# Deterministic and Stochastic Applied Physics

Pierre-Simon Laplace was one of the first mathematicians who took an interest in problems of probability and determinism.  It's surprising how much of the math and applied physics that Laplace developed gets used in day-to-day analysis. For example, while working on the ENSO and QBO analysis, I have invoked the following topics at some point:

1. Laplace's tidal equations
2. Laplace's equation
3. Laplacian differential operator
4. Laplace transform
5. Difference equation
6. Planetary and lunar orbital perturbations
7. Probability methods and problems
1. Inductive probability
2. Bayesian analysis, e.g. the Sunrise problem
8. Statistical methods and applications
1. Central limit theorem
2. Least squares
9. Filling in holes of Newton's differential calculus
10. Others here

Apparently he did so much and was so comprehensive that in some of his longer treatises he often didn't cite the work of others, making it difficult to pin down everything he was responsible for (evidently he did have character flaws).

In any case, I recall applying each of the above in working out some aspect of a problem. Missing was that Laplace didn't invent Fourier analysis but the Laplace transform is close in approach and utility.

When Laplace did all this research, he must have possessed insight into what constituted deterministic processes:

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

— Pierre Simon Laplace,
A Philosophical Essay on Probabilities[wikipedia]
This is summed up as:

He also seemed to be a very applied mathematician, as per a quote I have used before  “Probability theory is nothing but common sense reduced to calculation.”  Really nothing the least bit esoteric about any of Laplace's math, as it seemed always motivated by solving some physics problem or scientific observation. It appears that he wanted to explain all these astronomic and tidal problems in as simple a form as possible. Back then it may have been esoteric, but not today as his techniques have become part of the essential engineering toolbox. I have to wonder if Laplace were alive now whether he would agree that geophysical processes such as ENSO and QBO were equally as deterministic as the sun rising every morning or of the steady cyclic nature of the planetary and lunar orbits. And it wasn't as if Laplace possessed confirmation bias that behaviors were immediately deterministic; as otherwise he wouldn't have spent so much effort in devising the rules of probability and statistics that are still in use today, such as the central limit theorem and least squares.

Perhaps he would have glanced at the ENSO problem for a few moments, noticed that in no way that it was random, and then casually remarked with one his frequent idiomatic phrases:

"Il est aisé à voir que..."  ... or ..  ("It is easy to see that...").

It may have been so obvious that it wasn't important to give the details at the moment, only to fill in the chain of reasoning later.  Much like the contextEarth model for QBO, deriving from Laplace's tidal equations.

Where are the Laplace's of today that are willing to push the basic math and physics of climate variability as far as it will take them? It has seemingly jumped from Laplace to Lorenz and then to chaotic uncertainty ala Tsonis or mystifying complexity ala Lindzen. Probably can do much better than to punt like that ... on first down even !

# Confirmation Bias

Someone long ago must have stated that the El Nino/Southern Oscillation (ENSO) phenomenon was not related to lunisolar (lunar+solar) tidal forcing. This negative result (or null result) is not documented anywhere (AFAICT) but is likely considered conventional wisdom by climate scientists. The most direct evidence that climate scientists don't consider lunisolar forcing is that it appears nowhere in the parameterization of general circulation model (GCM) source code.

As a general rule, negative findings are rarely reported in research journals:

"As it stands now, researchers are typically rewarded (tenure, grants, better jobs, etc.) for publishing a quantity of publications in prestigious journals. They do this by

• Running small and statistically weak studies (they are easy to do) that produce only positive results, since journals tend to not publish negative findings.
• Ignoring negative findings.
• Publishing only new and exciting findings that journals are looking for.
• Never checking old findings for accuracy and replicability.
• Changing methodologies in mid-stream to assure positive results."

