“Two plus two no longer equals four, according to members of the Ontario Mathematics Coordinators Association (OMCA), who consider the equation to be a white-supremacist dog whistle instead of a basic mathematical truth.”
a philosophy based on the belief that the universe is irrational and meaningless and that the search for order brings the individual into conflict with the universe.
In his dystopian novel 1984, George Orwell wrote (pages 102-103 in this free edition),
He picked up the children’s history book and looked at the portrait of Big Brother which formed its frontispiece. The hypnotic eyes gazed into his own. It was as though some huge force were pressing down upon you—something that penetrated inside your skull, battering against your brain, frightening you out of your beliefs, persuading you, almost, to deny the evidence of your senses. In the end the Party would announce that 2 and 2 made 5, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense.
A bit further on, he wrote,
The Party told you to reject the evidence of your eyes and ears. It was their final, most essential command. His heart sank as he thought of the enormous power arrayed against him, the ease with which any Party intellectual would over-throw him in debate, the subtle arguments which he would not be able to understand, much less answer. And yet he was in the right! They were wrong and he was right. The obvious, the silly, and the true had got to be defended. Truisms are true, hold on to that! The solid world exists, its laws do not change. Stones are hard, water is wet, objects unsupported fall towards the earth’s centre. With the feeling that he was speaking to O’Brien, and also that he was setting forth an important axiom, he wrote:
Freedom is the freedom to say that 2 + 2 make 4. If that is granted, all else follows.
…pages 315-318…
Do you remember,’ he went on, ‘writing in your diary, ‘Freedom is the freedom to say that two plus two make four’?’ ‘Yes,’ said Winston. O’Brien held up his left hand, its back towards Winston, with the thumb hidden and the four fingers extended. ‘How many fingers am I holding up, Winston?’ ‘Four.’ ‘And if the party says that it is not four but five—then how many?’ ‘Four.’ The word ended in a gasp of pain. The needle of the dial had shot up to fifty-five. The sweat had sprung out all over Winston’s body. The air tore into his lungs and issued again in deep groans which even by clenching his teeth he could not stop. O’Brien watched him, the four fingers still extended. He drew back the lever. This time the pain was only slightly eased. ‘How many fingers, Winston?’ ‘Four.’ The needle went up to sixty. ‘How many fingers, Winston?’ ‘Four! Four! What else can I say? Four!’ The needle must have risen again, but he did not look at it. The heavy, stern face and the four fingers filled his vision. The fingers stood up before his eyes like pillars, enormous, blurry, and seeming to vibrate, but unmistakably four. ‘How many fingers, Winston?’
‘Four! Stop it, stop it! How can you go on? Four! Four!’ ‘How many fingers, Winston?’ ‘Five! Five! Five!’ ‘No, Winston, that is no use. You are lying. You still think there are four. How many fingers, please?’ ‘Four! five! Four! Anything you like. Only stop it, stop the pain!’ Abruptly he was sitting up with O’Brien’s arm round his shoulders. He had perhaps lost consciousness for a few seconds. The bonds that had held his body down were loosened. He felt very cold, he was shaking uncontrollably, his teeth were chattering, the tears were rolling down his cheeks. For a moment he clung to O’Brien like a baby, curiously comforted by the heavy arm round his shoulders. He had the feeling that O’Brien was his protector, that the pain was something that came from outside, from some other source, and that it was O’Brien who would save him from it. ‘You are a slow learner, Winston,’ said O’Brien gently. ‘How can I help it?’ he blubbered. ‘How can I help seeing what is in front of my eyes? Two and two are four.’ Sometimes, Winston. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. You must try harder. It is not easy to become sane.’ He laid Winston down on the bed. The grip of his limbs tightened again, but the pain had ebbed away and the trembling had stopped, leaving him merely weak and cold. O’Brien motioned with his head to the man in the white coat, who had stood immobile throughout the proceedings. The man in the white coat bent down and looked closely into Winston’s eyes, felt his pulse, laid an ear against his chest, tapped here and there, then he nodded to O’Brien. ‘Again,’ said O’Brien. The pain flowed into Winston’s body. The needle must be at seventy, seventy-five. He had shut his eyes this time. He knew that the fingers were still there, and still four. All that mattered was somehow to stay alive until the spasm was over. He had ceased to notice whether he was crying out or not. The pain lessened again. He opened his eyes. O’Brien had drawn back the lever. ‘How many fingers, Winston?’ ‘Four. I suppose there are four. I would see five if I could. I am trying to see five.’ ‘Which do you wish: to persuade me that you see five, or really to see them?’ ‘Really to see them.’ ‘Again,’ said O’Brien. Perhaps the needle was eighty—ninety. Winston could not intermittently remember why the pain was happening. Behind his screwed-up eyelids a forest of fingers seemed to be moving in a sort of dance, weaving in and out, disappearing behind one another and reappearing again. He was trying to count them, he could not remember why. He knew only that it was impossible to count them, and that this was somehow due to the mysterious identity between five and four. The pain died down again. When he opened his eyes it was to find that he was still seeing the same thing. Innumerable fingers, like moving trees, were still streaming past in either direction, crossing and recrossing. He shut his eyes again. ‘How many fingers am I holding up, Winston?’ ‘I don’t know. I don’t know. You will kill me if you do that again. Four, five, six—in all honesty I don’t know.’ ‘Better,’ said O’Brien. A needle slid into Winston’s arm. Almost in the same instant a blissful, healing warmth spread all through his body. The pain was already half-forgotten.
to the Marxist belief that the State is the ultimate truth and individuals with an alternate "truth" are dissidents. Some employers and leaders also fall into this belief that reality is nothing but paradigms despite empiric facts offered by "not a team player" people.
On July 8th, 2020, Twitter user @melvinmperalta posted a comic "about the relationship between '2+2=4' and notions of truth" (shown below).
On July 30th, Twitter user @kareem_carr tweeted that the "correct response" to someone saying "2 + 2 = 5" is to ask "What are your definitions and axioms?" (shown below).
That day, author James Lindsay posted a screenshot of the tweet on Twitter, [5]which mocked it as an "Orwellian." The same day, he posted an image macro of another tweet[6] by Carr juxtaposed next to a collapsed bridge (shown below).
