Final answer:
For de Botton, emotions projected from the courtyard arches of the Ducal Palace, embodying Romanesque solidness, differ from those at Bayeux Cathedral, which evoke Gothic spirituality and are designed to uplift towards the divine through the use of light and verticality.
Step-by-step explanation:
For de Botton, the emotions projected from the courtyard arches in the Ducal Palace and the arches at Bayeux Cathedral differ in a way that can be understood through the lens of architectural design and the emotional responses they elicit from viewers.
The Gothic architecture at Bayeux, with its emphasis on light and verticality, aimed to transport the viewer to a more spiritual, heavenly place - as Abbot Suger's application of divinity of light suggests. This contrasts with the solid, rooted feel of the Romanesque style found in the earlier Ducal Palace, where the weighty, rounded arches draw the eye downwards, instilling a sense of gravity.
The arches define not just the physical space but also the aesthetic experience and emotional reaction of the beholder. The contrasting use of geometry, light, and the modulation of arches in each architectural style communicates a different sense of the sacred and the nature of the human experience in relation to the divine.