The following conversation arose from a question raised by a reader about
the calculation used in the bridge
example in the section of Chapter 11 on "Trustworthy
Systems".
Thanks for putting Engines of Creation on the World Wide Web, it is a terrific book and I'm glad to have been able to read it.
I couldn't find K. Eric Drexler's email address so I am sending this to you in the hope that you can forward it to him.
In chapter 11, the probability of a bridge failure is discussed. The odds for failure for various cable configurations are given, but the derivation of these odds is not given. I tried to match the results given in the book but was unable to do so. My best analysis of the problem was that for probability p of single-strand failure per day (given as 1/365), the probability of simultaneous failure of k strands of an n-strand cable resulting in catastrophic bridge failure will be
(p^k)(C(n,k))
where C(n,k) is the number of combinations of n objects taken k at a time, or
n!/((n-k)!k!)
My reasoning is that p^k represents the chances of any specific k strands failing, and the C(n,k) accounts for the various combinations of k strands that could be chosen to result in failure.
My formula gives 12 years for failure of a six-cable bridge, 1.5E10 for 10 cables, and 3E32 for 15, which is slightly greater than your figure of 10 years for six cables but much greater for the other two cases.
I have no recollection of the origin of these numbers, but they look quite wrong; yours look better, and make the point better as well. Thank you.
- Eric
>Eric,
>Should I put a link in EOC pointing to a web page containing the text of this email
>thread, or a version of it?
>Russell
That would be fine.
- Eric