On August 1st, @kareem_carr[2] posted a Twitter thread clarifying her views on the equation, stating "as a former mathematician, I have things to say." On August 3rd, Twitter user @wtgowers[3] posted a similar thread, also claiming to come from the perspective of a mathematician.
On August 2nd, Twitter[4] user @Noahpinion tweeted "2+2=3."
The following statement appeared on Twitter recently:
“The idea of 2 + 2 being 4 is cultural and because of western imperialism/colonization, we think of it as the only way of knowing.”
It was actually part of a discussion among academic scholars about educational issues that K-12 teachers face all the time. But as sometimes happens, the Twitter-thread got derailed by trolls, most of whom who had no idea what they were talking about (they rarely do), and for the most part spouted nonsense about straw men of their own creation.
The Keith Devlin then states that
Though the Twitter storm flared up rapidly and then slowly died away, it got me thinking about the issues the tweet was addressing
and asks,
What do youmake of the statement that the identity 2 + 2 = 4 is cultural?
If we were to include a variable like x in an equation like 8x = 64, then that equation is not an identity because 8x only equals 64 if x = 8. If x = 2, then 8x = 16. Therefore, it would be incorrect that the equation 8x = 64 is true regardless of the value chosen. Keith Devlin will later discuss the identities 1 + 1 = 2 and 2 + 2 = 4. Devlin writes,
A storm in a twittercup
It’s a common practice in various academic disciplines to question how we come to know what we consider to be self-evident – even the most basic ideas that we regularly take for granted. Discussions are often couched in terms of simple examples, some of which come to be used repeatedly to illustrate and codify the issues. In the case of mathematics, 2 + 2 = 4 is one of them.
For instance, back at the start of the Twentieth Century, Alfred North Whitehead and Bertrand Russell produced a mammoth, three-volume work examining the logical foundations of mathematics, titled Principia Mathematica, in which they used the even simpler identity 1 + 1 = 2 as an illustrative example, taking over 350 pages to establish its truth by logical deduction from first principles.
The goal was not to check if the identity is correct in a real world sense. That’s obviously true. The issue was to determine the logical correctness of mathematics. The motivation was that Russell had shown some seemingly obvious mathematical facts led to contradictions. They proved 1 + 1 = 2 to demonstrate that the basic identities can be formally proved, and how it could be done.
Later, Devlin writes,
The key word in the 2 + 2 = 4 tweet that the Twitter trolls missed, and as a result lost their marbles, was the second one: idea.
In that particular context, the word packed a substantial punch. The underlying issues being discussed were (and are): what is the nature of mathematics, who gets to set the rules for how mathematics is done, who determines which people can participate, what constitutes correct–or good–math, what role does it play in society, and whose society are we talking about anyway?
The identity 2 + 2 = 4 is frequently used for that discussion precisely because it is noncontroversial in all human cultures that have counting numbers and arithmetic up to 4. Which is pretty well all cultures today. (Though you don’t have to go back very far in time to find anthropological studies of remote societies that organized counting in different ways.) Indeed, thinkers and writers have been using that very identity to illustrate an “obvious truth” since at least to the Sixteenth Century, often contrasting it to the “obvious falsity” of 2 + 2 = 5.
What makes the identity noncontroversial is that, if you count things in the world, four is what you get when you combine two with two. Being forced to think about the big idea of doing mathematics today in terms of that ridiculously simple, noncontroversial, universal example brings the much deeper underlying issues dramatically to the fore.
Before I look at some of the issues that tweet was really getting at, which will bring me back to my question about whether 2 + 2 = 4 is cultural, let me say it once more, just to be clear. The red-rag statement in the original tweet absolutely is not about whether, when you have two objects in one hand and two in the other, you have four objects altogether. By spouting off about that, the majority of Twitter trolls simply demonstrated their ignorance – to say nothing of a total lack of common sense. Social media can do that to people.
They ask readers,
Is mathematics cultural?
So, do you agree with the statement that 2 + 2 = 4 is cultural?
What follows is rather long and involved. You can read it here. Some, like the present editor, may find Devlin’s verbosity to be so mind numbing that any salient point he may be making is lost like a student who keeps falling asleep will lose the plot no matter how much wants to pay attention. He does, however, use the write such things as,
Indeed, from within theculture of contemporary professional mathematics, the claim that the identity is cultural is nonsense. Within that culture, it’s a universal fact, both theoretical and empirical. I’ve been in that culture my entire adult life, and I absolutely view 2 + 2 = 4 that way.
Why is that? In particular, where does the empiricism come in?
Also,
Having spent my entire adult life within that culture, I get that. But that’s the point. It is a view from within a culture. How well does it stand up to further analysis?
In the case of 2 + 2 = 4, if I seek some absolute certainty, I can fall back on my worldly experience. If I have two objects in my left hand and two more in my right, altogether I have four objects. There is absolutely nothing controversial about that. The scholars in the original Twitter discussion were certainly not questioning that. The Twitter commentators who claimed otherwise were, in the majority of cases I suspect, simply posturing that such was the issue in order to score some points in whatever culture war they are engaged in. But at best they just made themselves look silly. (And at worst malicious.
Additionally (pun intended) Devlin writes,
I think a lot of the talking-past-one-another you see on the “all mathematics is cultural” issue results from confusing “universality of truth” (of mathematical ideas) with the cultural basis of those ideas.
The reason we mathematicians think that mathematics does not depend on culture is that we are in that culture. Indeed, it’s probably more general than mathematicians. I suspect that most people in modern, industrialized societies think mathematics is a culture-free discipline.
I should add that it’s not by any stretch of the imagination Western Culture. It has roots in pretty well all cultures that developed anything we would regard as a civilization supported by engineering and technologies, going back at least 10,000 years to the introduction of counting numbers by the Sumerians.
Incidentally, the reference to “imperialism/colonialization” in the original tweet surely contributed to its red-flag effect. The tweet can be read at face value (as I did at first glance) as assuming counting-numbers arithmetic is an invention of western societies, which it was not. But the tweeter emphatically did not make that assumption. (I checked.)
Again, Devlin goes on (and on) and apparently has points to convey about things such as
K-12 math education, with a particular slant towards making the subject more welcoming to students from diverse backgrounds
and
Who are the gatekeepers who determine who gains accredited entry into the mathematical community?
