[P/E] vs growth of a stock

[FishHooks]

I was reading A Random Walk Down Wall Street (first investing book, just getting into this stuff only 18)and come upon something I was't too clear about. For those of you that have the book what i'm talking about is in Chapter 5.

He talkes about the [P/E] multiple with relation to the stock growth. He shows that the higher the [P/E] the higher the expected growth is. First of all why is this? Secondly how/if is this maintainable? You would think after the growth period the stocks [P/E] mulitple would be really high, even after the growth and the stock would just have to loose its value once it started to stable out. He might talk more indepth about this later in the book, just posted it now so I wouldn't forget.