David Silverman and “Woke Math”


Here we go again. David Silverman is racing rightwards, and is considering voting for Trump, because he doesn’t like the idea of defunding the police or what the Right are calling “Woke Math”.

Nobody changed, Dave. If you’re seriously considering voting Republican now, you were never on the side of the Left, which we should have figured out from all the CPAC chasing you were doing. Biden & Harris are very much center left politicians, so all the caterwauling about how radically socialist they are is absurd — the people I know who are unhappy with the Democratic candidates are rejecting them because they aren’t Left enough, which is actually an honest position.

But what about this “Woke Math” nonsense, which is a Fox News talking point? All this crap about schools not teaching 2+2=4 is made up propaganda. It’s not true.

You can look it up for yourself. Go to the Seattle Public Schools K-12 Math Ethnic Studies Framework, and read it. It doesn’t say anywhere that 2+2=5.

Here’s what it actually says. I don’t know how anyone can disagree with it.

Origins, Identity and Agency, as defined by ethnic studies, is the ways in which we view ourselves as mathematicians and members of broader mathematical communities. Mathematical theory and application is rooted in the ancient histories of people and empires of color. All human endeavors include mathematical thinking; from humanities to the arts to the sciences.

It’s saying that mathematics is a universal, multicultural thing. Do you disagree?

Power and oppression, as defined by ethnic studies, are the ways in which individuals and groups define mathematical knowledge so as to see “Western” mathematics as the only legitimate expression of mathematical identity and intelligence. This definition of legitimacy is then used to disenfranchise people and communities of color. This erases the historical contributions of people and communities of color.

They are explaining that math has often been used to justify oppression, whether it’s that slaves only count as 3/5ths of a person, or that the people of African nations have an average IQ of 70. Do you disagree?

The history of resistance and liberation, as defined by ethnic studies, is the stories, places, and people who helped liberate people and communities of color using math, engineering, and technology. Access to mathematical knowledge itself is an act of liberation.

What a radical idea, that knowledge is power and that learning math can set you free! Do you disagree?

Any atheist that doesn’t think that science and knowledge are vastly important can just fuck right off, Dave.

Student action, as defined by ethnic studies, is fostering a sense of advocacy, empowerment, and action in the students that creates internal motivation to engage in and contribute to their identities as mathematicians. Students will be confident in their ability to construct & decode mathematical knowledge, truth, and beauty so they can contribute to their experiences and the experiences of people in their community.

That’s a beautiful goal to have in any classroom. Do you disagree?

Even more dangerously, they have a list of questions that are appropriate for the subject. Oh no! QUESTIONS!

Where does Power and Oppression show up in our math experiences?
● Who holds power in a mathematical classroom?
● Is there a place for power and authority in the math classroom?
● Who gets to say if an answer is right?
● What is the process for verifying the truth?
● Who is Smart? Who is not Smart?
● Can you recognize and name oppressive mathematical practices in your experience?
● Why/how does data-driven processes prevent liberation?

How is math manipulated to allow inequality and oppression to persist?
● Who is doing the oppressing?
● Who does the oppression protect? Who does this oppression harm?
● Where is there an opportunity to examine systemic oppression?
● How can math help us understand the impact of economic conditions and systems that contribute to poverty and slave labor?
● How does math contribute to how we value natural resources?

My god, this is a recipe for making students think about the broader context, and also emphasizes over and over again how important it is for the students to understand math.

No wonder Fox News hates it and invents false claims about it, like that it’s all about teaching kids that 2+2 is not equal to 4. The far right has an anti-education agenda, and that’s why they’re spreading these lies.

And David Silverman has gullibly swallowed it whole. And is using it as an excuse to vote for Trump.

Comments

  1. whheydt says

    Hmmm.. I would have said that the Democratic party in general, and Biden in particular, is Center-Right. They only look “Left” because the Republicans are pinned to the extreme Right. Harris, at least, is Center or maybe a smidge towards Center-Left.

  2. mnb0 says

    “Biden & Harris are very much center left politicians”
    Yeah, sure. Centre left according to PZ: support death penalty (Harris as a prosecutor), oppose police reform (idem), voting for the Iraq War of 2002 (Biden) and refusing to speak out about the climate change, because economics (Biden).
    Which such centre left politicians the economical-political elite of the USA can keep on sleeping comfortably. PZ pseudoradical rants apparently are nothing but baked air – when it comes to making choices he’s just another lackey of USA’s one party system, making propaganda for Trump Light.

  3. christoph says

    @ Emily, # 1: You might enjoy Boolean algebra. It’s just like normal algebra, except in base 2. : )

  4. mnb0 says

    Ah, but they are better (read: not as bad) as Donald the Clown. Well, Brezhnev was better than Stalin.
    I won’t be surprised if the Afro-American electorate largely will stay at home this year. But PZ knows better than them, of course. No need to listen to criticism of Afro-Americans.

  5. Jemolk says

    Biden and Harris are very NOT center left. Sanders is center leaning left. AOC could be described as left of center. Biden and Harris are center right at best. The only reason they look halfway reasonable is that the Republicans are now barely left of Mussolini.

