I'd like to ask you guys a question. Do the shapes below look like they have the same area? Don't pull out your calculator or whatever, just tell me if they look like they occupy the same amount of 2D space. They're on the same x-y scale; 1 unit of length on one shape is the same unit of length on the other. I'll reveal the answer in... whenever I think I have enough answers.
-snip-
They are the same area.
Here's my count of responses:
Equal: 2 (+ 1?)
Not equal: 2
Indeterminate/Don't know: 2
The chance (from this tiny dataset) of getting the right answer is 43%. That's basically just random chance.
You see, I was motivated by a book I read (
Storytelling with Data: a Data Visualization Guide for Business Professionals; really good book if you visualize data for whatever reason). On page 61, the author talks about how pie charts "are evil". That is the exact phrasing. Then at page 63, the author then says the following: "The human eye isn’t good at ascribing quantitative value to two‐dimensional space. Said more simply: pie charts are hard for people to read"
That's what sparked my question. I knew of sin(x) and x
2, and I knew that those were fairly easy to end up with integrals with an area of 1. So I went into my graphing calculator software, and I asked it to calculate the definite integrals (non-math types: areas under the curve) of sin(x) between 0 and pi/2, and x
2 from 0 to ∛3. That's where the shapes come from.
Mathematically, you can show that both have the same area, but I knew that people are crap at determining (value from) area from that quote. I wanted to know, "how crap?" Maybe I should've asked "which of these shapes have the larger area", but you get the point.
As far as responses go... well.. I mean this in the most affectionate way possible, but y'all are smartasses. That's not a bad thing; questioning the things in front of you is a good skill to have. But, yeah, the straight answers (as opposed to the smartass answers) do pretty much show the point I was trying to make: people are crap at determining area.
Look at this clusterfuck of a before and after chart (credit to the book mentioned at the start; I'm straight plagiarizing it):
It took Rolan 5 seconds to come to their answer. Imagine doing that 5 times. 25 seconds. You're wasting huge amounts of time on processing time, just because you used a pie chart.
Here's a better version of that chart:
See, that's better. Part of the (huge) improvement comes from not making the audience try to gauge areas, because we're terrible at that. Instead, length is being used to illustrate relative difference.
The point I was trying to make was that people are bad at determining just similarities of area. I don't think it's anything profound, necessarily. I think it's a neat thing that can end up becoming profound with the right context. In the case of that book, it's "don't use pie charts". Maybe there's some value in this fact in other fields.