The Builders, who do the applied science in particular, are involved in invention, aqueducts, architecture, roads, civil engineering, and such, even the supervision of construction works.
Letter to the Gorean Group, Sept 20th 2000
Builders pray to the Priest-Kings for their prosperity
"In Ar, for example, early in the day, a member of the Builders will go to the roof on which the Home Stone is kept and place the primitive symbol of his trade, a metal angle square, before the Stone, praying to the Priest-Kings for the prosperity of his caste in the coming year; later in the day a Warrior will, similarly, places his arms before the Stone, to be followed by other representatives of each caste. Most significantly, while these members of the High Castes perform their portions of the ritual, the Guards of the Home Stone temporarily withdraw to the interior of the cylinder, leaving the celebrant it is said, alone with the Priest-Kings"
Tarnsman of Gor, page 68
Builders invented energy bulbs.
"Inside the tunnel, though dim, was not altogether dark, being lit by domelike, wire-protected energy bulbs. These bulbs, invented more than a century ago by the Caste of Builders, produce a clear, soft light for years without replacement."
Tarnsman of Gor, page 197
Builders take great care in their building and workmanship.
"The road, like most Gorean roads, was built like a wall in the earth and was intended to last a hundred generations. The Gorean, having little idea of progress in our sense, takes great care in his building and workmanship. What he builds he expects men to use until the storms of time have worn it to dust. Yet this road, for all the loving craft of the Caste of Builders which had been lavished upon it, was only an unpretentious, subsidiary road, hardly wide enough for two cars to pass. Indeed, even the main roads to Ko-ro-ba were a far cry from the great highways that led to and from a metropolis like Ar."
Outlaw of Gor, pg. 25
Builders use the fairs to exchange and show their crafts.
"...Similarly men of such castes as the Physicians and Builders make use of the fairs to disseminate and exchange information pertaining to their respective crafts."
Outlaw of Gor, pgs. 47-48