An eighth of an eighth

There is a Gemara in Sota 5a says that it is good to be humble, and quantifies this as an eighth of an eighth (1/64). This is seemingly arbitrary as the number is random, and how would we measure 1/64th of arrogance to find the suitable degree of humility?

The Vilna Gaon (biography here) has classic answer, that the 8th pasuk in the 8th parsha (Vayishlach) says "קָטֹנְתִּי מִכֹּל הַחֲסָדִים וּמִכָּל הָאֱמֶת אֲשֶׁר עָשִׂיתָ אֶת עַבְדֶּךָ - I have become small from all the kindnesses and from all the truth that You have rendered Your servant" - on which Rashi elaborates " קטנתי מכל החסדים : נתמעטו זכיותי על ידי החסדים והאמת שעשית עמי - I have become small: My merits have diminished because of the kindnesses and the truth that You have rendered me". This is a classic answer to what the Gemara is referencing, that we should assume that our merits have become small and that we are not actually all that, considering all G-d has done for us.

The Koheles Yitzchak delves deeper into the number 64, and says that the Gemara in Megila 29 tells the story of how all the mountains spoke to G-d, as it were, and competed for the right to have the Ten Commandents given on them, and Mt. Sinai "won" the right, and we are informed that one of the mountains was call Tabor.

In a Gemara in Bava Basra 73, the measurements of Tabor are listed, that it was 4 parsa tall, which is 16 mil, and a mil is the distance a person can walk outside a poulated area on Shabbos - 2,000 amot (cubits), so 16x2,000 cubits = 32,000.

There is a Mishna in Midos 2:1 that says that Mt Sinai was 500 cubits high. 500 fits 64 times into 32,000, ie Mt Sinai was 1/64th as tall as Tabor, and it was selected.

There is a third answered suggested by the Maharsha (biography here), that the word for arrogance in Hebrew - גס - has the numerical value of 63. Being a part of something greater (1/64th) is the way we should perceive things.