Friday, June 12, 2009

American Education - Take a Bow

Oh, dear. Another shortcoming of the overachieving class was brought home by an incident that occurred on the television show Cash Cab. It's a quiz show that plays out in a Manhattan taxi (seriously), and it's often a painful indictment of our country. Take, for instance, what happened when two young women were asked to name, in thirty seconds, the U.S. Presidents whose first and last names started with the same letter. I suppose there are a number of approaches to answering such a question. The approach these girls took was...hilarious, sad, and typical of people whose grades far outrun their intelligence.

One girl just started naming all the presidents, in order, starting with Washington. This is one approach! But a little thought will determine that this is a bad approach. To take one flaw (not the most serious flaw, but...), "Ronald Reagan" was unlikely to pass her lips within thirty seconds. To take the real flaw, she didn't actually know a damned thing. Like a .doc file or, hell, a piece of paper, all this chick could do was to repeat, thoughtlessly, a list of facts. Apparently the very idea of sorting the facts internally, selecting some, and focusing attention on them (you know, what we high-class intellectuals call "thinking") was foreign to her poor data-stuffed mind.

This sort of thinking-without-thinking can survive very long. All of the authors of this blog have spent substantial time in law school classes. All right, guys, how many times have you heard a student approach a complicated legal question by doing nothing more or less than listing elements? It is as if, to the question "How well does the application of the felony-murder rule advance the policy of retributivism?" these clever fools expect the answer "A criminal homicide constitutes murder of the second degree when it is committed while defendant was engaged as a principal or an accomplice in the perpetration of a felony" to score high marks. This kind of reasoning is over- and under-inclusive. Where some aspect of the answer isn't even arguably in dispute, it looks like ignorant redundancy (like answering "George Washington" to the original question); when the answer fails to address a relevant aspect of the question, it looks clueless.

This isn't smart. Stop rewarding it and these retards can skip seven years of schooling and go straight to their unrewarding desk jobs.

3 Comments:

At 12:56 PM, June 12, 2009 , Blogger Joshua said...

OK, I have to play devil's advocate on this one. Your points lower down are fine, and the American education system *does* suck, but I don't think that the girl's approach on Cash Cab is supportive of your argument. Sorting and selecting would be exactly the wrong approach on this one. The girl was correct, though I would have done it slightly differently.

For starters, being able to "name the president with first and last name starting with the same letter", is *not* the sort of metric by which we should measure the educational system. It's the epitome of a useless fact. In fact, in my field of work, we might select this as an interview specifically *because* it is so useless, and unlikely to be memorized -- and would have to be computed.

So, having set the context that this question is *only* useful for measuring someone's algorithmic approach and thinking process, let's evaluate the approaches.

Of course, any approach that a computer could take could also be taken by a human, with the understanding that humans are much slower at computation. The interesting thing in this case is that the brain-dead brute-force listing approach is actually smarter for *both* humans and computers. If anyone suggested the sorting or grouping approach, it would be an instant "no hire".

For a computer, the fastest sort is O(n log n), which is pretty fast, but a lot slower than brute force, which is O(n). The fastest way for a human to sort (with pencil and paper), would be to write all 26 letters on a piece of paper, and then categorize names. But it's obvious that you could easily stop when you hit a name that matches, which defeats the purpose of sorting.

The only time you would sort or group first is if you would have to do hundreds of similar lookups. It is not too hard to figure out how many you would need to do before sorting would be smarter. That would be a good interview question.

Finally, no reasonable human would have grouped (by first or last name) or sorted the presidents in long-term memory. Such information is completely useless, so it's no indictment of the American education system that the girl didn't have a pre-built index of presidential last names.

Now, although I think brute-force is the best, I personally would have started at the beginning and gone for 5 or 6, then started at the end and worked backwards, as a simple heuristic assuming that these names will be the quickest to recall, and also slightly more likely to be used for a trivia question.

 
At 8:53 PM, June 13, 2009 , Blogger Vernunft said...

I wasn't evaluating whether she could answer the question (in enough time, she could have). She knew MORE useless facts that necessary, clearly. I was evaluating the approach adopted. So whether she got the answer "right" is not really relevant.

I also don't see how your conclusion leads to anything but a paradox. The brute force method is the best ex ante but it'll turn out to fail this question every time ex post?

 
At 11:06 PM, June 13, 2009 , Blogger Joshua said...

Right, I was saying that the *approach* of iterating through them one at a time is the only right approach (and the only one that would get a "hire" for someone I interviewed). Even if some other approach got her the right answer quicker, it would be due entirely to dumb luck, and thus "incorrect".

The brute force approach won't fail this question. If the person is capable of getting the right answer (i.e. if they can even recall a subset of the presidents which contains the correct president), this approach will get the right answer for every class of this problem in the shortest possible time, every time. Of course, the answer may not come fast enough, but no other approach will be superior.

Anyway, I apologize for jumping in and harping on something so petty. I agree with the sentiment of the post, and I love this blog. I was hooked and subscribed after finding an old post about Kant, and I've found subsequent posts about German philosophers, religion, and law (among other things) to be extremely insightful and thought-provoking.

 

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