Circle graphs are the worst

Flashy animations are all the rage on cable news networks.  And people love infographics.  Both show a illogical love for graphs made out of circles.

From the :

radii measured with geogebra after constructing a circle through three points plotted on the edges of the graphics circles.

There are two issues: squared ratios, and packing.

The first arises that as you change the radius of the circle, the area will increase by the square of the radius.  So the designer has to choose one measurement to represent their unit.  It appears that they chose area for this graph.  The given scale seems accurate for the $100 billion circle’s area to the $10 billion circle’s area.  However, the $1 billion circle appears to be off, or I can’t measure it precisely enough.  The problem here is that we are better at recognizing linear relationships rather than square relationships.

The problem here is human intuition.  Does the largest circle look like 10 times as large as the medium one?

Consider these two representations of an area growing by a factor of 4.  Which is more natural?

To the unpracticed geometer, it may seem very difficult to believe four green circles fit into the large one.  Large area-scaled circles “seem smaller” than they should

That is the second issue: packing.  Rectangles are easy to pack.  Copy that green rectangle 3 more times and it will fit exactly in the area outlined.  But to fit the circle into its large circle of 4x the area, it requires distortions.  Those distortions harm the communication of knowledge.  Back in the first image, they attempt to pack a lot of various budget area’d circles in a large circle.  But the empty space makes the budget cover an area much larger than it should.

Infographics should always aim to present data in a way that makes it easier for the public to understand.  When style is chosen over substance, the information is distorted, literally.  Because of the competing effects of being too large or too small, I don’t believe the mis-communication was malicious.  Rather, it was ignorant.

“Very Lenient Umpire Tells Base Runner Next Time He Gets Tagged He’s Out”

I saw this great Onion Sports article today:,20903/

Umpire Laz Diaz displayed an unusual amount of leniency Sunday, allowing a clearly tagged Hanley Ramirez to take third base regardless of his failed steal attempt, on condition the Marlins shortstop understood he could not count on the same treatment next time. “I told him next time he’s tagged out, I’m calling him out,”

This Onion article should be shown to any new teacher.  Actually, it should be shown to all teachers.  How often do we make this mistake in our own classrooms?  We always think it will be easier to just let it go, but it always comes back to bite us.

I’m trying to take a tougher philosophy every year.  Not only in management, but in grading as well.  Especially when doing Standards Based Grading, I find it easy to tell a student: “nope, you didn’t get it,” because I can append “yet” to the end.

News Media

This XKCD comic reminded me of why I hate most of the News Media. The panel on the left is a pretty accurate rendition of a full screen graphic one of the 24 hour networks had up:

: $170 billion
Bonuses: $165 million

At first glance, one might arrive at the conclusion that AIG was using almost its ENTIRE bailout for these bonuses. “How irresponsible! What an outrage! Despicable!” But upon closer inspection, one notices the difference between the numbers. What if we actually took the difference?

– $165,000,000
= $169,835,000,000

There’s $165 million is a drop in the hat. Its about 0.1% of the bailout money. It pales in comparison! It should not be compared. I’m not defending AIG. That’s not the issue. The issue is the News Media is presenting information in a misleading format. I also assert the News Media is doing so purposely. They want the outrage, because outraged viewers will watch more. Everything is sensationalized and distorted.

The new propoganda isn’t for political gain. The Media wants your viewership and your money. They will distort the facts for it.

Our financial crisis is a result of people misrepresenting information about loans rates, feasibility of real estate transactions, investment options and the market in general. People would bend the truth to gain more money. Now, the News Media is now misrepresenting information… to gain more money. They mimic the actions of the very organizations they codemn.

“Why do we have to take math?” students ask me. Look at the world. Those who understand the system will take advantage of those who do not. A simple concept like orders of magnitude (billions vs. millions) will be lost on many viewers who have been in the habit of non-mathematical thinking.

The next time stats or data is thrown in your face, by the Media or anybody else, pause and think: “what does it really mean?

Wikipedia Crawl

I was channel surfing and stumbled upon The Late Late Show with Craig Ferguson. He was doing a Michael Caine impression and made some joke that I didn’t quite get. Wikipedia to the rescue! or so I thought…

1:36 am

1:58 am: I split into two simultaneous tabs:

Branch 1:
2:24 am

Branch 2:
2:24 am

There are some real gems in there. Never did find out what Ferguson was referencing though.

xkcd #214.


What a piece of work is iPhone, how noble in reason, how infinite in faculties, in form and moving how express and admirable, in action how like an angel, in apprehension how like a god.

Hamlet was one of the first people to get an iPhone but I was only 6 months behind! Scientifically speaking, it rocks.

Using elementary set theory, I will describe precisely every way in which it rocks, by articulating the complement.

{How the iPhone rocks}c

  1. No Copy/Paste. Well, no text highlighting in general. These are essential tools, and I feel handicapped without them.
  2. No GPS. This doesn’t sound so bad to most people, (“why do I need to know exactly where I am?”) but once you start playing around with the contacts and google maps then you realize you’d want some sort of functionality of “how do I get from HERE to there?” Basically, putting in GPS would have made the iPhone the closest thing to a URAT* modern society has to offer.
  3. Needs a search filter on Contacts. As fun as it is to flick my contact list to scroll through them all, I would like some sort of shortcut to get to a specific person.
  4. EDGE is slightly slow. But frankly, it works just fine for most of my needs. Even downloading stuff from YouTube isn’t bad with it. I sometimes even turn off Wi-Fi to go to Edge when the network signal is weak.
  5. Calendar only syncs with Outlook 2003 or 2007 on Windows. I would much prefer it to sync with Google Calendar directly. You can access Google Calendar through the web, of course, but I want to use the iPhone calendar “without all that tedious mucking about in hyperspace.”*
  6. Headphone jack is recessed. This is so the curved edge of the iPhone is still curved, and it actually protects the structure of the headphone jack, the internal card, and the plug. But it also means all standard headphones wont work without an adapter… $25.
  7. No 3rd party apps — yet. Sure I can go through Safari to do web-based apps, but that’s an inherently bulky way of doing things, and what did I just say about mucking about…
  8. No direct interaction with files — yet. I can’t see the files I have on there (“the files are in the computer*) or do anything with them, such as saving a picture off the internet, deleting songs, editing tags, editing documents.

That’s it. And essentially, most everything will be great when Apple puts out their Software Development Kit (SDK) and lets Google work their magic. Google people are SMRT*.