"Its end is embedded in its beginning and its beginning is embedded in its end... For the Master is Singular, He has no second.
And before One what do you count?" (Sefer Yetzirah 1:7)

Eight represents the realm of the Infinite, the miraculous, that which is beyond the limitations of nature. Circumcision is on the eighth day to initiate the child into the realm of the miraculous.
There are eight days of Chanukah, which is a festival for appreciating miracles. Appropriately, this figure eight placed on its side is also the mathematical symbol for infinity.