    As for Silverman — if he’s seriously considering the Republicans now, he’s not even a liberal in the sense we leftists use the term. If you have 10 people at a table listening to and nodding along with a Nazi, you have a table with 11 Nazis. Silverman appears to be perfectly willing to be one of those 10, so long as no one in his new party ever challenges the power structure he likes.

  6. patrisimo says

    One of my favorite examples of the Western-centric history of math is Eratosthenes vs al-Biruni for computing the radius of the Earth. Eratosthenes is cool because he did it so long ago, but his method is really difficult to do because you need to be near the tropics and be able to compute long distances over cardinal directions fairly precisely (and only shows the Earth’s curvature on one axis; Eratosthenes’ experiment equally supports even a cylindrical Earth). Al-Biruni on the other hand computed the radius without needing to travel very far at all, and his method can be done anywhere there are hills and in any direction that you can see the flat horizon from. It’s just so much better.

  7. says

    I can agree that they’re more center right than center left, but in the USA, that puts them pretty far left relatively.

    A majority of black Americans support Biden over Trump, and actually I was rather shocked during the primaries at how strong the black vote was for Biden. I didn’t understand it myself, but if we’re going to talk about bits and pieces of the electorate, telling me that black Americans don’t like Joe isn’t going to get you very far.

  8. says

    Why do I suspect the “due process” he’s concerned about has nothing to do with the courts and everything to do with the court of public opinion where due process isn’t a thing. Get back to me when you’re worried about the poor people being railroaded through the system because of overworked and underpaid public defenders, Dave.

    Now then, Dave, let’s discuss “free speech” and what has you so worked up that you are considering voting for a government official who has made actual attacks on free speech. https://pen.org/trump-timeline/

  9. consciousness razor says

    Emily, #1:

    But 2+2 doesn’t equal 4! It equals 11! …in base 3 :P

    11! = 39916800 = 2210002222120000 (base-3)

  10. Stacy says

    Regarding the strong black vote for Biden, I think it helps to consider the mostly older and southern African-American women who turned out especially in SC. They skew more conservative and religious. These voters have been called the backbone of the democratic party but they get little attention. They certainly had impact in 2018. Without them we would have ray moore in the Senate so I give them my heartfelt thanks.

  11. says

    TBH the “K-12 Math Ethnic Studies Framework” doc seems pretty weird. As in, I’m confused what its purpose is. Is it a guide to creating a class? If so, it seems to be for a social studies class not a math class. It’s also weird that it covers K-12, isn’t that kind of overly broad?

    If I had to guess, I’d say the audience of this doc is not K-12 kids, but rather social studies teachers who teach in that age range. Probably it’s part of one of those continuing education programs. That being the case, this feels like a lot of hot air over nothing.

  12. raven says

    Mathematical theory and application is rooted in the ancient histories of people and empires of color.

    I suppose this means David Silverman doesn’t use Arabic numerals, which they originally obtained from India.
    Or the numeral and idea of 0 which also came from the Indians.

    If he ever finds out the alphabet came from the Phoenicians, we are done with David Silverman.
    He can go back to painting in caves or whatever else the Europeans invented.

  13. says

    Oh gods, the maths thing again. I saw it over on Twitter, when Lindsay was dismissing actual mathematicians who said that “Well, actually, depending on your terms, 2+2 might be 5”. Which should be bloody obvious because for one thing, 5 is a sign we attached to a concept in the actual world and we could attach it to something else.

  14. says

    @6 Here’s an idea: How about we let black people decide for themselves who they’ll support rather than assuming that only the far left can speak for them? And while we’re at it, let’s apply the same logic to women and the LGBT community, shall we?

  15. says

    Followup to #16, a web search did not confirm my guess that it was part of a continuing education program. It seems to be a framework being considered by the Seattle school district. If approved, it would lead to the design of instructional units that teachers could optionally use. Since this comes from last year and there is no more recent news, I’m guessing it’s either still under consideration or was rejected.

    I still feel like this is nothing to get up in arms about.

  16. KG says

    A majority of black Americans support Biden over Trump, and actually I was rather shocked during the primaries at how strong the black vote was for Biden. – PZM@9

    Yes, yes yes, but those black Americans voting for Biden should be ignored, because they don’t agree with mnb0, consciousness razor and The Vicar .

  17. pilgham says

    God, I hate to talk about old I am, but decades and decades ago, math class started by spending a few days covering the math methods of ancient peoples, through the Romans and ending with the Arab world. It’s not new, is my point. On the other hand, they could have spent way more time on it and covered a lot more interesting topics. The Rhind Papyrus, for example, which starts “Accurate reckoning. The entrance into the knowledge of all existing things and all obscure secrets.” What kid wouldn’t love that?

  18. says

    Silverman:

    I’m literally thinking of voting red right now. Me. David Silverman.

