Why An Ark

Why the need for an ark? G-d could have saved Noach in any number of miraculous ways. 

There are several approaches to this question. A few of the approaches:

1. Rashi (7:14) says the point is the building of the ark so that people would ask and be told by Noach to repent. 

2. The Ramban says that G-d likes to minimize miracles and make events seem natural. Interestingly, the Ramban's reason for this idea is that humans must do their part, and Hashem completes the rest. This is a mussar idea that man must put in their full effort and ask Hashem to complete that which is beyond control. This is in contrast to the philosophical approach advanced by the Ralbag here in To'elet HaShevi'i, who emphasizes that Hashem only breaks natural law when absolutely necessary, because G-d wishes to uphold the perfect laws of nature which He designed. 

As mentioned on my father's blog 'Rogatchover on building the teivah: is the mitzvah the maaseh or the totza'ah?' the Rogatchover proves that Noach didn't have to build the teva himself from the fact that he got help, and אין שליחות לעכו" ם, it must be the point was just that the teva be built. We see from the Rogatchover that if the point is that the action is done, then one can perform the mitzvah through a gentile, and one does not need the parsha of shlichus. This yesod is also said by Rav Elchonon Betzah, siman 25, as to why one can fulfill the mitzvah of burial through gentiles. We can use the same idea to explain the opinion of the Magen Avraham (446:2) that one can fulfill the mitzvah of תשביתו שאור מבתיכם through a genile.  R' Akiva Eger asks אין שליות לעכו"ם?  According to this idea, the Magen Avraham holds that the mitzvah of תשביתו is to have the chametz removed (see Minchas Chinuch mitzvah 9), and for that one can fulfill the mitzvah even through the actions of a non-Jew.  

3. The ark was a miniature world. The world was created through kindness. That kindness was being obliterated by the חמס of the generation, and therefore they had to be destroyed. In order to keep the world going, Noach had to provide for the world around him to allow the world to continue to function (based upon Rav Dessler).  

4. Bereishis Rabbah 31:9: "Kanim ta'aseh es haTeivah" – like a bird's nest that purifies a metzora, so too the ark was a spiritual purification for Noach. How? Perhaps Noach was a צדיק בדורותיו ולא בדורו של אברהם because he was dragged down by his surrounding society. Instead of maxing out on his potential, he settled for being better than the rest. The teva was to teach Noach that one has to view themselves as their own little bubble and not be influenced by society at large. 

5. The Baal Shem Tov teaches that the word תיבה can also mean word. To escape the torrential מים רבים surrounding us, one must be able to retreat into the words of Torah and tefillah. The Kedushas Levi notes the dimensions of the teva, 300 = ש, 50 = נ, 30 = ל spell לשן tongue. The teva teaches us how to measure our speech properly. The Noam Elimelech adds צהר תעשה לתיבה, if speaking, one should ensure their words shine like the light from the ark.

Eight

The number eight is above teva. For the seven days of sukkot we offer korbanot to correspond to the gentiles. The 70 nations correspond to the middot* all ten mental and emotional powers. On Sukkot we celebrate our relationship to Hashem as is connected via our faculties. It is a celebration our our חיצוניות הלב connecting to Hashem, in the words of the Tanya, חיצוניות הלב היא התלהבות המתלהבת מבחי' הבינה והדעת בגדולת ה' א"ס ב"ה (להתבוננן) [להתבונן] בגדולתו ולהוליד מתבונה זו אהבה עזה כרשפי אש. We celebrate to the limit our our physical capabilities. On Shemini Atzeret (Shemini related to the word שמן, the fat, the meat, the essence) it is a private celebration between Hashem and Klal Yisrael.  This is a celebration of פנימי' הלב היא הנקודה שבפנימיות הלב ועומקא דליבא שהיא למעלה מעלה מבחי' הדעת והתבונה שיוכל האדם להתבונן בלבו בגדולת ה. We say from Elul לדוד ה אורי and we say לך אמר לבי בקשו פני. This culminates with Shemiini Atzeret. We celebrate the private,פנימיות connection to Hashem that is not limited by the faculties of a person. My father wrote about the last 8 pessukim in the Torah. The last 8 pessukim weren't written by Moshe in a coherent form, in a state of understanding, it was the pnemiuos of the Torah being written which then unscrambled into a physical state.           

Sukkah Dimensions

תשבו כעין תדורו says one should live in the sukkah as one lives in their house but sometimes it says the sukkah itself is invalid. A few examples of this principle. 

