## Honey, I Shrunk the Kids and the Science of Scale

As a parent, I feel it my duty to introduce my children to the classics of science fiction and fantasy. Arguably, some of the things we watch and read together are more classic than others, but all have their place in the spectrum of classic geekness. Interestingly, my kids immediately identified with the Szalinski family in the film Honey, I Shrunk the Kids (that’s the one with the nerdy dad whose crazy inventions littered the house and often resulted in smoke-filled explosions), while they thought that the sports-loving family next door seemed to be a bit weird—an observation that I must admit filled me with no small amount of irrational pride.

The next day while we were playing with Legos, one of my daughters announced that the movie we had just watched wasn’t very realistic. Interestingly enough, she had no problem with the plausibility of the main premise, that someone had invented a device capable of shrinking matter to an arbitrary size and had accidentally shrunk his children with it. Instead, her problem was that the scale of the film seemed to be inconsistent. This completely ruined her suspension of disbelief via an effect that John Scalzi has called “A Flying Snowman.”

Her reasoning was based on what she perceived as a logical contradiction between two claims made by the film:

1. Nick, the apparent scientist-in-training of the film, calculates that they have been shrunk to just 3/4 of an inch high (around 19 mm).
2. As the movie progresses and the children go forth on their tiny-sized adventures, one of the items they happen across is a toy block, which Nick identifies as a “Lego.” However the scale of this lego does not match the scale declared in the first statement.

Wanting to support her in this quest for truth, I took some screen captures of the film to make some calculations. The Lego in question appears to be a standard 2×3 brick (Lego element ID 300223), which the protagonists use as a safe-haven before being attacked by a giant scorpion.

If we assume that the block in the film is in fact a genuine Lego, and not some generic copy, the brick should be 23 mm tall when standing upright. Assuming Nick is in fact 19 mm tall as he claims, the brick he discovers in the film appears to be closer to 60 mm tall. This is about the size of a 2×8 brick, clearly not the one used in the film.

The next discrepancy we looked at was the relative size of “Aunty,” the ant they tame and then subsequently use as a mount. While ant sizes vary, the one in the film appears to be a little over five times as long as Nick is tall. This would place the ant at a little over 100 mm long. Considering the largest ant currently known (the fossilized Titanomyrma giganteum) was only 60 mm long, the ant in the film is unbelievably large.

The final discrepancy is the relative distance Nick calculates they need to travel to escape their back yard. He states in the film that since they are now 3/4 of an inch tall, the 64 feet they would normally have to travel is now the equivalent of 3.2 miles. Converting to metric, this is the equivalent of stating that 19.5 meters is now 5149 meters. This is an approximate ratio of 1:264. If we try to use the same ratio to calculate their original height, this would make their original height 19 mm x 264 = 5016 mm tall, an equivalent of 16 and a half feet.

Scaling Things Back

Can we attempt to reconcile these differences by assuming that Nick simply made a mistake in his calculations? If we take the Lego brick as a reference, knowing that it should be 23 mm tall and knowing that Nick’s head comes up about two-thirds of the way to the first post this would put Nick to be at 8 mm tall. This would put the ant’s size at around 40 mm, still a rather large ant for a North American garden, but well within the range of known ant sizes.

We could also assume that Nick’s size estimate is correct and that the block in the film is actually a Duplo block (still technically a Lego). A 2×3 Duplo block is 47 mm tall, which would fit the scale shown in the film. While this solves the child/block height discrepancy, it still leaves us with the problem of the gargantuan ant.

There are, of course, several possible ways to use science fiction to explain the overlarge ant. Perhaps the oversized ant is actually a result of experiments by Mr. Szalinski with the growth ray that is shown in the film’s sequel. Alternatively, it might not be an ant at all. It might just be an uncharacteristically kind-hearted Zanti.

Dr. Lee Falin is a Bioinformatician at the European Bioinformatics Institute, the host of the Everyday Einstein’s Quick and Dirty Tips podcast and the author of the “Science Fictioned” series, in which he takes scientific research articles and turns them into sciece fiction and fantasy short stories for middle grade and young adult readers. You can follow him on twitter at @qdteinstein.