[TUHS] Space Travel, was New: The Earliest UNIX Code

[Doug McIlroy]

I was about to add a footnote to history about
how the broad interests and collegiality of
Bell Labs staff made Space Travel work, when
I saw that Ken beat me to telling how he got
help from another Turing Award winner.

> while writing "space travel,"
> i could not get the space ship integration
> around a planet to keep from either gaining or
> losing energy due to floating point errors.
> i asked dick hamming if he could help. after
> a couple hours, he came back with a formula.
> i tried it and it worked perfectly. it was some
> weird simple double integration that self
> corrected for fp round off. as near as i can
> ascertain, the formula was never published
> and no one i have asked (including me) has
> been able to recreate it.

If I remember correctly, the cause of Ken's
difficulty was not roundoff error. It
was discretization error in the integration
formula--probably f(t+dt)=f(t)+f'(t)dt.
Dick saw that the formula did not conserve
energy and found an alternative that did.