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Thought for the Day: Havana, Bina, T'vuna -- Surface, Depth, New Surface

Anyone who has taught a class that requires problem solving has heard the following complaint:
I understand the material, I just can't do the problems.
As someone who has both taught and taken such classes, I can testify from bitter experience that the answer to this complaint is always the same,
Then you don't understand the material.
An answer which is both frustrating and irritatingly true.  In fact, I am sure that a non-negligible component of my tenacity in getting a Ph.D. in physics was to be able to give that answer back the newbies.  Pettiness knows no bounds and takes no prisoners.

In fact, however, the real problem here is that English does not have good words to express the different concepts being hidden by the word "understand".  The G"ra in his pirush on sefer Mishlei explains that Lashon HaKodesh does have such words.  The nouns havana, bina, and t'vuna all come from the same root that means to understand.  Havana is the simple, straightforward meaning that most closely aligns with the word "understanding" in English.  It's the other words that are tricky.  Since all of sefer Mishlei is about "understanding", having a good grasp on the intent of the different words in crucial to getting the message.  Since, however, we don't have the words in English, we'll have to be content with m'shalim/examples.

One approach: understanding that adding salt to bread dough counteracts the sweetness of the added sugar (as yeast food) is called "bina".  Understanding why salt is precisely the correct flavor to add is called
"t'vunah".  Another approach: understanding a process well enough to be able to successfully perform it is called "bina".  Understanding the process well enough to teach it to another person (or a computer, for that matter) is called "t'vuna".  (That is precisely the reason I started on this "Thought for the Day" programs..  I take just one (usually new) idea that I have learned each day and work on explaining it.  The process of explaining moves the idea from "bina" to "t'vuna".)

Of course, once one has move from bina to t'vuna, he quickly realizes that the new new depth of understanding simply opens up a new horizon of surface.  One is back to bina and needs to work on t'vuna.  Which is precisely the thrice daily directive of the Navi we quote a the end of the first paragraph of the Aleinu prayer:
And you shall know [bina] that day and take to heart [t'vuna] that HaShem is G-d in heavens above and the earth below.  There is none other.

And how does one move from one depth of understanding to the next?  That's the end Aleinu, which is a request for siyata d'shmaya (help from heaven); "Therefore we hope to You...."

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