Why Can't Winston Count?

Because Socially Constructed Math Is Simply Illogical

A dear friend is a math teacher who has a hard time understanding the new intersectional war on math, based on critical theory. Trying to explain it is frustrating. Like most opponents, she attempts logical refutations. But logic is the prime target in the war. A bit of recent history might help.

One of the earlier proposals was to abolish algebra at community colleges. By 2017, a growing number of educators wanted to dump it. NPR summarized the argument of Eloy Ortiz Oakley, chancellor of the California community college system, this way:

Algebra is one of the biggest hurdles to getting a high school or college degree—particularly for students of color and first-generation undergrads. It is also the single most failed course in community colleges across the country. So if you're not a STEM major (science, technology, engineering, math), why even study algebra?¹

A Movement Against Truths

It has become clear that a much more ambitious project is now in hand: to replace math with social justice math, including, perhaps, a name change. Educator Rochelle Gutierrez, whose specialty is "equity issues in mathematics education," was to give a keynote presentation, "Mathematx: Towards a Way of Being," at a Mathematics Education and Society Conference in India in early 2019. "Drawing upon Indigenous worldviews to reconceptualize what mathematics is and how it is practiced," she stated in the abstract of her talk, "I argue for a movement against objects, truths, and knowledge towards a way of being in the world that is guided by first principles—mathematx."²

By 2019, the movement was gaining strength. A preview of the new Seattle math curriculum gives some sense of it. British commentator Douglas Murray noted:

Just one of the sub-questions that students will be invited to consider here is "How can we use math to measure the impact of activism?" Because, of course, what matters most in this world is engaging in impactful activism. Elsewhere students will be invited to consider the following question, "Can you suggest resolutions to oppressive mathematical practices?"³

My math teacher friend would say, "It's not clear that Seattle students will be competent enough in math to reflect on its practices." No, but why assume that competence in math is the goal?

Attacking the Bedrock

One target has been the equal sign, =, once considered the bedrock of mathematics. As one tech writer explains,

It seems to make an entirely fundamental and uncontroversial statement: These things are exactly the same. But there is a growing community of mathematicians who regard the equal sign as math's original error. They see it as a veneer that hides important complexities in the way quantities are related—complexities that could unlock solutions to an enormous number of problems. They want to reformulate mathematics in the looser language of equivalence.⁴

For many, perhaps, it's a welcome deliverance from equations that don't equate. The new element is that mathematicians are getting behind this trend. That's doubtless for a variety of reasons, one of which must be, in these days, the risk of Cancellation.

They have reason to fear, given that the war has now spread to 2 + 2 = 4. In July of this year, teacher and Ph.D. student Brittany Marshall gained a good deal of attention on Twitter for proclaiming, "Nope the idea of 2 + 2 equaling 4 is cultural and because of western imperialism/colonization, we think of it as the only way of knowing." Paula Bolyard responded to one of Marshall's supporters, "The iPhone you typed those tweets on is based on the binary system—ones and zeroes, not fives and four thousands."⁵ True, but such facts have come to be seen as instruments of oppression. Bringing them up is hostility.

Author and scholar Nancy Pearcey notes that math is by no means exclusively Western:

We all use Arabic numerals, and in my college math class, we learned that the concept of zero as a place holder came from India; that the Babylonians gave us the 360-degree circle and the 60-minute hour; that the Babylonians, Egyptians, and Chinese all had a rough idea of the value of pi.⁶

Again, true, but hardly relevant in the Year Zero, when Western thinkers are denounced because they support objectivity and logical thinking, whatever its origin.

Academics Get Comfortable

Just to show how deep the rejection goes, one of the drivers in the war on 2 + 2 = 4 was the use of that concept by an opponent to explain the worldview of the new critical theorists. Social scientist James Lindsay quoted George Orwell's 1984: "Freedom is the freedom to say that 2 + 2 = 4. If that is granted, all else follows." He then found that many academics, including some mathematicians, are quite comfortable with the idea that 2 + 2 might equal 5. He later wrote,

I have to confess responsibility for this bizarre moment, which in some sense might be one of the greater achievements of my life thus far. There's an excellent case to be made that I have led a significant number of professionals who definitely should know otherwise—as effectively every six-year-old in a community with a school does—to dig deeply into tortured defenses of the proposition that two and two do not make four.⁷

There is a history here. Lindsay, with Helen Pluckrose, was one of Peter Boghossian's embattled Sokal hoaxers. They wrote clearly ridiculous papers that were accepted in social science journals. He and Pluckrose have now written a book, Cynical Theories (Pitchstone, 2020), addressing the underlying belief system of the war on math: "Knowledge is a social construct; science and reason are tools of oppression; all human interactions are sites of oppressive power play; and language is dangerous." The bizarre tricks that critical theorists use to try to make 2 + 2 come out to 5 underline a lack of acceptance of the need for rigorous thinking.⁸

Thus, when Brooklyn College Professor of Math Education Laurie Rubel announced in early August that 2 + 2 = 4 "reeks of white supremacist patriarchy,"⁹ she was speaking for surprising numbers of academics and teachers. Many rightly ask, what about the disadvantaged children who depend on public schools to provide basic literacy and numeracy skills? Well, there are two ways of looking at that. One would be to emphasize the skills; the other would be to undermine their value across society. Critical theory is firmly decided on the latter.

