From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Feb 1 10:50:04 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j11Go3oD027071 for ; Tue, 1 Feb 2005 10:50:03 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j11Go3Jc027070 for reliable_computing-outgoing; Tue, 1 Feb 2005 10:50:03 -0600 (CST) Received: from imap.univie.ac.at (mailbox-lmtp.univie.ac.at [131.130.1.27]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j11Gnrls027066 for ; Tue, 1 Feb 2005 10:49:59 -0600 (CST) Received: from [131.130.16.23] (theseus.mat.univie.ac.at [131.130.16.23]) by imap.univie.ac.at (8.12.10/8.12.10) with ESMTP id j11GniUW247612; Tue, 1 Feb 2005 17:49:47 +0100 Message-ID: <41FFB2FB.4050503 [at] univie [dot] ac.at> Date: Tue, 01 Feb 2005 17:48:59 +0100 From: Arnold Neumaier Organization: University of Vienna User-Agent: Mozilla Thunderbird 0.9 (X11/20041127) X-Accept-Language: en-us, en MIME-Version: 1.0 To: interval Subject: Interval arithmetic and the SIAM 100-digit challenge Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-DCC-ZID-Univie-Metrics: mx9.univie.ac.at 4248; Body=2 Fuz1=2 Fuz2=2 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk I just noticed that the review of the book F. Bornemann et al., The SIAM 100-digit challenge, SIAM, Philadelphia 2004 in the MathSciNet http://www.ams.org/msnmain?fmt=doc&fn=105&id=2076374&l=20&pg3=IID&r=1&s3=254928&v3=Bornemann%2C%20Folkmar refers to interval arithmetic for verifying the accuracy of the results. ''The authors second objective in each chapter is to validate the correctness of each calculated digit. This objective is achieved through various combinations of carefully designed computer experiments, a posteriori error estimates and computer-assisted proofs based on interval arithmetic.'' Arnold Neumaier From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Feb 1 11:12:11 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j11HCBwY027203 for ; Tue, 1 Feb 2005 11:12:11 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j11HCA03027202 for reliable_computing-outgoing; Tue, 1 Feb 2005 11:12:10 -0600 (CST) Received: from smtp2.rz.tu-harburg.de (smtp2.rz.tu-harburg.de [134.28.205.13]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j11HC1VJ027198 for ; Tue, 1 Feb 2005 11:12:07 -0600 (CST) Received: from mail2.rz.tu-harburg.de (mail2.rz.tu-harburg.de [134.28.202.179]) by smtp2.rz.tu-harburg.de (8.13.1/8.13.1) with ESMTP id j11HC0aa018352 (version=TLSv1/SSLv3 cipher=DHE-RSA-AES256-SHA bits=256 verify=NO); Tue, 1 Feb 2005 18:12:00 +0100 Received: from oem-9n90y5vdt8b (d187111.adsl.hansenet.de [80.171.187.111]) (user=ti3sr mech=LOGIN bits=0) by mail2.rz.tu-harburg.de (8.13.1/8.13.1) with ESMTP id j11HBxUi012448 (version=TLSv1/SSLv3 cipher=RC4-SHA bits=128 verify=NO); Tue, 1 Feb 2005 18:11:59 +0100 To: "Arnold Neumaier" , interval Subject: Re: Interval arithmetic and the SIAM 100-digit challenge References: <41FFB2FB.4050503 [at] univie [dot] ac.at> Message-ID: Date: Tue, 01 Feb 2005 18:11:55 -0100 From: "Siegfried M. Rump" Organization: Technical University Hamburg-Harburg Content-Type: text/plain; format=flowed; delsp=yes; charset=iso-8859-15 MIME-Version: 1.0 Content-Transfer-Encoding: 8bit In-Reply-To: <41FFB2FB.4050503 [at] univie [dot] ac.at> User-Agent: Opera M2/7.54 (Win32, build 3869) X-Scanned-By: TUHH Rechenzentrum content checker on 134.28.205.13 X-Scanned-By: TUHH Rechenzentrum content checker on 134.28.202.179 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Yes, one of the authors wrote me some time ago that five of the ten problems were solved using INTLAB. Best wishes Siegfried M. Rump On Tue, 01 Feb 2005 17:48:59 +0100, Arnold Neumaier wrote: > I just noticed that the review of the book > F. Bornemann et al., > The SIAM 100-digit challenge, > SIAM, Philadelphia 2004 > in the MathSciNet > http://www.ams.org/msnmain?fmt=doc&fn=105&id=2076374&l=20&pg3=IID&r=1&s3=254928&v3=Bornemann%2C%20Folkmar > refers to interval arithmetic for verifying the accuracy of the results. > > ''The authors second objective in each chapter is to validate the > correctness of each calculated digit. This objective is achieved through > various combinations of carefully designed computer experiments, a > posteriori error estimates and computer-assisted proofs based on > interval arithmetic.'' > > > Arnold Neumaier > -- ================================================= Prof. Dr. Siegfried M. Rump Arbeitsbereich Informatik III Technische Universität Hamburg-Harburg Schwarzenbergstr. 95 21071 Hamburg Germany phone +49 40 42878 3027 secr. +49 40 42878 3227 fax +49 40 42878 2489 From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Feb 1 18:32:54 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j120Wsiv027831 for ; Tue, 1 Feb 2005 18:32:54 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j120WswF027830 for reliable_computing-outgoing; Tue, 1 Feb 2005 18:32:54 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j120WqTo027826 for ; Tue, 1 Feb 2005 18:32:52 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j120WpiP027825 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 1 Feb 2005 18:32:51 -0600 (CST) Received: from postfix3-2.free.fr (postfix3-2.free.fr [213.228.0.169]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j0S9Pjxc018202 for ; Fri, 28 Jan 2005 03:25:51 -0600 (CST) Received: from Tartaros (longchamp44-3-82-224-250-165.fbx.proxad.net [82.224.250.165]) by postfix3-2.free.fr (Postfix) with ESMTP id 036C8C24B; Fri, 28 Jan 2005 10:25:32 +0100 (CET) From: "Christophe Jermann" To: "Christophe Jermann" Subject: Postdoctoral position in Nantes, France Date: Fri, 28 Jan 2005 10:25:31 +0100 MIME-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Mailer: Microsoft Office Outlook, Build 11.0.6353 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 Thread-Index: AcUFG09tET/E1MVVR6u+NucyvlbdxQ== Message-Id: <20050128092532.036C8C24B@postfix3-2.free.fr> Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk [apologies if you receive multiple copies of this message] POSTDOCTORAL POSITION in COMPUTER SCIENCE and INTERVAL MATHEMATICS University of Nantes, LINA laboratory, CoCoA Team ----- The CoCoA (Continuous Constraints and Applications) team of the LINA (Computer Science Laboratory of Nantes Atlantique) laboratory invites applications for a postdoctoral position. The appointment will be for one year, starting between September 2005 and December 2005. The CoCoA team will support candidates into applying to fellowships and grants programs. For this purpose, interested candidates should send their application the sooner. Context ------- The CoCoA team consists of 15 researchers who aim at solving general first-order formulas over integers and reals, involving non-linear constraints, uncertainty, preferences on the data and efficiency criteria. The base tools we use are interval analysis, constraint propagation (CP), symbolic computation and tree-search methods. Constraint programming provides a declarative and natural way of formulating problems as constraint satisfaction problems (CSPs) by stating the requirements (constraints) that must be fulfilled by the solutions. The CoCoA team is especially interested in numerical CSPs which involve constraints over real numbers. Such CSPs appear in industrial applications like conceptual design, computer aided design, robotics and molecular biology, which are the main applications the CoCoA team is tackling. Objectives ---------- The postdoctoral fellow will be involved into one of the ongoing research projects of the team, contribute to the development of the ELISA platform for constraint programming and optimization, and pursue researches in one of the following directions (depending on her/his abilities and desires): * hybridization of solving/optimization techniques (local/global, numeric/symbolic, ...) * design of solving/optimization methods for composite problems (hierarchical conjunctive/disjunctive models, mixed problems) * definition of systems and languages for constraint programming and optimization * study of a given application field (design, bioinformatics, ...) Candidate profile ----------------- Interested candidates should send an application letter including detailed CV (with a list of publications and a description of research interests) to the contacts below. The candidate must hold a recent PhD (within 5 years) at the appointment time. Applicants must have sound publications and expertise in one or more of the following areas (in a broad sense): * Programming languages and constraint programming * Optimization techniques (interval, convex, local, global, ...) * Cooperative problem solving Environment ------------ The city of Nantes is ideally located, only two hours from Paris by TGV (high-speed train, 20 shuttles per day) and about two hours by plane from most European capitals. Gateway to the Brittany ports, just a step away from major tourist sites such as Mont Saint-Michel, the Puy du Fou, the Futuroscope or the "Chateaux de la Loire", Nantes is also only 50km away from the renown coasts of Brittany and beaches of Vendee. The LINA laboratory offers a friendly working environment and excellent computational facilities. Contacts -------- Laurent Granvilliers or Christophe Jermann Laboratoire LINA - University of Nantes 2 rue de la Houssiniere BP 92208 F-44322 Nantes CEDEX France Phone: +33 251 125 851 or +33 251 125 840 Fax: +33 251 125 812 email: {laurent.granvilliers, christophe.jermann}@univ-nantes.fr http://www.sciences.univ-nantes.fr/lina/en/research/teams/COCOA/index.html From owner-reliable_computing [at] interval [dot] louisiana.edu Thu Feb 3 18:39:35 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j140dZeG000952 for ; Thu, 3 Feb 2005 18:39:35 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j140dZ13000951 for reliable_computing-outgoing; Thu, 3 Feb 2005 18:39:35 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j140dQYj000944 for ; Thu, 3 Feb 2005 18:39:32 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j140d3x28149; Thu, 3 Feb 2005 17:39:03 -0700 (MST) Message-Id: <200502040039.j140d3x28149 [at] cs [dot] utep.edu> Date: Thu, 3 Feb 2005 17:39:02 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: a book of potential interest to interval researchers: forwarding To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: Michael.Oberguggenberger [at] uibk [dot] ac.at MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: 8Djyq/w7zFLESJDm2PgDCg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk From: "Michael Oberguggenberger" ... Dear colleagues, It is my pleasure to bring your attention to the edited monograph W. Fellin, H. Lessmann, M. Oberguggenberger, R. Vieider: Analyzing Uncertainty in Civil Engineering. Springer-Verlag, Berlin 2005. You can find the table of contents at http://www.cs.utep.edu/interval-comp/fellin.pdf Interval-related papers are in this book in as much as random sets and fuzzy sets are employed, and this implies using evaluations of functions on intervals. In my review article, intervals as models of uncertainty are discussed as well; in addition, there is a paper on sensitivity analysis. Thus the book might be of interest to the interval community. On behalf of the editors, I thank you for your interest. With best regards, Michael Oberguggenberger Institut fuer Technische mathematik, Geometrie und Bauinformatik Universitaet Innsbruck Technikerstr. 