From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: X-Spam-Checker-Version: SpamAssassin 3.4.2 (2018-09-13) on inbox.vuxu.org X-Spam-Level: X-Spam-Status: No, score=-0.8 required=5.0 tests=HEADER_FROM_DIFFERENT_DOMAINS, MAILING_LIST_MULTI,RCVD_IN_DNSWL_NONE autolearn=ham autolearn_force=no version=3.4.2 Received: from minnie.tuhs.org (minnie.tuhs.org [45.79.103.53]) by inbox.vuxu.org (OpenSMTPD) with ESMTP id 795afe15 for ; Sat, 19 Oct 2019 14:40:39 +0000 (UTC) Received: by minnie.tuhs.org (Postfix, from userid 112) id 46C2D9B844; Sun, 20 Oct 2019 00:40:38 +1000 (AEST) Received: from minnie.tuhs.org (localhost [127.0.0.1]) by minnie.tuhs.org (Postfix) with ESMTP id DFE4F9B5C2; Sun, 20 Oct 2019 00:40:19 +1000 (AEST) Received: by minnie.tuhs.org (Postfix, from userid 112) id DC01D9B5C2; Sun, 20 Oct 2019 00:40:17 +1000 (AEST) Received: from mail.cs.Dartmouth.EDU (mail.cs.dartmouth.edu [129.170.212.100]) by minnie.tuhs.org (Postfix) with ESMTPS id A81D09B57F for ; Sun, 20 Oct 2019 00:40:16 +1000 (AEST) Received: from tahoe.cs.Dartmouth.EDU (tahoe.cs.dartmouth.edu [129.170.212.20]) by mail.cs.Dartmouth.EDU (8.15.2/8.15.2) with ESMTPS id x9JEe8wD012961 (version=TLSv1.3 cipher=TLS_AES_256_GCM_SHA384 bits=256 verify=NO); Sat, 19 Oct 2019 10:40:08 -0400 Received: from tahoe.cs.Dartmouth.EDU (localhost.localdomain [127.0.0.1]) by tahoe.cs.Dartmouth.EDU (8.15.2/8.14.3) with ESMTP id x9JEe8qO035922; Sat, 19 Oct 2019 10:40:08 -0400 Received: (from doug@localhost) by tahoe.cs.Dartmouth.EDU (8.15.2/8.15.2/Submit) id x9JEe8PB035921; Sat, 19 Oct 2019 10:40:08 -0400 From: Doug McIlroy Message-Id: <201910191440.x9JEe8PB035921@tahoe.cs.Dartmouth.EDU> Date: Sat, 19 Oct 2019 10:40:08 -0400 To: tuhs@tuhs.org, dbrock@computerhistory.org User-Agent: Heirloom mailx 12.5 7/5/10 MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Subject: Re: [TUHS] Space Travel, was New: The Earliest UNIX Code X-BeenThere: tuhs@minnie.tuhs.org X-Mailman-Version: 2.1.26 Precedence: list List-Id: The Unix Heritage Society mailing list List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Errors-To: tuhs-bounces@minnie.tuhs.org Sender: "TUHS" 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.