Who determines where any available funding goes to support mathematical research?
Is consideration of the ethical aspects of mathematics something mathematicians should be concerned about, or is that the job of others?
Immediately following - after many thousands of words, mind you - he adds,
I could go on, but hopefully you get the point.
This may induce one to ask (especially if you read it all) why the author doesn’t just make his point. Brevity is the soul of wit, it is said. Does this mean that verbosity is the soul of dullness? Can it not be said that at times verbosity is used like a smokescreen? At any rate, Devlin’s point is, apparently, that
the idea that there is a single body of knowledge or a single way of thinking that we call “mathematics” is a myth.
The debate over double-speak has heated up to the point where leftists have actually been posting "2+2=5" without any hint of irony at all.
It began when James Lindsay, of New Discourses, posted a meme that read "2+2=4: A perspective in white, Western mathematics that marginalizes other possible values."
The meme is a send-up of the current culture wherein virtually everything is labeled as racist, white supremacist, misogynist, homophobic, transphobic, xenophobic, otherizing, shaming, or problematic. That should have been clear. It wasn't.
It led people to begin posting "2+2=5" instead.
And these were just a few of the responses justifying that a doubling of two is not equivalent to a doubling of two but a number higher than that, namely, five.
The contradiction of basic math was to claim that Lindsay and his approach to discourse is incorrect, and undoubtedly problematic. Perhaps they realize in posting that two doubled is equivalent to two and a half doubled makes them and their positions look absurd.
Those mathematicians that jumped onto the 2+2=5 bandwagon are being disingenuous when they cite complex equations and theoretical propositions. That there can be obtuse, obscure, and theoretical ways of attaining mathematical probabilities of correctness through intensive mental machinations does not negate the fact that for all practical matters, if you have two apples, and you add two more, you will have four apples.
Additionally, the missive that 2+2=5 was posted by trans rights activists, who see the equation 2+2=4 as an attack on the concept that "trans women are real women," and refuse to let logic, reason, or biology stand in the way of that. The stating of 2+2=5 is their way of saying that men are women.
Emmons later concludes,
The teaching of history has been called into question, as well as the foundations of America itself. Calls for that which was founded or begun with a whiff of prejudice have been deemed to be wholly suspect, and removal of said stain has been targeted for eradication. It began with statues and police, and has moved on to schools, curriculum, and the foundations of government and civil order.
The eradication of basic mathematical principles, the push for people to believe what they are told to believe as opposed to that which is logical, reasoned, and proven, is a push toward creating more manageable humans that will be more susceptible to authoritarian control.
in early august a Harvard Ph.D. student in biostatistics Kareem Carr ignited another math-related debate online over the proposal that 2 + 2 could = 5 under certain circumstances which sparked a wider discussion on the inequality that apparently mathematics and objectivity represent to minority groups.
The following tweet is then featured.
The following response is also featured.
Paladin continues,
Carr isn't inherently wrong but you have to bend the rules for him to be right. For example 2 plus 2 would equal 5 if we were rounding up to the nearest whole and both values of 2 were truncated forms of 2.4.
The following is shown.
Paladin continues,
But instead of explaining a case where that actually might be true, he used a bizarre example about chicken reproduction.
Paladin continues,
Either way in almost every case 2 + 2 does in fact = 4 regardless.
Out of this came an explosion of tweets claiming that the basic equation was evidence of everything from western imperialism and colonialism, racism, transphobia, discrimination towards women of color, white supremacy, patriarchy and was just generally oppressive.
The video displayed the following as Paladin stated the words above.
She continues,
Others chimed in with far less coherent explanations than Carr’s, suggesting that two is just a variable, that all of math is a social construct - like, apparently, the age of consent - using word problems phrase in a precise way to confuse or maybe impress those not paying too much attention and a few actually being able to replicate the same explanation I provided albeit often in a weird word problem manner all to prove the validity of the claim that two plus two really can equal five.
Of course the irony of the twitter left being up in arms defending that two plus two should really equal five being directly lifted from George Orwell was lost on this lot.
A clip from what seems to be a comedic TV series is featured for a few moments of relevant dialogue (see below).
Paladin discusses Common Core math and No Child Left Behind and other changes to the way math was taught under Obama’s presidency. She also discusses what come call 'creative math’ and other such difficulties. Beginning at 29:34, she states,
that brings us back to the very onus of what I believe the intent is behind the push for 2 + 2 to equal 5. It's not about improving education. It's to make it so that there is no wrong answer and thus there can be no differences between students.
Will this flatten the curve of academic achievement? Well, I guess of course, but it will also disallow for the concept of academic exceptionalism and this concept and call is not new to academia, only now seeing more mainstream attention as an article from Gutierrez 2008 illustrates. Dr. Gutierrez insists in her piece that the problem with education is not the education gap between students of different backgrounds but the fact that we measure said gap at all.
She describes this as gap gazing and as a fetishization of measuring the differences between students rather than a real concern with an attempt to mitigate the causes that lead to said gap. She posits that within-group differences are more important than between-group differences. And while this may be more the case for boys, it's unlikely to be the case for girls who tend to have a very small standard deviation within their scores in math.
And yet differences between racial groups persist despite these gendered facts. She also argues that any differences observed are socially constructed and a failure of the researchers who identified said differences. Just like thinking 2 + 2 = 4 is a social construct I guess.
The video cuts to Captain Piccard yelling…
She continues,
Further she contends that data concerning the gap does not consider the possibility that some students may fall into multiple categories. For example, both black and impoverished and speaking English as a 2nd language which is a real concern but easily assuaged by utilizing data from multiple sources that examine those different individuating factors.
Her 3rd concern is that comparing groups to one another is simply unfair and groups need be examined in isolation which is hey true. But both are important in order for the latter to have any meaning in the wider dialogue and the realm of scientific discourse. Hence, why I utilize sources that contrast and focus on different groups in this analysis making evident that such analyses are clearly extent.
4th she believes that white people's concerns with narrowing the gap is due to their own prejudice and taints research; a bold and rather scathing indictment on the many hundreds of scientists of all backgrounds who were studying this topic, Dr. Gutierrez.
