What does voice/data service have to do with math performance?

[kirisutogomen]

"" (Watch on YouTube)

Comments

[billmarrs.livejournal.com]

I like the part in the middle when the support guy put him on hold and he let out this fairly long and quite audible sigh of exasperation.

I thought his explanations and examples, though futile, were quite good. I doubt I could have come up with anything better in his shoes.

I get the impression that each of the people he talked to didn't have much confidence in their math skills. The last person even admitted this. I think this is part of the reason why the conversation went on so long.

The calculator usage was interesting, especially how each of the support people he talked to seemed to rely on it to give correct answers. Which it did, but...

[firstfrost.livejournal.com]

After reading the transcript of this and beating my head on the desk for a while, I think I do understand what's going on.

Dollars are the *units*. If you have 1,000,000, you have One Million Dollars. So, you might say "Win $1,000,000 - a million dollars!" and not really mean "a billion dollars", because you aren't trying to multiply the quantity times the description. Similarly, if you have .01, you have One Cent. .03 is Three Cents, which is the same things as ".03 cents". Because in your head, the dollars are still the units, and the cents are just what you're using to describe pieces of dollars.

[readsalot.livejournal.com]

I'm about 4 minutes into it, and I'm not sure I can stand to listen to much more. It is clear that the support person does not get the whole idea of units--once they start getting into fractions, he doesn't think that the words "dollars" and "cents" are meaningful any longer. There's just some absolute unit (probably dollars) and the word (dollars/cents) used to modify the rate is not relevant.

It's very sad.

[treptoplax.livejournal.com]

Incidentally, Google has a marvelous calculator with units built into their search page now. I use it at work all the time, eg:

http://www.google.com/search?hl=en&lr=&safe=active&q=10+TB+%2F+%2890%25+*+1+GB%2Fs%29+in+hours

[kirisutogomen.livejournal.com]

As part of the inevitable and interminable follow-up, the customer included a Google link in some e-mail (http://verizonmath.blogspot.com/2006/12/my-email-response-to-verizon.html). I was vaguely wondering what was up with that, and it's hard to tell from his page, where some of the link is missing. Now I know. That's pretty nifty.

[kirisutogomen.livejournal.com]

But 0.5 cents isn't the same as 0.5 dollars. So when does it switch over?

I suspect 0.03 cents is actually $0.0003, and cents don't mean dollars until you get below 0.01, but I'm really not sure.

I also feel like if we could really understand what's going on here, it could be really useful. If I could have predicted this as well as mjperson's Diet Coke Incident (http://mjperson.livejournal.com/11227.html), I'd have a much better understanding of my species.

[kirisutogomen.livejournal.com]

Well, if you didn't get into the second half, you missed

G: 0.002 cents is different than 0.002 dollars. I'm being charged 0.002 dollars per kilobyte. 0.002 dollars is one tenth of one... I mean, two tenths of one cent.

A: Okay, well, I mean it's obviously a difference of opinion...

[kirisutogomen.livejournal.com]

I agree that the customer seemed to be genuinely trying to help them out. I probably couldn't have done better, but I'd like to find out what I'd need to know to be able to do better.

The calculator thing is definitely interesting. I think some people might be tempted to blame over-reliance on calculators for the lack of math intuition, but I would guess that's not the problem. I suspect that if you take away the calculators people just transfer their trust to a mindlessly-executed pencil-and-paper algorithm.

[jdbakermn.livejournal.com]

Wow, that just made my head hurt. BTW, transcript, if you're not interested in listening to the whole thing (Thanks FirstFrost).

http://verizonmath.blogspot.com/2006/12/transcription-jt.html

[firstfrost.livejournal.com]

I think it switches over when the word "point" enters into it. Point zero one means that one is a cent. You can see it when they're talking about .5 dollars - that's confusing, so he says "half a dollar". Sure, half a dollar is not the same as half a cent. But what the heck is point five dollars? Point notation is supposed to have two decimal places!

