Did Aboriginal Australians predict solar eclipses?

“Mathematics has been gatekept by the West and defined to exclude entire cultures” declares Professor Rowena Ball of the Australian National University, who wants mathematics to be “decolonised”. In one sense she is right, mathematics is indeed “a universal human phenomenon” that transcends individual cultures. But she is wrong to suppose that anyone disagrees; she is wrong to claim that there are people who think of mathematics as having “an exclusively European and British provenance” and want it to remain that way. Rebutting a strawman serves only to signal one’s superior attitudes.

Professor Ball claims that “Almost all mathematics that students have ever come across is European-based”, and yet “algebra” is an Arabic word and so is “algorithm”. Foundational concepts such as the number zero and negative numbers originated in the Middle East, India and China before being adopted by Europeans. The mathematics now taught to schoolchildren in Mumbai and Tokyo is the same as that taught in London.

Being Australian, Ball’s primary concern is to laud the mathematics of indigenous Australians as being of equivalent merit to globally mainstream mathematics, so she wants a “decolonised” curriculum in which “indigenous mathematics” has equal standing.

But how much substance is there to her case? What would actually be taught? Professor Ball’s article gives only one anecdote about signalling with smoke rings, and based on that alone concludes that: “Theory and mathematics in Mithaka society were systematised and taught intergenerationally”.

In a longer, co-authored article, she reviews evidence of mathematics among indigenous Australians prior to Western contact, but finds little beyond an awareness of counting numbers and an ability to divide 18 turtle eggs equally between 3 people. She recounts that they had concepts of North, South, East and West, could travel and trade over long distances, and knew about the relationship between lunar cycles and tides, and had an understanding of the seasons and the weather. And yes, I’m sure that they were indeed expert in the forms of practical knowledge needed to survive in their environment. But there is no indication of a parallel development of mathematics of equal standing to that elsewhere.

The two authors assert: “We also illustrate that mathematics produced by Indigenous People can contribute to the economic and technological development of our current ‘modern’ world”. But nowhere is that actually illustrated. There is no worked example. The suggestion is purely hypothetical. And there is no exposition of what a “decolonised” mathematics curriculum would actually look like.

There is one claim in the article that did seem intriguing:

But Deakin (2010, p. 236) has devised an infallible test for the existence of Indigenous mathematics! This is that there must be ‘an Aboriginal method of predicting eclipse’. To predict an eclipse, one needs clear and accurate understanding of the relationships between the motions of the Sun and Moon. In spite of the challenge, the answer is yes. Hamacher & Norris (2011) report a prediction by Aboriginal people of a solar eclipse that occurred on 22 November 1900, which was described in a letter dated in December 1899.

Predicting solar eclipses is indeed impressive. It requires considerable understanding and long-term record-keeping over many centuries, in order to discern patterns in eclipse occurrences, or it requires some sophisticated mathematics coupled with measuring and recording the locations of the sun and moon to good accuracy. Either is hard to do in a society lacking a written language. (English astronomer Edmond Halley is best known for having predicted the return of a comet and for predicting a solar eclipse over London in 1715, the first secure example of that feat, though it is likely that Babylonian, Chinese, Arabic or Greek astronomers, such as Thales, possibly using something like the Antikythera Mechanism, had done so centuries earlier.)

This geoglyph in the Ku-ring-gai Chase National Park has been interpreted as a record of a solar eclipse, depicting the eclipsed crescent above two figures.

Hence, Professor Ball’s claim of a successful prediction of a solar eclipse is vastly more significant than anything else in her paper. So I looked up the source, a paper by Hamacher & Norris (2011). The evidence is a letter written in December 1899 by a Western woman who says: “We are to witness an eclipse of the sun next month. Strange! all the natives know about it; how, we can’t imagine!”.

Afterwards the same correspondent wrote: “The eclipse came off, to the fear of many of the natives. It was a glorious afternoon; I used smoked glasses, but could see with the naked eye quite distinctly”. But there was no eclipse until a year after the first letter (Nov 1900), not “next month”; the “fear of many of the natives” is incongruous with the suggestion that they had predicted it; and the text of the letters comes from a later compilation in 1903. This is the only piece of evidence given that Aboriginal Australians had developed the ability to predict eclipses; Professor Ball presents nothing else, and nothing from Aboriginals themselves. She gives no account from any Aboriginal about how this is done, and if that’s because she cannot find anyone who could give that account, then doesn’t that count for more than one anecdote that could have been misunderstood or miscommunicated?