And finally her 5th issue is that analyzing the gap causes scientists to see students in aggregate rather than as individuals when that, Richelle, is the exact purpose of statistical analysis; to remove personal bias from the analysis of data. So should we give students A's for effort and allow 2 + 2 to = 5 if a student can explain it? Well teachers influence grades and generally it seems they don't play a positive role when they grade students easily. As data from Westerhoff, Creemer's and Jong 2000 found, it turns out that going light on students and, say, reinventing math in a misguided attempt to make it easier actually isn't better for students.
On the topic of decolonizing mathematics and flattening the gap that exists between students of different racial and ethnic backgrounds, the government doesn't seem terribly good at improving education via large-scale initiatives from new math to no child left behind to common core, problems persist and there is no real reason to believe that giving good grades for effort is an effective strategy.
Either this is a complex topic though, and for that reason I am not done analyzing it as there are many other factors to consider including math anxiety, stereotype threat and the influence of the family, but from the data that we've seen today, it seems unlikely that allowing 2 + 2 to = 5 will overwhelmingly positively influence education outcomes for US students, at least if other government attempts are any indication, and I believe they are. In the same way, government inclusion of anti-science initiatives such as those present in critical theory scholarship are probably best left out as I believe trump was right to do.
She then wraps up her video by asking what the viewer to comment and so on.
On November 12, 2020, Aydin Paladin’s video “2+2=5 Critical Theory : This is What CRT Scholars Actually Believe” was published. Paladin, in her scholarly, insightful and witty way, discusses not so much the 2 + 2 = 5 debate by itself as much as she discusses trends and problems in math education. She uses the 2 + 2 = 5 idea as an exemplar of the “no wrong answers” approach and, thus, it serves as an indication of problems with our education system. She states that in
September of 2020 president Trump placed a ban on the teaching of critical race theory in government programs to which various media outlets proclaimed that he had instead banned diversity training and that this action was intended as discriminatory.
These complaints which inflamed social media discourse coincided with many in the same spaces expressing dismay at the idea that 2 + 2 should = 4, instead suggesting that such an equation was also discriminatory and that a basic mathematical calculation was instead a manifestation of every imaginable form of bigotry and prejudice known to humankind from transphobia to sexism to colonialism racism and so on.
The claims did not just arise from randos on Twitter with rose emojis in their handles but also from scholars as well, including Harvard bio statistics Ph.D student Kareem Carr, Rutgers mathematics education Ph.D student Brittney Marshall and, earlier in the year, Dr Michael J. Barony, a professor in the Science Technology and Innovation Studies Department at the University of Edinburgh among many others.
This image is shown in the video as it is discussed (see below).
Barony contests that 1 + 1 equaling 2 is nothing more than hegemonic discourse.
That is, that it's concerned with political power and not objective truth. Others were even more direct that the problem was not relegated to a mathematical equation but rather to the concept of reality itself as expressed by Dr. Eve Ewing, a professor with an emphasis on the sociology of education at the University of Chicago who, by the way, also has her hands in the comic book industry, who claimed that racism is real but objectivity is not in reference to Trump's ban of critical race theory. But just what is critical race theory and how does it relate to the idea that 2 + 2 equaling 4 is oppressive?
We highly recommend that you see the entire video. We will, here, say that near the end of a roughly hour-long high-quality, informative and entertaining lesson, Paladin states (at 1:03:10),
Overall, neither cultural values nor extrinsic motivation were significantly associated with mathematics achievement the most important single factor in this analysis was the family, particularly when its various aspects were concerned and taken into consideration. This means that educational changes are unlikely to do anything if the home environment is not conducive to education. I'm sorry, but the data seem pretty clear here: no matter how much money is provided for students and schools, if the student doesn't have a positive home environment, there's just nothing the government can do to fix that detriment and presumably, that involves reinventing 2 + 2 to equal 5.
So, knowing everything that we know about government attempts at education overhaul to reduce the gaps between students of different backgrounds and, arguably, different skill levels, the importance of math and the hindrances of math anxiety as well as the influence of stereotype threat and, finally, the influence of the family and home life, let's come to some conclusions about shutting down STEM, 2 + 2 = 5 social pushes and the influence of Trump's ban on critical race theory.
Education is obviously important. It affects us all and ensuring that everyone has a fair and, well, edifying education is an no goal. But I doubt attempts to redefine math so that all answers are valid or to highlight that STEM simply isn't a one-to-one representative of social demographics are helpful and I believe that Trump was right to ban courses that teach division rather than unity and I don't believe so in a data void vacuum.
Not only are government programs designed to improve math scores typically failures at doing anything to help improve the math outcomes of students, they often seem to make things worse, particularly when it comes to parents instructing their children in a novel way of doing math. Given the stagnant scores in math since the rise of CRT there's no reason to believe it would be any different than new math or the No Child Left Behind program.
Some of the problems students face in math are often due to math anxiety which, while it may be higher in women, does not seem to uniquely affect black students more than it does students of other backgrounds. Instead, math anxiety seems to be something of a universal variable and, therefore, something we can't fix with a government program, although perhaps it could be ameliorated by just saying all answers to 2 + 2 are valid.
But I have my doubts. While stereotype threat - feeling like one is destined to be bad at math due to inalienable characteristics - is a problem, it seems unlikely to be mitigated by simply telling students there are no wrong answers and pushing them forward regardless of their results as the No Child Left Behind experiment so thoroughly Illustrated.
Moreover, while you can give kids an A for effort in the classroom, you can't really when they're an architect. Finally, for all the failures of government initiatives (and that logically includes CRT) the family seems to consistently be a source of hope when it comes to leveling the achievement gaps in math, be that between racial and ethnic groups, the sexes or groups of different socio-economic status.
But unfortunately for activists, that's something they themselves have to do and not something that the government can just sign away via legislation. And even then, the reality is that outcomes will probably never truly be equal, only opportunities. And if your family doesn't provide an equal opportunity, how could we possibly ask the government to fix that? By breaking families apart?
Seems to me that change needs to start in the home not in the state.
Thus ends her discussion of that subject in this video.
insecure math educators across the country, the ones trying to justify how 2+2 could in fact =5.
There's a subtlety there I should highlight. The contention is not that 2+2=5. The contention is that 2+2 could =5. Or anything else, really. The former is patently ridiculous. The latter is, too, but also much more dangerous as it is an attack on objective truth, it is bringing the concept of deconstruction to mathematics.