I imagine that if a budding graduate student devised a hypothetical ENSO/lunar tidal connection as a potential thesis topic, it would be rejected by his advisor. The advisor would not want to risk his reputation or track record by going down a potential dead end. The same is perhaps true of the recent case of NASA JPL rejecting the proposal of one of their research teams who suggested funding for this actual topic.  Read an excerpt from this footnote:

"None of the peer-reviewers nor collaborators in 2006 had anticipated that the most remarkable large-scale process that we were going to find comes from ocean circulations fueled by Luni-Geo-Solar gravitational energy. We found evidence of the existence of this energy in the data produced by satellites like QuikSCAT and ASCAT. Following the standard
from the 1970’s of using these satellite data as winds in numerical modeling of oceans and climate has created and continues to create significant errors in the simulated ocean temperature, salinity, and currents as well as in the atmosphere. Together with our co-workers, we chose not to publish the errors until a solution to appropriately use

satellite data in numerical modeling was found. However, over the following years, proposed solutions were not considered because of various factors including economic and scientific pressure to publish and continue the standard agenda."

This is a clear example of confirmation bias stalling promising research. Yet, apparently there are no issues with pushing iffy models of ENSO based on nebulous chaos theory by climate change deniers such as Anastasios Tsonis.
Hmmm ... something is not right with this picture.

So if this lunisolar model of ENSO pans out, it is an excellent example of how confirmation bias impeded scientific progress, but with the scientific method eventually winning out.

Fig 1: Top is the ENSO model trained on NINO3.4 data from 1880 to 1920, with the lower curve providing a calibration of the lunar forcing based on sensitive LOD measurements of the earth's rotation. ENSO is not a chaotic process if it can be stimulated directly by the known lunisolar forcing.

And we can do the same confirmation bias exercise with the quasibiennial oscillation (QBO) phenomenon, substituting the climate change denier Richard Lindzen for Tsonis as the impediment to progress.  Lindzen couldn't find the lunar connection (even though there is plenty of evidence he tried), so just assumed it wasn't there.  Everyone that followed Lindzen's original model essentially confirmed his bias and so no progress was made, until the bias was removed and the lunisolar forcing re-evaluated.

The difference here is that I am not preparing a thesis or working for NASA. This is one way of inoculating oneself from historical confirmation biases -- by not being part of an inside consensus, there is no one to suggest to "not go there".  By the same token, I now possess an apparent confirmation bias that a lunisolar forcing plays a primary role in certain climate phenomena.  Yet, it's a weak confirmation bias because I didn't start with this view, but it gathered steam based on all the evidence accrued over the past few years. It is now up to others to use the scientific method to reject this model. And, of course, I will be the first to abandon this model if I come across strong evidence to reject it. After all, I don't have any particular allegiance to the moon gods, only in the learned view that oscillations of this nature do not occur via spontaneous resonance.

As an important footnote to this post, consider the recent admission that lunar forces play a significant role in triggering earthquakes. Up to the last year, the confirmation bias was that the lunar gravitational forcing was too weak to trigger earthquakes, and so the onset was historically described in statistical terms. The earthquake itself triggered by the passage and time and the slow creep of a fault. But the tide turned in 2016 when two independent groups found significant correlations with lunar cycles -- a Japanese group led by Ide [1] and a US Geological Survey group led by van der Elst [2]. These are the same fortnightly lunar cycles (see Figure 2 below) that are used in the ENSO model described above (compare to lower chart in Figure 1).  So the new thinking is that indeed the gravitational pull of the moon will trigger the slipping of a fault, and this happens enough that future predictions of earthquakes (for example along the San Andreas fault [3]) can use tidal tables to aid the analysis.

Fig 2: Lunar forced earthquake analysis by van der Elst et al [2]. Note the fortnightly cycles similar to Fig 1 above.

The bottom-line is that we need to monitor the earth sciences consensus regarding lunar forcing in the next few years, both in terms of ENSO and QBO climate behavior and with regard to earthquake analysis.   Scientific theories are not binding, unlike sporting events -- "World cup matches cannot be replayed, but science can be corrected afterwards.". Thus, the confirmation bias of "no lunar forcing" is not necessarily set in stone.

## References

1. Ide, Satoshi, Suguru Yabe, and Yoshiyuki Tanaka. "Earthquake potential revealed by tidal influence on earthquake size-frequency statistics." Nature Geoscience 9.11 (2016): 834-837.
2. van der Elst, Nicholas J., et al. "Fortnightly modulation of San Andreas tremor and low-frequency earthquakes." Proceedings of the National Academy of Sciences (2016): 201524316.
3. Delorey, Andrew A., Nicholas J. van der Elst, and Paul A. Johnson. "Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault." Earth and Planetary Science Letters 460 (2017): 164-170.