In this task, you are given a question and a context passage. You have to answer the question based on the given passage.

What is needed to prove the theory?, Context: In the early 11th century, the Muslim physicist Ibn al-Haytham (Alhacen or Alhazen) discussed space perception and its epistemological implications in his Book of Optics (1021), he also rejected Aristotle's definition of topos (Physics IV) by way of geometric demonstrations and defined place as a mathematical spatial extension. His experimental proof of the intromission model of vision led to changes in the understanding of the visual perception of space, contrary to the previous emission theory of vision supported by Euclid and Ptolemy. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things."
vision

What do you need to happen if you want the water in the water experiment to have a greater arc?, Context: Mach argued that, in effect, the water experiment in an otherwise empty universe would remain flat. But if another object were introduced into this universe, perhaps a distant star, there would now be something relative to which the bucket could be seen as rotating. The water inside the bucket could possibly have a slight curve. To account for the curve that we observe, an increase in the number of objects in the universe also increases the curvature in the water. Mach argued that the momentum of an object, whether angular or linear, exists as a result of the sum of the effects of other objects in the universe (Mach's Principle).
an increase in the number of objects in the universe

What is the second mentioned neighborhood?, Context: The city has many distinct neighborhoods. In addition to Downtown, centered on the central business district and the Green, are the following neighborhoods: the west central neighborhoods of Dixwell and Dwight; the southern neighborhoods of The Hill, historic water-front City Point (or Oyster Point), and the harborside district of Long Wharf; the western neighborhoods of Edgewood, West River, Westville, Amity, and West Rock-Westhills; East Rock, Cedar Hill, Prospect Hill, and Newhallville in the northern side of town; the east central neighborhoods of Mill River and Wooster Square, an Italian-American neighborhood; Fair Haven, an immigrant community located between the Mill and Quinnipiac rivers; Quinnipiac Meadows and Fair Haven Heights across the Quinnipiac River; and facing the eastern side of the harbor, The Annex and East Shore (or Morris Cove).

Dixwell