The author later writes,
I recall when deconstructionism swept the world of literary, film, and art criticism in the 1980s, and was horrified at the manner in which it rejected the notion of the existence of objective truth and elevated the observer to the role of arbiter of what is or is not truth, rather than the creator. In other words, works could mean whatever you wanted them to mean.
(I believe this laid the foundation for the concept of "lived experience" or "my reality" being more important than, you know, "reality." It's also where the notion of offense being taken is elevated over whether the offense was intended.)
That was harmless as far as it went. I don't particularly care if you think an Imperial Star Destroyer could take out the USS Enterprise because it doesn't really matter and also you are wrong.
However it didn't end there.
The notion went on to infect pretty much every other academic discipline and in many ways forms the intellectual underpinnings of wokism. Everything is a social construct. All the things you believe are simply power systems put in place to further the hegemony of the dominant culture.
First they came for the authors, and I did not speak out— Because I was not an author.
Then they came for the historians, and I did not speak out— Because I was not an historian.
Then they came for the scientist, and I did not speak out— Because I was not a scientist.
Then they came for mathematics—and there was no one left to speak for math.
Math may have been the last stronghold, but no more. Even math, the one discipline that genuinely resides outside the scope of humans and that in its purest form is wholly objective, is under assault.
Why?
In answer, they quote James Lindsay thusly,
There's no other reason to deny something so fundamental as "2+2=4" than to generate precisely this kind of confusion, and then into that confusion it is repeatedly asserted that "objectivity" in mathematics, even elementary arithmetic, is the kind of illusion that the powerful delude themselves and others into believing so that they can exclude other possibilities.
after calling everyone who disagrees with him stupid, he actually made a sound argument: 2+2 does =4, but the application of math is affected by culture.
Well, yeah, of course he conveyed that. But was that all? Moron continues,
True enough, what math is focused on, how it is used in real life, has cultural elements but he unwittingly became the useful idiot for those who are not making that argument.
Not only are math educators arguing that 2+2 does not have to equal 4, they are doing so to promote an agenda, to further the deconstruction of everything and to, you guessed it, fight for social justice.
A few examples.
“Nope, the idea that 2+2 equaling 4 is cultural because of Western imperialism/colonization, we think of it as the only way of knowing.”
Before she deleted her account at some point in the last few months (and had protected her tweets since July at least), Marshall was a,
“she/her, teacher, scholar, social justice change agent, Chicagoan, PhD student, architecture enthusiast, wannabe math person, BLM always..”
She continued to defend her position, being unfailingly polite, but clearly frustrated we just weren't getting it.
This is where purported mathematicians lose their focus.
Do the people in Papua New Guinea count differently from us?
“In Alamblak, a language of Papua New Guinea, there are only words for 1, 2, 5, and 20, and all other numbers are built out of those. So 14 is (5×2)+2+2, or tir hosfi hosfihosf, and 59 is (20×2)+(5x(2+1))+(2+2) or yima hosfi tir hosfirpati hosfihosf.”
Yes, they do, but as Devlin already pointed out above, using their symbols, 2+2 still equals 4.
It's the equivalent of saying Spanish-speaking people don't believe two plus two equals four but rather that dos más dos es igual a cuatro.
The Japanese use different numbering systems depending on the characteristics of the object. Long skinny things are counted using different words from wide things.
But 2 long skinny things plus 2 long skinny things still equals 4 long skinny things.
If you really wanted to be an anthropologist or a linguist, maybe you should have majored in that instead.
Would you want to fly on a plane designed using metaphors?
2+2 = 5?
It "starts an awesome discussion."
Like, "why am I failing math?"
2+2 = 4?
Stop being so stubborn!
Instead, insist that 2+2 = 5, because it's particularly elegant to live in a fantasy world of your own making.
Interesting example. Could be economics. Could be ethics.
But math? No.
Incidentally, Mitchell blocked me at some point.
I honestly don't remember ever having any exchange with this person.
Maybe it was preemptive!
To be completely fair to the mathematicians using arithmetic to fight imperialism, they just might have a point from time to time.
Decolonize English measurements!
I probably shouldn't encourage them.
Incidentally, if you have some time it's worth diving into the comment threads on any of these. The amount of push back is both epic and encouraging.
George Orwell's dystopian novel, 1984, is referenced so often these days it's become a trope, but it is referenced with good reason.
“"The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable—what then?"
"Freedom is the freedom to say that 2+2=4. If that is granted, all else follows" -George Orwell, Nineteen Eighty-Four”
In other news, China's math majors are focusing on, get this, math.
On paper, it’s one of the simplest math problems in the world: 2+2. If you’re counting something, like screws at the hardware store, it’s pretty straightforward. But the lines blur in other contexts. If you add 2 cups of vinegar to 2 cups of baking soda, and the reaction produces 5 cups of a fizzy mess, does that mean 2+2=5?
Is this not an other way of saying that 2 + 2 can = 5 if we substitute these values with other values? Delbert later writes that in
his Twitter thread, Carr pointed out that counting numbers “are abstractions of real underlying things in the universe,” so we should be mindful of how those abstractions distort truth when introduced to real-world scenarios.
I find this to be interesting because it seems that we are dealing with a number of cases of people more-or-less arguing that 2 + 2 = 5 can be correct if we change 2 + 2 from what it is - a mathematical abstraction - into something it is not such as a hen and a rooster or rounding up 2.4 to 2.5 and rounding up an other 2.4 to 2.5 and adding them. She writes,
Carr’s tweet received some replies displaying other examples of arithmetic’s real-world limitations. Many people pointed out that two animals can become three through reproduction (1+1=3, or 1+1=1, depending on your parameters), or that two machines could become three machines if you had some spare parts from each machine and a little elbow grease. Others pointed out that 2.3 rounds down to 2, but 2.3+2.3 rounds up to 5, making it possible through a certain filter that 2+2=5.
The author goes on and on with other invalid examples. She is more-or-less arguing that if we pretend that 2 means something other than 2 and/or that 5 means something other than 5, than it can be true that 2 + 2 = 5.
I have heard that if wishes were horses, beggars could ride.
