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Valentine is the voice of modern science in the play. As a mathematician, he explains to Hannah (and, by extension, to the audience) exactly what's going on with fractals and grouse and Thomasina's rabbit equations. And he not only knows math, he's more excited about it than a tween girl at a Twilight release party:
VALENTINE: The future is disorder. A door like this has cracked open five or six times since we got up on our hind legs. It's the best possible time to be alive, when almost everything you thought you knew is wrong. (1.4)
Look, Ma, no first-person singular pronouns! The lack of any kind of "I" in this passage suggests that Valentine more interested in the march of knowledge itself than in being its drum major. He's happy to be wrong, because that means that progress can be made – in stark contrast to Bernard, who fears being wrong like Superman fears kryptonite. This, not surprisingly, leads to conflict between the two:
VALENTINE: Well, it's all trivial anyway. [...] The questions you're asking don't matter, you see. It's like arguing who got there first with the calculus. The English say Newton, the Germans say Leibnitz. But it doesn't matter. Personalities. What matters is the calculus. Scientific progress. Knowledge. (2.5)
Valentine's insistence that personalities don't matter is the polar opposite of Bernard's point of view, which is that they're the only thing that does. This debate could be as simple as the scientific point of view vs. the humanistic one, but there's also something deeper here: conflicting views of history.
Valentine sees history like a kid making a rock pile. You find a new rock of knowledge, add it to the pile – clunk – and voilà, you have more knowledge. It doesn't matter that one rock came from a forest and the other from a parking lot, just that they're both in the pile now. Bernard, on the other hand, sees history like a story: imagine a kid writing a power ballad about the day she found this shiny green rock, and the trouble she went to in order to add it to her pile, and how happy she is that now the rock is hers.
So what does it matter for Valentine that he thinks of history the way he does? Well, for starters, it means he has a lot of trouble believing that Thomasina was doing anything important. If the good stuff is like a pile of rocks, the fact that Thomasina's discoveries didn't have any effect – she didn't add a new rock to the pile – means that, to him, they don't matter. For all his enthusiasm for Knowledge, Valentine seems to have a fairly narrow definition of what Knowledge might mean.
And as we all know, character development involves someone seeing the error of their ways and gaining an open mind and learning the true meaning of Christmas. So does Valentine cast off his Scrooge-like ways and make a big donation to the Tiny Tim Memorial Orphanage and Math Tutoring Center? Well, at the very least he does soften towards Thomasina. By the end of the play he admits that she was on to something:
VALENTINE: She didn't have the maths, not remotely. She saw what things meant, way ahead, like seeing a picture. (93)
While Valentine sticks to his assertion that she simply didn't have the tools to make anything big out of her ideas, he does realize that the inspiration was in itself meaningful. Does that mean that Valentine is going to give up math and take up literary criticism? Probably not, but perhaps he won't be so hasty to dismiss those who think outside the box – and through him, the play suggests that we don't need to side with either Valentine or Bernard. There's some wiggle room between their approaches.