    I love how these people love to try to rope others into their bullshit narrative, like people reading his tweet are gobsmacked at this development. Anyone paying attention over the past several years would have seen the reflexively reactionary douchebaggery leading to this moment. Even the people whose trajectory has most saddened me, if I look back honestly at their history, showed the signs long before they went full misogynist/racist/transphobe/imperialist/…

    I adore these approaches (here’s an effort to decolonize fashion and fashion history), but the writing of these plans often leaves a good deal to be desired.

    Power and oppression, as defined by ethnic studies, are the ways in which individuals and groups define mathematical knowledge so as to see “Western” mathematics as the only legitimate expression of mathematical identity and intelligence.

    Who gets to say if an answer is right?…

    You’re already facing an uphill battle, and you know the Right will mobilize to attack any such efforts. It would help to use language that’s much more clear and resistant to distortion and misrepresentation. And as Siggy mentions @ #16, the whole purpose/audience of the document seems confusing. I love the concept, and think it should be integrated into math education, but the execution isn’t great.

  19. Devious Brownies says

    Damn it, there ought to be some sort of meme for when someone says something so blindingly dumb that your face sort of screws up in an “did you really just say that” expression!

  20. wzrd1 says

    @Christoph, boolean is fine, but regular expressions gives one an enhanced toolbox. ;)

    Still, gotta love all of the “Biden’s gonna defund the police”, no, just nope.
    Trump’s doing that by refusing to help states, counties and cities who have lost most of their tax revenue, but still have to keep essential services running. So, do we get rid of EMS and fire during a pandemic or police? Or simply disband our local governments, essentially ridding ourselves of all essential services and enjoy our eventual dirt road infrastructure and go back to storing shit under our houses?
    I’ll further predict that Trump’s next budget will defund the SDNY, while shouting on Twaddle, “LAW AND ORDER”.

  21. philipelliott says

    Biden willingly held the #2 slot backing up a black man for 8 years, without complaint, or any hint of anything but loyalty. I think that explains his strong support in the Black community. But what do I know? I’m just some idiot on the internet.

  22. says

    Biden and Harris are american center left which means center right.

    Well, math is math. It is universal. There is no power dynamics in math, you are either correct or not.

    All of those issues mentioned are applications of math and those can be skewed or misused.

    In school kids should learn not only how math works but also how to use it, so all those social based issues may be an element of education in math, why not.

  23. mailliw says

    raven @17

    I suppose this means David Silverman doesn’t use Arabic numerals, which they originally obtained from India.

    Here in Germany someone told a candidate for the far right NPD that there were whole suburbs in the town where all the houses had Arabic numerals. A complaint about “Islamisation” on this ground subsequently turned up in the party’s election material.

  24. gedjcj says

    @1, 12

    But 2+2 doesn’t equal 4! It equals 11! …in base 3 :P

    11! = 39916800 = 2210002222120000 (base-3)

    In base 3, 11! = 220 ;-)

  25. wzrd1 says

    @Gorski, you’ve not watched me do math. If I don’t have a calculator of some sort, even abacus or my favorite alternative, a slide rule, doing it by hand tends to be a disaster and a protracted exercise.
    Algebra, trig and even a touch of calculus is OK, the actual number crunching, legendary in gaffes. Dyslexia and all.
    So, when sleep deprived for several days, taking a 15 second pulse just isn’t destined to be. After three days, even taking a full minute pulse becomes problematic.
    But, at optimal, bare numbers, I’m good when counting to 20 – with my shoes and socks off and the last time I counted to 21, I was arrested. ;)

    Not joking about comfortable using an abacus and preferring a slide rule. But, using a computer is easier and superior, given a computer is frequently also a communications device.

  26. says

    #16: Yes, it’s for teachers. I’ve got guides like this for teaching biology, and especially for meeting the requirements for certification for graduates of the school of education. I think this one is fairly well thought out for its purpose, and really is no big deal.

  27. wzrd1 says

    @30, consciousness razor, I disagree. Some citizens are not permitted to vote for valid reasons, such as engaging in willful voter fraud. They’re rare, so my proposal would be equitable and quite reasonable, given the origination of our nation. No taxation without representation and one cannot be represented if one isn’t part of the selection process via ballot. So, no vote, that citizen is exempt from all taxation.
    And whenever someone wants to repress a segment of the population and succeeds, as has frequently happened, the disenfranchised are now tax exempt – for all taxes and social security credits are applied to replace the shortfall to those programs.
    What do you want to bet we’d see zero disenfranchisement?

  28. monad says

    I remember seeing a problem in university that most of the class got wrong. We missed that the answer was different when 13 = 0. In real math, you don’t insist on what things like 2+2 must be, you look for what they else they could consistently be and what consequences that would have.

  29. consciousness razor says

    gedjcj:
    Yes, but 220 (base-3) = 4! and “2+2 doesn’t equal 4!” which is certainly true: 2+2 doesn’t equal 4! It’s obviously 11!

