Sometimes even smart and literate people are somewhat naïve when it comes to science. We had an example just recently when educated and sophisticated people compared prevalent conservative skepticism about climate change / global warming with almost non-existent skepticism about the causes of the recent solar eclipse. But this turns out to be a case of dueling misconceptions about differences in scientific methodology: the methodology used to substantiate climate change and the methodology used to account for solar eclipses. The differences are subtle, requiring a working knowledge of the history of science, but important in appreciating the extent to which the two cases – climate change and eclipses – are not *quite* comparable. Almost. But not *quite*.

I am riding this particular horse off a rhetorical cliff, rather like Butch Cassidy and the Sundance Kid, because, ever since the recent eclipse, I have heard people compare the popular reactions to the eclipse and to climate change along the following general lines. The following is one of the two dueling misconceptions. Everyone, even the most hard-core climate change deniers -- literally *every*one -- grants science unconditional trust when it comes to eclipses, accounting for when and why they occur, predicting them, etc. But those same skeptics, who so readily believe in scientific accounts of celestial events like eclipses, balk like a recalcitrant mule – this is the second dueling misconception -- when presented with equally massive evidence substantiating climate change / global warming. The conclusion is that such an attitude is an explicit contradiction: after all, so the argument goes, **the same** scientific method that accounts for, e.g., climate change is **the same** scientific method that accounts for solar eclipses. **Why grant the latter a level of credibility that is denied to the former?** Is that not like calculating the square root of 2 on my Android and believing it, while doubting the value of the square root of 2 if calculated on my iPhone?

Problem is, it really is not quite the same thing as Android v. iPhone. And here is why …

Think about how Johannes Kepler, very early in the 1600s, developed Kepler’s Laws of planetary motion. Remember: *Kepler accomplished this feat well over 80 years before Newton developed his laws of motion* – and, by the by, the mathematical discipline of differential calculus – in the great *Principia*. All Kepler had to go on were the voluminous but **purely empirical** **naked-eye** observations of the great Dutch astronomer Tycho Brahe (rhymes with “fry”), who ranks as one of the two or three greatest observational astronomers who ever lived, not least because *Brahe made his observations well before the invention of the telescope*. (Galileo would not peer through a telescope until around 1610, maybe slightly later.) Brahe was also an unrepentant party animal – when Brahe gazed at the night sky, his eyes were probably not all that were naked! -- whereas Kepler was a driven, dour, straight-laced Reformed Protestant, who had to wait for Brahe to take time out from his (Brahe’s) bibulous dissipations just long enough to dribble out a few more precious pages of astronomical observations.

Notwithstanding, this was a marriage made in heaven: Brahe was almost OCD-like in the meticulous precision of his (again: **naked-eye**) observations and in the organization and recording of same, but lacked mathematical imagination; Kepler was a virtuoso mathematician, in fact, a kind of mathematical mystic – he wasted time trying to account for the motion of the planets by using the Platonic solids – but lacked raw data until he met Tycho Brahe. *Kepler’s seismic discovery was that, hidden within the apparent chaos of Brahe’s mega-reams of individual observations, there was a sublime and elegant pattern: Kepler’s Laws of planetary motion.* Eighty-plus years later, Sir Isaac Newton – like Kepler, also a 17

^{th}-century mega-nerd and a radically

**non**-party-animal – would formulate his laws of motion that account for why Kepler’s laws are as they are. In fact, if you take a decent course in celestial mechanics these days, you will probably derive Kepler’s laws as

*purely analytical theorems*: special cases of Newton’s laws. If you start with Newton’s laws, plus the values of some fundamental parameters like Newton’s gravitational constant, you don’t even need to go outside and look up at the sky to derive Kepler’s laws. All you need is pencil and paper.

The reason I describe this as a “seismic” result is because, from Kepler and Newton on, all you needed to describe the entire Universe **in classical-physics terms** was the value of a few – maybe a dozen-plus – constants like pi, Newton’s gravitational constant, something called the “fine-structure” constant, the value of the unit charge on various particles like the electron, etc., etc., and the rest was sheer pencil-and-paper calculation. Predicting eclipses, as Newton’s friend Sir Edmund Halley demonstrated in the late 1600s when he predicted the return of what came to be known as Halley’s Comet, became a simple (seriously! it really is!) exercise in spherical trigonometry, no gazing through a telescope needed. (Quantum mechanics is **non**-classical, so you have to learn to live with arrays – “vectors” – of probabilities instead of determinate values; hence the “classical-physics” qualifier above.) The point is that the entire zoo, the whole riot of individual, discrete empirical observations, the eye-crossing jumble of numbers, had been corralled into an all-encompassing set of mathematical rules. The most highly developed sciences – physics, cosmology, eventually relativity, and even quantum theory (with the above *caveat* about living with probabilities) -- became *exercises in pure mathematics*. At the most fundamental level, the Universe is elegantly, astoundingly **simple**.

