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In this paper, page 7 (160 of the Journal), Fig 3, there is a particularly amusing (not to the authors!) caption:

"... On April 1 of year 2 in the $S_0$ experiment, the computer was hit by a cosmic ray or some other disturbance which caused improper numbers to be stored in the ground temperature array."

Note that the temperature array they are referring to is NOT a physical probe; the entire experiment was done numerically on what's probably a room sized computer for the duration of at least a year. The authors even plot a dashed corrected curve in the figure to try and account for this.

Are there any other documented cases of numerical errors arising from physical phenomena affecting older computers? I'm aware of stuff like the Pentium FDIV bug and the collection from this question but, I was wondering of examples more in line with the above caption from seemingly ridiculous sources like cosmic rays?

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closed as off-topic by j.c., Ramiro de la Vega, David White, Chris Godsil, Daniel Moskovich Oct 10 '13 at 5:14

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about research level mathematics within the scope defined in the help center." – j.c., Ramiro de la Vega, David White, Chris Godsil, Daniel Moskovich
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Nothing ridiculous about cosmic rays. See cs.toronto.edu/~bianca/papers/sigmetrics09.pdf $\endgroup$ – Dan Piponi Oct 9 '13 at 23:13
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    $\begingroup$ Odd that it happened on April 1 though! $\endgroup$ – Gordon Royle Oct 10 '13 at 3:10
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    $\begingroup$ I feel that this question is off-topic because it's about history of computing and hardware design, as opposed to being about mathematics. $\endgroup$ – Daniel Moskovich Oct 10 '13 at 5:20
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They were having some trouble with the Harvard Mark II in 1945, when Grace Murray Hopper found a moth stuck in the machine --- the first (and, so far as I know, only) literal computer bug. Mentioned at http://www.computerhistory.org/tdih/September/9/ and elsewhere on the web.

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In the 1970s, or was it the 1980s, IBM ran a large number of computers for months down a deep mineshaft and another lot at ground level, to test the hypothesis that cosmic rays were responsible for rare memory errors. They found that the main culprit was alpha decay of impurities in the memory chips and their packaging, with cosmic rays also contributing. These days alpha decay is no longer much of a problem due to more pure materials, but cosmic rays keep on coming.

The error rate is a lot higher than you imagine. If you ran a computation for a month there was probably a few hits. I have encountered events with no better explanation several times. Error-correcting memory helps a lot.

A technical article with facts and figures is here.

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    $\begingroup$ " I have encountered events with no better explanation several times" curious on what events? $\endgroup$ – Brout Oct 9 '13 at 23:42
  • $\begingroup$ I mean very long computations that obtained slightly incorrect answers but when rerun with the same program on the same computers got the right answer. $\endgroup$ – Brendan McKay Oct 10 '13 at 10:43
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This would have been in the 1930's. Lehmer and Lehmer invented a factoring machine with lots of gears and an electric eye. This would misbehave at random intervals. Eventually it was traced to a short-wave radio enthusiast in the neighborhood; when he broadcast, the eye thought it was succeeding. Page 242 in Recreations in the Theory of Numbers, by Albert H. Beiler.

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Yes. This problem is particularly salient for satellite systems, which are less shielded than regular terrestrial electronics. As transistors get smaller, particles are ever more likely to cause logical errors.

You have to design HW that is robust to these sorts of particles: Wikipedia:Radiation Hardening

I have friends that have gotten PhDs in this field: http://www.isde.vanderbilt.edu/wp/tag/radiation-effects/

I think it's pretty cool stuff.

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Actually, bits get flipped in DRAMs quite often due to physical phenomena, including hard enough radiation. Besides DRAMs I've seen GPUs misbehave like that. The sensitivity of many computational components to disturbances like these depends in part on the temperature. This is one of the reasons why most DRAMs have ECC bits and logic for error correction: it periodically checks for inconsistencies in main memory and tries to correct the errors.

Actually the theory behind some of the error correction schemes has some interesting mathematics, including polynomials over finite fields and information theory. The questions raised there is how to correct up to E errors in a block of B bits, B >> E, using no more than 2E redundant bits, what would be the optimal block size given the dependency of error probability on the size of the block, etc.

Another related subject would be fault-tolerant computing.

Here's a Wiki article on ECC: http://en.wikipedia.org/wiki/Error_Control_Coding

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It is not that uncommon that external physical phenomena influence computer hardware. Cosmic rays are indeed known to cause problems. Sun (the computer company) ran into a similar problem around year 2000, as they delivered and installed lots of high end server CPUs, which would sporadically fail. The problem was alpha radiation from either the packaging or cooling fins on the cache memory chips, causing bits to flip if the actual memory location was hit by alpha particles:

http://www.sparcproductdirectory.com/artic-2001-dec-1.html

At the particle accelerator in CERN, the researchers thought they had a computer bug depending on the moon phase. The issue eventually turned out to be that the moon position actually causes the geometry of the particle accelerator to change slightly, causing the moon phase to influence the measurements themselves (and not the following calculations on the collected data):

http://www.catb.org/jargon/html/P/phase-of-the-moon.html

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