The Rema (640:4) rules like the Yeriam who is of the opinion that if one constructs their sukkah in a place where part of the time it will be a place where the they will be מצטער then one can't fulfill their obligation in the sukkah at all even at points where one is not בצער. In other words, he holds כעין תדורו defines the building of the sukkah to the extent that one can't fulfill their obligation if it is not constructed to make it livable for the duration of sukkot. The Chacham Tzvi (cited in Sharey Teshuva) disagrees and holds one can fulfill their obligation at the time one is not בצער. In other words, he views that one's residing in the sukkah has to be in a manner of כעין כדורו but it doesn't define the building.    

Shibulay HaLeket (347) ומצאתי שהשיב רבינו האיי גאון ז"ל. וששאלתם מהו למיעבד סוכה האידנא בבתי כנסיות ובבתי מדרשות. כך ראינו שאינו חייב למיעבד [סוכה] האידנא אלא בביתיה בדירתיה היכא דאכיל ושתי וגני שדירתו שם כל השנה דקא אמרה תורה כל שבעת הימים צא מדירת קבע ושב בדירת עראי. שנו חכמים מיכן אמרו יש לו כלים [נאים] מעלן לסוכה אוכל ושותה בסוכה ומטייל בסוכה אבל בתי מדרשות ובתי כנסיות אין מיחדין אלא לתפלה ולהתעסק בה בתורה לבד אבל אם עושין לכתחילה בשביל עוברי דרכים שאוכלים וישנים שם יפה עושין אבל בני העיר לסמוך על סוכה שבבית הכנסת לצאת בה ידי חובתן אינם יוצאין אלא בסוכה שלכל אחד ואחד בביתו. ולפיכך כשעושין אותה סוכה של בית הכנסת אינן צריכין לברך שלא לעצמן הן עושין אותה אלא לעוברי דרכים. וגם בשם ר' נטרונאי גאון ז"ל [מצאתי] שאין בני העיר יכולין לסמוך על סוכה שבבית הכנסת לצאת בה ידי חובתן ואין יוצאין אלא בסוכה שעושה כל אחד ואחד בחצירו לפיכך אסור לברך בסוכה של בית הכנסת. Why does he hold you can't be yotzei with the sukkah of the shul? He says אמרה תורה כל שבעת הימים צא מדירת קבע ושב בדירת עראי, in other words, this is not just a separate law of how one should design and adorn the sukkah but is part of the definition of sitting in a sukkah. One can only fulfill the obligation of being in a sukkah when it is a sitting that can be a permanent fashion (Rav Dovid Solevetchik.) 

Another example is the opinion of Ravah (Sukkah 4a) is that a sukkah that has ends of the scach hanging in the sukkah so that the airspace is less than 10 טפחים it is pasul.  According to many Rsihonim it invalidates the sukkah and that is the ruling of the Shulchan Aruch (633:9.) The Rambam is of the opinion that the sukkah does not become entirely invalidated, it is merely something that ne should try to avoid. The Briskor Rav says the reason for the Rambam is that he holds the sukkah itself must have a height of 10 tefachim, the law of the sukkah being fit for living in all 10 tefachim is only required according to the opinion that sukkah is דירת קבע not according to the halacha of דירת ארעי. However, the other Rishonim hold that if the sukkah is unlivable it creates a pesul in the sukkah itself.  

Sukkah Soul

The Sfas Emes (5650) says the two mitzvot of Sukkos, the lulav and the sukkah parallel the two names or two different approaches of Yaakov, the approach of Yaakov and of Yisrael.  The mitzvah of lulav corresponds to the name Yaakov which is the avodah of fighting against evil forces.  The mitzvah of sukkah is the level where the evil forces can't touch.  That is why חל שם שמים on the sukkah.  The sukkah is above our understanding, it is the point above reason which is connected to the deepest part of our soul. It is interesting that sukkah is deemed above logic when it is also the mitzvah linked to למען ידעו. But it is no contradiction. The understanding of sukkah is beyond our understanding but it is engrained within us. דעת as explained by the Tanya and Nefesh Hachaim means connection.  It is the point of connection of the neshama that is not defined by reason but is felt by the person.  That is what sukkah represents.  It is not that sukkah is beyond sechel, it is deeper.  The lulav is the spear we use to combat the forces around us while the sukkah is the point of sitting back and take in our connection to Hashem.