13 A - 6020 Innsbruck, Austria Tel ++43 (0)512 507 6824 Fax ++43 (0)512 507 2941 E-Mail michael.oberguggenberger [at] uibk [dot] ac.at From owner-reliable_computing [at] interval [dot] louisiana.edu Fri Feb 4 23:28:54 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j155Sr1j001928 for ; Fri, 4 Feb 2005 23:28:53 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j155SrHO001927 for reliable_computing-outgoing; Fri, 4 Feb 2005 23:28:53 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j155SgGL001923 for ; Fri, 4 Feb 2005 23:28:48 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j155SYH06877; Fri, 4 Feb 2005 22:28:34 -0700 (MST) Message-Id: <200502050528.j155SYH06877 [at] cs [dot] utep.edu> Date: Fri, 4 Feb 2005 22:28:36 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: interval talks welcome at an El Paso 2006 conference To: reliable_computing [at] interval [dot] louisiana.edu, interval [at] cs [dot] utep.edu Cc: solin [at] math [dot] utep.edu, rafi.muhanna [at] gtrep [dot] gatech.edu, Robert.Mullen [at] case [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: QsgFWChbVEPTbqBHgz88wg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, FEM CONFERENCE: IN BRIEF In the second week of December 2006, El Paso, Texas will host an international workshop on Finite Element Methods (FEM) and their applications to Science and Engineering. Several renowned researchers are planning to come, some funding has already been secured, and the organizers are actively applying for additional support. This workshop is organized by an enthusiastic inter-disciplinary team: * Pavel Solin (http://www.math.utep.edu/Faculty/solin/) is an applied mathematician specializing in higher order finite element methods; he is the author of a research monograph Higher-Order Finite Element Methods (Chapman & Hall/CRC Press, 2003) * Jack Chessa (http://www.dmc.utep.edu/chessa) is a professor of mechanical engineering department, a specialist in finite element methods for non-linear problems such as fracture, shear band and localization phenomena as well as fluid structure interaction and multi-phase flow, and, more generally, problems that deal with moving interfaces and discontinuities. INTERVAL TALKS ARE VERY WELCOME Both Pavel and Jack have heard a lot of good things about interval techniques in FEM as techniques that provide guaranteed error bounds, they are very much interested to learn more about these techniques and they strongly believe that the interaction between leading FEM researchers and interval researchers interested in FEM applications will be very beneficial to both sides. POTENTIAL COMPLEMENT TO REC WORKSHOPS This aspect of the planned workshop makes is a nice complement to the Second International Workshop on Reliable Engineering Computing (REC) that Rafi Muhanna and Robert Mullen plan to organize in Savannah, Georgia, in February 2006 - after the success of their first workshop in September 2004: * the REC bring together researchers who use validated techniques in engineering (not necessarily in FEM), where we can exchange our ideas and techniques and advertise our successes to the larger engineering community * on the other hand, the planned FEM workshop will give us an opportunity to make our ideas, techniques, and results more known in the general engineering computation community, especially among those who use FEM methods. PLEASE EXPRESS YOUR INTEREST ASAP If you are potentially interested in coming, please let Pavel know ASAP by email to solin [at] math [dot] utep.edu (copy to me at vladik [at] cs [dot] utep.edu). By March 1, 2005, he would like to have a preliminary list. The more impressive the resulting list, the larger potential for collaboration and applications, the better chances for getting additional funding (for some of the grants to support 2006 conferences, early March 2005 is the deadline). By March 1, the workshop dates will be decided exactly. INTERVAL TUTORIAL SOLICITED In view of the collaboration potential, in addition to the research interval-related talks of interest to the FEM community, the organizers would like to include a description of interval techniques with an emphasis on FEM as a tutorial and/or one of the keynote talks. They will try their best to fund potential keynote speakers. During several interval-related conferences and at the REC meeting in Savannah, I have heard many interesting talks and tutorials that, in my opinion and in the opinion of other participants, are very clear so that they can be rather easily understood by the engineering-related audience and very enthusiastic so that they can enthuse participants into using these verified (reliable) techniques. If you are interested in presenting such a tutorial and/or keynote talk or if you would like to suggest someone who, in your opinion, would be the best person for this job, please do not hesitate to email Pavel (copy to me) about these possibilities. VENUE The workshop will be held either on campus or at the new Hilton hotel that Hilton is currently building on our campus (it is scheduled to open in February 2006). In any case, a block of rooms will be reserved at the Hilton hotel for the out-of-town guests. The local tradition is that in early December, a Season of Light is officially opened, with thousands of holiday lights decorating the trees and the Bhutanese-style buildings on campus. These lights are on every evening in December, so you will have an opportunity to enjoy them. From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 11:58:28 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15HwRrI003670 for ; Sat, 5 Feb 2005 11:58:27 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15HwRLn003669 for reliable_computing-outgoing; Sat, 5 Feb 2005 11:58:27 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15HwIAR003665 for ; Sat, 5 Feb 2005 11:58:24 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j15HwEi09476; Sat, 5 Feb 2005 10:58:14 -0700 (MST) Message-Id: <200502051758.j15HwEi09476 [at] cs [dot] utep.edu> Date: Sat, 5 Feb 2005 10:58:12 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: FW: calculators To: reliable_computing [at] interval [dot] louisiana.edu Cc: pjwilkinson [at] pasadena [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: yYYk0bJ9UaAUABPK6y/rQQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Re need to teach kids (and adults) about accuracy and maybe intervals. And maybe in favbor of interval calculators. ------------- Begin Forwarded Message ------------- Date: Sat, 5 Feb 2005 09:46:52 -0800 From: "Paul Wilkinson, Ph. D." Subject: FW: calculators To: SIGCSE-MEMBERS [at] LISTSERV [dot] ACM.ORG I spent a long time teaching mathematics ... I have found that if you take the calculator away from the student, they cannot add, subtract, multiply, or divide, let alone doing fractions. An example that I have had arguments with students over is (2/3)^4 * (3/2)^4. The answer we all know is 1, but they argue their calculator says the answer is not one, but something, depending upon the calculator brand, like 1.00000001. ... From my observations, it appears as if all they know how to do is punch buttons when they get out of high school when calculators are used in the classroom. Paul J. Wilkinson, Ph. D. Chair Department of Information Systems and Computer Science Pasadena City College Pasadena, California ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 12:07:37 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15I7aJe003788 for ; Sat, 5 Feb 2005 12:07:36 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15I7aAS003787 for reliable_computing-outgoing; Sat, 5 Feb 2005 12:07:36 -0600 (CST) Received: from ms-smtp-02-eri0.ohiordc.rr.com (ms-smtp-02-smtplb.ohiordc.rr.com [65.24.5.136]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15I7Ro7003783 for ; Sat, 5 Feb 2005 12:07:33 -0600 (CST) Received: from Moore (wor226111.columbus.rr.com [204.210.226.111]) by ms-smtp-02-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j15I7EXV004870; Sat, 5 Feb 2005 13:07:14 -0500 (EST) Message-ID: <000701c50bad$912cd790$1702a8c0@Moore> From: "Ray Moore" To: "Vladik Kreinovich" , Cc: References: <200502051758.j15HwEi09476 [at] cs [dot] utep.edu> Subject: Re: calculators Date: Sat, 5 Feb 2005 13:07:33 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Virus-Scanned: Symantec AntiVirus Scan Engine Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk No, I think the point is that we still need to teach kids mental arithmetic when it is that easy. Ray Moore ----- Original Message ----- From: "Vladik Kreinovich" To: Cc: Sent: Saturday, February 05, 2005 12:58 PM Subject: FW: calculators > Re need to teach kids (and adults) about accuracy and maybe intervals. And > maybe in favbor of interval calculators. > > ------------- Begin Forwarded Message ------------- > > Date: Sat, 5 Feb 2005 09:46:52 -0800 > From: "Paul Wilkinson, Ph. D." > Subject: FW: calculators > To: SIGCSE-MEMBERS [at] LISTSERV [dot] ACM.ORG > > I spent a long time teaching > mathematics > ... > > I have found that if you take the calculator away from the student, > they cannot add, subtract, multiply, or divide, let alone doing fractions. > > An example that I have had arguments with students over is (2/3)^4 * > (3/2)^4. The answer we all know is 1, but they argue their calculator says > the answer is not one, but something, depending upon the calculator brand, > like 1.00000001. > > ... > > From my observations, it appears as if all they know how to do is punch > buttons when they get out of high school when calculators are used in the > classroom. > > Paul J. Wilkinson, Ph. D. > Chair > Department of Information Systems and Computer Science > Pasadena City College > Pasadena, California > > > ------------- End Forwarded Message ------------- > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 12:17:13 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15IHDTS003906 for ; Sat, 5 Feb 2005 12:17:13 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15IHCwE003905 for reliable_computing-outgoing; Sat, 5 Feb 2005 12:17:12 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15IH4ld003901 for ; Sat, 5 Feb 2005 12:17:10 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j15IGxF09561; Sat, 5 Feb 2005 11:16:59 -0700 (MST) Message-Id: <200502051816.j15IGxF09561 [at] cs [dot] utep.edu> Date: Sat, 5 Feb 2005 11:16:58 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: calculators To: vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu, rmoore17 [at] columbus [dot] rr.com Cc: pjwilkinson [at] pasadena [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: ou5pGfWUswYyj1huM+3pHQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Ray, >From your reply, I realize that I did not make my point right. I agree with what you said, the need to teach mental arithmetic was the main point (and a valid point) of the posting, a point that I did not emphasize because it is of general interest, not specific to our interval area. What I wanted to say that is that on top of this point, adding uncertainty to calculators - whether in explanations in the class or explicitly in hardware -- would further help students. In the example given by Dr. Wilkinson, yes, mental arithmetic would help, but if they try square