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.

Humanists UK demands a blasphemy law

“Blasphemy laws are NEVER justifiable” declares Andrew Copson, Chief Executive of Humanists UK. “Freedom of speech, freedom of expression, and freedom of religion or belief are the very bedrock upon which our humanist ideals rest”, and in response to the disappointing news that Denmark wants to make it a criminal offence to burn the Koran in public, he adds: “appeasing bullies doesn’t work – it merely emboldens them”. As a member and supporter of Humanists UK I entirely agree.

The very next segment of the Humanists’ newsletter, however, declares: “Humanists protest ongoing delays to conversion therapy ban”. Reports are that the UK government is dropping its committment to such a ban, “with ministers concluding it has proven problematic or ineffective in other countries”. Meanwhile, Humanists UK complain that: “LGBT people continue to be subjected to harmful attempts of so-called ‘conversion therapy’”.

I can’t help thinking that a ban on “conversion therapy” amounts to a blasphemy law, a ban on saying something that offends secular norms. As regards sexuality, pretty much the only form of conversion therapy that exists these days is speech, speech that “can include exorcisms and forced prayer” and that occurs “in closed-off religious communities”.

“Humanists UK is strongly committed to freedom of religion or belief, but that freedom should be limited where it causes harm, and conversion therapy is harmful”.

But I have a hard time accepting that such speech meets a legal definition of “harm” sufficient to justify making it a criminal offence. The whole basis of enlightenment values is that we outlaw physical violence and threats thereof, but accept people speaking freely even if others find it offensive and distressing. If we allow “psychological harm” as a reason to shut down speech, then anyone can censor speech simply by claiming to be upset. And that is exactly what activists do these days, claiming that any opinion they disagree with is “hate” speech that makes them feel “unsafe”.

Yes, it may well be psychologically distressing for a young gay adult to be told by their religious mentor that Jesus wants them to be straight, but I have little doubt that it is psychologically distressing for a devout Muslim to hear of their prophet being denigrated or their holy book being treated with disrespect. If we want to say “tough” to the latter, telling them that in a free society they must accept it, then, as I see it, we must also allow a Christian to proclaim that Jesus deplores homosexuality.

I am puzzled that Humanists UK can adopt a hard-nosed attitude to the “harm” caused to Muslims by Mohammed cartoons or burned Korans, but then go with the nebulous and un-evidenced concept of “harm” to a gay person on being told that Jesus could make them straight. It may be that their postion is a knee-jerk opposition to religion in each case, but humanism should not be anti-religion. If we really think that “Freedom of speech, freedom of expression, and freedom of religion or belief are the very bedrock upon which our humanist ideals rest”, then we need to mean it, and reject the idea that such speech causes “harm”. “I support free speech but not where it causes harm …” is how all requests for blasphemy prohibitions start, religious or secular.

As for “forced” prayer and “closed-off religious communities”, any adult can walk away, and if they choose not to then that’s up to them. Humanists UK talk of “harrowing case studies” of “starvation”, though that exposé related only that: “On his first visit to the church, our reporter was invited to take part in a separate three-day residential programme, where those participating would be expected to pray for up to three hours at a time without eating or drinking until the third day”. Unless they were locking the doors, preventing him walking down to the nearest McDonald’s should he choose to (which, of course, would already be illegal), I’m not harrowed. Do we want to outlaw religiously-motivated fasting?

Humanists UK also link to a study of psychiatrists reporting that: “17% [of therapists] reported having assisted at least one client/patient to reduce or change his or her homosexual or lesbian feelings. […] counselling was the commonest treatment offered …” and that some therapists “… considered that a service should be available for people who want to change their sexual orientation”.

If someone goes voluntarily to a therapist and asks for it, I don’t see that it should be a criminal offence for the therapist to offer religious-based counselling, even though that counselling will likely not work. Acupuncture, Reiki and homeopathy also don’t work, but are not illegal.

