LSAT Logic, Math, and Verizon's Epic Fail

(aka "One of My Stupidest LSAT Blog Posts Ever." You probably won't learn a single thing from this blog post, but I hope you'll find it as hilarious as I do and forward it to your friends.)

"Wait a second," you say. "There's no math on the LSAT."

Yes and no.

The LSAT doesn't ask you to solve math problems, but it does ask you to understand the differences between percentages and absolute numbers. It also asks you to perform basic deductive reasoning.

You can see my explanation for one basic deductive reasoning question in Formal Logic Inference Questions.

However, this blog post will cover a simpler real-world example. In this epic fail, Verizon customer service reps embarrassed themselves and achieved Internet notoriety by demonstrating their inability to make some very basic math deductions.

Via NYTimes:

A few years ago... a frustrated customer named George Vaccaro recorded and posted his phone conversation with two service representatives at Verizon Wireless. Vaccaro’s complaint was that he’d been quoted a data usage rate of .002 cents per kilobyte, but his bill showed he’d been charged .002 dollars per kilobyte, a hundredfold higher rate. The ensuing conversation [SS: mp3 via xkcd] climbed to the top 50 in YouTube’s comedy section [SS: link added].

About halfway through the recording, a highlight occurs in the exchange between Vaccaro and Andrea, the Verizon floor manager:

V: “Do you recognize that there’s a difference between one dollar and one cent?”
A: “Definitely.”
V: “Do you recognize there’s a difference between half a dollar and half a cent?”
A: “Definitely.”
V: “Then, do you therefore recognize there’s a difference between .002 dollars and .002 cents?”
A: “No.”
V: “No?”
A: “I mean there’s … there’s no .002 dollars.”

A few moments later Andrea says, “Obviously a dollar is 1.00, right? So what would .002 dollars look like? I’ve never heard of .002 dollars… It’s just not a full cent.”

The challenge of converting between dollars and cents is only part of the problem for Andrea. The real barrier is her inability to envision a portion of either.

If you like reading instead of listening, here's a full transcript of the 27-minute conversation where George encountered multiple Verizon reps, none of whom understood his argument.

Since the Verizon reps didn't understand George's argument, it's entirely possible that someone reading this blog doesn't understand it either.

As the NYTimes blog post notes, the Verizon reps commit more than one logical fallacy, so it's worth taking a bit of time to review their arguments.

The simpler (aka stupider) fallacy:

V: “Do you recognize that there’s a difference between one dollar and one cent?”
A: “Definitely.”
V: “Do you recognize there’s a difference between half a dollar and half a cent?”
A: “Definitely.”
V: “Then, do you therefore recognize there’s a difference between .002 dollars and .002 cents?”
A: “No.”

George makes a simple deductive argument that all of you should have understood.

In case you're reading this while under the influence (I really hope you'd do more exciting things in those magical moments), I'll take a moment to explain.

Using symbols, we could say if A (a dollar) doesn't equal B (a cent), then A multiplied by 0.5 doesn't equal B multiplied by 0.5, and A multiplied by 0.002 doesn't equal B multiplied by 0.002.

(We can also say if A = B, then A +1 = B + 1. On the other hand, if A doesn't equal B, then A + 1 doesn't equal B + 1, but George doesn't get into addition.)

Basically, once you accept the basic premise that dollars and cents are not equivalent, you're also committed to accepting several other statements regarding their different values.


More-interesting fallacy:

Andrea: "Obviously a dollar is 1.00, right? So what would .002 dollars look like? I’ve never heard of .002 dollars… It’s just not a full cent.”

She uses this to support her answer of "No" to the question of whether there's a difference between .002 dollars and .002 cents.

Putting this into an Evidence-Conclusion framework gives us:

Evidence: [Because] .002 dollars is not a full cent (it's 2/10 of a cent)
Evidence: [Because] Andrea has never heard of .002 dollars
Conclusion: [Therefore] .002 dollars is no different than .002 cents


Andrea fails to consider that just because:

-we don't create hard currency in such small amounts (like 2/10 of a cent), AND
-we don't usually charge for things in such small increments

THAT

this doesn't mean that if we were to do so, that these small amounts would have no unique value of their own.

The Verizon mp3 conversation is about cost per kilobyte transmission, which some of you might not know much about.


Here's a simpler example:

Suppose you were 5 years old and bought a jar of sand. (Little kids get a kick out of things like jars of sand.)

Each jar costs $1.00 and contains exactly 50,000 grains of sand. If all grains of sand are identical, then you've just bought sand at a rate of .002 cents per grain.

(50,000 grains/100 cents = 1 grain/.002 cents)

Just because there's no coin representing .002 cents and just because people are unlikely to buy only a grain or two of sand, this doesn't mean the "sand store" can't charge for sand at that rate.

(They'd probably impose some sort of minimum on the amount of sand you can purchase in order to avoid wasting their time with purchases of only a couple hundred grains.)

And this, my dear readers, nearly concludes my simplest blog post ever.

***

Before I go, I wanted to share a funny image I came across while searching "Epic Fail" on flickr. Seems like I'm not the only one interested in the dollar/cents confusion.

Enjoy.

(Comments are from the person who uploaded the photo to flickr - not me. Click image to enlarge.)






























Photo by weatherpattern / CC BY-NC-SA 2.0
Photo by kt / CC BY-NC-ND 2.0