root of 2 then they need to know that the result is also not exact. >From the viewpoint of a kid, a weight measured by a scale is more accurate that a weight guessed by a human being; a velocity measured by a radar is more accurate than estimated visually. A natural kid's conclusion is that whatever calcuator produces shouldbe more accurate than what we do by hand. This is one of the sources of confusion. Honestly, when I balance by checkbook by hand, I trust myself less (and make mistakes more often) then if I use the corresponding software. Calculator is capable of correct (guaranteed) computations, but we need to program and modify it accordingly, or at least explain. I think the need felt by educators may be a good opportunity for us to educate people more in uncertainty issues. Vladik > From: "Ray Moore" > To: "Vladik Kreinovich" , > Cc: > Subject: Re: calculators > Date: Sat, 5 Feb 2005 13:07:33 -0500 > MIME-Version: 1.0 > Content-Transfer-Encoding: 7bit > X-Priority: 3 > X-MSMail-Priority: Normal > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 > X-Virus-Scanned: Symantec AntiVirus Scan Engine > > No, I think the point is that we still need to teach kids mental arithmetic > when it is that easy. > > Ray Moore > > ----- Original Message ----- > From: "Vladik Kreinovich" > To: > Cc: > Sent: Saturday, February 05, 2005 12:58 PM > Subject: FW: calculators > > > > Re need to teach kids (and adults) about accuracy and maybe intervals. And > > maybe in favbor of interval calculators. > > > > ------------- Begin Forwarded Message ------------- > > > > Date: Sat, 5 Feb 2005 09:46:52 -0800 > > From: "Paul Wilkinson, Ph. D." > > Subject: FW: calculators > > To: SIGCSE-MEMBERS [at] LISTSERV [dot] ACM.ORG > > > > I spent a long time teaching > > mathematics > > ... > > > > I have found that if you take the calculator away from the student, > > they cannot add, subtract, multiply, or divide, let alone doing fractions. > > > > An example that I have had arguments with students over is (2/3)^4 * > > (3/2)^4. The answer we all know is 1, but they argue their calculator says > > the answer is not one, but something, depending upon the calculator brand, > > like 1.00000001. > > > > ... > > > > From my observations, it appears as if all they know how to do is punch > > buttons when they get out of high school when calculators are used in the > > classroom. > > > > Paul J. Wilkinson, Ph. D. > > Chair > > Department of Information Systems and Computer Science > > Pasadena City College > > Pasadena, California > > > > > > ------------- End Forwarded Message ------------- > > > > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 13:29:16 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15JTGZo004116 for ; Sat, 5 Feb 2005 13:29:16 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15JTFdv004115 for reliable_computing-outgoing; Sat, 5 Feb 2005 13:29:15 -0600 (CST) Received: from relay.pair.com (relay00.pair.com [209.68.1.20]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with SMTP id j15JT6SQ004111 for ; Sat, 5 Feb 2005 13:29:12 -0600 (CST) Received: (qmail 81823 invoked from network); 5 Feb 2005 19:29:05 -0000 Received: from unknown (HELO ?192.168.1.100?) (unknown) by unknown with SMTP; 5 Feb 2005 19:29:05 -0000 X-pair-Authenticated: 24.244.69.242 Mime-Version: 1.0 X-Sender: jat711k [at] www [dot] peda.com Message-Id: In-Reply-To: <200502051816.j15IGxF09561 [at] cs [dot] utep.edu> References: <200502051816.j15IGxF09561 [at] cs [dot] utep.edu> Date: Sat, 5 Feb 2005 11:28:04 -0800 To: reliable_computing [at] interval [dot] louisiana.edu From: Jeff Tupper Subject: Re: calculators Cc: pjwilkinson [at] pasadena [dot] edu Content-Type: text/plain; charset="us-ascii" ; format="flowed" Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Back in 2000, I worked (through my company) with Hewlett-Packard on the Xpander calculator project. The calculator, which could have introduced some interval concepts to a larger audience (I was responsible for the reliable graphing portion), was cancelled---after prototypes were built and demonstrated---as upper management at HP unexpectedly decided to put nearly all calculator development on hold. The large manufacturers have some interest in interval methods but want to see demand for such methods from their customers. Jeff From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 13:49:46 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15JnkEB004243 for ; Sat, 5 Feb 2005 13:49:46 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15JnjP4004242 for reliable_computing-outgoing; Sat, 5 Feb 2005 13:49:45 -0600 (CST) Received: from ms-smtp-01-eri0.ohiordc.rr.com (ms-smtp-01-smtplb.ohiordc.rr.com [65.24.5.135]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15Jnb3b004238 for ; Sat, 5 Feb 2005 13:49:42 -0600 (CST) Received: from Moore (wor226111.columbus.rr.com [204.210.226.111]) by ms-smtp-01-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j15JnUHu002885; Sat, 5 Feb 2005 14:49:34 -0500 (EST) Message-ID: <001201c50bbb$dcc2a1e0$1702a8c0@Moore> From: "Ray Moore" To: "Jeff Tupper" , Cc: References: <200502051816.j15IGxF09561 [at] cs [dot] utep.edu> Subject: Re: calculators Date: Sat, 5 Feb 2005 14:49:50 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=response Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Virus-Scanned: Symantec AntiVirus Scan Engine Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Jeff and all, And how could such "demand" be demonstrated ? Ray Moore ----- Original Message ----- From: "Jeff Tupper" To: Cc: Sent: Saturday, February 05, 2005 2:28 PM Subject: Re: calculators > Back in 2000, I worked (through my company) with Hewlett-Packard on > the Xpander calculator project. The calculator, which could have > introduced some interval concepts to a larger audience (I was > responsible for the reliable graphing portion), was cancelled---after > prototypes were built and demonstrated---as upper management at HP > unexpectedly decided to put nearly all calculator development on > hold. The large manufacturers have some interest in interval methods > but want to see demand for such methods from their customers. > > Jeff > From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 14:04:39 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15K4ccV004361 for ; Sat, 5 Feb 2005 14:04:39 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15K4ca7004360 for reliable_computing-outgoing; Sat, 5 Feb 2005 14:04:38 -0600 (CST) Received: from ms-smtp-01-eri0.ohiordc.rr.com (ms-smtp-01-smtplb.ohiordc.rr.com [65.24.5.135]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15K4TB0004356 for ; Sat, 5 Feb 2005 14:04:35 -0600 (CST) Received: from Moore (wor226111.columbus.rr.com [204.210.226.111]) by ms-smtp-01-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j15K45Hu017850; Sat, 5 Feb 2005 15:04:05 -0500 (EST) Message-ID: <002001c50bbd$e43bdca0$1702a8c0@Moore> From: "Ray Moore" To: "Vladik Kreinovich" , Cc: References: <200502051816.j15IGxF09561 [at] cs [dot] utep.edu> Subject: Re: calculators Date: Sat, 5 Feb 2005 15:04:24 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Virus-Scanned: Symantec AntiVirus Scan Engine Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Vladik, > What I wanted to say that is that on top of this point, adding uncertainty > to > calculators - whether in explanations in the class or explicitly in > hardware -- > would further help students. HOW would it help them ? > In the example given by Dr. Wilkinson, yes, mental arithmetic would help, > but > if they try square root of 2 then they need to know that the result is > also not > exact. WHY would they "need to know that the result is also not exact" ? > From the viewpoint of a kid, a weight measured by a scale is more accurate > that > a weight guessed by a human being; a velocity measured by a radar is more > accurate than estimated visually. A natural kid's conclusion is that > whatever > calcuator produces shouldbe more accurate than what we do by hand. This is > one > of the sources of confusion. HOW does this cause confusion ? > Honestly, when I balance by checkbook by hand, I trust myself less (and > make > mistakes more often) then if I use the corresponding software. A pocket calculator is perfectly capable, if used correctly, and without any intervals, of balancing your checkbook correctly; and so you are by hand if you take the time. > Calculator is capable of correct (guaranteed) computations, but we need to > program and modify it accordingly, or at least explain. That is not necessary for just checkbook calculations. Better examples are needed to generate "demand" from prospective.customers. Ray Moore From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 14:26:03 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15KQ3wp004495 for ; Sat, 5 Feb 2005 14:26:03 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15KQ3d0004494 for reliable_computing-outgoing; Sat, 5 Feb 2005 14:26:03 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15KPpt4004490 for ; Sat, 5 Feb 2005 14:26:00 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j15KPkD10036; Sat, 5 Feb 2005 13:25:46 -0700 (MST) Message-Id: <200502052025.j15KPkD10036 [at] cs [dot] utep.edu> Date: Sat, 5 Feb 2005 13:25:45 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: calculators To: vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu, rmoore17 [at] columbus [dot] rr.com Cc: pjwilkinson [at] pasadena [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: ZhWkHH1U9RKpikV4+njlmg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Ray, Dear participants of the mailing list, I seem to be not in my clearest today, my apologies. Of course, I did not mean that interval calculators somehow help in balancing a checkbook. I apologize for creating this false impression. Let me try to state my case clearer. Let me describe a scenario how current calculators can cause confusion and how interval calculators can help. * First, a student balances a checkbook by hand and then again by using a calculator. In many such cases, the two results are somewhat different. So, the student checks again and again, and find the mistake in what he did by hand. This happens several times, with different examples. As a result, the student acquires the following rule: if a calculator produces one result and computations by hand produce a different result, then, most probably, a calculator is right and calculations by hand are wrong. * Now, a student computes the square root of 2 and then squares the resulting number. If he or she does it "by hand" (i.e., without using a calculator, in this case, by writing expressions on a sheet of paper, by using reasoning), this student should get the exact same value 2. The student is well aware that he sometimes makes mistakes. So, to be on the safe side, this students checks his or her result on the calculator. The result is not exactly 2, but something like 2.00000001. The student already knows, from earlier painful experience, that when the calculator and his manual results differ, there is a serious probability that the calculator is right. (Even when the results of, say, checkbook balancing were differing by 1 cent between what the student got by hand and what the student got by using a calculator, still the most usual case was a student's