Does Frye’s statement "you can see why we tend to think of the sciences as intellectual and the arts as emotional: one starts with the world as it is, the other with the world we want to have" and the explanation that follows imply he believes art and science cannot overlap? Does he think that science or the actions that lead up to scientific revelations cannot come from the thoughts of what we want the world to be? Do the arts have to be based on the world we want to have, or can they be based solely on what is already on the earth?

Northrop Frye wrote this statement in one of his most famous essays on critical theory. However, he does not mean to suggest that science is purely the arena of intellectual reality, and the arts the arena of imagination and a dream of what is yet to come. Indeed, Frye describes science and the arts as both operating "on a mixture of hunch and common sense," with science and art, in their highly developed forms, being very close to each other. Frye's understanding of art and science is that they meet in the middle.
What he does seem to believe about art and science is that they "start from opposite ends." That is, science evolves and improves from a technical, measurable point of view: a modern scientist will necessarily know a lot more about the scientific world than Newton did, even though he may not be such a brilliant or accomplished scientist. Meanwhile, there can be no similar sense in which art "improves." Frye gives the examples of King Lear and Oedipus as representing the peak of human achievement in terms of drama: while other, equally good plays may be produced over time, they will not be "better," measurably, than these plays. This, Frye says, is the key difference between science and art, rather than the stipulation that art is emotional and science is intellectual.
Certainly, some scientific endeavors can be driven by the idea of how we would like the world to be. Frye gives the example, in art, of human beings imagining flying machines, but of course this same hope that we would one day fly drove science, too. Leonardo da Vinci represents the epitome of a crossover between science and art with his drawings of flying crafts, some of which scientists believe he really built. Likewise, a lot of our novels, in particular, Frye says, are representations of the world around us, drawing from the "immediate" experience of the writer. Frye questions whether we really need art when the world around us is so scientifically advanced, but the reason we do still need it is because we also enjoy reading about the world as it is—we do not only want to read about a dream world, a futuristic vision of life.
Ultimately, there is necessarily an overlap between science and art, with both scientists and artists being, sometimes, driven by imagination. The key difference between the two disciplines is that science can measurably improve, while literature cannot.