In the book Mathematical GeoEnergy, I mention the word heuristic or heuristics 82 times. In scientific research, it’s an important signpost because it identifies where a physical understanding is lacking, which is the point I was trying to make in a recent online discussion.
In the preface, I specifically cite the sunspot cycle as a heuristic, which I commented on:
“For example, the 11 -year sunspot cycle is considered a heuristic but not the annual or daily cycles, which are trivially explained. Tried to get ChatGPT to agree with me:
https://chat.openai.com/share/2706730c-2767-4060-b65e-08549b538d0e“chatGPT is correct.
whats your problem
I responded with two examples of heuristics that can conceivably be replaced by plausible and parsimonious physics.
Heuristic: The wobble is approximately 433 days, thought to be excited by fluctuations of mass on Earth achieving a natural resonance condition.
Physics: The wobble of precisely 433 days is a frequency side-band of the lunar draconic cycle interacting with the annual cycle. Not resonant just as the annual wobble is not resonant, and due to a forced angular momentum response.
QBO.
Heuristic: The oscillation is approximately 2+ years, thus the name “quasi-biennial”, thought to be excited by atmospheric waves.
Physics: The oscillation of 2.37 years period follows from the semi-annual oscillation at higher altitudes locked to the longer period by the lunar tidal forcing at lower altitudes of the stratosphere. The cycle is commensurate with simultaneous nodal crossings of both the moon and sun across the ecliptic plane.
In both these cases, the heuristic could be discarded and the description of the behaviors updated. Another example may be Milankovitch cycles, which replaces the heuristic of glacial cycles with a plausible physical mechanism that matches the observations. Whether Chandler, QBO, or Milankovitch will stand the test of time is another question, but these new models aren’t considered heuristics because they predict precise values for the observations. Discovering replacements for heuristics are rare nowadays as most of the heuristics (such as ocean tidal cycles) were resolved long ago. Circadian rhythms were a heuristic replaced by an encoded mechanism 20-30 years ago. Explaining predator-prey population cycles are at the heuristic stage still, IMO and may not get resolved as humans modify the environment.
The suggestion is that an unresolved heuristic is always a good candidate for a thesis topic.
NEW
Discussing relatively recent discoveries that replaced a heuristic, one that also came up is the Quantum Hall Effect. This is a subtle one because although the effect was experimentally discovered by von Klitzing, a Japanese team did roughly predict it a few years earlier, but added a caveat that they did not believe their own calculations! They also did not predict the quantization was in exact integer multiples. So that remained a heuristic for only a short time until it was physically explained (I remember giving a talk on this derivation for my solid-state physics class, which the instructor was very happy about). But then the experimental discovery of a fractional Quantum Hall Effect occurred, which apparently is still a heuristic because a strong consensus has yet to emerge on the physics behind it. Over the years, there have been at least 3 Nobel Prizes shared among 7 physicists to topological QHE research.
I bring this up because there’s a recent Quanta Magazine article dated July 18 titled “How Quantum Physicists Explained Earth’s Oscillating Weather Patterns” which describes how the QHE math can be conceivably applied to making predictions for equatorial patterns, and thus removing at least some of the heuristic nature. Geoffrey Vallis, who is an expert on geophysical fluid dynamics, is quoted in the article saying that the new result is a significant advance that will provide a “foundational understanding” of Earth’s fluid systems. The intriguing aspect is that this did not require the periodic order of a lattice — quoting from the article:
“I was surprised to see that topology could be defined in fluid systems without periodic order,” said Anton Souslov, a theoretical physicist at the University of Bath
Curry has a tweet on this, a reply tweet here because I am blocked
GeoEnergy Math 