Listen to this review! 
Maria Hill: When did you become an expert in thermonuclear astrophysics?
Tony Stark: Last night.
The Avengers brings together a who’s who of Marvel superheroes, including Iron Man, the Hulk, Captain America, Black Widow, Thor, and Hawkeye, to save Earth from the evil plot of Thor’s adopted brother, Loki. I have seen and reviewed several other films based on comic books, though it is not my favorite genre. What brought me into the theater for The Avengers is Joss Whedon’s involvement in the project. I have been a fan of his work for years, since TV’s Buffy the Vampire Slayer, so I was interested to see his take on the superhero movie. I was not disappointed. For a summer blockbuster, this film offers some intriguing math and science to discuss. (I understand the Science and Entertainment Exchange—the National Academy of Sciences program that connects entertainment industry professionals with top scientists—is at least partially responsible.)
As the film opens, S.H.I.E.L.D. (a secret law enforcement agency) is attempting to use an object called the “tesseract” to generate unlimited renewable energy. Loki attacks the facility where the experimentation is occuring to steal the tesseract and enslaves a key scientist and Hawkeye. Loki intends to use the tesseract to transport an army to Earth to enslave the planet. S.H.I.E.L.D. brings the Avengers team together to locate and retrieve the tesseract.
Math teachers might be interested in using this film to generate interest in the real geometric object of the same name. A tesseract is sometimes called a hypercube or four-dimensional cube. Since our everyday world has just three spatial dimensions (length, width, and height), it is very difficult to envision how a 4-D object would appear. The best way I know of to imagine a tesseract is to consider how you get from a two-dimensional square to a three-dimensional cube. A cube can be unfolded to make six squares, one for each face. A 4-D tesseract would unfold into eight 3-D cubes.
Another way to visualize the tesseract is to consider time as the fourth dimension—see the animation at left.
To find the tesseract, the Avengers search for the gamma radiation it emits. Gamma rays are high-energy photons released during nuclear decay. (The two other kinds of radioactive emission are alpha and beta particles.) Gamma rays are more difficult to block than alpha or beta particles, and their energy means that gamma rays can cause cancer by damaging DNA. To harness the power of the tesseract, Loki steals a large quantity of iridium from a government laboratory. Iridium, atomic number 77, is an extremely rare metallic element in Earth’s crust. Iridium is usually found in very small quantities alloyed with platinum, itself a rare element. Iridium is very dense (approximately twice the density of lead!), hard, and brittle, and there is good reason to connect a gamma ray source with iridium metal.
The 1961 Nobel Prize in Physics was awarded to Rudolph Mössbauer for his discovery of resonant absorption and emission of gamma rays in a solid iridium sample. This example of resonant absorption and emission in a solid is now known as the Mössbauer Effect. Because of this relationship between iridium and gamma rays, I found it reasonable in the film’s plot to require a large sample of iridium to make the tesseract work.
Though The Avengers contains some examples of thoughtful science, it has other scenes that are a bit far removed from reality. The mobile base of operations for S.H.I.E.L.D. is a helicarrier, or flying aircraft carrier. As if it isn't challenging enough to imagine lifting the mass of an aircraft carrier thousands of feet into the air, this ship is somehow able to remain in stable flight with one of its four turbines out of commission. The four turbines on the four corners of the ship each provide an upward force to keep the ship aloft, so if one is missing, the ship should tilt like a loaded table that suddenly loses a leg. (Conventional airplanes can maintain flight with an engine out because the engines are not providing lift; they are providing thrust. As long as the airplane is moving forward fast enough, the wings will provide enough lift to keep the plane aloft.) In the film, we see only minor flight problems with one engine out, which is hard to imagine with the design depicted.
The Avengers will give science and math teachers the chance to talk about gamma radiation, four-dimensional objects, and the Nobel Prize when classes resume in September.
Jacob Clark Blickenstaff is teacher education programs manager for the American Physical Society. He can be reached at blickenstaff@aps.org.
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