mistake, not the calculator's mistake.) This is where the student is confused: instead of trusting the results of his own work, he trusts the calculator instead, and this is a wrong occasion to trust the calculator: because with real numbers, calculators are only approximate devices. * How would an interval calculator help: to check the value 2 that the student got by arguing on a sheet of paper, the student runs the same computations on a calculator. As a result, the student gets an interval [1.99999999,2.000001] that clearly contains his result 2. So, instead of being confused (as with the traditional calculator), the student is reassured that his or her original sheet-of-paper calculations were correct. I hope I made my case clearer now. Vladik P.S. I agree that balancing a checkbook is not the right example for convincing the general audience, I am simply trying to explain why I forwarded the original email to the interval mailing list in the first place. > From: "Ray Moore" > To: "Vladik Kreinovich" , > Cc: > Subject: Re: calculators > Date: Sat, 5 Feb 2005 15:04:24 -0500 > MIME-Version: 1.0 > Content-Transfer-Encoding: 7bit > X-Priority: 3 > X-MSMail-Priority: Normal > X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 > X-Virus-Scanned: Symantec AntiVirus Scan Engine > > Vladik, > > > What I wanted to say that is that on top of this point, adding uncertainty > > to > > calculators - whether in explanations in the class or explicitly in > > hardware -- > > would further help students. > > HOW would it help them ? > > > In the example given by Dr. Wilkinson, yes, mental arithmetic would help, > > but > > if they try square root of 2 then they need to know that the result is > > also not > > exact. > > WHY would they "need to know that the result is also not exact" ? > > > From the viewpoint of a kid, a weight measured by a scale is more accurate > > that > > a weight guessed by a human being; a velocity measured by a radar is more > > accurate than estimated visually. A natural kid's conclusion is that > > whatever > > calcuator produces shouldbe more accurate than what we do by hand. This is > > one > > of the sources of confusion. > > HOW does this cause confusion ? > > > Honestly, when I balance by checkbook by hand, I trust myself less (and > > make > > mistakes more often) then if I use the corresponding software. > > A pocket calculator is perfectly capable, if used correctly, and without > any intervals, > of balancing your checkbook correctly; and so you are by hand if you > take the time. > > > Calculator is capable of correct (guaranteed) computations, but we need to > > program and modify it accordingly, or at least explain. > > That is not necessary for just checkbook calculations. Better examples > are needed > to generate "demand" from prospective.customers. > > Ray Moore From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 14:35:55 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15KZtPs004605 for ; Sat, 5 Feb 2005 14:35:55 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15KZtg1004604 for reliable_computing-outgoing; Sat, 5 Feb 2005 14:35:55 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15KZktX004600 for ; Sat, 5 Feb 2005 14:35:52 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j15KZgm10081; Sat, 5 Feb 2005 13:35:42 -0700 (MST) Message-Id: <200502052035.j15KZgm10081 [at] cs [dot] utep.edu> Date: Sat, 5 Feb 2005 13:35:41 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: calculators To: vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu, rmoore17 [at] columbus [dot] rr.com Cc: pjwilkinson [at] pasadena [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: ptRKLpr7lX1jsykyQ2swuQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk P.S. Same thing in the original example given by Dr. Wilkinson: if instead of 1.000001, students would see the interval [0.999999,1.00001] that clearly contain their own result 1, they would not perceive any discrepancy between what they did mentally and what the calculator did. On the other hand, with the existing calculator, when they get one result by thinking (1) and another result by using a calculator (1.000001), all they see is that there are two different results, so they are confused into thinking that one of these results is wrong. Of course, as Dr. Moore has absolutely correctly stated, the main point of Dr. Wilkinson's posting was that the students are unable to think about this problem at all. What I am saying is that even if they learn to think (but they are not 100% sure in themselves), and by thinking, they will come up with a correct result 1, they will still encounter potential confusion if they get a different number 1.000001 by using a calculator; this confusion will be elimintade (and thus, the students' progress improved) if the calculator, instead of providing the students with an approximate value with no guartantees of its accuracy, would istead provide them with a guiaranteed interval that is guaranteed to contain the actual result of the calculations. From owner-reliable_computing [at] interval [dot] louisiana.edu Sat Feb 5 16:07:02 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15M71nL004800 for ; Sat, 5 Feb 2005 16:07:01 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j15M71BM004799 for reliable_computing-outgoing; Sat, 5 Feb 2005 16:07:01 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j15M6qiF004795 for ; Sat, 5 Feb 2005 16:06:58 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j15M6g610517; Sat, 5 Feb 2005 15:06:42 -0700 (MST) Message-Id: <200502052206.j15M6g610517 [at] cs [dot] utep.edu> Date: Sat, 5 Feb 2005 15:06:41 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: calculators To: vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu, rmoore17 [at] columbus [dot] rr.com, pjwilkinson [at] pasadena [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: QWP5puicj43eCKgOlx6fUw== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Dr. Williamson, I agree (and have always agreed) with your main point: that if people cannot think and cannot do the computations by hand, then they should learn how to do it. I am NOT arguing against it. I am all for it. It was never my intent to argue that students should not learn how to think or that they should not learn how to add by hand. They should, you are absolutely right. What I am making is another claim. But what I am doing is making one step forward. Let us consider the students who have learned how to think and how to do computations in their heads (and there are such students). For such students, I argue that interval calculator will be less confsuing than the existing one. This is what my argument was about. I hope that this (fifth?) time I have made my argument clearer. Vladik > User-Agent: Microsoft-Entourage/11.1.0.040913 > Date: Sat, 05 Feb 2005 13:25:51 -0800 > Subject: Re: calculators > From: "Paul Wilkinson, Ph. D." > To: Vladik Kreinovich , , > Mime-version: 1.0 > Content-transfer-encoding: 7bit > > Your example here of when a student sees that a calculator gives a different > answer than by doing the same task by hand, and then going on to rely on the > calculator's answer is how I have been able to get more change back from a > purchase than what it was supposed to be. For example, if the total was > $3.72 I have put down $4.02, and sometimes $4.22. The look on the people's > faces behind the counter when I do this is that of total confusion. They > then enter something into the "machine" and then give me what the "machine" > tells then to give me. On more than one occasion, even when pointing this > out to the store manager, I have been told that if the "machine" tells then > to give that amount of change, they have to give that change and that the > "machine is always right." One time, to see how far this perpetuated through > the organization, I called the district manager, and then the regional > manager. Both sent me complimentary food coupons for "my troubles" and > "assured" me that the "machine is always right." Finally, at a VP level, > things changed -- but they still sent me free coupons for "my troubles and > honesty." > > So, if even making change cannot be done correctly without a calculator, > which uses only two decimal digits and subtraction / addition, what good > would an interval calculator do to this people? > > (BTW The US Stock Exchange went to doing things in total decimal format > several years ago because it was "more accurate." I think the real reason > was that most new stock brokers could not do the fractions in their head, or > that most calculators of that time could not do fraction arithmetic. > Depending upon how many digits are used in the calculation, we are not > getting our full "share" of a stock purchase any more) > > > On 2/5/05 12:25 PM, "Vladik Kreinovich" wrote: > > > Dear Ray, Dear participants of the mailing list, > > > > I seem to be not in my clearest today, my apologies. > > > > Of course, I did not mean that interval calculators somehow help in balancing > > a > > checkbook. I apologize for creating this false impression. > > > > Let me try to state my case clearer. > > > > Let me describe a scenario how current calculators can cause confusion and how > > interval calculators can help. > > > > * First, a student balances a checkbook by hand and then again by using a > > calculator. In many such cases, the two results are somewhat different. > > > > So, the student checks again and again, and find the mistake in what he did by > > hand. > > > > This happens several times, with different examples. > > > > As a result, the student acquires the following rule: if a calculator produces > > one result and computations by hand produce a different result, then, most > > probably, a calculator is right and calculations by hand are wrong. > > > > * Now, a student computes the square root of 2 and then squares the resulting > > number. If he or she does it "by hand" (i.e., without using a calculator, in > > this case, by writing expressions on a sheet of paper, by using reasoning), > > this student should get the exact same value 2. > > > > The student is well aware that he sometimes makes mistakes. > > > > So, to be on the safe side, this students checks his or her result on the > > calculator. The result is not exactly 2, but something like 2.00000001. > > > > The student already knows, from earlier painful experience, that when the > > calculator and his manual results differ, there is a serious probability that > > the calculator is right. > > > > (Even when the results of, say, checkbook balancing were differing by 1 cent > > between what the student got by hand and what the student got by using a > > calculator, still the most usual case was a student's mistake, not the > > calculator's mistake.) > > > > This is where the student is confused: instead of trusting the results of his > > own work, he trusts the calculator instead, and this is a wrong occasion to > > trust the calculator: because with real numbers, calculators are only > > approximate devices. > > > > * How would an interval calculator help: to check the value 2 that the student > > got by arguing on a sheet of paper, the student runs the same computations on > > a > > calculator. As a result, the student gets an interval [1.99999999,2.000001] > > that