# Analogies, Numeric Sequences, and Balls of Wax

Is it just me, or has there been an almost annoying increase in the number of “Let’s see how smart you are” ads on the Web these days? From self-propelled pseudo-IQ tests to numeric sequences to who-knows-what-else, I see these little buggers pop up on all manner of pages. I find them to be a waste of time, not because I think any form of testing is bad, but because the very premise of a correct answer is sometimes flawed. In some cases, all they tell you is whether or not you think like the person who wrote the test.

A case in point: The other day while checking the weather forecast, I saw one of these little irritants off to the side of the page. It started with a simple analogy “teaser” in the hope that you’d follow the link. Here’s what it was. There was a picture of three items; a very green, somewhat elliptically shaped lime, an orange, and a bright red tomato, complete with green leafy bits at the stem. The question posed was “Which is not like the others?” I imagine that a typical person might say “the tomato”, perhaps because gastronomically-speaking, the first two are fruits and the tomato is a vegetable. But what’s so special about that reasoning? Depending on your perspective, you might also pick the tomato because it’s not citrus, or because it was the only one that included leafy bits, or because it’s the only item of the three that doesn’t grow on a tree.

This would be a moot point if we couldn’t make similar arguments for the other items. For example, someone could pick the lime because it’s the only one that’s not at the red end of the color spectrum or because it’s not spherical. Similarly, one might choose the orange because it’s the only one of the group that most folks would eat “out of hand” by peeling or because there’s no green in the picture at all. Is the fact that a tomato is not citrus really any more important than the fact that the lime is not spherical or that people don’t usually peel limes and tomatoes and eat them as snacks? I argue that the question as posed is ambiguous. It’s not like the question was “which of these is least closely related to the others botanically?”

Perhaps these get under my skin because they remind me of those analogies from the old SAT, things like:
Fire hydrant is to cat as eyeglass case is to
A) German Shepard
B) atomic nuclei
C) that funny little drainage divot under your nose and above your lip, also known as the philtrum

Then again, I’m equally aghast at those “Guess the next number in this sequence” tests. Heck, I can create all manner of answers for that one, in some cases it’s just a matter of creating an interesting polynomial, and in others, a tendency to think in alternate domains. If there’s no clue as to what the rule for the sequence entails, then the sky’s the limit. For example, while I’d wager that most people would continue the sequence “100, 200, 400, 800” with “1600”, I imagine quite a few runners (or at least fans of track and field) might say “1500”. With no other guidance, is a doubling in any way more meaningful than a listing of Olympic standard race distances? Being both an electrical engineer who works with numbers every day, and a distance runner who logs many miles every day, I declare “No”. That is, what seems obvious, and thus logical, to me in this instance will depend on my state of mind at the moment. If a student offered up this sequence at the close of an electrical circuits lecture, I’d be very likely to say “1600”, but if that same person asked me just as I was finishing up some speed work or viewing an IAAF meet featuring Alan Webb and Bernard Lagat, “1500” would be the clear favorite.

Granted, this is perhaps a whole lot about nothing, considering I’m just talking about some dumb, little, Web sites. The problem I see is that some people take these sorts of tests seriously, and seriously enough to subject a whole lot of students to them via standardized testing. But that’s a whole ‘nother ball of wax.

1. #1 kemibe
August 26, 2006

Which of these doesn’t belong?

* A triceratops

* A calf (i.e., a young cow)

* A fiery flying serpent

* Zacharius (son of Elisabeth)

Bible scholars will immediately realize that the correct answer is obviously “A,” the only one of the four organisms listed that the Bible does not characterize as a fruit.

2. #2 Jim
August 26, 2006

Ahh, but the real question is whether or not Zacharius was capable of riding a triceratops like a pony. I’m sure some folks in Florida can shed a little light on that subject.

3. #3 Irrelephant
August 26, 2006

Hum. Yep, I have also seen some proliferation of ads for pseudo-IQ measurements. I guess they’re tapping on some Perelman effect; several articles I saw about him had headlines like “Smartest man on Earth refuses prize”, and people may wonder about their own intelligence (and perhaps their chances to win a million bucks). The part I least like about these tests is that they lead people to identify their intellectual value with a number which is fixed, like their height. No reason then to spend time learning, or to put some effort into thinking.

4. #4 Aerik
August 26, 2006

It’s been my understanding that the tomato is a fruit because It’s obviously a kind of berry. What do you mean to illustrate by “gastronomically-speaking?”

5. #5 Jim
August 27, 2006

A botanist may classify a tomato as a fruit, but it is sold and prepared as a vegetable. Ask almost any cook, farmer or grocer whether a tomato is a fruit or a vegetable, and they’ll say “vegetable”.

I put berries on my cereal every morning, but tomatoes and raisin bran isn’t going to cut it.

6. #6 Aerik
August 27, 2006

I know different trades sort them differently Jim – we all do – but I think we need a biologist’s opinion on the matter, or at least something more scientific than what it looks like or how we use it. That’s why I am asking the Doc to elaborate what she means by “gastronomically-speaking.”

7. #7 llewelly
August 28, 2006

Step (1): Write down a definition of ‘fruit’.
Step (2): Write down a definition of ‘vegetable’.

Step (3): Using the definitions from (1) and (2), sort each of the following into either the ‘fruit’ category or the vegetable category. Justify each decision.

Banana
Cucumber
Eggplant
Honey-Dew melon
Lime
Plantain
Coffee
Tomato
Zucchini

8. #8 Jim
August 28, 2006

Aerik, take a closer look at the by-line of that piece. I’m assuming that you weren’t aware that this is a group blog.

9. #9 Ryan
August 28, 2006

llewelly,

step 1: Friuts are things that form from flowers and contain seeds.

Step 2: vegetables are plant parts that we eat that don’t form from flowers and contain seeds (and are consumed in sufficient quantities to not be considered herbs).

Step three. All examples are fruits. Except probably coffee. Coffee, as we know it, is a roasted seed.

I understand your point though. Different people categorize things different ways. To a lot of people a fruit is something that comes froma plant and is sweet and a vegetable is something that comes from a plant and goes well with savory flavors.

If you go by that definition then you have a list that breaks down about 1/3 fruit, 1/3 vegetable and 1/3 shrug and make it up.

Basically all the wrangling plays up the fact that humans are great at sorting things into artificial boxes. Nature doesn’t care so much.