That Professor Ball accepts such weak evidence uncritically shows that she is driven by an agenda, not by a fair assessment of the development of mathematics or of the history of indigenous peoples. There is no substance here, no account of what an “indigenous mathematics” curriculum would look like. It does students from indigenous backgrounds no favours to divert then away from global mathematics into “ethnomathematics”. Ironically, it is people like Professor Ball who are telling them that mathematics is “colonised” and European and not for them. This is the wrong message. Mathematics and science are universal, and should be open to everyone, and we should not be dividing universal enterprises into silos with ethnic labels attached.

This piece was written for the Heterodox Academy STEM Substack and is repoduced here.

Confusion over causation, both top-down and bottom-up

I’m becoming convinced that many disputes in the philosophy of science are merely manufactured, arising from people interpreting words to mean different things. A good example is the concept of “reductionism”, where the meaning intended by those defending the concept usually differs markedly from that critiqued by those who oppose it.

A similar situation arises with the terms “top down” versus “bottom up” causation, where neither concept is well defined and thus, I will argue, both terms are unhelpful. (For examples of papers using these terms, see the 2012 article “Top-down causation and emergence: some comments on mechanisms”, by George Ellis, and the 2021 article “Making sense of top-down causation: Universality and functional equivalence in physics and biology”, by Sara Green and Robert Batterman.)

The term “bottom-up” causation tends to be used when the low-level properties of particles are salient in explaining why something occurred, while the term “top-down” causation is used when the more-salient aspect of a system is the complex, large-scale pattern. But there is no clear distinction between the two, and attempts to propose one usually produce straw-man accounts that no-one holds to.

Human brains have to be deterministic (though indeterminism would not give us free will anyhow)

Are human brains deterministic? That is, are the decisions that our brain makes the product of the prior state of the system (where that includes the brain itself and the sensory input into the brain), or does quantum indeterminacy lead to some level of uncaused randomness in our behaviour? I’ll argue here that our brains must be largely deterministic, prompted by being told that this view is clearly wrong.

First, I’ll presume that quantum mechanics is indeed indeterministic (thus ignoring hidden-variable and Everettian versions). But the fact that the underlying physics is indeterministic does not mean that devices built out of quantum-mechanical stuff must also be indeterministic. One can obtain a deterministic device simply by averaging over a sufficient number of low-level particle events. Indeed, that’s exactly what we do when we design computer chips. We build them to be deterministic because we want them to do what we program them to do. In principle, quantum fluctuations in a computer chip could affect its output behaviour, but in practice a minimum of ~50 electrons are involved in each chip-junction “event”, which is sufficient to average over probabilistic behaviour such that the likelihood of a quantum fluctuation changing the output is too small to be an issue, and thus the chip is effectively deterministic. Again, we build them like that because we want to control their behaviour. The same holds for all human-built technology.

Confusion about free will, reductionism and emergence

Psychology Today has just published: “Finding the Freedom in Free Will, with the subtitle: “New theoretical work suggests that human agency and physics are compatible”. The author is Bobby Azarian, a science writer with a PhD in neuroscience. The piece is not so much wrong — I actually agree with the main conclusions — but is, perhaps, rather confused. Too often discussion in this area is bedevilled by people meaning different things by the same terms. Here is my attempt to clarify the concepts. Azarian starts:

Some famous (and brilliant) physicists, particularly those clearly in the reductionist camp, have gone out of their way to ensure that the public believes there is no place for free will in a scientific worldview.

He names Sabine Hossenfelder and Brian Greene. The “free will” that such physicists deny is “dualistic soul” free will, the idea that a decision is made by something other than the computational playing out of the material processes in the brain. And they are right, there is no place for that sort of “free will” in a scientific worldview.

Here’s GJ 367b, an iron planet smaller and denser than Earth

This is an article I wrote for The Conversation about a new exoplanet, for which I was a co-author on the discovery paper. One reason for reproducing it here is that I can reverse any edit that I didn’t like!