clearly contains his result 2. > > > > So, instead of being confused (as with the traditional calculator), the > > student > > is reassured that his or her original sheet-of-paper calculations were > > correct. > > > > I hope I made my case clearer now. > > > > Vladik > > > > P.S. I agree that balancing a checkbook is not the right example for > > convincing > > the general audience, I am simply trying to explain why I forwarded the > > original email to the interval mailing list in the first place. > > > >> From: "Ray Moore" > >> To: "Vladik Kreinovich" , > > > >> Cc: > >> Subject: Re: calculators > >> Date: Sat, 5 Feb 2005 15:04:24 -0500 > >> MIME-Version: 1.0 > >> Content-Transfer-Encoding: 7bit > >> X-Priority: 3 > >> X-MSMail-Priority: Normal > >> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 > >> X-Virus-Scanned: Symantec AntiVirus Scan Engine > >> > >> Vladik, > >> > >>> What I wanted to say that is that on top of this point, adding uncertainty > >>> to > >>> calculators - whether in explanations in the class or explicitly in > >>> hardware -- > >>> would further help students. > >> > >> HOW would it help them ? > >> > >>> In the example given by Dr. Wilkinson, yes, mental arithmetic would help, > >>> but > >>> if they try square root of 2 then they need to know that the result is > >>> also not > >>> exact. > >> > >> WHY would they "need to know that the result is also not exact" ? > >> > >>> From the viewpoint of a kid, a weight measured by a scale is more accurate > >>> that > >>> a weight guessed by a human being; a velocity measured by a radar is more > >>> accurate than estimated visually. A natural kid's conclusion is that > >>> whatever > >>> calcuator produces shouldbe more accurate than what we do by hand. This is > >>> one > >>> of the sources of confusion. > >> > >> HOW does this cause confusion ? > >> > >>> Honestly, when I balance by checkbook by hand, I trust myself less (and > >>> make > >>> mistakes more often) then if I use the corresponding software. > >> > >> A pocket calculator is perfectly capable, if used correctly, and without > >> any intervals, > >> of balancing your checkbook correctly; and so you are by hand if you > >> take the time. > >> > >>> Calculator is capable of correct (guaranteed) computations, but we need to > >>> program and modify it accordingly, or at least explain. > >> > >> That is not necessary for just checkbook calculations. Better examples > >> are needed > >> to generate "demand" from prospective.customers. > >> > >> Ray Moore > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Feb 6 04:40:39 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j16AedoS006298 for ; Sun, 6 Feb 2005 04:40:39 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j16Aec5M006297 for reliable_computing-outgoing; Sun, 6 Feb 2005 04:40:38 -0600 (CST) Received: from interval.louisiana.edu (rbk5287@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j16AeavW006293 for ; Sun, 6 Feb 2005 04:40:36 -0600 (CST) Received: (from rbk5287@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j16AeaOs006292 for reliable_computing [at] interval [dot] louisiana.edu; Sun, 6 Feb 2005 04:40:36 -0600 (CST) Received: from adminmail.paccd.cc.ca.us (adminmail.paccd.cc.ca.us [198.188.4.35]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j167pGR0005654 for ; Sun, 6 Feb 2005 01:51:22 -0600 (CST) Received: from Spooler by adminmail.paccd.cc.ca.us (Mercury/32 v4.01b) ID MO041F7A; 5 Feb 2005 23:44:07 -0800 Received: from spooler by adminmail.paccd.cc.ca.us (Mercury/32 v4.01b); 5 Feb 2005 23:43:48 -0800 Received: from [10.0.1.2] (64.170.175.75) by manage.paccd.cc.ca.us (Mercury 1.48); 5 Feb 05 23:43:29 -0700 User-Agent: Microsoft-Entourage/11.1.0.040913 Date: Sat, 05 Feb 2005 23:50:43 -0800 Subject: Re: calculators From: "Paul Wilkinson, Ph. D." To: Vladik Kreinovich , , Message-ID: In-Reply-To: <200502052206.j15M6g610517 [at] cs [dot] utep.edu> Mime-version: 1.0 Content-type: text/plain; charset="US-ASCII" Content-transfer-encoding: 7bit Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk I do understand your point.. But, I think, where we differ is where calculators should be used. The longer I am in higher education, the more I am becoming convinced that calculators should be removed from all levels of education below the collegiate level, and then used only in "advanced" classes where they are used as tools to assist. Examples of such classes would be organic chemistry, mechanics, optics, etc. Just as a side note, one of the courses that I taught when I was teaching mathematics on a part-time basis was a preparation course for the CBEST (California Basic Education Skills Test) for elementary and secondary school teachers. In California all elementary and secondary teachers, before getting their "Clear Credential," must pass a state-administered test on basic skills (such as mathematics, writing, etc). Every individual that was in these classes already was a college graduate with the additional year of teacher preparation (and some had graduate degrees). All of them had great difficulty in doing the mathematics of the course without a calculator. The course content included addition, subtraction, multiplication, division, fractions, percentages (and conversion between fraction and percentage), and volume / area calculations. Several of the students had taken the CBEST at least once, and failed the mathematics portion. On 2/5/05 2:06 PM, "Vladik Kreinovich" wrote: > Dear Dr. Williamson, > > I agree (and have always agreed) with your main point: that if people cannot > think and cannot do the computations by hand, then they should learn how to do > it. I am NOT arguing against it. I am all for it. It was never my intent to > argue that students should not learn how to think or that they should not > learn > how to add by hand. They should, you are absolutely right. > > What I am making is another claim. > > But what I am doing is making one step forward. > > Let us consider the students who have learned how to think and how to do > computations in their heads (and there are such students). For such students, > I > argue that interval calculator will be less confsuing than the existing one. > > This is what my argument was about. > > I hope that this (fifth?) time I have made my argument clearer. > > Vladik > >> User-Agent: Microsoft-Entourage/11.1.0.040913 >> Date: Sat, 05 Feb 2005 13:25:51 -0800 >> Subject: Re: calculators >> From: "Paul Wilkinson, Ph. D." >> To: Vladik Kreinovich , > , >> Mime-version: 1.0 >> Content-transfer-encoding: 7bit >> >> Your example here of when a student sees that a calculator gives a different >> answer than by doing the same task by hand, and then going on to rely on the >> calculator's answer is how I have been able to get more change back from a >> purchase than what it was supposed to be. For example, if the total was >> $3.72 I have put down $4.02, and sometimes $4.22. The look on the people's >> faces behind the counter when I do this is that of total confusion. They >> then enter something into the "machine" and then give me what the "machine" >> tells then to give me. On more than one occasion, even when pointing this >> out to the store manager, I have been told that if the "machine" tells then >> to give that amount of change, they have to give that change and that the >> "machine is always right." One time, to see how far this perpetuated through >> the organization, I called the district manager, and then the regional >> manager. Both sent me complimentary food coupons for "my troubles" and >> "assured" me that the "machine is always right." Finally, at a VP level, >> things changed -- but they still sent me free coupons for "my troubles and >> honesty." >> >> So, if even making change cannot be done correctly without a calculator, >> which uses only two decimal digits and subtraction / addition, what good >> would an interval calculator do to this people? >> >> (BTW The US Stock Exchange went to doing things in total decimal format >> several years ago because it was "more accurate." I think the real reason >> was that most new stock brokers could not do the fractions in their head, or >> that most calculators of that time could not do fraction arithmetic. >> Depending upon how many digits are used in the calculation, we are not >> getting our full "share" of a stock purchase any more) >> >> >> On 2/5/05 12:25 PM, "Vladik Kreinovich" wrote: >> >>> Dear Ray, Dear participants of the mailing list, >>> >>> I seem to be not in my clearest today, my apologies. >>> >>> Of course, I did not mean that interval calculators somehow help in > balancing >>> a >>> checkbook. I apologize for creating this false impression. >>> >>> Let me try to state my case clearer. >>> >>> Let me describe a scenario how current calculators can cause confusion and > how >>> interval calculators can help. >>> >>> * First, a student balances a checkbook by hand and then again by using a >>> calculator. In many such cases, the two results are somewhat different. >>> >>> So, the student checks again and again, and find the mistake in what he did > by >>> hand. >>> >>> This happens several times, with different examples. >>> >>> As a result, the student acquires the following rule: if a calculator > produces >>> one result and computations by hand produce a different result, then, most >>> probably, a calculator is right and calculations by hand are wrong. >>> >>> * Now, a student computes the square root of 2 and then squares the > resulting >>> number. If he or she does it "by hand" (i.e., without using a calculator, > in >>> this case, by writing expressions on a sheet of paper, by using reasoning), >>> this student should get the exact same value 2. >>> >>> The student is well aware that he sometimes makes mistakes. >>> >>> So, to be on the safe side, this students checks his or her result on the >>> calculator. The result is not exactly 2, but something like 2.00000001. >>> >>> The student already knows, from earlier painful experience, that when the >>> calculator and his manual results differ, there is a serious probability > that >>> the calculator is right. >>> >>> (Even when the results of, say, checkbook balancing were differing by 1 > cent >>> between what the student got by hand and what the student got by using a >>> calculator, still the most usual case was a student's mistake, not the >>> calculator's mistake.) >>> >>> This is where the student is confused: instead of trusting the results of > his >>> own work, he trusts the calculator instead, and this is a wrong occasion to >>> trust the calculator: because with real numbers, calculators are only >>> approximate devices. >>> >>> * How would an interval calculator help: to check the value 2 that the > student >>> got by arguing on a sheet of paper, the student runs the same computations > on >>> a >>> calculator. As a result, the student gets an interval [1.99999999,2.000001] >>> that clearly contains his result 2. >>> >>> So, instead of being confused (as with the traditional calculator), the >>> student >>> is reassured that his or her original sheet-of-paper calculations were >>> correct. >>> >>> I hope I made my case clearer now. >>> >>> Vladik >>> >>> P.S. I agree that balancing a checkbook is not the right example for >>> convincing >>> the general audience, I