  30. brucegee1962 says

    Leaving Silverman and his self-justifying politics aside for a moment, though — I’m kind of surprised that PZ so eagerly defends that curriculum. At least the part that he quoted looks dangerously akin to anti-science woo. I’m a humanities guy, not a math guy, but if as a student I had seen a class textbook with that stuff in it, I would have been eying the exits.
    Obviously, if a math class is taught with a “history of mathematics” component, then the contributions of non-Western mathematicians should certainly be brought to the foreground. That seems self-evident. And like all of the sciences which are based upon it, math is a tool which can be used for good or ill — also self-evident. I could even see room for discussion of how modern math departments can be bastions of retrograde thinking, though that seems a bit heavy for K-12.
    But none of these points seem to be what the curriculum is stressing — instead, it seems to be arguing that the premises of math itself are somehow tainted by evil Westerners and need to be questioned and overturned. This sounds like an outgrowth of the standard woo mantra “Western medicine is corporate and evil due to big pharma, so open your mind to homeopathy and Eastern mystic treatments” and the rest of that codswollop.
    PZ quotes:

    Power and oppression, as defined by ethnic studies, are the ways in which individuals and groups define mathematical knowledge so as to see “Western” mathematics as the only legitimate expression of mathematical identity and intelligence. This definition of legitimacy is then used to disenfranchise people and communities of color. This erases the historical contributions of people and communities of color.

    and comments

    They are explaining that math has often been used to justify oppression, whether it’s that slaves only count as 3/5ths of a person, or that the people of African nations have an average IQ of 70. Do you disagree?

    I agree with what PZ says in his comments that math has been used to justify oppression, but I don’t think that’s a reasonable paraphrase or extrapolation from what he’s quoting. What’s with the scare quotes around “Western” mathematics? I had always been taught that mathematics and the other sciences are a universal body of knowledge, independent of originating cultures — indeed, that one of the purposes of the scientific method was to reduce cultural influences on universal knowledge. The real kicker of the quote comes at the end of the first sentence — what, exactly, is the non-Western version of mathematics that is a “legitimate expression of mathematical identity and intelligence”? This seems to be arguing that, just as we should toss out Western medicine and explore other forms untroubled by pesky requirements like “evidence,” we should do the same with math and every other scientific discipline as well.
    Also, the examples they seem to be giving come primarily from the fields of sociology and politics, which, sure, can twist math to do some pretty awful things. But that is just a small subsection of math’s applications as a whole. The bridge does not care about your race, ethnicity, or culture. The bridge just knows whether it was built with the strength to stay up or fall down. I don’t see how you can teach “mathematical knowledge, truth, and beauty” without teaching that.

  31. a_ray_in_dilbert_space says

    David Silverman needs to be sentenced to a period of 2 weeks performing long division using only roman numerals, but I suspect the Geneva convention would be all over my ass on that punishment.

  32. mailliw says

    The bridge does not care about your race, ethnicity, or culture. The bridge just knows whether it was built with the strength to stay up or fall down. I don’t see how you can teach “mathematical knowledge, truth, and beauty” without teaching that.

    Mathematics is a branch of philosophy, not of science or engineering.

  33. mailliw says

    monad @36

    In real math, you don’t insist on what things like 2+2 must be, you look for what they else they could consistently be and what consequences that would have.

    Exactly.

  34. consciousness razor says

    The real kicker of the quote comes at the end of the first sentence — what, exactly, is the non-Western version of mathematics that is a “legitimate expression of mathematical identity and intelligence”?

    There have been important mathematical traditions in non-Western (or non-European) cultures throughout history. China, India, and the Islamic caliphates have been some of the largest, which made huge contributions to the field over many centuries. It is not just a history of some ancient Greeks and Romans, followed by other Europeans like Fibonacci, Cardano, Newton, Leibniz, Euler, Gauss, etc.

  35. wzrd1 says

    @38, brucegee1962, western or non-western, mathematics are invariant depending upon location, east, west, north, south, Andromeda galaxy, mathematics by nature must remain invariant upon location, lest all natural laws become variable and observations support that theory.
    As for western, non-western mathematics altering medicine, medicine is physics and hence, chemistry and again, are invariant. What is different is the social construct and approach, with loads of woo in different directions when people attempt to mix various nonsense into evidence based science. Where things work are examination of herbs, one of which is relatively recently discovered artemisinin based antimalarial drugs, to use one dated example (artemisinin resistance has already been observed, as that damnable parasite is quite adaptable).
    Nothing changed in the science, but we also didn’t bother with something as random as freeze dried seahorse or similar insanity that would have so many compounds present to instantly confound any attempt at study.
    But, artemisinin works on some variants of malaria, east, west, north or south, for precisely the same reason, as biochemistry within an organism remains invariant upon where that specific organism is found. The mechanism of action remains ill understood with artemisinin, but appears oxidative in nature and iron and oxygen reacting in a manner not controlled within a cell is infamous for wreaking havoc.
    So, the entire western/non-western argument is well, bullshit on rye and being called a Reuben sandwich. It isn’t, it’s simply shitting up a perfectly delicious bread, rendering it useless.

