[The FAQ says](https://en.bitcoin.it/wiki/FAQ#Why_don.27t_we_use_calculations_that_are_also_useful_for_some_other_purpose.3F):

> 
> **Why don't we use calculations that are also useful for some other purpose?**
> 
> 
> To provide security for the Bitcoin network, the calculations involved
>  need to have some very specific features. These features are
>  incompatible with leveraging the computation for other purposes.
> 
> 
> 

That's a rather generic explanation. What are these "very specific features" that Bitcoin calculations need?