am simply trying to explain why I forwarded the >>> original email to the interval mailing list in the first place. >>> >>>> From: "Ray Moore" >>>> To: "Vladik Kreinovich" , >>> >>>> Cc: >>>> Subject: Re: calculators >>>> Date: Sat, 5 Feb 2005 15:04:24 -0500 >>>> MIME-Version: 1.0 >>>> Content-Transfer-Encoding: 7bit >>>> X-Priority: 3 >>>> X-MSMail-Priority: Normal >>>> X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 >>>> X-Virus-Scanned: Symantec AntiVirus Scan Engine >>>> >>>> Vladik, >>>> >>>>> What I wanted to say that is that on top of this point, adding > uncertainty >>>>> to >>>>> calculators - whether in explanations in the class or explicitly in >>>>> hardware -- >>>>> would further help students. >>>> >>>> HOW would it help them ? >>>> >>>>> In the example given by Dr. Wilkinson, yes, mental arithmetic would help, >>>>> but >>>>> if they try square root of 2 then they need to know that the result is >>>>> also not >>>>> exact. >>>> >>>> WHY would they "need to know that the result is also not exact" ? >>>> >>>>> From the viewpoint of a kid, a weight measured by a scale is more > accurate >>>>> that >>>>> a weight guessed by a human being; a velocity measured by a radar is more >>>>> accurate than estimated visually. A natural kid's conclusion is that >>>>> whatever >>>>> calcuator produces shouldbe more accurate than what we do by hand. This > is >>>>> one >>>>> of the sources of confusion. >>>> >>>> HOW does this cause confusion ? >>>> >>>>> Honestly, when I balance by checkbook by hand, I trust myself less (and >>>>> make >>>>> mistakes more often) then if I use the corresponding software. >>>> >>>> A pocket calculator is perfectly capable, if used correctly, and > without >>>> any intervals, >>>> of balancing your checkbook correctly; and so you are by hand if you >>>> take the time. >>>> >>>>> Calculator is capable of correct (guaranteed) computations, but we need > to >>>>> program and modify it accordingly, or at least explain. >>>> >>>> That is not necessary for just checkbook calculations. Better examples >>>> are needed >>>> to generate "demand" from prospective.customers. >>>> >>>> Ray Moore >>> >> > From owner-reliable_computing [at] interval [dot] louisiana.edu Sun Feb 6 05:03:59 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j16B3xEx006429 for ; Sun, 6 Feb 2005 05:03:59 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j16B3whI006428 for reliable_computing-outgoing; Sun, 6 Feb 2005 05:03:58 -0600 (CST) Received: from lakermmtao01.cox.net (lakermmtao01.cox.net [68.230.240.38]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j16B3oLW006424 for ; Sun, 6 Feb 2005 05:03:55 -0600 (CST) Received: from Inspiron-8200 ([68.226.133.93]) by lakermmtao01.cox.net (InterMail vM.6.01.04.00 201-2131-117-20041022) with SMTP id <20050206110344.VEED11542.lakermmtao01.cox.net@Inspiron-8200>; Sun, 6 Feb 2005 06:03:44 -0500 Message-Id: <2.2.32.20050206110339.00a0a4b8 [at] pop [dot] louisiana.edu> X-Sender: rbk5287 [at] pop [dot] louisiana.edu X-Mailer: Windows Eudora Pro Version 2.2 (32) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Date: Sun, 06 Feb 2005 05:03:39 -0600 To: Vladik Kreinovich , vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu, rmoore17 [at] columbus [dot] rr.com From: "R. Baker Kearfott" Subject: Re: calculators Cc: pjwilkinson [at] pasadena [dot] edu Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk All, Yes, I see "sloppy thinking" frequently on students' papers in upper division undergraduate courses. For example, when a student is exhibiting a computation of the form (3+2) * 5 + 4, I might see the following on the paper: "5 = 25 = 29" I suspect this is at least partially a consequence of repeatedly pushing a button on a calculator that, although labelled "=" actually has the functionality of "accumulate partial result". In my undergraduate numerical analysis course (as many on this list probably also teach), we teach roundoff error in introductory sessions. I assigned some problems from a text in which students were to do some floating point computations on a moderately sensitive polynomial, using a 3-digit "toy" system and first rounding, then chopping. Carefully reading the students' papers, about 70% missed it. Several came up to me beforehand, totally befuddled. I saw liberal use of the "=" symbol, both as in my example above and as a substitute for "approximately equal." In 30 years of teaching this course, my impression is that this is the worst I have seen it. (However, several students DID get it. In fact, one did the assignment by producing an object-oriented class in Matlab that did decimal arithmetic to a prescribed number of places and with a prescribed rounding mode. However, amazingly, that student is apparently weak with other mathematical concepts.) Best regards, Baker At 01:35 PM 2/5/2005 -0700, Vladik Kreinovich wrote: >P.S. Same thing in the original example given by Dr. Wilkinson: if instead of >1.000001, students would see the interval [0.999999,1.00001] that clearly >contain their own result 1, they would not perceive any discrepancy between >what they did mentally and what the calculator did. > >On the other hand, with the existing calculator, when they get one result by >thinking (1) and another result by using a calculator (1.000001), all they see >is that there are two different results, so they are confused into thinking >that one of these results is wrong. > >Of course, as Dr. Moore has absolutely correctly stated, the main point of Dr. >Wilkinson's posting was that the students are unable to think about this >problem at all. > >What I am saying is that even if they learn to think (but they are not 100% >sure in themselves), and by thinking, they will come up with a correct result >1, they will still encounter potential confusion if they get a different >number 1.000001 by using a calculator; this confusion will be elimintade (and >thus, the students' progress improved) if the calculator, instead of providing >the students with an approximate value with no guartantees of its accuracy, >would istead provide them with a guiaranteed interval that is guaranteed to >contain the actual result of the calculations. > > > > --------------------------------------------------------------- R. Baker Kearfott, rbk [at] louisiana [dot] edu (337) 482-5346 (fax) (337) 482-5270 (work) (337) 993-1827 (home) URL: http://interval.louisiana.edu/kearfott.html Department of Mathematics, University of Louisiana at Lafayette (Room 217 Maxim D. Doucet Hall, 1403 Johnston Street) Box 4-1010, Lafayette, LA 70504-1010, USA --------------------------------------------------------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Feb 8 13:36:29 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j18JaT0x012156 for ; Tue, 8 Feb 2005 13:36:29 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j18JaTKD012155 for reliable_computing-outgoing; Tue, 8 Feb 2005 13:36:29 -0600 (CST) Received: from mx2.mail.ru (mx2.mail.ru [194.67.23.122]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j18JaJ9m012151 for ; Tue, 8 Feb 2005 13:36:25 -0600 (CST) Received: from [62.152.83.86] (port=1191 helo=slava) by mx2.mail.ru with smtp id 1Cyb9k-000PY8-00 for reliable_computing [at] interval [dot] louisiana.edu; Tue, 08 Feb 2005 22:36:17 +0300 Message-ID: <00b201c50e15$5f996e40$4652983e@slava> From: "Slava Nesterov" To: "RC mailing list" Subject: Reliable Computing, Vol.11, issue 3, 2005 Date: Tue, 8 Feb 2005 22:30:42 +0300 MIME-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_NextPart_000_00A6_01C50E2D.D2C1F190" X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 X-Spam: Not detected Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. ------=_NextPart_000_00A6_01C50E2D.D2C1F190 Content-Type: text/plain; charset="koi8-r" Content-Transfer-Encoding: quoted-printable Reliable Computing Volume 11, issue 3, 2005 Mathematical Research Enclosing Solutions of Singular Interval Systems Iteratively Goetz Alefeld, Guenter Mayer 165-190 Fast Inclusion of Interval Matrix Multiplication=20 Takeshi Ogita, Shin'ichi Oishi 191-205 Exact Bounds on Finite Populations of Interval Data Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Luc Longpre, Monica = Aviles 207-233 Tolerances in Geometric Constraint Problems Johannes Wallner, Hans-Peter Schroecker, Shi-Min Hu 235-251 ------=_NextPart_000_00A6_01C50E2D.D2C1F190 Content-Type: text/html; charset="koi8-r" Content-Transfer-Encoding: quoted-printable
          &nbs= p; =20 Reliable=20 Computing
          =  =20 Volume 11, issue 3, 2005
 
          &nbs= p;=20 Mathematical Research
 
Enclosing Solutions of Singular = Interval Systems=20 Iteratively
Goetz Alefeld, Guenter Mayer
165-190
 
Fast Inclusion of Interval Matrix = Multiplication=20
Takeshi Ogita, Shin'ichi Oishi
191-205
 
Exact Bounds on Finite Populations of = Interval=20 Data
Scott Ferson, Lev Ginzburg, Vladik Kreinovich, Luc Longpre, = Monica=20 Aviles
207-233
 
Tolerances in Geometric Constraint=20 Problems
Johannes Wallner, Hans-Peter Schroecker, Shi-Min=20 Hu
235-251
------=_NextPart_000_00A6_01C50E2D.D2C1F190-- From owner-reliable_computing [at] interval [dot] louisiana.edu Tue Feb 15 23:27:50 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1G5RoNx028120 for ; Tue, 15 Feb 2005 23:27:50 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1G5RoI9028119 for reliable_computing-outgoing; Tue, 15 Feb 2005 23:27:50 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1G5RfVh028114 for ; Tue, 15 Feb 2005 23:27:47 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1G5RBt19348; Tue, 15 Feb 2005 22:27:11 -0700 (MST) Message-Id: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu> Date: Tue, 15 Feb 2005 22:27:11 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: a book of potential interest to interval researchers To: reliable_computing [at] interval [dot] louisiana.edu Cc: chleb [at] math [dot] cas.cz MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: eUVL2bxhxe4PovM/tDhigQ== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Forwarding, from NA Digest ****************************************** From: Jan Chleboun Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET) Subject: New Book on Uncertain Input Data Uncertain Input Data Problems and the Worst Scenario Method by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska; North-Holland Series in Applied Mathematics and Mechanics, Volume 46, Elsevier, Amsterdam, December 2004. Hardback, xxvi+458 pages, ISBN: 0-444-51435-X This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data. A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included. More details can be found at http://books.elsevier.com/elsevier/?isbn=044451435X Jan Chleboun Mathematical Institute Academy of Sciences Zitna 25 ( TeX: \v{Z}itn\'a ) 115 67 Prague 1 Czech Republic e-mail: chleb [at] math [dot] cas.cz From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 06:38:02 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GCc2J9029074 for ; Wed, 16 Feb 2005 06:38:02 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GCc2EC029073 for reliable_computing-outgoing; Wed, 16 Feb 2005 06:38:02 -0600 (CST) Received: from ms-smtp-03-eri0.ohiordc.rr.com (ms-smtp-03-smtplb.ohiordc.rr.com [65.24.5.137]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GCbrdY029069 for ; Wed, 16 Feb 2005 