  36. brucegee1962 says

    @42 consciousness razor

    There have been important mathematical traditions in non-Western (or non-European) cultures throughout history. China, India, and the Islamic caliphates have been some of the largest, which made huge contributions to the field over many centuries. It is not just a history of some ancient Greeks and Romans, followed by other Europeans like Fibonacci, Cardano, Newton, Leibniz, Euler, Gauss, etc.

    Was there anything in my comment that contradicted or disagreed with what you say here? I said

    Obviously, if a math class is taught with a “history of mathematics” component, then the contributions of non-Western mathematicians should certainly be brought to the foreground. That seems self-evident.

    What I was trying to say was that math should be viewed and taught as a unified field of knowledge which has been created and built upon by multiple cultures working in concert. The K-12 curriculum PZ presented, at least as I read it, seemed to imply that there are multiple, culturally dependent strains of math, which may be mutually contradictory but which are nevertheless all equally valid. I don’t even find that line of reasoning convincing when it comes to social sciences, let alone math.

    @40 mailliw

    Mathematics is a branch of philosophy, not of science or engineering.

    I would say rather that science and engineering are branches of math. As for math being a branch of philosophy, I’ll grant you that if you like.

    @43 wzrd1
    We’re in complete agreement, I think?

  37. says

    brucegee1962 @ #45:

    The K-12 curriculum PZ presented, at least as I read it, seemed to imply that there are multiple, culturally dependent strains of math, which may be mutually contradictory but which are nevertheless all equally valid.

    I agree that it implies this, but I assume it’s more the result of sloppy writing than intent.

  38. Rich Woods says

    Maybe I’ve turned up too late in the game to say that the claim “Biden & Harris are very much center left politicians” is bollocks by European standards. Those two are centre-right at best. I’d have to hold my nose to vote for either of them, although I’d do so just to get that shitstain ignoramus Trump out of office.

    I’m not claiming that in contrast my country, the UK, has a perfect system for allowing the electorate to express their opinion and not see it ignored by the methodology of electoral calculus, let alone the impact of the explicitly non-democratic elements of formal governance, but the US does claim to have a reliable and democratic functioning republican system while in practice having so many gaping holes you could crash-land a space shuttle through any one of them.

  39. consciousness razor says

    SC:
    That’s difficult to spell out, and it should go without saying that I’m not a historian or philosopher of mathematics. Let me start by saying that I don’t think there’s only a single type of thing that does (or could) meaningfully distinguish one from another. There are lots of commonalities here and differences there…. Like many other things that involve a complicated process of cultural transmission over long periods of time (as I could much better explain in the context of musicology), there isn’t a very clean way to separate one from the other, especially not if you were making the same type of cut in each case. And over time, they have (in some sense and to some degree) merged into the modern forms of math that we recognize and use today. So it’s complicated. (Obviously.)

    With that said, a few examples of some basic differences come to mind…. The types of arguments or proofs that are used, which topics are even being studied extensively (e.g., geometry, number theory, probability, etc.), and perhaps most noticeable are the ways that mathematical ideas are expressed/represented/notated. We’re so accustomed to algebraic formulas now that I don’t think many appreciate just how much of it used to be done verbally or pictorially.

    That may not seem like much at first but shouldn’t be discounted, given that whenever it’s applied, what people are doing with math is exactly to represent other things. So, it makes sense that different representations can make a big impact on how you go about solving problems (if you can), how you might approximate solutions (if necessary/practical), how you might generalize results, how you might come up with new problems or new concepts altogether, and so forth.

  40. nomdeplume says

    You guys are SO unfair to Silverman. I mean, he would LOVE to vote for progressive Democrat candidates, but some people in the community just keep coming up with these awful progressive ideas that he can’t support because reasons, so what is the poor bluer than blue fellow meant to do? Eh?

  41. brucegee1962 says

    @48 consciousness razor

    The types of arguments or proofs that are used, which topics are even being studied extensively (e.g., geometry, number theory, probability, etc.), and perhaps most noticeable are the ways that mathematical ideas are expressed/represented/notated. We’re so accustomed to algebraic formulas now that I don’t think many appreciate just how much of it used to be done verbally or pictorially.

    That may not seem like much at first but shouldn’t be discounted, given that whenever it’s applied, what people are doing with math is exactly to represent other things. So, it makes sense that different representations can make a big impact on how you go about solving problems (if you can), how you might approximate solutions (if necessary/practical), how you might generalize results, how you might come up with new problems or new concepts altogether, and so forth.

    I’ll agree that all of this seems worthy of study — at an undergraduate/graduate level. But in K-12? Anything that’s taught in K-12 ought to be “This is something that every adult American ought to be familiar with to function in modern society.” Given the general level of innumeracy in our society, alternative/abandoned systems of notion don’t seem to be worth precious time, when many adults don’t understand how fractions work: https://www.smbc-comics.com/comic/fractions

  42. brucegee1962 says

    @46 SC

    I agree that it implies this, but I assume it’s more the result of sloppy writing than intent.

    I would love to believe this, but it sounds depressingly similar to other “This field/work/author should be rejected because it’s Western and therefore imperialist” line that some people have been using against the sciences.

