There was at least one Mars probe that crash landed due to unit conversion (or lack there of) between subcontractors. And I believe there was an early launch failure (perhaps a Venus probe?) due to a minus sign. And I recall a space shuttle laser experiment that ended up pointing the laser up instead of down. Not sure I'd classify any of these as true math failures. And there was the case of the atrium that collapsed, killing a bunch of people, due to the contractor placing fasteners in the wrong place, doubling the load. But that wasn't a math error either. I think it was similar to the classic physics problem with window washers deciding to tie one end of their rope to their building rather than their platform, instantly doubling the load on the rope. (The other end of the rope is tied to the platform, and the rope goes over a pulley above that is fastened to the roof.) --ms On 20-Dec-15 20:21, James Propp wrote:

Has anyone compiled a list of disasters caused by errors in basic math?

I don't mean things like the vibration-induced collapse of the Tacomah Narrows Bridge; that involved a fairly sophisticated mistake and a lack of imagination. I mean things like the Hubble Telescope debacle, which I gather in part stemmed from a failure to keep track of units and do necessary conversions.

I'm asking because on their final exams, many of my students changed 3^n + (-2)^n to 3^n - 2^n. Next time I teach the course, I plan to explicitly remind them about this common mistake (and to exhort them not to commit it), but even more than that, I'd like to tell them about some memorably terrible thing that happened as a result of somebody somewhere neglecting to use parentheses where they were needed, or misusing them in some fashion.

And even more, I'd like to see a compendium of such adverse outcomes, so that any time I want to warn the students away from a particular kind of mistake, I can say something like "If you make this mistake on my exam, you might lose points. And if you make this mistake after you graduate, you might kill hundreds of people."

(I don't know if crosses-along-highways are a universal thing, so I'll pause to explain that here in the U.S. they signify places along a roadway where a fatal accident occurred.)

Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

Hello, I know that Paul Zimmermann told me a series of catastrophes that occured because of a miscalculation in a computer, data exception, division by zero, almost collisions of planes because of the computation of tan(Pi/2) , I had the reference about it, lost it. I will try to get my hand on it. Best regards, Simon Plouffe

On Dec 20, 2015, at 8:21 PM, James Propp <jamespropp@gmail.com> wrote:

And even more, I'd like to see a compendium of such adverse outcomes, so that any time I want to warn the students away from a particular kind of mistake, I can say something like "If you make this mistake on my exam, you might lose points. And if you make this mistake after you graduate, you might kill hundreds of people."

Those students will increasingly be using automated tools for avoiding those fatal minus signs, so diligence of that sort may not be what your students need the most. A more troublesome thing, in my mind, is illustrated by a correspondence I had with a young research intern at the Federal Reserve (the US institution that sets interest rates). The question concerned a line of code in a software package that was developed in-house. This line of code computes the logarithm of a number, but first checks that the number is positive. When the check fails, the logarithm is replaced by a fixed constant. The intern wanted to know the rationale for choosing this constant. I think I did the right thing by pointing out to the intern that the code surely suffers from more serious problems if that check fails with any regularity!

On 2015-12-20 17:21, James Propp wrote:

Has anyone compiled a list of disasters caused by errors in basic math?

I don't mean things like the vibration-induced collapse of the Tacomah Narrows Bridge; that involved a fairly sophisticated mistake and a lack of imagination. I mean things like the Hubble Telescope debacle, which I gather in part stemmed from a failure to keep track of units and do necessary conversions.

https://www.ssl.berkeley.edu/~mlampton/AllenReportHST.pdf I haven't plowed though this, but I recall reading that the grinding was to be guided by a highlight off a metallic calibration bead, but a misaligned guidance lens deceived a technician into mistaking the highlight off some protective plastic goop for the metallic bead. This would have been caught by "all-up" testing, which was skipped due to cost and time overruns. --rwg

I'm asking because on their final exams, many of my students changed 3^n + (-2)^n to 3^n - 2^n. Next time I teach the course, I plan to explicitly remind them about this common mistake (and to exhort them not to commit it), but even more than that, I'd like to tell them about some memorably terrible thing that happened as a result of somebody somewhere neglecting to use parentheses where they were needed, or misusing them in some fashion.

And even more, I'd like to see a compendium of such adverse outcomes, so that any time I want to warn the students away from a particular kind of mistake, I can say something like "If you make this mistake on my exam, you might lose points. And if you make this mistake after you graduate, you might kill hundreds of people."

(I don't know if crosses-along-highways are a universal thing, so I'll pause to explain that here in the U.S. they signify places along a roadway where a fatal accident occurred.)

Jim Propp