Two plus two no longer equals four, according to members of the Ontario Mathematics Coordinators Association (OMCA), who consider the equation to be a white-supremacist dog whistle instead of a basic mathematical truth.
According to a webinar created by OMCA president Jason To, proponents of math’s political neutrality who use the phrasing “2 + 2 = 4” are engaged in an act of “Covert White Supremacy.”
To’s presentation, released in September of last year, features a pyramid of “White Supremacy in Math Education.” The apex of the pyramid features examples of “overt white supremacy” — classroom offenses any reasonable person would consider racist — while the base includes more nebulous examples of what To calls “covert white supremacy.” The covert forms of white supremacy allegedly plaguing mathematical education include “Eurocentric math curriculum,” “Standardized testing,” and exhortations such as “Just stick to math,” “I don’t see colour in my math class,” and “Of course math is neutral because 2+2=4.”
They then include the following blurry chart.
Bliff continues,
Former OMCA president Heather Theijsmeijer, who originally publicized the webinar, lives on picturesque Manitoulin Island, in Georgian Bay, and serves as the program coordinator for middle- and high-school math students in the Rainbow District School Board, the largest district in northern Ontario. Her social-media history conveys a deep support for OMCA’s view of mathematics as a potentially malign force. In one tweet, Theijsmeijer pointed her followers to commentary by Laurie Rubel, an associate professor of mathematics education, explaining that proponents of “2 + 2 = 4” are grounded “in white, Western mathematics that marginalizes other possible values.”
Rubel argued that supporters of math’s political neutrality were oblivious to a deeper point: “It’s about truth: who holds the truth, who decides what is true, and how open we are as a society to multiple truths.”
One could say that it is indeed about who decides what is true. They want to decide that falsehoods are true when it serves them. This means, of course, that they would be able to decide that truth is false when it serves them. All the while, they are accusing others of what they are guilty of doing themselves; of trying to wield the power to decide what 2 + 2 can equal. Regular people and almost all mathematicians would say that they are not deciding that 2 + 2 = 4 but rather, they know that 2 + 2 = 4. It seems that those who would say that 2 + 2 = 5 are deciding to be wrong while insisting that they are right. Blaff continues,
Although Rubel acknowledged the equation “literally” equals four, the statement is “used as a kind of basic truth & way to ridicule many critiques of mathematics as white and as western and as exclusionary.”
Rubel’s beliefs are becoming widespread among Ontario’s leading mathematics bodies, senior administrators, and a compliant academic establishment, according to several teachers whose accounts were substantiated by educational materials reviewed by National Review.
As math has become hyper-politicized, test scores have continued to plummet.
Not even half of sixth-grade students meet provincial math standards at present; 52 percent of ninth-graders met the bar during the 2021–2022 school year, down from 75 percent just three years prior, according to provincial standardized testing administered by the Education Quality and Accountability Office (EQAO). Woke Math advocates have doubled down in the face of falling performance, seeking to incorporate so-called Indigenous Knowledge Systems and anti-racism.
Theijsmeijer and OMCA did not respond to a request for comment.
It seems as if they are intentionally sabotaging math education. Blaff goes into more depth and expands to considerable breadth. We recommend you read the entire article. But we will not that they state that
when the Ford government released its long-awaited curriculum update in June 2021, the document was littered with Woke Math concepts, leading policy analysts like Zwaagstra to question whether elected officials or the provincial bureaucracy had truly steered the agenda.
The new curriculum was prefaced with a disclaimer that math “has been used to normalize racism and marginalization of non-Eurocentric mathematical knowledges, and a decolonial, anti-racist approach to mathematics education makes visible its historical roots and social constructions.” Embedded throughout the proposal were references to “anti-racist and anti-oppressive teaching and learning opportunities” as well as “the colonial contexts of present-day mathematics education.”
The precise sentiment could have been ripped directly out of an OMCA seminar.
Public pushback led the government to abandon the hyper-politicized language. The premier’s insistence that Ontarians “stick with math” ignited a firestorm among activist teachers. Jamie Mitchell, who leads the computer science, math, and innovation, science, technology, engineering, and mathematics (I-STEM) program at Aldershot School in the Halton District School Board (HDSB), was apoplectic.
“You can talk about history and social studies while also teaching math. In fact, positioning math as separate from history and social studies is white supremacy in action,” tweeted Mitchell, a recipient of the prestigious Prime Minister’s Award for Teaching Excellence. “I guess what I’m saying is @fordnation is a racist windbag.” The sentiment was defended by a fellow award winner on whom Justin Trudeau had personally conferred the prize.
Ford failed to realize that the sentiment “stick with math,” per OMCA’s pyramid, constitutes a subtle form of white supremacy.
Mitchell boasts an active social-media presence and unabashedly broadcasts his radical politics. In September 2022, the math teacher shared an article arguing that “silence is violence” and that “progressive politics so often let us down because of white fragility and respectability politics.” Mitchell underscored a specific sub-section — “It’s Time to Be Intolerant” — as his “fav” part.
“You want to be progressive? Then you have to accept that sometimes you are going to have to get messy, ruffle feathers, and break with decorum. You cannot be antiracist, decolonial, queer-affirming, etc., while still tolerating and celebrating the presence, lives, or actions of those who are not.”
Blaff also reports,
On a previous occasion, Mitchell, a middle-aged white man, shared a photo of himself wearing a T-shirt proclaiming “Dismantle Oppressive Systems” at school and tagged the organization Human Restoration Project (HRP).
The group, according to its website, aims to “bring together a network of radical educators who are transforming classrooms across the world.” HRP’s goals include ending “dehumanizing practices” such as “grading” and “radically reduc[ing] homework.” Members of the group strive to entrench social justice as a “cornerstone to educational success” while demanding “anti-racist, inclusive spaces” and adopting “critical pedagogy.”
A similar sentiment was expressed by To, whose position as Toronto’s coordinator of secondary mathematics makes him one of the most influential educational figures in Canada shaping math instruction. The impulse behind antiracist math, To explained to TVO Today, is to lift the “veil of objectivity” surrounding the subject. “Now we can start interrogating some of the dangers of how mathematics has been practiced and how it’s used.”
Later Blaff reports that
teachers are encouraged to “co-conspire” with a list of stakeholders, including students.
