## ENGINES OF DESTRUCTION

*(Chapter 11)*
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".

From: Brian Henry [SMTP:BRIANHE@Attachmate.com]

Sent: Tuesday, October 29, 1996 10:58 AM

To: 'whitaker@best.com'

Subject: Question about math in Engines of Creation

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.

From: K. Eric Drexler

Sent: Tuesday, November 19, 1996 10:32 PM

To: BRIANHE

Cc: Russell Whitaker

Subject: Re: Question about math in Engines of Creation (fwd)

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

From: K. Eric Drexler

Sent: Wednesday, December 11, 1996 5:38 PM

To: Russell Whitaker

Subject: RE: Question about math in Engines of Creation (fwd)

>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

[**Return to Bridge
Discussion in Chapter 11**]

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© Copyright 1986, K. Eric Drexler. All rights reserved.

Published and maintained by Russell Whitaker.

Last updated: 23 September 1996