What is the significance of the Scottish Rite cap?

Meaning of the Scottish Rite Cap

“In the Scottish Rite, the caps [indicate] the consecration of one’s physical and spiritual (material and intellectual) attributes to the betterment of humanity. On the one hand, the caps are an inheritance from our chivalric tradition, as similar ones were associated with European Orders of Knighthood, where they evolved from the Arming Bonnet, worn under the helmet. On the other hand, they are also worn as a type of prayer cap, a tradition which also survives in some religions. Thus, the caps are a constant reminder that the physical must be subject to the spiritual and that, like knights, we must valiantly endeavor to maintain honor and virtue by applying the Moral Sense and Reason.” —From Arturo de Hoyos, Scottish Rite Ritual Monitor and Guide, 3rd Ed., Corrected (Washington, DC: The Supreme Council, 33°, SJ, 2010), 135.

Official Caps

Below are the official caps of the Scottish Rite of Freemasonry, SJ, USA, as listed in Article XIII, Sections 15–22, of the Statutes (bylaws) of the Supreme Council, 33°, SJ, USA:
32°, Master of the Royal Secret 32° Scottish RIte cap
Fifty-year Member Fifty-year Member Scottish Rite cap
32°, Knight Commander of the Court of Honour 32°, Knight Commander of the Court of Honour, Scottish RIte cap
33°, Inspector General Honorary  33°, Inspector General Honorary, Scottish RIte cap
33°, Grand Cross of the Court of Honor 33°, Grand Cross of the Court of Honour, Scottish RIte cap
Deputy of the Supreme Council, 33°, SJ Deputy of the Supreme Council, 33°, SJ, Scottish Rite cap
Sovereign Grand Inspector General of the Supreme Council, 33°, SJ Sovereign Grand Inspector General of the Supreme Council, 33°, SJ, Scottish Rite cap
Sovereign Grand Commander of the Supreme Council, 33°, SJ Sovereign Grand Commander of the Supreme Council, 33°, SJ, Scottish Rite cap