An Ig Nobel for Mathematics
On October 5, 2006, photographer Nic Svenson (eyes open) and physicist Piers Barnes (eyes closed) were awarded an Ig Nobel at Harvard University by the Annals of Improbable Research magazine. The award was for their calculation of the number of photographs that a person must take to ensure that nobody in the group had their eyes closed. Who says that mathematics does not have value!
The problem is modeled after the solution of the infamous birthday problem. Their approach is as follows:
It turns out that this model follows the normal distribution (or bell curve). To be 99% certain of getting a good picture (i.e. no blinks), Piers caclulated that Svenson needed to take 30 photos. With a group of 50 people, it becomes almost impossible to get a good picture.
- A person being photographed blinks an average of 10 times/minute
- The average blink lasts 250 milliseconds
- A camera shutter stays open about 8 milliseconds
- Assume that the eye blinks of group members being photographed are random and independent
- Probability of one person blinking and spoiling photo is product of x (expected # blinks) and t (time during which photo could be spoiled)
- Probability of one person not blinking and spoling photo is (1-xt)
- And for a group, the probability of n people not blinking is (1-xt)n
- Therefore, the number of photos needed is 1/(1-xt)n
As a rule of thumb when taking a group photo of less than 20 people, Piers suggests that you divide the number of people by 3 if there is good light and by 2 if there is bad light. Again, who says that mathematics has no value!