Computerized navigation machines were invented by Normal Cenva to mitigate the navigational hazards of foldspace travel, while they were not completely reliable, they managed to cut losses in half before they were banned due to fear of thinking machines. A few were secretly installed in a handful of key vessels, including Vorian Atreides's flagship. Eventually, she found an alternate solution to the foldspace navigation problem: melange-induced prescience, becoming the first Guild Navigator.
Navigation machines were reinvented by Ixians at some point after the death of Leto II, Ixian navigation machines broke the Spacing Guild's monopoly on FTL space travel, and, by the time of the discovery of the Dar-es-Balat hoard, had supplanted guild navigators as the primary means of foldspace navigation. While these machines allowed foldspace navigation without spice or guild navigators, they were described as "primitive" and "inferior substitutes".
A mathematical compiler was an advanced navigation machine which originated with the Thinking Machines during the time of the advent of Kralizec. Unlike the more primitive Ixian navigation machines, a mathematical compiler could successfully guide a ship through fold space almost as well as a Guild Navigator.
Khrone Introduces the DeviceEdit
As the New Sisterhood held a vise-like grip on the production of melange, the Administrator branch of the Guild became increasingly desperate to find new sources of the spice. Khrone, an Enhanced Face Dancer, and servant of the Thinking Machine rulers, Omnius and Erasmus, was instructed by the duo to introduce human-kind leaders to the concept of using machines to fold space for their starship vessels.
In his guise as an assistant researcher to the Ixian Chief Fabricator Shayama Sen, Khrone over a period of six years, purported to have completed the testing of a device, that once installed to a spacecraft's Holtzman engine; could fold space successfully—which Khrone dubbed a "mathematical compiler" to avoid association with thinking machines. In actuality, the device was one that the Thinking Machines had provided, and had been using for decades. The Ix starship foundries announced that mathematical compilers were available to all who could purchase them. Little did the Ixians know that already many of their personnel and managers had already been replaced by Enhanced Face Dancers, and that the compilers would self-sabotage when the machine armada attacked the human core worlds a few years later.
Gorus Uses the DeviceEdit
The Guild Administrator Rental Gorus immediately ordered all Heighliners that came in for routine maintenance to be retro-fitted with the device, and the ship's Steersman to be left to die. In the following five years, up to five hundred Navigators perished as Gorus's orders were ruthlessly enforced across human space.
On the Day of KralizecEdit
As the Machine armada swept a devastating path through human space; Murbella, her Supreme Bashar Janess Idaho, the Ixian-built New Sisterhood fleet; readied a last-stand effort above the skies of Chapterhouse and Junction. On the day of Kralizec, the Thinking Machine fleet attacked in a giant tens of thousands of starship wave. As they came into contact with the Ixian ships which contained mathematical compilers, the Machine armada sent out a carrier signal, which completely disabled the compilers on the human ships.
The human ships were left to drift aimlessly in space, and could not navigate at all. However, the day turned out differently due to the intervention of the Oracle of Time, and her remaining Navigator heighliner fleet; as well as the astounding events that occurred on Synchrony, with the captured crew of the Ithaca, the banishment of Omnius, and revelation of Duncan Idaho as the Ultimate Kwisatz Haderach.
As Idaho united man and machine into a brighter future; the Guild used both mathematical compilers and Navigators, in future commerce and travel.