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Hyperacute Interdynamics

|< < Prev #3178 (December 8, 2025)

Title text: Our models fall apart where the three theories overlap; we're unable to predict what happens when a nanometer-sized squirrel eats a grapefruit with the mass of the sun.

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Explanation

Miss Lenhart is teaching a class, a recurring theme on xkcd. She correctly describes two of the three pillars of physics: general relativity, concerning very large objects, and quantum mechanics, concerning very small objects. The third pillar is thermodynamics, but she replaces this with the fictional hyperacute interdynamics, which supposedly specifically covers objects 10 – 30 cm (~4" – ~12") in size and 200 – 700 g (0.44 lb – 1.54 lb) in mass.

When a student points out that the application of hyperacute interdynamics is quite limited, Miss Lenhart responds by stating that this is made up for by the fact that it is apparently very accurate and precise, and states that it is able to perfectly describe squirrels and grapefruit, two objects which fit the necessary size and weight specifications (though see below). Her comment that there are hopes to unify this system with the other two reflects the efforts of physicists to unify general relativity with quantum mechanics, so far without success.

While there is no actual field called hyperacute interdynamics, there is one of mesoscopic physics, described as the study of materials of an "intermediate size". The upper end of mesoscopic physics studies objects whose length is measured in micrometers — much smaller and lighter than what hyperacute interdynamics would study, so the analogy is not perfect. On the other hand, it happens fairly frequently in science that two separate length scales may be studied by different fields with no overlap. In this situation, innovations are, in principle, possible by trying to fill in this gap. An example is that structural biology is concerned with proteins and protein-sized objects, while cell biology is concerned with organelles; experimental techniques for studying phenomena between these two scales were less well-established until the development, in the 2010s, of cryo-electron microscopy.

The title text extends the riff on unification, noting that, under the current system, measurements which require elements from all three pillars are impossible. The example given — when a nanometer-sized squirrel (suggesting an understanding of equivalence across both quantum mechanics and hyperacute interdynamics) eats a grapefruit with the mass of the Sun (similarly, general relativity meshing with hyperacute interdynamics) — would cover all three domains. Such objects are not known to occur in real life, so it is unknown how or why scientists would be trying to measure them. A black hole with the mass of the Sun would have a Schwarzschild radius of 2.95 km, so it would take some significant revisions to theory to accommodate a grapefruit-sized object with that mass, before even considering how a squirrel of that small size (but of more normal mass) could exist and eat the former object.

The eastern gray squirrel, which is the most prevalent squirrel in Massachusetts (where Randall lives), measures 16-20 inches (approx. 40-50 centimeters) on average when fully grown — outside the range of sizes given for hyperacute interdynamics to apply. It does, however, weigh between 400 and 600 grams — within the weight range. Whether hyperacute interdynamics would apply, then, would appear to depend on whether the 'and' in Miss Lenhart's statement is inclusive (a union of candidates from the two separately applicable ranges) or exclusive (only items within the intersection of both stipulations), though the title text suggests that the former is the more logical.

Individually, the head-and-body size and the tail size of the eastern gray squirrel are each within the hyperacute effective size (though potentially not mass). If they were modelled individually, or if the squirrel curled up, then they may become able to be effectively modelled by hyperacute interdynamics, even if the entire, stretched out squirrel cannot. This shows the absurdity of hyperacute physics, with such a strict cut-off making it easy for objects to enter and exit the hyperacute effective size. By contrast, relativity and quantum mechanics slowly become worse at describing reality as size increases/decreases.

Some squirrels, such as the Borneo black-banded squirrel do entirely fit into the hyperacute effective size and mass.

Transcript

[Miss Lenhart is teaching a classroom holding a finger up in front of the class. Two students can be seen sitting at desks in front of her, a Cueball like boy is on the first row and Jill, taking notes, is in the second row.]

Miss Lenhart: Modern physics rests on three main pillars:

General relativity, which describes very massive objects,

[Close up of Miss Lenhart.]

Miss Lenhart: Quantum Mechanics, which describes very small objects,

[In a frame-less panel the view zooms back out, but shows only Miss Lenhart.]

Miss Lenhart: and Hyperacute Interdynamics, which describes objects 10-30cm in size and 200-700g in mass.

[The panel zooms back in to a close up of Miss Lenhart.]

Student (off-panel): That last one seems kind of limited.

Miss Lenhart: Yeah, but over it's domain it's really precise. Absolutely nails squirrels and grapefruit.

Miss Lenhart: Someday we hope to unify it with the other two.

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