This is one of the technological/mathematical developments, along with multi-sig, that has great promise for improving the security and flexibility of Bitcoin. One of the worries for people with large bitcoin holdings is the being-hit-by-a-bus problem. With normal property the legal system provides the flexibility and rules by which valuable goods can be passed on to heirs. With Bitcoin, the loss of keys can mean huge amounts of value are irrecoverably lost. I hope that Shamir Secret Sharing is used as the basis for a bitcoin startup that allows bitcoin users to easily specify a set of trusted people who can come together to reconstruct keys on the event that the original holder of the keys is incapacitated or deceased.