical universe.
b. Languages — they try to describe the stories in that meta-space.
c. A meaning-space — the meaning of the meta-space story is understood by people.
In general, a meta-space story could be understood differently by different people who have different world views. However, we could exclude the culture element and deal the issue strictly linguistically, that is, in terms of translation among languages only. Then, the meaning-space for all languages is identical.
Now, for all languages (including mathematics), they share two identical continents (meta-space and meaning-space). That is, “all” languages are permanently linked among one another by these two continents. And, every language can be “translated” to any other language. Math is the “simplest” language in linguistics. When one cannot translate a math equation to a nature language, he does for sure not truly understand that math equation.
In this view, different languages are only different translation machines. More of this is meta-language issue is available at (http://www.chineselanguageforums.com/linguistics-f25/language-types-and-second-language-acquisition-t222.html#p1930 ).