06:37:59 -0600 (CST) Received: from Moore (wor226111.columbus.rr.com [204.210.226.111]) by ms-smtp-03-eri0.ohiordc.rr.com (8.12.10/8.12.7) with SMTP id j1GC0jwZ018590; Wed, 16 Feb 2005 07:00:45 -0500 (EST) Message-ID: <000701c5141f$364f8550$1702a8c0@Moore> From: "Ray Moore" To: "Vladik Kreinovich" , Cc: References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu> Subject: Re: a book of potential interest to interval researchers Date: Wed, 16 Feb 2005 07:00:51 -0500 MIME-Version: 1.0 Content-Type: text/plain; format=flowed; charset="iso-8859-1"; reply-type=original Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2900.2180 X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 X-Virus-Scanned: Symantec AntiVirus Scan Engine Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk It seems odd to me that there is no mention of interval computation in the book. Ray Moore ----- Original Message ----- From: "Vladik Kreinovich" To: Cc: Sent: Wednesday, February 16, 2005 12:27 AM Subject: a book of potential interest to interval researchers > Forwarding, from NA Digest > ****************************************** > From: Jan Chleboun > Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET) > Subject: New Book on Uncertain Input Data > > Uncertain Input Data Problems and the Worst Scenario Method > by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska; > North-Holland Series in Applied Mathematics and Mechanics, Volume 46, > Elsevier, Amsterdam, December 2004. > Hardback, xxvi+458 pages, ISBN: 0-444-51435-X > > This book deals with the impact of uncertainty in input data on the > outputs of mathematical models. Uncertain inputs as scalars, tensors, > functions, or domain boundaries are considered. In practical terms, > material parameters or constitutive laws, for instance, are uncertain, and > quantities as local temperature, local mechanical stress, or local > displacement are monitored. The goal of the worst scenario method is to > extremize the quantity over the set of uncertain input data. > > A general mathematical scheme of the worst scenario method, including > approximation by finite element methods, is presented, and then applied to > various state problems modeled by differential equations or variational > inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, > plate buckling, contact problems in elasticity and thermoelasticity with > and without friction, and various models of plastic deformation, to list > some of the topics. Dozens of examples, figures, and tables are included. > > More details can be found at > http://books.elsevier.com/elsevier/?isbn=044451435X > > Jan Chleboun > Mathematical Institute > Academy of Sciences > Zitna 25 ( TeX: \v{Z}itn\'a ) > 115 67 Prague 1 > Czech Republic > e-mail: chleb [at] math [dot] cas.cz > > From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 09:26:51 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GFQpoe029452 for ; Wed, 16 Feb 2005 09:26:51 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GFQo3g029451 for reliable_computing-outgoing; Wed, 16 Feb 2005 09:26:50 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GFQgju029447 for ; Wed, 16 Feb 2005 09:26:47 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GFQao21752; Wed, 16 Feb 2005 08:26:36 -0700 (MST) Message-Id: <200502161526.j1GFQao21752 [at] cs [dot] utep.edu> Date: Wed, 16 Feb 2005 08:26:36 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: Re: a book of potential interest to interval researchers To: vladik [at] cs [dot] utep.edu, reliable_computing [at] interval [dot] louisiana.edu, rmoore17 [at] columbus [dot] rr.com Cc: chleb [at] math [dot] cas.cz MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: XTf0GpWmKSCp5/BA/vzTOg== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Ray, I agree with you 100%. There may be a mention of intervals inside, but it is unusul that these techniques are not mentioned in the general description - while the topic seems to be taylor-made for the interval techniques. That is why I forwarded this information to the interval mailing list: that this is an overview of the problems where interval will probably help and are not under-used. As you may remember from some of my previous email, I am currently starting to work together with Dr. Pavel Solin, one of the former co-workers of Dr. Babuska (he invited Babuska to El Paso last year). From my experience of working with Dr. Solin, he is enthusaistic about all possible techniques, he is just not that familiar with interval techniques and their capabilities. I think this is one more opportunity for us to teach our techniques to a new set of folks, and by collaborating with them convince them that interval techniques should definitely be a part of their toolbox. In my experience of working with engineers and applied mathematicians, sometimes the problem is that they do not appreciate th eneed for validated guaranteed worts-case estimates. This book is an example of an area where the problem is well-understood and since this problem is exactly what our interval techniques are good at solving, there is a great potential of using these techniques. This is one of the reasons why I am so enthusiastic about this book and potential for usese of interval techniques. Vladik > From: "Ray Moore" > To: "Vladik Kreinovich" , > Cc: > Subject: Re: a book of potential interest to interval researchers > Date: Wed, 16 Feb 2005 07:00:51 -0500 > MIME-Version: 1.0 > Content-Transfer-Encoding: 7bit > X-Priority: 3 > X-MSMail-Priority: Normal > X-MIMEOLE: Produced By Microsoft MimeOLE V6.00.2900.2180 > X-Virus-Scanned: Symantec AntiVirus Scan Engine > > It seems odd to me that there is no mention of interval computation in the > book. > > Ray Moore > > ----- Original Message ----- > From: "Vladik Kreinovich" > To: > Cc: > Sent: Wednesday, February 16, 2005 12:27 AM > Subject: a book of potential interest to interval researchers > > > > Forwarding, from NA Digest > > ****************************************** > > From: Jan Chleboun > > Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET) > > Subject: New Book on Uncertain Input Data > > > > Uncertain Input Data Problems and the Worst Scenario Method > > by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska; > > North-Holland Series in Applied Mathematics and Mechanics, Volume 46, > > Elsevier, Amsterdam, December 2004. > > Hardback, xxvi+458 pages, ISBN: 0-444-51435-X > > > > This book deals with the impact of uncertainty in input data on the > > outputs of mathematical models. Uncertain inputs as scalars, tensors, > > functions, or domain boundaries are considered. In practical terms, > > material parameters or constitutive laws, for instance, are uncertain, and > > quantities as local temperature, local mechanical stress, or local > > displacement are monitored. The goal of the worst scenario method is to > > extremize the quantity over the set of uncertain input data. > > > > A general mathematical scheme of the worst scenario method, including > > approximation by finite element methods, is presented, and then applied to > > various state problems modeled by differential equations or variational > > inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, > > plate buckling, contact problems in elasticity and thermoelasticity with > > and without friction, and various models of plastic deformation, to list > > some of the topics. Dozens of examples, figures, and tables are included. > > > > More details can be found at > > http://books.elsevier.com/elsevier/?isbn=044451435X > > > > Jan Chleboun > > Mathematical Institute > > Academy of Sciences > > Zitna 25 ( TeX: \v{Z}itn\'a ) > > 115 67 Prague 1 > > Czech Republic > > e-mail: chleb [at] math [dot] cas.cz > > > > From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 10:24:41 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGOfOW029595 for ; Wed, 16 Feb 2005 10:24:41 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GGOfJb029594 for reliable_computing-outgoing; Wed, 16 Feb 2005 10:24:41 -0600 (CST) Received: from cs.utep.edu (mail.cs.utep.edu [129.108.5.3]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGOWSv029590 for ; Wed, 16 Feb 2005 10:24:38 -0600 (CST) Received: from aragorn (aragorn [129.108.5.35]) by cs.utep.edu (8.11.7/8.11.7) with SMTP id j1GGORf22170; Wed, 16 Feb 2005 09:24:27 -0700 (MST) Message-Id: <200502161624.j1GGORf22170 [at] cs [dot] utep.edu> Date: Wed, 16 Feb 2005 09:24:27 -0700 (MST) From: Vladik Kreinovich Reply-To: Vladik Kreinovich Subject: a course of potential interest to interval researchers To: reliable_computing [at] interval [dot] louisiana.edu Cc: mceberio [at] utep [dot] edu MIME-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii Content-MD5: +AhxrwbWrsBRJfWo9oDWOA== X-Mailer: dtmail 1.3.0 @(#)CDE Version 1.4 SunOS 5.8 sun4u sparc Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk Dear Friends, As many of you know, I have recently joined a group of people interested in extended interval techniques to the situations when, in addition to guaranteed (interval) bounds, we also have some partial information about the probability of different values within the corresponding intervals. This activivity was pioneered by Ray Moore himself in his 1980s papers, Dan Berleant has a website (easily acceissble from the interval webpage) on probabilities and intervals. For control applications, this activity was done in 1990s by Bob Barmish, the author of one of the most well-known books on interval-based (robust) control. >From this viewpoint, the following course may be of interest to many researchers from our community. Many thanks to Greg Coxson for brining this to our attention. ------------- Begin Forwarded Message ------------- Date: Wed, 16 Feb 2005 09:19:51 -0500 From: "Coxson, Gregory E" I wonder if those in the group would be interested in this that I took off the Control Theory eLetter. ... Course on Randomized Algorithms for Analysis and Control of Uncertain Systems Lecturer: Roberto Tempo IEIIT-CNR Politecnico di Torino, Italy tempo [at] polito [dot] it Date: March 14-18, 2005 Place : Dept. Ing. de Sistemas y Automatica Escuela Superior de Ingenieros, Univ. Sevilla, Spain Summary This course concentrates on nonstandard tools for control of uncertain systems with main emphasis on the interplay of probability and robustness. The objective is to combine hard bounds, which are frequently used in classical robust control, with probabilistic information which is often neglected in this context. The main advantage is to provide additional insight to the control engineer. This insight may be very useful in analyzing and designing complex control systems in the presence of uncertainty. The interplay of probability and robustness also leads to innovative concepts such as the probabilistic robustness margin and the probability degradation function. The algorithms obtained are low complexity (polynomial-time) and are associated to robustness bounds which are generally less conservative than the classical ones, obviously at the expense of a small risk expressed in probability. These algorithms are usually called "randomized algorithms." In the first part of the course, we concentrate on analysis and, in particular, we address the issue of finite sample size. Subsequently, we present results for sample generation