The “co-conspirator” concept was popularized by Brazilian academic Paulo Freire, whose Pedagogy of the Oppressed is considered one of the foundational academic texts of the 20th century. Freire packaged Marxist and post-colonialist thinking together, arguing that education is a political tool used by the privileged to oppress and dominate the lower classes. Fostering a “Critical Consciousness” translates to “a state of mental and spiritual development that confers upon its subject a morally progressive, engaged, and holistic view of life,” as one proponent summarizes it.
This philosophy is now the guiding principle at Toronto schools, the most influential district in the country, and has been embraced by Ontario’s leading teachers unions.
OMCA’s list of recommended books for teachers to assign makes clear just how deeply radical politics has infiltrated Canadian education. One book — High School Mathematics Lessons: To Explore, Understand, and Respond to Social Injustice — features contributor biographies that reflect an obsession with identity politics, including one bio that describes “a white, cisgender woman” who “strives to interrogate her privilege and understand how mathematics education perpetuates yet can intervene to challenge oppression.”
There are four “critical” reasons, the textbook argues, for teaching the field of mathematics for social justice including empowering students “to confront and solve real-world challenges they face” as well as to “learn to use mathematics as a tool for social change.”
Every single case study the textbook cites applies unambiguously to a progressive cause: “Culturally Relevant Income Inequality,” “Climate Change in Alaska,” “Intersectionality and the Wage Gap,” “Humanizing the Immigration Debate,” and “Making Mathematical Sense of Food Justice.” The textbook also warns teachers to be careful when discussing “wealth redistribution” because it “may cause improper inference or political associations to socialism.”
Are you fuzzing out yet? Are your eyes glazing over? Are you asking yourself why the hell don’t they shut the hell up about anything other than math, teach the kids math and leave it at that. Later, Blaff writes of
a ritzy getaway to the Hockley Valley Resort, where members can pay up to $300 per night to learn about Indigenous Knowledge Systems.
Understandably, Blaff later notes that it is
unclear exactly how Indigenous Knowledge contributes to basic mathematics.
There is apparently a method of teaching kids the mathematical skill of estimating that involves drying and baling seaweed. Furthermore,
Middle-schoolers are asked to practice “two-step equations” featuring integers and constants by using “spirit canoe journey calculations.”
Most teachers simply go along with the zeitgeist for fear of being considered a racist, Jeffrey said. “I’m sure there’s interesting things in here,” Jeffrey said of Indigenous Knowledge. Yet, the math teacher questioned whether such “skills are still relevant to the workforce today.”
Many teachers and parents have become deeply uneasy about the injection of politics. It is so alarming that many are petrified to speak — even anonymously — about their experience for fear of losing their jobs. Wayne, a lifelong educator, confessed his misgivings about Ontario’s education by saying if this “gets out, I’m done.”
While many are still afraid to speak out, some parents have begun to quietly band together and organize to oppose the relentless political creep.
Catherine Kronas, a concerned mother and former trustee candidate from Hamilton, reflected that “there are parents who are completely alarmed at what’s happening, but fearful of speaking up more.”
“I was broaching some of these issues in Facebook groups and getting shut down, my posts deleted. But talking to parents on the ground, individually, people are beginning to notice something is going on. People are very concerned to the point where they are afraid to discuss it,” she said.
Still, proponents of Woke Math insist that the politicization of education is simply a fiction concocted by reactionaries. In November 2022, several Ontario math teachers shared pictures of themselves on social media wearing “Woke Math” T-shirts, many seemingly on school property. Apart from To and Mitchell, the group included Devan Singh, the head of mathematics at Elsie MacGill Secondary School in HDSB.
The author then calls a particular portion to our attention with the following graphic.
The author then states,
There you have it: "Covert white supremacy!" White supremacy so covert that it looks like a normal, inarguable, incontestable universal mathematical proof! What more evidence do you need?
The article concludes,
(Fair warning: If you need more evidence, that makes you a white supremacist.)
And yes, this is a big, important group. The OMCA says on its website that its members "support the effective teaching and learning of mathematics in K-12 classrooms across Ontario," including working with government offices.
Folks, be aware of what your kids are learning. And don't hesitate to protect them from this rotten stuff.
the idea is that in a totalitarian system - and George Orwell was criticizing the Nazis within that book - is the fact that there is no more reality there is no more things that have meaning and they are grounded. Everything is movable, everything can depend on what the party is saying. So, this particular viral clip shows this lady talking about exactly that: that it's happening in Canada and we're going to listen to it.
He plays the clip and in it, a woman says,
“The Ontario Mathematics Coordinators Association has officially deemed the equation 2 + 2 = 4 to no longer be objectively correct because instead of being a mathematically proven equation, instead they are calling it a white supremacist dog whistle.”
Vee comments on this,
So, when they are calling something a ‘white-supremacist dog-whistle,’ they're basically enforcing that authority. They are saying that if you do not comply with their new way of thinking, if you challenge it, that you should get fired, you should get ostracized, you should get pressure; bad things should happen to you.
So, when they say something is white supremacist they don't actually mean that the person is within the ideology that believes white people are superior. No, no, no. What they are saying is that you are not allowed to question this particular thing, like, we have decided that this is the case and anyone that goes against us is an enemy and they're going to be persecuted. So the interesting thing about 2 + 2 = 4 is that you have different cultures around the world using different language, using different terminology, using different numbers and they all come to the same conclusion.
And obviously mathematics is very important when it comes to engineering. Like, you can have bridges collapse, you can have nuclear reactors melt down, you can have airplanes not flying properly. Messing with this thing, right, like, considering that 2 + 2 does it equal 4, you are basically messing with science as we know it.
But of course, these individuals aren't interested in science (these) individuals are interested in spreading wokeness. They are interested in creating sheep. They are interested in creating individuals that will think whatever is necessary. Because the moment you agree that 2 + 2 = anything else besides 4 that you can agree to anything else and this is what post-modernism is.
I heard the very beautiful explanation of what post-modernism is, in that of the following example. Imagine that you are sitting in your personal vehicle in the parking lot of a supermarket and all of a sudden the vehicle next to you starts to slowly move away and it creates the illusion that you are moving. So, what do you do? Well, the first thing you do is you're going to hit the brakes and then you're going to look around for another building, other cars, something in the distance; maybe a hill, a sign, and you want to see something stationary so that you can understand if you are the one moving or if it's the car next to you. That's reality.
