The number of billionaires has increased sharply in recent years — and they are using their charitable giving to influence the direction of a host of issues, such as education, the environment, science, among others, according to a new book, The Givers: Wealth, Power, and Philanthropy in a New Gilded Age . Author D avid Callahan, founder and editor of the website Inside Philanthropy, leads a team whose goal is to shed light on the intentions of foundations and donors. He recently joined the  Knowledge at Wharton show, which airs on SiriusXM channel 111 , to talk about his book.  An edited transcript of the conversation follows. Knowledge at Wharton: What do you see as the state of philanthropy right now? David Callahan: There’s a lot of it going on. It’s the next chapter, what I call this new gilded age, that got going in the 1980s when Forbes first published that list of the wealthiest Americans. It had only 13 billionaires, but you could get on the list if you had $80 million.…