Captain Pike tells Commander Burnham that Spock has a way of "making people see that logic was the beginning of the picture, not the end". This is a lesson Spock himself tries to impart to fellow Vulcan Lieutenant Valeris in Star Trek VI: The Undiscovered Country (1991) when he tells her that "logic is the beginning of wisdom, Valeris, not the end".
The images in the opening credits have changed since last season to reflect this season's storyline--the empty captain's chair, the Red Angel, the Vulcan hand gesture with the IDIC - Infinite Diversity in Infinite Combinations - symbol, the Section 31 badge, and the three badges transporting in new personnel (Pike, etc).
Captain Pike's biography, displayed on the main bridge display, includes, in addition to the F in astrophysics he mentions, the Okuda Award, a reference to Michael Okuda, the Scenic Art Supervisor for Star Trek: The Next Generation (1987) and the Campbell Award, a real award named after John W. Campbell Jr., the editor of the magazine "Astounding Science Fiction".
When Captain Pike asks the bridge crew for a roll call without rank, "because it doesn't matter," The entire crew sounds off giving their names with no rank except for Lt. Commander Airiam who gives her rank first.
Beginning with this episode, a conscious effort was made to "course correct" the series. A version of the franchise's traditional primary-color uniforms were introduced and the holographic communicators would be removed. The entire bridge crew was called by name, owing to criticisms that they had previously been treated as background extras lacking in character development. Pike was made a more lighthearted and heroic character than Lorca.