Downgrading PS3
For anyone looking to run homebrew on their PS3, an older version of the PS3's operating system is a necessity, as many homebrew applications are designed to run on version 3.41 or lower. Downgrading the PS3 is also a step in jailbreaking it to run other custom applications.
TI-84 Plus Graphing Calculator
The TI-84 Plus graphing calculator is most frequently used to perform mathematical equations and chart graphs. However, it also features the ability to load applications and games. Coupled with USB connectivity, this app-loading capability makes the TI-84 an effective, albeit unorthodox, method of downgrading the PS3's firmware.
Advantages
Downgrading the PS3 firmware gives the PS3 a far greater range of capability than it normally has, and gives creative programmers the ability to share their own personal creations with the world. It also gives you the ability to step back to an earlier OS version if you don't like the current one.
Disadvantages
Downgrading and jailbreaking the PS3 is a hit-and-miss endeavor, even with the TI-84 method. While it is rare to brick the system and render it useless, it is possible to unintentionally disable the system's Blu-ray playback capability. Downgraded systems may also occasionally freeze or experience other unexpected glitches. Jailbreaking or downgrading your PS3 also may void your warranty, so do so at your own risk.