Last week I visited my dad and step-mom in St. Joseph, Missouri (home of the Pony Express). My dad is a medical physicist. He used to be a professor in the Department of Radiology at Vanderbilt, but left for reasons that are best left unstated, since I don't know what the statute of limitations is on these things. Let's just say that I was well aware of the existence and nastiness of academic politics well before I became a participant myself. And I still don't trust doctors.
Anyway. Dad told me the single most WTF-inspiring education story I've ever heard. Some thirty-odd years ago, he was supervising a visiting student from another country. As a sort of warm-up exercise, he asked the student to measure the dead time for a scintillation camera. A scintillation camera consists of a radioactive source and a screen of material that converts charged particles into visible photons. Basically, it's a Geiger counter, only with flashes of light instead of ticks of sound. After each flash, a scintillator element needs some time to recover before it can flash again; this interval is the camera's dead time. There's a standard experiment to estimate dead time called the two source method: measure the response to two calibrated sources, both separately and together, all for the same duration, and plug those three measurements into a simple formula.
Anyway, the student went to the lab, did the experiment, and came back with a dead time of minus 3 milliseconds.
Confident that the scintillation camera had not spontaneously mutated into a time machine, my dad asked the student to repeat the experiment while he watched. She set up the the first source, set the timer on the camera, and pushed the start button.
Click, click, ding!
Now, the experiment called for a twenty-second measurement interval, and ‘click click ding’ was just way too short. Rather than correct her directly, my dad asked the student, "How much time was that?"
Dad looked at the camera and realized the problem. The camera's timer had a Nixie tube display. The decimal point in the second-to-last tube was defective, so the display read 20 (or 2.0) when it was set to 2.0 seconds.
But she should have noticed that. So Dad asked the student to run the test again.
The student checked the sample, set the Nixie timer to "2.0" again, and pushed the button. Click, click, ding!
"So how long was that?"
"Do you see that clock on the wall over there? I want you to look at the clock, and watch how long it takes the second hand to go from the 12 to the 4."
The student looked at the clock. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. Tick. "Okay."
"How much time was that?"
"Now run the test again."
Click, click, ding!
"Now how long was that?"
The student simply could not conceive of the idea that the timer display could be wrong. The display said "20", so the time must have been set to twenty seconds, no matter how much time it seemed to take.
That's where Dad's story ended, but it doesn't explain the student's original answer. A shorter experiment would give a less accurate estimate of the dead time, but it would still be positive. The only way to get a negative solution from the two-source formula is to take one measurement over a longer time period than the others. Since the student was a physics major who had won a scholarship to study in the US, she probably did the high-school math correctly and followed the experiment's directions slavishly. I can only surmise that the decimal point on the Nixie tube went out during the experiment, and the student didn't notice the discrepancy.