But if you live in post-modernism world and you see the car next to you moving and then you hit the brakes and you look around and you see that the building next to you is moving, the hill in front of you is moving, the signs are moving, the sun is moving, everything is moving, you do not have any point that's grounded. You you do not have any point of reference. There is nothing. Everything is moving. So you can't really tell if you are the one moving or the car next to you is moving. Could be either/or this is what post-modernism tries to accomplish. And the reason for doing this is to give the people in power - those that have the ability to decide what is white supremacy or not - to be able to decide your reality, to be able to decide how you're going to think. Now of course they're not going to actually influence your reality. They can't literally do mind control. But they can persuade you to only say things that are considered acceptable by other people or at least that you think are considered acceptable by other people. So, in this situation you know that 2 + 2 = 4. They're not going to try to persuade you that it's not. But they are going to try to persuade you that if you say that 2 + 2 = 4, there will be consequences done against you. And this is just one example with mathematics, but, like, you can go through political correctness and you can see many things that if you do not say the correct phrase or if you say something wrong, you are going to get persecuted.
He continues playing the video featuring the woman and she says,
“Apparently if you are emotionally neutral about the equation 2 + 2 = 4, then you are participating in covert white supremacy.”
Vee pauses the video and comments
Ah, the best type of supremac- the covert, cov- und- splinter cell.
He continues playing the video and the woman says
“A This is insane but
B This is”
Vee pauses her video and says,
It's not insane. It's working. Like, that's why they are doing it. Right? So, you have all these activists now, they don't know mathematics. I can guarantee you that most of them are probably clueless at best. You may have someone that's, like, a university professor and he has like some superficial knowledge of mathematics but he's, like, one of those really bad university professors that everyone fails to join their class because he is incompetent and can't teach for shit.
So, you have, like, these people and the first thing they do is they latch on to the things that gravitate around the subject that they want to subvert. So, in this case, you know, they can graft it around magazines that talk about mathematics or certain groups that talk about mathematics. But they're not really creating mathematics. And once they convert those institutions, you know, maybe they can manage to convert something that gives prizes or awards, or they can create their own things. Right? They can start making their own peer review and they do this circle jerk where they peer review other’s literature. And then they gain some level of power within the field. And then they start calling the actual mathematics professor to be racist, white supremacist, yada yada.
So now the mathematic professors are starting to bend the knee because they want to be acknowledged by the public. They want to get the awards they want to get the fame that comes from being in those publications. So they're going to start to bend over, you know, they're going to start to allow- you go, ‘well let's get some activists in our university to make sure that we don't have any white supremacists that believe that 2 + 2 = 4.’
This is a tactic that has been employed in many other fields. Comic books, movies, video games, like, entertainment, whatever you want. Right? Like, the comic book critics don't read comic books, the video game critics don't play video games, because it's not about the actual hobby. It's not about improving the hobby. It's about subverting it.
He plays more of the woman’s video and she says,
“-verbatim exactly what happened in George Orwell's 1984.
You tell me if this sounds like 2023 America; “In the end the party would announce that 2 and 2 made 5 and you would have to believe it. It was inevitable that they should make that claim sooner or later”
Vee pauses and says,
I mean, we already have seen this during COVID, right? The party demanded that asking people to get ideas to vote is racist because people cannot afford to buy an ID; there are some individuals that are so poor they cannot afford the 20 bucks to buy an ID and therefore requiring them to get one would be racist. But then they said no, you actually need to have a QR code in order to enter McDonald's, so a person that can't have 20 bucks to buy an ID all of a sudden has the money to buy a cell phone to install the apps required, to do the traveling expenses required, to get the vaccine, to to get the QR code to install it; all of that, right?
They also claimed at one point, I think it was Biden that said, uh, it's difficult for minorities to get online. But at the same point, you know, they go on and say, ‘Well, actually, you need to have a QR code.’
So, you can see that one day they can say, ‘No you need to stay at home stay safe.’
Literally the next day, they say, ‘No, you need to go out and protest because BLM is important and you need to go out and, uh, you know, like, advocate for civil rights and stuff.’
And then, it's like, ‘Okay, well, now that Biden won, you need to go back home and stay safe.’
They are literally training people to think this way. Like, there are no more principles. There are not, like, whatever you're being told today that you have to do, well, you have to do it. No questions. No, no ifs, no buts. It's just executing orders like good little soldiers. This is a of course a sign of fascism and this is what George R.R. Martin (?) was criticizing in his book.
But, but, yeah, I mean, verbatim it is now being said that uh 2 + 2 doesn't equal 4 and I've seen people justifying it in different ways. First of all, they started saying that 2 + 3 = 4 only in base 10 and in other bases it doesn't. And I'm like, ‘Yes, but in mathematics, if you don't mention the base, then it's implied that it's base 10.’
Right? Like, when you go to the shopping mall, you don't ask in what base are these prices, right? Is it base 3? Base 4? No. You know, it's in base 10 and no one does that because it's basically an understanding. Then they said, ‘Yeah, but like there are situations where if you take 2 squares and you take 2 other squares that you put them together you have 1, 2, 3, 4 squares and another square. That's, like, all 4, so you have, actually, 2 + 2 = 5.’
And I'm like, ‘Yeah, sure, but you're just playing a language game now. You know, the Greeks called the sky green because they didn't have a word for blue. But that doesn't mean that the sky was green. The sky was still blue. So what you're doing is, like, you're, you're counting different things. Like, the the question was, like, ‘How many squares are the exact same shape are there there?’
What you're doing is, you're, like, trying to play a little magician game.
He then asks for audience input in the comments. By the way, give us some input in the comments.
Closing Words
When Julian Assange, Tommy Robinson and Dr. Jordan Peterson tenaciously refuse to surrender the truth, they are, in that sense, like WinstonSmith in 1984 or Captain Picard in a particular episode of Star Trek the Next Generation (see below).
Winston and Piccard were tortured. Both are fictional. Julian Assange and Tommy Robinson are humans who have suffered the torture of solitary confinement. As I write this, Robinson has been in solitary for months and still is. We should hang our heads in shame over this. Better yet, we should get him out and put those who persecute him in his place.