As our Solar System formed, 4.6 billion years ago, small grains of dust and ice swirled around, left over from the formation of our Sun. Through time they collided and stuck to each other. As they grew in size, gravity helped them clump together. One such rock grew into the Earth on which we live. We now think that most of the stars in the night sky are also orbited by their own rocky planets. And teams of astronomers worldwide are trying to find them.

The latest discovery, given the catalogue designation GJ 367b, has just been announced in the journal Science by a team led by Dr Kristine Lam of the Institute of Planetary Research at the German Aerospace Center.

The first signs of it were seen in data from NASA’s Transiting Exoplanet Survey Satellite (TESS). Among the millions of stars being monitored by TESS, one showed a tiny but recurrent dip in its brightness. This is the tell-tale signature of a planet passing in front of its star every orbit (called a “transit”), blocking some of the light. The dip is only 0.03 percent deep, so shallow that it is near the limit of detection. That means that the planet must be small, comparable to Earth.

Science does not rest on metaphysical assumptions

It’s a commonly made claim: science depends on making metaphysical assumptions. Here the claim is being made by Kevin Mitchell, a neuroscientist and author of the book Innate: How the Wiring of Our Brains Shapes Who We Are (which I recommend).

His Twitter thread was in response to an article by Richard Dawkins in The Spectator:

Dawkins’s writing style does seem to divide opinion, though personally I liked the piece and consider Dawkins to be more astute on the nature of science than he is given credit for. Mitchell’s central criticism is that Dawkins fails to recognise that science must rest on metaphysics:

Eddington did indeed validate Einstein at the 1919 eclipse

You’re likely aware of the story. Having developed General Relativity, a theory of gravity that improved on Newton’s account, Einstein concluded that the fabric of space is warped by the presence of mass and thus that light rays will travel on distorted paths, following the warped space. He then predicted that this could be observed during a solar eclipse, when the apparent position of stars near the sun would be distorted by the mass of the sun. Britain’s leading astronomer, Arthur Eddington, set out to observe the 1919 solar eclipse, and triumpantly confirmed Einstein’s prediction. The story then made the front pages of the newspapers, and Einstein became a household name.

You’re also likely aware of the revisionist account. That the observations acquired by Eddington were ambiguous and inconclusive, and that he picked out the subset of measurements that agreed with Einstein’s prediction. Thus Eddington’s vindication of Einstein was not warranted on the data, but was more a “social construction”, arrived at because Eddington wanted Einstein’s theory to be true. Thus Einstein’s fame resulted, not from having developed a superior theory, but from the approval of the high-status Eddington.

The story is often quoted in support of the thesis that science — far from giving an objective model of reality — is just another form of socially-constructed knowledge, with little claim to be superior to other “ways of knowing”. Even those who may grant that science can attain some degree of objectivity can point to such accounts and conclude that the acceptance of scientific ideas is far more about the social status of their advocates than is commonly acknowleged.

Albert Einstein and Arthur Eddington

A new paper by Gerry Gilmore and Gudrun Tausch-Pebody reports a re-analysis of the data and a re-evaluation of the whole story. Their conclusion, in short, is that Eddington’s analysis was defendable and correct. Where he placed more credence on some observations than others he was right to do so, and the measurements really did favour Einstein’s value for the deflection of the stars’ positions.

Thus, the later revisionist account by philosophers John Earman and Clark Glymour, taken up in accounts of science such as The Golem by Harry Collins and Trevor Pinch, are unfair to Eddington.

Images on the 1919 Solar eclipse. Faint stars are marked.

Gilmore and Tausch-Pebody say in their article:

Earman and Glymour conclude: “Now the eclipse expeditions confirmed the theory only if part of the observations were thrown out and the discrepancies in the remainder ignored; Dyson and Eddington, who presented the results to the scientific world, threw out a good part of the data and ignored the discrepancies. This curious sequence of reasons might be cause enough for despair on the part of those who see in science a model of objectivity and rationality.”

Our re-analysis shows that these strong claims are based entirely on methodological error. Earman and Glymour failed to understand the difference between the dispersion of a set of measurements and an uncertainty, random plus systematic, on the value of the parameter being measured. They speculated but did not calculate, and their conclusions are not supported by evidence.

