Saturday, May 19, 2018
Happy Metrology Day!
I'll call this my annual Metrology Day item. I'm too busy to run up a really proper animation.
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Another excellent piece by the NON-NEWS departments of BBC. A well-researched article on shrinkflation.
They miss two important points.
On toilet paper, the width of the roll has been shrinking along with the total length of the paper. I was accidentally able to document this. Width makes a difference. When the paper is narrower, you need to pull more squares to get the same effect. Each roll is necessarily used up faster. Double benefit to the seller. Less material per roll, more rolls per month.
On food pleasure, they get the non-linear nature of perception right, but miss on the math needed to sum up the pleasure.
Each curve represents the pleasure of eating, with the x-axis representing 20 spoonfuls.
Each bite gives you a delta of pleasure, indicated by the little arrow roughly between Bite 2 and Bite 3. The real pleasure goes up fast at the start, peaks in the middle, and goes down fast. (I've shown it as a sine for easy math, but it's probably more like a rounded trapezoid.)
The lower curve indicates the linear pattern that we assume if we don't understand perception.
Figuring the sum of the deltas on each curve:
Chandon, who also studies the pleasure of eating, thinks that there's a way to downsize some products, like chocolate, that doesn't irritate so many people but doesn't fool them either. That's because the enjoyment we get from food doesn't grow in lockstep with amount consumed. “The first bite of a chocolate mousse is usually the most pleasurable,” he says. “After that it decreases. The last bite, honestly, it's the one you regret. We all know that. The thing we fail to realise – and it's super-important – is that the pleasure of this entire chocolate mousse you're eating is not the sum of the pleasure of each bite. It is the average.”Exactly right on the curve, but the result is NOT the average. Graphically:
Each curve represents the pleasure of eating, with the x-axis representing 20 spoonfuls.
Each bite gives you a delta of pleasure, indicated by the little arrow roughly between Bite 2 and Bite 3. The real pleasure goes up fast at the start, peaks in the middle, and goes down fast. (I've shown it as a sine for easy math, but it's probably more like a rounded trapezoid.)
The lower curve indicates the linear pattern that we assume if we don't understand perception.
Figuring the sum of the deltas on each curve:
import math
# Figure sum of deltas on the top curve:
total=20
spoon=0
sum=0.0
oldY=0.0
newY=0.0
for spoon in range(total):
rads = float(spoon) * math.pi / float(total)
newY = math.sin(rads)
sum = sum + (newY-oldY)
oldY = newY
print "sin",sum
# Figure sum of deltas on the bottom curve:
total=20
spoon=0
sum=0.0
oldY=0.0
newY=0.0
for spoon in range(total):
newY = float(spoon) / float(total-1)
sum = sum + (newY-oldY)
oldY = newY
print "linear",sum
The results: Total pleasure on the sin version is 0.15, and total on the linear (as you'd expect) is 1.
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Later editorial quibble: If I'd been writing the original article and wanted to use a food example just after discussing toilet paper, I probably wouldn't have chosen chocolate mousse for the example.Labels: Metrology, Real World Math
¶ 8:41 AM