  43. says

    wzrd1. Rather than freeze dried seahorse, what about Gila Monster venom? One of the first of a class of drugs I take for diabetes was based on a compound in Gila Monster venom.

  44. Allison says

    Even within modern higher math, there are cultural differences. French mathematics is noticeably different from the sort of mathematics done in the English-speaking world. For a long time, there were two schools of doing what we now call calculus; the names Leibnitz and Newton come to mind. What we have now is really an amalgam of the two. Even within the USA, there are definite styles of math that differ from research university to university. And this despite the fact that everyone knows pretty much everyone else.

    Of course there are commonalities. They are trying to describe more or less the same world. It’s like how different cultures have recognizably different ways of building boats, despite dealing with the same physics.

  45. says

    consciousness razor @ #48, I don’t really see how that’s different from people participating in a global knowledge project from a variety of perspectives. Also, there’s no “Western” mathematics or “Western” anything – Greeks, Romans, Christians, Enlightenment philosophers,… – there were wildly different approaches both amongst and within these groups. An important project would look at the distortions and limitations caused by religious/political ideologies on the broader project (which I’ve been thinking about even more after reading Caroline Winterer’s American Enlightenments…). But it’s all mathematics.

  46. Allison says

    brucegee1962 @51

    “This field/work/author should be rejected because it’s Western and therefore imperialist”

    A lot of stuff that we white Euro-Americans uncritically take as good is imperialist. And that includes a fair amount of what people think of as “science.” We live in a culture which encourages us to not notice the ways in which science, philosophy, arts and literature are biased. Because these biases are seen as rationality, and anything which disagrees with those biases is dismissed as illogical, emotional, or “political correctness gone amok.” I think that pretty much everything “Western” deserves to be examined for the ways in which it is imperialist. Only after serious, critical examination will we know if there is anything of value left after the imperialism is removed.

  47. consciousness razor says

    I’ll agree that all of this seems worthy of study — at an undergraduate/graduate level. But in K-12?

    I don’t think it ought to be too much of a focus when the basics are still being sorted out, but it wouldn’t have to be too much. It’s important to gain some recognition that math has come in many different forms, from many different places over many years, because that’s just the truth.

    Anything that’s taught in K-12 ought to be “This is something that every adult American ought to be familiar with to function in modern society.”

    I wouldn’t say that. Functioning in our modern society (specifically the US) isn’t the kind of aspiration I think we should have, at least not as long as the society in question is the thoroughly dysfunctional system of oppression and exploitation that we actually have. If some people get confused about fractions, as you claim, that suggests the current way of doing things isn’t accomplishing what you wanted. So whatever you may take from that, this doesn’t make for a valid argument against doing something else.

    I think the purpose of education should be (very roughly) to learn about yourself and the world around you. It shouldn’t be about training people for jobs, so that they may “function” for their society. What I don’t want are cogs that will fit nicely into the machine that’s been crafted for us, because that machine is awful.

    So we’re clear: I’m not subscribing to what’s quoted in the OP, but at the same time, I have no problem with teaching kids more about the cultural/historical side of things in math classes, including some amount of that in elementary schools.

    Personally, I always found that kind of stuff pretty interesting, and it did not hinder my interest in or ability to do math. It’s really sort of exciting to learn about this big, long, messy, worldwide endeavor that people have undertaken for as long as anyone can remember, which had all sorts of dead ends and confusing twists and turns along the way. Compared to that, some abstract symbols written on a chalkboard, by a teacher who’s not explaining much of anything about where any of it came from, probably seems very dull or even useless. And I don’t think that’s the kind of experience students should have.

  48. wzrd1 says

    @robertbaden, I remember seeing a blurb about that. Forgot to follow it up, so I left a tab open for later.
    Gotta run off to the store to pick up some odds and ends. I’ve been minimizing major provisions runs of late, the fridge died and cold storage is limited to coolers until I can get a new fridge installed.
    Annoyingly, a very full fridge. Like there’s any other time a refrigerator fails, save right after you’ve just stocked it up… :/
    Murphy was ever so much an optimist!

  49. says

    Allison @ #58, that’s a great model and should be applied to everything, whether it’s labeled “Western” or not. I completely agree that much of what is accepted in Europe, the US, and everywhere that’s felt our influence needs special scrutiny given the history, but the argument is a more general one with wider applicability. Asking what religious, political, and/or economic interests have (mis-)shaped an approach should be fundamental. (And kids are probably more able to do it than we think!)

  50. consciousness razor says

    I don’t really see how that’s different from people participating in a global knowledge project from a variety of perspectives. Also, there’s no “Western” mathematics or “Western” anything – Greeks, Romans, Christians, Enlightenment philosophers,… – there were wildly different approaches both amongst and within these groups. An important project would look at the distortions and limitations caused by religious/political ideologies on the broader project (which I’ve been thinking about even more after reading Caroline Winterer’s American Enlightenments…). But it’s all mathematics.

    I agree with that. It’s the same thing in music: the term “Western music” gets tossed around a lot, which is just as confusing in that context. And like you say above, it is all still music.

