Mathematics & The Imposing Your Beliefs Fallacy

I blush as I write the truism that it is possible, given obvious reasons, that anybody anywhere might discover or hit upon a mathematical truth. Any body. Even NPR listeners. Even DIE commissars. Even, yes, female professors.

I blush because this is not only obvious, but it is idiotically obvious, and when you are forced to write something idiotically obvious, you cannot escape a sting to your conscience.

You felt it, too, that hot stab of inflamed hackles, if you were a woman or a white-knighting beta male and you read the obvious statement that even women professors can discover mathematical truths. He must mean it isn’t true!, the constantly aggrieved internally emoted, Which is why he wrote it was true!

Which brings up the difference between might and likely. Because if you emoted in that fashion you fell out of the likely camp and into the might. Let that pass for the moment.

Let’s instead discuss why you and I are forced onto this dismal subject, and why we have say things that should “go without saying”.

But first a small thought experiment. Which of these three sentences give you the most cringe?

1. Of course men can discover mathematical truths;

2. Of course women can discover mathematical truths;

3. Of course Indigenous and First Nations peoples around the world can discover mathematical truths.

Well, it’s no secret. There is no cringe for the first sentence, given the (again, obvious) observation that nearly all the most important mathematicians were and are men. I say obvious because everybody who cares to think about this know this. The sentence becomes a banality.

There is some cringe with the second sentence, the level according to how earnestly Equality is believed. There is in many minds the question Why is he saying this? By which they mean, what motive do I have. They ask themselves this because they know it is false that the most important mathematicians were and are women. But they also know they should not want this to be so. And so anybody who brings up the “disparity” in this underhanded way must be against Equality, or that they seek to discourage women from discovering mathematical truths.

But that is like arguing a man who said “The sun rises in the east” is against rotational freedom and works actively in preventing the sun rising in the west.

The third sentence I borrowed in part from lady professor Rowena Ball, from Australia. There is no cringe in the third sentence. Instead, many will find themselves nodding along with it. They do this because they know there have been very few “Indigenous and First Nations peoples around the world” who have been among the most important mathematicians. Yet, one feels, like with women, there have been certain anti-mathematical obstacles put into the paths of these fine people; obstacles which, when removed by Education, will allow Indigenous mathematicians to flourish.

Doubtless this is so in some cases. There may be a Ramanujan hiding among some Aboriginal tribe, just waiting for the right government grant to come along and free him—or her—to theorize. Of course, this might be a bad example, because Ramanujan’s genius was readily recognized under less than ideal circumstances. And he rose to prominence at a time in which the near totality of feverish craving for uncovering hidden gems did not yet exist; indeed, something like the opposite was the case, or so we are always told we must believe.

Now our Ball would, the linked article indicates, certainly enjoy uncovering a few gems. But it seems she has formed the tacit premise that gem searching has been going on for some time now, and without much success. And so the real problem must be in the definition of what counts as a gem.

Indigenous societies haven’t contributed much to mathematics as it is traditionally understood, but that is because they “often excel at non-numerical mathematics”. Like?

One interesting example that we are currently investigating is the use of chiral symmetry to engineer a long-distance smoke signalling technology in real time,” Professor Ball says. “If you light an incense stick you will see the twin counter-rotating vortices that emanate ? these are a chiral pair, meaning they are non-superimposable mirror images of each other.”

A memoir by Alice Duncan Kemp, who grew up on a cattle station on Mithaka country in the early 1900s, vividly describes the signalling procedure, in which husband-and-wife expert team Bogie and Mary-Anne selected and pulsed the smoke waves with a left to right curl, to signal “white men”, instead of the more usual right to left spiral….

To create and understand these signals, you have to be a skilled practical mathematician, Professor Ball says.

To which the only rational response is, No, you don’t. You can be utterly ignorant on the workings of internal combustion engines, not having a clue what a piston is or how it might function, and still be able to drive a car. Yet if you were to cruise past Ball, she would say “There goes a mechanical engineer.”

Incidentally, one also wonders if in addition to the chiral-paired smoke signal for “white men” there is another for “mathematicians.” Or is that considered a redundancy?

Here are two more important truths, both as obvious as the truth with which we began: (1) All of mathematics has not been discovered; (2) Many discoveries to come will arise from unexpected directions.

For instance, a great many interesting things were learned from the Mayan base-20 mathematical system after it became known. (And, by coincidence, has curious connections with Ramanujan’s thesis on highly composite numbers; i.e. those numbers with lots of divisors.)

So it remains possible that a form of mathematics, as yet unknown to the larger world, is operating quietly or in secret among “Indigenous and First Nations peoples”, a form that will in time become better known. But it won’t be of the chiral-smoke signal type, because that is an ordinary (to us) mathematician noticing a new application of ordinary (to us) mathematics.

The mistake egalitarians make is easy to identify. It is the opposite of the one a man makes when he observes only men who are taller than their mates, and concludes, falsely, that therefore all men are taller than all women. Ball argues that of all the mathematicians she knows the great majority are not “Indigenous and First Nations peoples”, and concludes, falsely, that therefore “Indigenous and First Nations peoples” are equally adept at mathematics as other groups.

To prove this, as said, she needs to redefine what mathematics means. And to do that she invokes the Imposing Your Beliefs Fallacy (blog, Substack). Which she does by “decolonizing”.

“Mathematics is a universal human phenomenon, and students of under-represented and minority groups and colonised peoples are starting to be more critical about accepting unquestioningly the cultural hegemony of mainstream European-based mathematics,” says Professor Rowena Ball from the ANU Mathematical Sciences Institute…

“Mathematics has been gatekept by the West and defined to exclude entire cultures. Almost all mathematics that students have ever come across is European-based,” she explains. “We would like to enrich the discipline through the inclusion of cross-cultural mathematics.”

Somebody or some group must gatekeep and impose their beliefs on what mathematics is, by setting its limits and purposes. One can, à la Ball, say that mathematics is whatever anybody wants it to be, but that makes it nothing. You reading this now is “mathematics” if you are a Victim. Ball is right that almost all mathematics in European-based, and that the people in this system (who now come from many races) continue to impose these beliefs on the practice of mathematics. She is being absurd and libelous to say that mathematics is “defined to exclude entire cultures.” No, it is not.

The author of the article says, “Here, in Australia, we are still in the early stages of the decolonisation journey. There is a curiously persistent trope that Aboriginal and Torres Strait Islander peoples had only rudimentary mathematical knowledge, despite widespread evidence to the contrary.”

Dividing through for the nauseating effeminate language (“decolonisation journey”), the author makes the same egalitarian error. There is no such evidence of mathematical equality, therefore equality must actually exist, she says.

What else can you say to such an absurd mistake except that is it absurd?

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