Reduced to Prejudice

Is there a way of critiquing this mass flight from fact? In the current environment, that's harder than some might think. For example, in an excerpt from Cynical Theories, Pluckrose and Lindsay note that the new progressive theory explains too much: "It reduces everything to one single variable, one single topic of conversation, one single focus and interpretation: prejudice, as understood under the power dynamics asserted by Theory."

But why should that be seen as a problem when it is precisely the intention? They then argue, "The entire backbone of the theory is affirming the consequent. True logical statement: if there's prejudice, then there's disparity. Logical fallacy: there's disparity, so there's prejudice." But with the abolition of logic, logical fallacies are no longer a problem. People who don't accept fallacies, however, are a problem.¹⁰

Douglas Murray sums up the current situation:

When do you come to realise that a movement has made a clean sweep through the culture? It isn't the moment when the disciplines that you know succumb to it. It isn't when the ideas that you are familiar with suffer from the contamination. Rather it is when subjects you took to be serious, solid and immune from such things end up spouting exactly the same degraded mantras as everyone else.¹¹

Winstons in Danger

Part of the problem may be that the very nature of mathematics is problematic in a naturalist (nature is all there is) environment. Philosopher Edward Feser puts it this way:

Mathematics appears to describe a realm of entities with quasi-divine attributes. The series of natural numbers is infinite. That one and one equal two, and two and two equal four could not have been otherwise. Such mathematical truths never begin being true or cease being true; they hold eternally and immutably. The lines, planes, and figures studied by the geometer have a kind of perfection that the objects of our experience lack.¹²

That realm—recognized across the world—is increasingly seen as a problem at universities today. One commentator quoted G. K. Chesterton (1874-1936):

We shall soon be in a world in which a man may be howled down for saying that two and two make four, in which people will persecute the heresy of calling a triangle a three-sided figure, and hang a man for maddening a mob with the news that grass is green.13

Orwell's hapless central character in 1984, the one who insisted that 2 + 2 = 4, was named Winston. If universities come to be dominated by critical theorists in all disciplines, they will not be slow to deal with the Winstons who show any attachment to fundamental facts, let alone eternal truths.

Notes:
1. Kayla Lattimore and Julie Depenbrock, "Say Goodbye To X+Y: Should Community Colleges Abolish Algebra?", NPR (July 21, 2017): https://n.pr/2QMzueo.
2. Greg Piper, "Professor proposes 'mathematx' to fix pro-human bias in math," The College Fix (Aug. 21, 2018): https://bit.ly/2QKvKKf. Note: It is not clear that she actually gave the presentation, because the conference page no longer exists. But she is prolific within the discipline, as a list of her publications demonstrates: https://bit.ly/3gS4u7j.
3. Douglas Murray, "Will maths succumb to the woke wave?", UnHerd (Oct. 4, 2019): https://bit.ly/2QLF7cF.
4. Kevin Hartnett, "Is the Equal Sign Overrated? Mathematicians Hash It Out," Wired (Oct. 13, 2019): https://bit.ly/32R9cgN.
5. Paula Bolyard, "Orwellian: Teacher Blames 'Western Imperialism,' 'Colonization' for Concept of 2+2=4," PJ Media (July 8, 2020): https://bit.ly/335q2IX.
6. Nancy Pearcey, "Does Mathematics = Western Imperialism?", The Federalist (July 26, 2020): https://bit.ly/32T35rZ.
7. James Lindsay, "2+2 Never Equals 5," New Discourses (Aug. 3, 2020): https://bit.ly/2EWC0Mo.
8. Ibid.
9. Ben Zeisloft, "Math education prof: 2+2 = 4 'trope' 'reeks of white supremacy patriarchy'," Campus Reform (Aug. 9, 2020): https://bit.ly/34Y4yA5.
10. Helen Pluckrose and James Lindsay, "Intersectionality: An Excerpt from Cynical Theories," Areo (June 6, 2020): https://bit.ly/34Ya7OR.
11. Douglas Murray, "Will maths succumb," Ibid., note 3.
12. Edward Feser, "Keep It Simple," First Things (April 2020): https://bit.ly/3jJsrj7.
13. Kurt Mahlberg, "Is it racist to say that 2+2=4?", MercatorNet (Aug. 19, 2020): https://bit.ly/31PIVA6.