Their error was left unchallenged and the strong conclusions and accusations they derived from it were used not only to question the scientific method then applied, but also to undermine the scientific integrity and reputation of an eminent scientist.

The crucial observations came from two different telescopes, a 4-inch telescope at Sobral, in Brazil, and an astrograph sent to Principe Island, off West Africa. Einstein’s theory of gravity predicted a deflection (for a star at the sun’s limb) of 1.75 arcsecs, while a calculation based on Newtonian gravity predicted half that value, 0.87 arcsecs.

Gilmore and Tausch-Pebody present the table below, listing the measured deflection, and how much it differed from the Einsteinian, Newtonian and zero-deflection models. The z value is the difference, in units of the measurement’s error bar, and P(z) is the probability of obtaining that measurement, were the model correct. The data clearly prefer Einstein’s value for the deflection.

Observations were also made with a third instrument, an astrograph taken to Sobral. However, the resulting images were “diffused and apparently out of focus”, resulting in a systematic error that was large and unquantifiable. Crucially, being unable to evaluate the systematic distortion, the observers could not arrive at a proper uncertainty estimate for these data points, without which they could not be combined with the measurements from the other two telescopes.

Gilmore and Tausch-Pebody conclude:

The original 1919 analysis is statistically robust, with conclusions validly derived, supporting Einstein’s prediction. The rejected third data set is indeed of such low weight that its suppression or inclusion has no effect on the final result for the light deflection, though the very large and poorly quantified systematic errors justify its rejection.

Scientists, being human, are of course fallible and prone to bias. To a large extent they are aware of that, which is why techniques such as double-blinded controlled trials are routinely adopted. And in some areas, such as the replication crisis in psychology, scientists have certainly not been careful enough. But, overall, it does seem that science succeeds in overcoming human fallibility, and that the consensus findings arrived at are more robust than critics sometimes allow.

Are predictions an essential part of science?

Theoretical physicist Sabine Hossenfelder recently wrote that that “predictions are over-rated” and that one should instead judge the merits of scientific models “by how much data they have been able to describe well, and how many assumptions were needed for this”, finishing with the suggestion that “the world would be a better place if scientists talked less about predictions and more about explanatory power”.

Others disagreed, including philosopher-of-science Massimo Pigliucci who insists that “it’s the combination of explanatory power and the power of making novel, ideally unexpected, and empirically verifiable predictions” that decides whether a scientific theory is a good one. Neither predictions nor explanatory powers, he adds, are sufficient alone, and “both are necessary” for a good scientific theory.

Science Unlimited, Part Three: Philosophy

This is the Third Part of a review of Science Unlimited? The Challenges of Scientism, edited by Maarten Boudry and Massimo Pigliucci. See also Part 1, focusing on pseudoscience, and Part 2, focusing on the humanities.

Science started out as “natural philosophy” until Whewell coined the newer name “science”. As a scientist I have a PhD and am thus a “Doctor of Philosophy”. And yet many philosophers assert that today “philosophy” is an enterprise that is distinct from “science”.

The argument runs that philosophy is about exploration of concepts, and what can be deduced purely by thinking about concepts, whereas science is heavily empirical, rooted in observation of the world. Thus philosophy (exploration of concepts) and science (empirical observation) are fundamentally different beasts. And both are necessary for a proper understanding.

Science Unlimited, Part One: Pseudoscience

Philosophers Maarten Boudry and Massimo Pigliucci have recently edited a volume of essays on the theme of scientism. The contributions to Science Unlimited? The Challenges of Scientism range from sympathetic to scientism to highly critical.

I’m aiming to write a series of blog posts reviewing the book, organised by major themes, though knowing me the “reviewing” task is likely to play second fiddle to arguing in favour of scientism.

Of course the term “scientism” was invented as a pejorative and so has been used with a range of meanings, many of them strawmen, but from the chapters of the book emerges a fairly coherent account of a “scientism” that many would adopt and defend.

This brand of scientism is a thesis about epistemology, asserting that the ways by which we find things out form a coherent and unified whole, and rejecting the idea that knowledge is divided into distinct domains, each with a different “way of knowing”. The best knowledge and understanding is produced by combining and synthesizing different approaches and disciplines, asserting that they must mesh seamlessly.