OK, one might respond, but what about children, what about gay teenagers who may not be able to walk away? And yes, that’s a harder case. In general I want to protect children from religious coercion. But how far would we take it? Should it be illegal for a Catholic parent to teach their child about hell? Should we outlaw cults, outlaw Scientology, indeed outlaw Haredi Judaism or Catholicism or Islam? The teachings of all of these could be fairly regarded as abusive ideas to put in the mind of a child, and yet we tolerate them; indeed we even promote religions by handing over state-funded schools to them and by granting them charitable status.

If we are making it illegal for a religious leader to tell a teenager that gay acts are immoral, should we make it illegal for them to tell that teenager that sex before marriage is immoral, or that they should wear a hijab? I don’t think we should, since if we want freedom from religion and the freedom to blaspheme then we need to accept freedom of religion and their right to broadcast their views, however much we deplore those views.

We already have a problem with British police telling street preachers that they cannot proclaim Christianity. It’s precisely because I want the right to denigrate religion, including being disrespectful to the Prophet Mohammed, that I support their right to broadcast views that might upset others. A better approach is to remove schools from religious institutions, giving kids a right to a secular education, thus ensuring that they can also obtain views and perspective from other than their parents’ religion.

In the current climate, the really contentious issue is not so much sexuality, but “gender identity”. A ban on “conversion therapy” would include a ban on attempts to change a teenager’s “gender identity”. But our understanding of such issues is poor and is evolving rapidly, such that it could be calamitous for the clod-hopping criminal law to step in. We don’t even have an agreed definition of “gender identity”. Heck, we’d have a hard-enough time agreeing a definition of “woman” these days!

Unlike sexuality, “gender identity” seems to be fluid. The evidence is that, of young teenagers who declare a “gender identity” different from their biological sex, many, perhaps most, will desist and come to identify with their sex by early adulthood. Do we want to deny such kids access to professional counselling because the counsellors are worried that, if a teenager does come to desist, then they’ll have committed the criminal offence of “conversion therapy”? Of do we want to ensure that only gung-ho counsellors, who will push an ideological approach whatever, will take on such kids? If you think such a law is a good idea, please could you at least read this account by the parent of a trans-identifying child.

OK, you might reply, we’ll draft the law with an exemption for well-meaning professional counselling. But what about a parent, or an aunt who has doted on the kid since birth and who has their best interests at heart, or a trusted teacher? Are they allowed to talk through the kids’ feelings with them, without risk of being hauled into court? Activists will use accusations to try to silence anyone who disputes their ideology; they already do.

Then there’s the issue that “affirming” a teenager’s self-declared gender identity, that is, going along with a social transition, “is not a neutral act”, in the words of the authoratitive Cass Review, but is instead “an active intervention because it may have significant effects on the child or young person in terms of their psychological functioning”. Refusing to acquiesce with a social transition might thus be in the child’s best long-term interests (we don’t know, Dr Cass says “better information is needed about outcomes”), while being exactly the sort of thing that activists want to prohibit.

Then there’s the issue that social transition often pushes the child towards medical and surgical transition, which can leave the young person permanently without sexual function and unable to have children, and turns them into a medical patient for life, requiring ongoing maintenance — and yet evidence that this improves their psychological well-being or reduces their suicide rate is simply not there.

Given the uncertainties, this is no place for the criminal law and I’m glad that the UK government is realising the problems with any such law and is shelving the idea. Those advocating such a law must believe that they know what’s best for trans-identifying youths, but the evidence base is meagre. Discouraging open enquiry is the opposite of what we need. Any entry of the criminal law into the contested arena of “gender identity” is likely to do much more harm than good.

The proper scope of academic freedom

This piece was written for and first appeared on the Heterodox STEM Substack, and was inspired by this Tweet:

“You can’t complain about attempts to shut down gender critical views in universities, and support the closing down of gender studies depts or courses on queer theory. You either support academic freedom or you don’t. Unfortunately, many people, including many academics, don’t understand academic freedom, or why it’s so important.” — Colin Wight, Professor Emeritus (International Relations)

Perhaps I’m one of the many academics who don’t understand academic freedom, but oh yes I can do both of those things! I don’t see academic freedom in such stark terms, and want to make a distinction between teaching and scholarship.

