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Rounding error is ubiquitous and unavoidable in digital computers, but with high precision computing (64-bit, 128-bit) it’s so small as to be negligible.
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<div class="">However, in cases where the same computation is performed many thousands or millions of times, it can still accumulate to a point that it’s significant. </div>
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<div style="margin: 0px; font-stretch: normal; line-height: normal;" class=""><font face="Arial" style="font-size: 11px;" class="">MacKenzie, D. (1993). Negotiating Arithmetic, Constructing Proof: The Sociology of Mathematics and Information Technology. Social
Studies of Science, 23(1), 37-65.</font></div>
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<div style="margin: 0px; font-stretch: normal; line-height: normal;" class=""><font face="Arial" style="font-size: 11px;" class="">Also see the short examples of this in my book <i class="">A Vast Machine: Computer Models, Climate Data, and the Politics of
Global Warming</i> (MIT Press, 2010), pages 177-178.</font></div>
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<div style="margin: 0px; font-stretch: normal; line-height: normal;" class=""><font face="Arial" class=""><span style="font-size: 11px;" class="">Best,</span></font></div>
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<div style="margin: 0px; font-stretch: normal; line-height: normal;" class=""><font face="Arial" class=""><span style="font-size: 11px;" class="">Paul</span></font></div>
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<div class="">On Jul 3, 2020, at 10:54, Matthew Kirschenbaum <<a href="mailto:mkirschenbaum@gmail.com" class="">mkirschenbaum@gmail.com</a>> wrote:</div>
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<div class="">Hello all,</div>
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<div class="">I am interested in a better understanding of the nature of computational error. My sense is that actual, literal (mathematical) mistakes in modern computers are quite rare; the notorious Pentium bug of the early 1990s is the exception that proves
the rule. Most bugs are, rather, code proceeding to a perfectly correct logical outcome that just so happens to be inimical or intractable to the user and/or other dependent elements of the system. The Y2K "bug," for instance, was actually code executing in
ways that were entirely internally self-consistent, however much havoc the code would wreak (or was expected to wreak).<br class="">
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<div class="">Can anyone recommend reading that will help me formulate such thoughts with greater confidence and accuracy? Or serve as a corrective? I'd like to read something fundamental and even philosophical about, as my subject line has it,
<i class="">the nature of computational error</i>. I'd also be interested in collecting other instances comparable to the Pentium bug--bugs that were actual flaws and mistakes hardwired at the deepest levels of a system.<br class="">
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<div class="">Thank you-- Matt</div>
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<div dir="ltr" class="">Matthew Kirschenbaum<br class="">
Professor of English and Digital Studies<br class="">
Director, Graduate Certificate in Digital Studies<br class="">
Printer's Devil, BookLab<br class="">
University of Maryland</div>
<div class=""><a href="mailto:mgk@umd.edu" target="_blank" class="">mgk@umd.edu</a><br class="">
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<div>________________________</div>
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<div class=""><a href="https://profiles.stanford.edu/paul-edwards" class="">Paul N. Edwards</a><br class="">
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<div class="">Director, <a href="http://sts.stanford.edu" class="">Program on Science, Technology & Society</a></div>
<div class="">William J. Perry Fellow in International Security and Senior Research Scholar</div>
<div class=""><a href="http://cisac.fsi.stanford.edu/" class="">Center for International Security and Cooperation</a></div>
<div class="">Co-Director, <a href="https://cisac.fsi.stanford.edu/stanford-existential-risks-initiative" class="">Stanford Existential Risks Initiative</a></div>
<div class="">Stanford University<br class="">
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Professor of <a href="http://www.si.umich.edu/" class="">Information</a> and <a href="http://www.lsa.umich.edu/history/" class="">History</a> (Emeritus)</div>
<div class="">University of Michigan</div>
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