    It doesn’t seem like we disagree. I was responding to a statement that doubted that there was any such thing as legitimate “non-Western” math, supposedly analogous to “non-Western medicine,” but in the process I didn’t mean to imply that I think “Western” actually is a helpful description. That’s partly why I started with all of those caveats and complications, but obviously that point was not very clear.

  51. says

    “Bluer than blue”? Is that sort of like “being a Daley”? Remember, the police aren’t here to create disorder, they’re here to preserve disorder!

    Party allegiance doesn’t have an awful lot to do with ideological purity. If it did, the Illinois Speaker of the House — whose entire law practice revolves around (arguably corruptly, but in Cook County who could tell?) winning appeals for rich landowners against real-estate tax assessments. Now, someone please show me how that’s a partisan or ideological purity test?

    The Democratic Party is center-right. The Republican party is right tending toward outright reactionary. And if center-right is too far to the left for Mr Silverman, one wonders what too far to the right looks like…

  52. brucegee1962 says

    @58 Allison

    I think that pretty much everything “Western” deserves to be examined for the ways in which it is imperialist. Only after serious, critical examination will we know if there is anything of value left after the imperialism is removed.

    See, this is one of the attitudes I have trouble with — the equivalency of imperialism with Western society. Every culture has historically been imperialist whenever it gets the opportunity to be. It’s not just Western — it’s a universal human trait.
    In the seventeenth century, more slaves were taken from Europe to Africa than went in the opposite direction — entire coastal villages from Italy to Ireland were depopulated by Barbary raiders. (Of course, the flow decidedly reversed in the eighteenth and nineteenth centuries.) One of the reasons the British were able to colonize India were that it had already been colonized by Mughals a few centuries earlier, so the locals were used to being ruled over by foreigners from a different culture. Jared Diamond wrote a lot that I didn’t know in Guns, Germs and Steel about how the current Indonesians were the conquerors of the earlier inhabitants of the islands. Japan, China, the Khmer in Vietnam — everybody was constantly conquering everybody else. Westerners just happen to get most of the blame for it because theirs happened in recent memory, the technological difference between conquerors and conquered was somewhat greater, and they tended to be somewhat more systematic and bureaucratic about the process.

  53. consciousness razor says

    The Democratic Party is center-right. The Republican party is right tending toward outright reactionary. And if center-right is too far to the left for Mr Silverman, one wonders what too far to the right looks like…

    A little too far to the left: money is speech, and corporations are people

    Perfectly balanced and moderate: money is speech, and corporations are the only people

    A little too far to the right: money is speech, and corporations are the only people, other than the reptilian communists who poisoned us with cell phones, faked the moon landing, blew up the twin towers, and must be destroyed at all costs

  54. UnknownEric the Apostate says

    The only thing that matters to David Silverman is David Silverman. And since we were all meany pants to him, he’s gonna take his football and go play with the kids at the other park, where they let him do whatever he wants.

  55. chrislawson says

    brucegee1962–

    Look at those points again. Not one of them suggests that mathematics should be rejected because it is imperialist. It even asks students to think about how maths can be used to analyse issues like economics and the environment.

  56. chrislawson says

    To everyone insisting that maths is some kind of pure essence that transcends culture: yes, of course, it’s true in the obvious sense that, say, Pythagoras’ Theorem isn’t dependent on you ethnicity or culture. But the examples of mathematics being used for oppression are not exactly hard to think of.

    The Laffer Curve
    The Black-Scholes Equation
    The Bell Curve (the book)
    Medical data collected on white males extrapolated without thought to women and non-whites, resulting in severe undertreatment of those groups.
    The Prosecutor’s Fallacy (there’s a reason it’s not known as the Defence Attorney’s Fallacy)

    A more obscure one: The argument that Tasmanians were too stupid to maintain their technology level after the land bridge to mainland Australia was flooded.

  57. klatu says

    Biden & Harris are very much center left politicians

    The US does not have a left worth talking about. Not when your so-called left is also invested in never-ending war and profit-driven climate extinction.

    And that is exactly why you (Americans, I mean. I’m not one) need to build one. Collectively hold your noses in November and vote Biden. And then stop voting for Dems altogether. Stop rewarding shitty people for being slighty less shitty than they could be.
    At least start supporting local DSA chapters or the Greens or whatever else actually left-adjacent choices you have available. And if none are available, create them.
    You guys NEED a viable third party. Fuck, the rest of the world needs you to have a third party, because that septic tank you call a democracy keeps spilling over to everyone else.

  58. logicalcat says

    A viable third party cannot exist. Our system doesnt allow it. Forming a third party splits the vote and ensures only republicans win. Basicaly turning the country into a one party state.

    The only viable option is if leftist take over the democratic party. And they dont want to do that because leftists either are too dumb, dont actually care and pretend they do, or are too in love woth their antiestablishmentarian status.

  59. says

    That material from Seattle is among the most arrant nonsense I ever read. Sorry, Prof. Myers, I have read your blog for years and agree with almost everything you say, but if you can’t see how unutterably stupid this is, I just don’t know what to say.