in various norm-bounded sets of interest in robust control. These results are based on methods of statistical analysis and of the theory of random matrices. The construction of specific randomized algorithms concludes this part of the course. In the second part, we study probabilistic robust design of uncertain systems. We show how this problem can be formulated in the context of classical optimal control and then we discuss how randomization and stochastic gradient methods can be successfully used. We also consider extensions of this approach to linear parameter-varying systems. Other topics that will be addressed is the design of randomized algorithms for model predictive control and for robust fault-tolerant control. The course will end with a description of a number of open problems which may be important to consider in the near future. The course is focused on the exposition of the theoretical developments as well as on simulations showing the efficacy of these techniques. Main list of topics - Preliminaries and Motivations for a Probabilistic Approach - Uncertain Systems - The Interplay of Probability and Robustness - Randomized Algorithms - Sample Size Bounds and Statistical Learning Theory - Sample Generation Theory - Probabilistic Robust Design with Linear Quadratic Regulators - Probabilistic Design for Linear Parameter-Varying Systems - Randomized Algorithms for Model Predictive Control - Applications (robustness of high-speed networks, stability of quantized sampled-data systems, performance of flexible structures) - Discussion of Open Research Problems The course is funded by the Spanish Ministry of Education and and no fees will be charged. The number of places is limited and a first in first served system will be used. Registration: e-mail to eduardo [at] esi [dot] us.es ------------- End Forwarded Message ------------- From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 10:49:14 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGnDse029756 for ; Wed, 16 Feb 2005 10:49:13 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GGnDei029755 for reliable_computing-outgoing; Wed, 16 Feb 2005 10:49:13 -0600 (CST) Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGn3ll029750 for ; Wed, 16 Feb 2005 10:49:09 -0600 (CST) Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com (Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004)) with ESMTP id <0IC00063UK15PV00@mail-mta.sfvic.sunlabs.com> for reliable_computing [at] interval [dot] louisiana.edu; Wed, 16 Feb 2005 08:48:41 -0800 (PST) Received: from [129.146.72.246] by mail.sunlabs.com (Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004)) with ESMTPSA id <0IC000BK0K14MH10 [at] mail [dot] sunlabs.com> for reliable_computing [at] interval [dot] louisiana.edu; Wed, 16 Feb 2005 08:48:41 -0800 (PST) Date: Wed, 16 Feb 2005 08:48:44 -0800 From: "G. William Walster" Subject: Re: a book of potential interest to interval researchers In-reply-to: <000701c5141f$364f8550$1702a8c0@Moore> To: Ray Moore Cc: Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu, chleb [at] math [dot] cas.cz Reply-to: Bill.Walster [at] sun [dot] com Message-id: <4213796C.3080008 [at] sun [dot] com> Organization: Sun Microsystems Laboratories MIME-version: 1.0 Content-type: text/plain; charset=us-ascii; format=flowed Content-transfer-encoding: 7BIT X-Accept-Language: en-us, en References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu> <000701c5141f$364f8550$1702a8c0@Moore> User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7) Gecko/20040616 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk I agree. I have ordered it from Amazon. Perhaps the authors don't know about intervals. Many people still do not. The encouraging thing is that even point people are starting to realize the importance of input uncertainty. This can only be good for us. :) Cheers, Bill P.S. If nothing else, this is a source of good examples for you to use in your talk. :) Ray Moore wrote: > It seems odd to me that there is no mention of interval computation in > the book. > > Ray Moore > > ----- Original Message ----- From: "Vladik Kreinovich" > To: > Cc: > Sent: Wednesday, February 16, 2005 12:27 AM > Subject: a book of potential interest to interval researchers > > >> Forwarding, from NA Digest >> ****************************************** >> From: Jan Chleboun >> Date: Wed, 9 Feb 2005 12:09:50 +0100 (CET) >> Subject: New Book on Uncertain Input Data >> >> Uncertain Input Data Problems and the Worst Scenario Method >> by Ivan Hlavacek, Jan Chleboun, and Ivo Babuska; >> North-Holland Series in Applied Mathematics and Mechanics, Volume 46, >> Elsevier, Amsterdam, December 2004. >> Hardback, xxvi+458 pages, ISBN: 0-444-51435-X >> >> This book deals with the impact of uncertainty in input data on the >> outputs of mathematical models. Uncertain inputs as scalars, tensors, >> functions, or domain boundaries are considered. In practical terms, >> material parameters or constitutive laws, for instance, are uncertain, >> and >> quantities as local temperature, local mechanical stress, or local >> displacement are monitored. The goal of the worst scenario method is to >> extremize the quantity over the set of uncertain input data. >> >> A general mathematical scheme of the worst scenario method, including >> approximation by finite element methods, is presented, and then >> applied to >> various state problems modeled by differential equations or variational >> inequalities: nonlinear heat flow, Timoshenko beam vibration and >> buckling, >> plate buckling, contact problems in elasticity and thermoelasticity with >> and without friction, and various models of plastic deformation, to list >> some of the topics. Dozens of examples, figures, and tables are included. >> >> More details can be found at >> http://books.elsevier.com/elsevier/?isbn=044451435X >> >> Jan Chleboun >> Mathematical Institute >> Academy of Sciences >> Zitna 25 ( TeX: \v{Z}itn\'a ) >> 115 67 Prague 1 >> Czech Republic >> e-mail: chleb [at] math [dot] cas.cz >> >> > From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 10:50:14 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGoDR7029804 for ; Wed, 16 Feb 2005 10:50:13 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GGoDQD029802 for reliable_computing-outgoing; Wed, 16 Feb 2005 10:50:13 -0600 (CST) Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GGo0KV029793 for ; Wed, 16 Feb 2005 10:50:06 -0600 (CST) Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com (Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004)) with ESMTP id <0IC000644K37PV00@mail-mta.sfvic.sunlabs.com> for reliable_computing [at] interval [dot] louisiana.edu; Wed, 16 Feb 2005 08:49:55 -0800 (PST) Received: from [129.146.72.246] by mail.sunlabs.com (Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004)) with ESMTPSA id <0IC000BK6K36MH10 [at] mail [dot] sunlabs.com> for reliable_computing [at] interval [dot] louisiana.edu; Wed, 16 Feb 2005 08:49:55 -0800 (PST) Date: Wed, 16 Feb 2005 08:49:58 -0800 From: "G. William Walster" Subject: P.S. In-reply-to: <000701c5141f$364f8550$1702a8c0@Moore> To: Ray Moore Cc: Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu, chleb [at] math [dot] cas.cz Reply-to: Bill.Walster [at] sun [dot] com Message-id: <421379B6.6050504 [at] sun [dot] com> Organization: Sun Microsystems Laboratories MIME-version: 1.0 Content-type: text/plain; charset=us-ascii; format=flowed Content-transfer-encoding: 7BIT X-Accept-Language: en-us, en References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu> <000701c5141f$364f8550$1702a8c0@Moore> User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7) Gecko/20040616 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk P.S. Did you have any comments about the short note I sent regarding the use of Popper's ideas? Cheers, Bill From owner-reliable_computing [at] interval [dot] louisiana.edu Wed Feb 16 11:04:39 2005 Received: from interval.louisiana.edu (daemon@localhost [127.0.0.1]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GH4dPx029984 for ; Wed, 16 Feb 2005 11:04:39 -0600 (CST) Received: (from daemon@localhost) by interval.louisiana.edu (8.13.1/8.13.1/Submit) id j1GH4cuV029983 for reliable_computing-outgoing; Wed, 16 Feb 2005 11:04:38 -0600 (CST) Received: from mail-mta.sunlabs.com (dyn50.sunlabs.com [204.153.12.50]) by interval.louisiana.edu (8.13.1/8.13.1/ull-interval-math-majordomo-1.5) with ESMTP id j1GH4INq029979 for ; Wed, 16 Feb 2005 11:04:28 -0600 (CST) Received: from mail.sunlabs.com ([152.70.2.186]) by mail-mta.sfvic.sunlabs.com (Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004)) with ESMTP id <0IC00064NKQTPV00@mail-mta.sfvic.sunlabs.com> for reliable_computing [at] interval [dot] louisiana.edu; Wed, 16 Feb 2005 09:04:05 -0800 (PST) Received: from [129.146.72.246] by mail.sunlabs.com (Sun Java System Messaging Server 6.1 HotFix 0.02 (built Aug 25 2004)) with ESMTPSA id <0IC000BL9KQPMH10 [at] mail [dot] sunlabs.com> for reliable_computing [at] interval [dot] louisiana.edu; Wed, 16 Feb 2005 09:04:02 -0800 (PST) Date: Wed, 16 Feb 2005 09:04:05 -0800 From: "G. William Walster" Subject: Re: P.S. In-reply-to: <421379B6.6050504 [at] sun [dot] com> To: Bill.Walster [at] sun [dot] com Cc: Ray Moore , Vladik Kreinovich , reliable_computing [at] interval [dot] louisiana.edu, chleb [at] math [dot] cas.cz Reply-to: Bill.Walster [at] sun [dot] com Message-id: <42137D05.2040003 [at] sun [dot] com> Organization: Sun Microsystems Laboratories MIME-version: 1.0 Content-type: multipart/mixed; boundary="Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA)" X-Accept-Language: en-us, en References: <200502160527.j1G5RBt19348 [at] cs [dot] utep.edu> <000701c5141f$364f8550$1702a8c0@Moore> <421379B6.6050504 [at] sun [dot] com> User-Agent: Mozilla/5.0 (Macintosh; U; PPC Mac OS X Mach-O; en-US; rv:1.7) Gecko/20040616 Sender: owner-reliable_computing [at] interval [dot] louisiana.edu Precedence: bulk This is a multi-part message in MIME format. --Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA) Content-type: text/plain; charset=us-ascii; format=flowed Content-transfer-encoding: 7BIT Sorry, everybody, but Ray. I intended this only for him, for now. The note I referred to is still a "work in progress". Nevertheless, I would appreciate any feedback regarding it. Thanks in advance, Bill G. William Walster wrote: > > P.S. > > Did you have any comments about the short note I sent > regarding the use of Popper's ideas? > > Cheers, > > Bill > --Boundary_(ID_U3KS6C0RmmCtPus/Fz0qAA) Content-type: application/pdf; x-mac-type=0; x-mac-creator=0; name=draft03.pdf Content-transfer-encoding: base64 Content-disposition: inline; filename=draft03.pdf JVBERi0xLjMKMyAwIG9iaiA8PAovTGVuZ3RoIDI3OTcgICAgICAKL0ZpbHRlciAvRmxhdGVE ZWNvZGUKPj4Kc3RyZWFtCnjajVndj9vGEX/3X3GPJGCx3OV3XorEbuI0gOvaQoOi7gOPok5E KVEhqbtc//rOb2Z2Sd3JSBFEtzszOzvfM0ubu5j+M3cmqaK4zO5yk0VJVdw1xzc/bN/86cc0 uTNFZE12t90z6Xb3r+DH0JgyqMMkDvqQVlNok6ALTRHssX0OEyvbU5gkwUO4saUNZhAdAGgB yINtmHqAzYMhTEwwYvUMvMGBVPB80wxoFbzDqQGAY5jFwRn4C36YnDkRk4JkYvJPYRoLYAjT YOepGxC24b+3f70rbFSU5d3GmqgyJSv4OUyZVwH9CtGFhbjHWdaZlVAoq7kDIA7+ERqSw9mG z5YO59jmsFgqgjARyz5BGrE4SZKxxdOEZDN3m8RGsUlZtp9wIAoJFAe/hhaWzomL/I91Td4h 42ySuCICEycCAXoKS7oLwldkFCifRGVZke7k9bxQ51Y5E9zj1IifC35qvyX/JCYLDNYpXRC8 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