Ernie pretends to be a doctor.
Today we get a new facet to Bert's personality: hypochondria. It isn't a prominent trait in that we don't necessarily see it outside of this sketch, but it is in keeping with his concerned and cautious nature.
In Muppet time, Big Bird is always six, Elmo is always three and a half, and Oscar the Grouch is always 43, "because it's a funnier number than 42." So how old are Bert & Ernie? As far as I know, there's not an official numerical answer to that question. The closest thing to an official answer that I've ever come across is that sound bite from Joan Ganz Cooney to which I am so fond of linking.
There are some people who insist that Bert & Ernie are grown men, probably based on the fact that they live in an apartment with no parents. These people have clearly never learned the difference between a man and a Muppet. Who knew that song was filling such an educational void?
In this sketch, Ernie says that he won't be able to become a doctor until he goes through, "eight years of grade school, four years of high school..." etc., which would imply that either he is involved in a proto version of Billy Madison1 or else he's only five or six years old.
So there we have our answer, right? Well, no; it's not quite as simple as that. On the 1983 album Sesame Street Sing-Along!, Ernie drives a bus, and in the movie Follow That Bird he flies a plane. So in those instances, Ernie has to be at least the minimum age to get a driver's license and a pilot license, respectively (both of which probably vary by state).
And what about Bert? In a few weeks, we will meet Bert's twin brother, Bart, who seems to be an adult, which would imply that Bert is also an adult.2 I also remember another specific instance in which Bert makes reference to having spent "10 years at Julliard," which could mean that he's a child prodigy but would more likely mean that he's an adult. On the other hand, in some sketches he seems more like a kid, specifically the "I Wish I Had a Friend" sketch that we watched last month.
So here's the answer to the question: Bert & Ernie are whatever age they need to be in any given sketch in order for it to be funny. This means that their ages can vary from sketch to sketch, even between two sketches in the same episode! This same principle applies to Grover; Grover seems like a little kid, but if they need him to be a waiter, then he's old enough to be a waiter, and if they need him to be a taxi driver, then he's old enough to be a taxi driver, etc.
The one constant with regards to Bert's & Ernie's age(s) is that Bert always seems to be more mature than Ernie. That doesn't necessarily mean that he's an adult, however. Ernie could be five and Bert could be 12 or 14. But if they are both youngsters, then why do they live in an apartment by themselves? This is just my unsubstantiated opinion, but I think it's supposed to represent a child's fantasy of living in an apartment with your best friend without any responsibilities (or at least very few). Think of it this way: they don't have jobs, they don't seem to ever go to school, they never complain about bills or worry about paying rent, and really, the only time they have responsibilities is when it's in service of comedy. Also, their landlords are Susan and Gordon, who are essentially the surrogate parents of everyone on Sesame Street. They have the best of both worlds; the benefits of both childhood and adulthood without the negative aspects of either.
Well, that's not entirely true. Gossip is almost always a negative aspect of life no matter whether it occurs among children or adults, and in the world outside of Sesame Street, poor Bert & Ernie are plagued by it. But we'll talk about that next week.
1Which would probably be a lot funnier than the real version.
2Bert also has a baby nephew whom we will also meet in a few weeks, but that doesn't necessarily indicate his age. Under certain circumstances, anyone can become an aunt or uncle at almost any age.