That is, 1.59 is a unit of money. One is in dollars, and .59 is in cents. Sure, .59 cents.

.5 is not a coherent unit of money. Nor is .002.

[kirisutogomen.livejournal.com]

There's an interesting bit right before George hands off to Andrea, when George seems to be saying that "0.002 cents" is equivalent to "two-tenths of a penny." Do we think that "penny" means something different from "cent" to George?

[firstfrost.livejournal.com]

(as I hone my explanation)

I think it's that any amount which has a decimal point in it is essentially in the unit "moneys". 0.002 moneys is a hard amount of moneys, because it's not anything you can count out, but it's "two tenths of a penny". Not .02 pennies, because .02 has a decimal point in it, so that would be .02 moneys, or two pennies.

In English, how do you say $1.59? You don't actually say one point five nine dollars. You say "a dollar and fifty nine cents." 1.xx = one dollar. .59 = fifty nine cents. Cents aways have .s in front of them!

[readsalot.livejournal.com]

I did keep listening after I wrote my reply, though I nearly gave up again when the woman doing support insisted that 0.002 dollars was not a real rate, but 0.002 cents was.

I wonder what would have happened if he'd tried to explain that you can get from any dollar amount to any cents amount by dividing the dollar amount by 0.01, and that you go from cents to dollars by multiplying cents by 0.01.

[thatwesguy.livejournal.com]

Okay, first, this is incredible.

Second, this is part of why I'm a math tutor.

Third, this seems to me to be an example of the all-too-common tendency to conflate units with quantity. All day, every day, many laypeople (in contrast to engineers and scientists) assume units based on the quantity involved -- or, at least, based on the way the quantity is expressed. This is a useful tendency for people to have; it provides error correction.

If I said that something cost 0.05, we would all understand that I meant a nickel. If I said 0.1, we would not necessarily understand that I meant a dime, because the way that that is normally quoted is either 0.10, or 10. This, too, is no problem, because context usually makes clear in the case of "10" whether I mean cents or dollars.

But if I say 0.10, most people know what I mean because that pattern is well-established as a synonym for $0.10, even though any engineer or scientist will confirm that it is in a strict sense no such thing.

Now, having bent over backwards defending this customer support reps in this example, I will point out that while all this error correction and context-dependence is usually useful, it's also occasionally necessary to be able to employ stricter terminology, so that when context doesn't make it clear, one can distinguish between half a cent and half a dollar.

In short, they may not be idiots, they are most assuredly stupid.

It breaks my heart a little.

[kirisutogomen.livejournal.com]

Excellent!

If the length is 1.5m, I don't say "one meter, fifty centimeters," but if it's 1.5ft I do say "one foot six inches."

Similarly, "one hour, twelve minutes, fifteen seconds."

And I wouldn't blame you for being confused if I said "0.0625 gallons," because I'm violating the standard for what units to use for that order of magnitude.

The insight involved must actually be pretty sophisticated, because it's essentially what's necessary to stop using MCMLXVIII and go decimal, and some pretty smart guys went pretty far without ever figuring that one out.

(All this said, I still blame Verizon, for quoting the price per kilobyte instead of per megabyte. "Two dollars per Mb" makes everything perfectly clear.)

[billmarrs.livejournal.com]

Yes! I think this is exactly what was going on! nice hone!

[kirisutogomen.livejournal.com]

Let's test our comprehension. Is "point five nine cents" the same as "fifty-nine cents"?

It sounds like you're saying it is, because cents always have .s in front of them. But I find it hard to believe that people would claim that 0.59 cents = 59 cents.

Then again, I still find the original conversation difficult to understand, and the Diet Coke sympathetic magic still blows my mind.

[firstfrost.livejournal.com]

I think "point five nine cents" might be like "$1 dollar", with redundant units, so yes, equal to fifty-nine cents.

(So point five cents is *not* the same as half a cent, for example.)

I'm trying to think of another example where the "units" come before the number, but haven't thought of one yet.