Since writer Ryan North’s Fantastic Four series began in 2022, it’s basically become Marvel’s science communication book. That makes sense, considering Mister Fantastic (Reed Richards) is supposedly the foremost authority on the Marvel Universe. In nearly every issue, North fills the dialogue and story with so many fun, and sometimes puzzling, scientific facts and ideas that it’s enough to make this comic book-loving physics teacher smile every time.
The recent Fantastic Four #23 illustrates this well. While the main plot involves time dilation due to special relativity and some of the fastest particles ever discovered, I want to focus on a very brief moment where Reed mentions the anti-square law. It’s interesting to see Reed suggest that magic must obey this scientific law.
Marvel Comics
So what exactly is the inverse square law?
Well, most people think of this law in relation to Newton’s law of gravity between two point-like or spherical masses (such as the Sun and a planet), or Coulomb’s similar law of the electrical force between two charged particles, but it actually applies to any phenomenon in which something is radiating in all directions at the same time. This is because the inverse square law is actually a mathematical law based in geometry, rather than a scientific law.
Imagine a room with nothing in it except a small table in the middle, with a single lit candle in the middle of the table. Let’s assume that there are no other sources of light, and that the light from the candle flame radiates evenly in all directions.
If you could see the rays of light moving outwards from a candle as arrows, the tips of the rays would form a perfect sphere around the flame. Thus, the light emanating from a candle flame should be evenly distributed across the surface of any given sphere.
http://230nsc1.phy-astr.gsu.edu/hbase/Forces/isq.html
We all know that the surface area of a sphere is equal to 4πr2, where r is the radius of the sphere, and π = 3.14. Therefore, as we move away from the candle and the distance (or radius) from the flame increases, the intensity of the light must decrease as the inverse of r2, since the light is distributed over a surface area of 4πr2.
So if you double the distance from the candle, the light intensity drops to one-quarter, or 25%, of what it was before. If you triple the distance, the intensity drops to one-ninth, or about 11.1%. This is all for simple geometric reasons.
Is this Latveria?
In Fantastic Four #23, Reed seems to assume that when Doctor Doom uses his Sorcerer Supreme magic in Latveria, some kind of magical energy or aura radiates from Doom in all directions. If that’s true, and I agree, the strength of that aura should follow the law of inverse proportion.
But as Reed says, Latveria isn’t that close to his and Ben’s current state of Arizona (I grew up in Arizona, so I know where it is). In Marvel Universe lore, Latveria is located in Eastern Europe, where Hungary, Serbia, and Romania meet. Using the approximate latitude and longitude coordinates of Phoenix, Arizona, and where Latveria is supposed to be, I crunched the numbers and calculated the shortest distance between the two places: about 9,000 kilometers (about 5,600 miles). Of course, the shortest distance is a straight line through the Earth, so I’m not sure why Reed thinks being outdoors would allow the machine to better detect the Sorcerer Supreme’s magic, but oh well.
According to the law of inverse proportions, 9,000 km away in Arizona, the magical “aura” emanating from Doctor Doom would be roughly 81 million times weaker than it would be just 1 km away from Doom, meaning either the Sorcerer Supreme’s aura was extremely powerful to begin with, or Reed’s detectors were very, very sensitive.
Marvel Comics
But first, one wonders whether magic even obeys the anti-square law: does magic radiate equally from the magician in all directions?
Returning to the example of light, many light sources (probably most of the light sources we use every day) do indeed radiate in all directions at once, but some do not: lasers direct light in approximately straight lines, and even a simple lens can focus a group of light beams in one direction, whose intensity does not fall off according to the anti-square law.
Plus, don’t most wizards in the Marvel Universe cast their magic in a specific direction? Usually by shooting magical energy beams or casting curses on specific people? When magic is concentrated in a specific direction, the inverse square law no longer applies.
On the other hand, it’s not hard to imagine a very powerful magician constantly emitting some kind of magical aura as a by-product of their energy. In that case, the law of inverse proportions certainly makes sense. But as we’ve seen, an inverse relationship is just a rate that weakens with distance. It’s hard for me to imagine that Reed’s device in Fantastic Four #23 would detect any measurable magic — that is, unless it gets destroyed by a ridiculously fast cosmic particle in the next panel (spoiler alert).
AIPT Science is co-hosted by AIPT and New York City Skeptics.