This is where the analogy to the reasoning behind global warming and eclipse predictions breaks down. The latter is an instance, in fact, a classical instance, of the mathematically rigorous discipline of celestial mechanics – an extension of Newton’s and Kepler’s laws. With Newton and Kepler and comets, we have an excellent and exhaustive grasp of what the general laws / rules are, and can express these laws and rules *quantitatively* via the medium of mathematics, e.g., we know with excruciating precision when Halley’s comet will return and when there will be another solar eclipse over the American mainland. *But we do not have anything even remotely approximating that kind of predictive, quantitative power in fields like climatology, paleo-climatology, etc.* If we did, we could have predicted the origin and path of, e.g., Hurricanes Katrina, Harvey, and Irma years … decades … ago, and would not have to settle for multiple model-based “spaghetti diagrams” of all their possible paths. Weather is different from climate, but the two do have this in common: *both weather and climate are inherently, intrinsically *chaotic systems. We can model both, but after a very limited period of time -- typically a few days for weather – the predictions based on those models “diverge”, i.e., cease to accord with empirical reality.

Does this mean that the climate change skeptics may be right? **Absolutely not. Climate change is real. Period. Full stop. **But the *reason we know* climate change is real is not because we have anything analogous to Kepler’s laws of planetary motion or Newton’s laws. Unlike planets’ orbits, climate and weather, and changes thereto, are chaotic systems. (Actually, in the very strictest technical sense, planetary motions are also chaotic, but over spans of time measured in multiple billions of years, not the eye-blink of a few millennia. So celestial mechanics affords us the *temporally grounded illusion* of permanence and stability.) With climate and weather, we have to do what Brahe and other astronomers did, pre-Newton and pre-Kepler: make the best we can of large samples comprising petabytes of climatological and paleo-climatological information. This is the 21^{st}-century version of the 17^{th}-century Big Data-mining that Kepler performed with Brahe’s astronomical observations. Try to imagine predicting solar eclipses using sheer masses of Brahe-like individual, empirical, naked-eye observations: that is why Kepler’s accomplishment is so drool-inducingly awesome.

Will there come a day when, as with Brahe and Kepler, we can comprehend the complexity of climate exhaustively in a set of mathematical expressions that will have the same precision, the explanatory, and the predictive power *vis a vis* climate that Kepler’s and Newton’s laws possess *vis a vis* astronomy? Well … never say “never” … but given that, with climate, we are dealing with chaotic systems constrained by relatively short (on a cosmic scale) time-frames, I would make bold to say “No”. Large-scale quantum computing might, and most likely will, extend the time before the models’ predictions diverge, but I expect there will always be a limit. Chaotic systems are **deterministic**, but that does not mean they are exhaustively **predictable**. I mean "exhaustively predictable" in the sense that the models' predictions will accord with empirical observations for a span of time at least as great as the period of time before "dark energy" causes the Universe to evaporate. That is to say, while I do not know, I do seriously doubt, that even the application of massive quantum processing will yield models that are -- quite literally -- valid for all Eternity: eventually *every*thing turns to *dreck*.

(Even within chaotic systems, however, there is a deep order. It turns out that if we take all the relevant parameters of any chaotic system, we can construct a multi-dimensional "phase space" of all the possible states that any chaotic system can occupy at any given time. The topology of a chaotic system's "phase space" is always an elegantly beautiful fractal which is invariant with respect to scale, i.e., the "phase space" looks the same, no matter how microscopically you examine it. Zoom in on the "phase space". Zoom out on the "phase space". *It always looks the same.* Chaos theoreticians talk about "scale-invariance" of phase spaces in chaotic phenomena. If you find this side-note confusing, just ignore everything between the parentheses.)

The point of all the foregoing is that, yes, **in the foregoing limited sense** eclipses and climate change studies do share a common generic methodology, but only in the sense that, as is always the case with science, observation always constrains theory. In that sense, again yes, both climatology and eclipse prediction are instances of the scientific method. Beyond that, the methodologies are different in that eclipse prediction and description have the luxury of being describable in terms of very terse mathematical algorithms, whereas fields like climatology are always working “down in the weeds” with pure data.

Asserting without qualification or nuance that the two methodologies are “the same” is just true enough to be misleading, and so only muddies the water.

**James R. Cowles**

Image credits

Desert with tree ... PublicDomainPictures ... CC0 Public domain

Polar bear on ice floe ... PublicDomainPictures ... CC0 Public domain

Hurricane Fran, 1996 ... NOOA ... Public domain

Katrina flood, New Orleans ... US Coast Guard, PO-2 Kyle Niemi ... Public domain

Eclipse 2017 ... Pixabay ... CC0 Creative Commons

Eclipse 2017 (color) ... Pixabay ... CC0 Creative Commons