By “teaching” I’m referring to official courses run by a university, usually for credit towards a degree. I argue that academics don’t have “academic freedom” to do as they wish when teaching. A university should be dedicated to truth-seeking enquiry based on evidence and reason, and the courses it runs and the degrees that it awards carry its imprimatur. I don’t think that a university should run courses that promote creationism or Mormon theology or Queer Theory, or anything else where evidence and reason take a back seat to ideology, even if some academics want to teach it and even if some students want to take it.

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.

What counts as evidence? Or why Bayesian analysis of religion convinces no-one.

When arguing about religion on Twitter, there’s a common notion that if (say) consciousness is more expected under theism than under atheism, then consciousness is “evidence for” theism. The argument is that, while an atheistic universe might develop conscious life, equally an atheistic universe could be utterly devoid of life. In contrast, a universe founded by the Abrahamic god would always include God-created conscious life. Hence, consciousness is better predicted by theism and is thus evidence for theism.

I regard this as cheating. The Abrahamic-god hypothesis was designed to explain conscious life. You can’t use known information to construct a hypothesis, and then evaluate your hypothesis as probable just because it explains that very same information.

If the hypothesis successfully predicts new information, not already used in constructing that hypothesis, then, yes, that’s strong evidence. But if the information is not new, then one needs to fall back on evaluating the competing explanations overall. I do not regard “consciousness was put there by God” as being a better explanation for consciousness than “consciousness evolved because it aided animals’ survival”, and thus do not regard consciousness as evidence for theism.

Neutral standards for advertisers are not a blasphemy law

The right to offend religious sentiment is a necessary part of a free society where we are not subject to religion. So, when Humanists UK protest about a recent ruling by the UK’s Advertising Standards Authority, I might be expect to join in. But I’m not.

“Demi Lovato must have the right to blaspheme”, declares Stephen Knight, a writer I usually agree with. But a right to blaspheme is not the same as the right to display a blasphemous poster on an advertising billboard in a public place. I will strongly defend the publication of Charlie Hebdo cartoons, but that doesn’t mean they would be appropriate on billboards in Piccadilly Circus.

The standard for acceptable advertisements is tighter than for publication in one’s own magazine or on one’s own website. That’s because the public encounters adverts when going about their daily life. They aren’t opting in to seeing them, as they would be when picking up a copy of Charlie Hebdo. As a result, the Advertising Standards Authority requires that adverts not cause “serious or widespread” offence, taking into account “prevailing standards in society”. The threshold will, of course, be subjective, but the ASA take their role seriously, including the polling of public opinion.

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.

Why did Psychology Today publish woo?

Psychology Today sets itself high standards. “We are proud to be a trusted source for clinical and scientific information … we hold this content to the highest standards”, it says. “All expert author content is reviewed, edited and fact-checked for accuracy, objectivity and to ascertain that the author has relevant domain expertise”.

So why did it publish a recent interview of Jeffrey Kripal by Dinesh Sharma, a piece filled with what can be fairly summed up as “woo”.

Dinesh Sharma’s background is in the social sciences and Jeffrey Kripal is a theologian. The editor, whose job it is to uphold the above standards, was Tyler Woods, whose degree was in politics and English. None of them has any standing in the physical sciences, which might explain why the article goes badly wrong when it starts talking about physics. Let’s take it bit by bit.

Is science “plagued” by “rife” harassment and discrimination?

Given society-wide soul-searching over issues of race and gender today, many scientific institutions are conducting surveys to assess the prevalence of harassment, bullying and discrimination within their fields. In principle this is a good thing, since scientific institutions should, of course, be open to all, and the work environment should feel welcoming. But we also need a degree of rigour when designing and interpreting such surveys.

Nature is the world’s leading scientific magazine (though being a commercial product it also has a predilection for click-bait). A recent headline claims that science is “plagued” by discrimination.

The survey that led to this conclusion is summarised in this table.

So two thirds of scientists respond that they have not experienced nor seen bullying, nor harassment, nor discrimination — not even one incident — in the whole of their current job, a length of typically two to eight years. Does that amount to their institutions being “plagued” by such behaviour?