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Hex
From Discworld & Pratchett Wiki
Hex is the Unseen University's organic super-computer, located in the High Energy Magic Building, whose initial components were a mouse-wheel and an ant-colony (the sum in this case is far greater than the parts) tended by Ponder Stibbons and a group of like-minded, spotty, if-only-we-had-anoraks undergraduates. Hex can be cranky, recalcitrant, demand more cheese, occasionally be of use, and exhibit disturbing signs of sentience. Apart from the odd banana, not too much difference from here. Hex makes a major appearance in Interesting Times, Hogfather and The Science of Discworld where it helped facilitate the Roundworld project, and has also been used at other times to do complicated calculations for how exactly a spell is to be performed, or to control the operations of complicated magical instruments.
Hex is able to cast a huge amount of spells in a very small amount of time (similar to early computers that were used to do multiple calculations in a short space of time), thus reducing the need for humans to do so (a source of disgruntlement to the Faculty), and garnering results that it would take a team of research wizards weeks, months or even years to get.
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A lot of the technical jargon that Ponder and the team use around Hex is based on computer-speak on Roundworld.
There is a motto attached to Hex saying Anthill Inside, a reference to Intel Inside.
While Hex is pondering a question, it will shut down all other functions, and an hourglass on a spring will descend and slowly turn, indicating that its runtime is being applied to the issue. This is akin to the cursor transforming into a picture of an hourglass in some OSs.
Hex occasionally demands cheese for his/its mouse. If the mouse is not fed, Hex stops working. This is a reference to the Roundworld 'mouse', which controls the cursor.
Sometimes when Hex is baffled by a question, it produces random error messages - as incomprehensible as Roundworld computers' "An error of type 5307 has occured.' or '[Something] failure', but with a more arcane bent. 'Eternal domain error' = 'Internal domain error'.
When Hex appears to 'catch' the Bursar's daftness, its behaviour may echo the Red Dwarf concept of 'computer senility': an android which had contracted it preferred to be known as 'Ramses Niblick III Kerplunk Kerplunk Whoops! Where's My Thribble?' - Hex says 'Whoops! Here Comes The Cheese!'.

