An Eighth of an Eighth

"I have become unworthy through all the acts of kindness" [Vayishlach 32:11]

The Vilna Gaon was once asked to explain Chazal's statement [Sotah 5a]  "Said R'Chiya bar Ashi in the name of Rav: A Talmid chacham must have one-eighth of an eighth [of haughtiness]".  

Rashi explains that it is essential for a talmid chacham to possess this minute amount of pride in order to prevent those who are ignorant in Torah learning from making light of him and his words.  Why did Chazal choose specifically the measure of one-eighth of an eighth?

The term "one eighth of an eighth" answered the Gaon, is not a reference to a particular measure. Rather it is hinting at the eighth verse of the eighth parsha of the Torah.  The eighth portion in the Torah is Parshas Vayishlach, and the eighth verse of the parsha [32:11] begins with the word "katonti" - "I am very small".

While a talmid chacham must possess a certain amount of arrogance, it must be a "very small" amount.

Source: Rabbi Yisrael Bronstein