“I’ve got a plan,” I said to Pedro. He looked at me. “Have you heard of the ‘wisdom of crowds’?”
Alex, one of the students had. He span around in his chair to explain.
“It was a long time ago, I think, a bunch of people tried to guess the weight of a cow or something. It turned out that the closest answer was the average of all their guesses and it’s a thing! Like a mathematical thing where all the guesses of the crowd focus on roughly the correct answer.”
I told them I had a plan. Take a photo of the guesses so far, put them into a spreadsheet and work out the average.
We all discussed it at length. Pedro had already decided to guess the maximum number of eggs by calculating the area of a cross section of the jar, then roughly dividing it by the length of each egg. If he then multiplied that number by the height, he’d have a good estimate for the total. His guess was 270 eggs.
I thought there would be more than 300 eggs in the jar, simply based on observation, but I was so intrigued by the scientific approach that we talked about it further. What about the way the eggs tesselate between the layers, how they nestle into spaces below their layer, or pack like close-packed atoms in a solid? I thought 270 would be an underestimate.
Pedro was equally fascinated by my wisdom of crowds method. I agree, it is quite extraordinary, but I was pretty sure it would work. I got the numbers and turned them into data, then turned that data into a histogram.
Two guesses were high: 500 and 600. Two were low, and the others were no more than 40 apart. With only 28 guesses, I knew it would be risky to rely on the crowd, so I decided to wait until around 4pm for other guesses to come in. 311, 323, 290… I kept nipping out to collect the latest guesses.
“When did you put yours up?” I asked. “The other day,” said Pedro. Fair enough. I was calculating the standard deviation on a sample of 31 guesses, but of course the variation was huge - about 115. Should I hold to the wisdom of the crowd, I wondered, or listen to the wisdom of Pedro?
I’ve always thought science and statistics were reliable. Logic tumbles into maths, and becomes science - immutable, open-minded, correct, based on the purity of an objective viewpoint. How the wisdom of crowds works I don’t know, but hey, if it the language of the universe could work, if it could inform me, guide me, lead me to a jar packed with chocolate eggs, then surely it was worth a go. I decided to stick with the crowd. The mean average was 301. Someone of course had already guessed 300 and so at 4pm, armed with a pen, I popped back to reception, one final time to make my scientific, logical, statistical guess, based on the wisdom of the crowd. 301 eggs.
-
A few moments later, I swung back into the office.
“You know what the crowd could never have predicted?” I asked, sardonically. Three faces turned blankly. “I’ll tell you,” I said, “That reception would take the jar back in at 3:30.”
Gone. No jar, no sign up sheets, no little yellow chicks pecking around on top of the desk - just the sound of the reception team in their office counting and laughing to themselves behind a half-open door.
My friends chuckled. They told me they would let me know when the eggs were counted, just how close I would have come. Meanwhile, I closed down my spreadsheet and its mocking bar chart.
You know, I’m sure there’s a lesson in there somewhere. I told Sammy about it and she guffawed into her pillow. Did the science work? Is there wisdom in a crowd? Did those outliers shift the numbers way off target? Was the sample too small and were the guessers unreliable? Should I have just entered into the spirit of the thing and plumped for a guess? Probably. I might easily have saved some time.
I closed my eyes and listened to the rain. The lesson is probably to stop overthinking everything, isn’t it. Perhaps it’s not all a problem to be solved.
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