  60. mailliw says

    @45 brucegee1962

    I would say rather that science and engineering are branches of math.

    Scientists and engineers use mathematics, mathematicians study mathematics. In the same way as people use language, but linguists study language.

  61. nomdeplume says

    @68 Thanks for the Tasmanian reference Chris. I was a significant player in that debate in the 1970s – odd to see a mathematical treatment of it. I have followed up by writing to the author.

  62. chrislawson says

    @71–

    If you can’t put into words why it’s so unutterably stupid, than maybe it’s not as stupid as you think.

  63. chrislawson says

    nomdeplume@73–

    …on the right side I hope :-)

    I would be interested in hearing your experiences with the controversy.

  64. lotharloo says

    I’m sorry PZ but this is an astoundingly stupid post.

    Power and oppression, as defined by ethnic studies, are the ways in which individuals and groups define mathematical knowledge so as to see “Western” mathematics as the only legitimate expression of mathematical identity and intelligence. This definition of legitimacy is then used to disenfranchise people and communities of color. This erases the historical contributions of people and communities of color.

    I read this multiple times and I don’t think it has any meaning. Mathematical knowledge is not defined through “power and oppression”. The statement is meaningless.

    “Western” mathematics as the only legitimate expression …”

    Total nonesense. Meaningless dribble. Ramanujan, disconnected from “western mathematics” discovered the same things the “western Mathematician” had discovered, so I guess we can conclude he was a FUCKING AGENT OF THE BRITISH EMPIRE!! Or how else do you explain his “Western Mathematical knowledge”? Eh? EH??

    And I also read your explanation and it really missed the mark:

    They are explaining that math has often been used to justify oppression, whether it’s that slaves only count as 3/5ths of a person, or that the people of African nations have an average IQ of 70. Do you disagree?

    How is it related to math? Numbers =/= math. Arithmetic is not math. Running a statistical regression algorithm is not math.

    The history of resistance and liberation, as defined by ethnic studies, is the stories, places, and people who helped liberate people and communities of color using math, engineering, and technology. Access to mathematical knowledge itself is an act of liberation.

    As much as I love math, I disagree. It’s not “math” that helped people, it’s morality and empathy and realization that people with different colors are still human. Access to mathematical knowledge has nothing to do with liberation. Math can help your thinking and logical skills but it won’t help you see others as human. For that you need humanity and empathy. All the evil people, all the capitalist fucks, all the psychopathic CEOs are also very good with their critical skills and foresight and they are very good in extracting tiny amount of value out of exploiting people. The IT world is full of brilliant people with excellent mathematical skills who can design complex system that are highly optimized to let their machinery run without any regard for the morality of what they are doing.

  65. lotharloo says

    Also, after reading that document, it is clear that its authors have no clue what is mathematics and I doubt they have even an understanding of mathematics at the level of an undergrad student studying pure math:

    SWBAT demonstrate mathematical literacy by applying concepts to real world problems through dialogue and story telling.

    SWBAT re-humanize mathematics through experiential learning and answering “why?”.

    Right, “experiential learning”. Something tells me they have never taken a course on topology.

  66. nomdeplume says

    @76 Yes, the right side Chris! My conclusion, briefly, was that the economy, culture and technology said by Rhys Jones to be evidence of intellectual decline, the result of “too few people”, was in fact the adaptive response to the Tasmanian environment. In the paper you linked to, the author is showing mathematically that the idea that the population was “too small” makes no sense. So this is a complementary finding to my work. While my work was largely ignored (Jones was a much more powerful academic figure than I was in 1979) it did effectively put a stop to people developing the “intellectual decline” nonsense in the academic literature, though it continued to be used in the Right Wing popular press.

  67. chrislawson says

    @79–

    I remember swallowing that hypothesis completely when I was younger. Now that I’m a lot more skeptical, I’d look to see if there truly was a reduction in complexity vs. an archeological confounder at work, and if there was an observable reduction in complexity, if it was due to adaptation of the culture to the environment rather than “decline”. After all, complexity has its costs and if a simpler tool achieves the same ends, then it’s a step forward.

    I can imagine an ill-informed future anthropologist might argue that our shift to electric vehicles, with their much simpler engineering, is a sign of technological regression.

  68. KG says

    KG, #22:
    Bullshit. I don’t think any voters should be ignored. – consciousness razor@30

    Your constant whining about how your “standards” won’t allow you to vote to end the rule of Trump says otherwise.

  69. mailliw says

    lotharloo @77

    The IT world is full of brilliant people with excellent mathematical skills who can design complex system that are highly optimized to let their machinery run without any regard for the morality of what they are doing.

    But isn’t that a reason why people should be taught about the moral implications of what they are doing in their discipline?

  70. lotharloo says

    @mailliw

    Yes, but it should not be limited to math, and it should include most areas of science.

  71. says

    I can’t even keep track of who’s arguing exactly what in this thread and doubt very much that people are sharing the same definitions of the things they’re arguing over and I blame the document in the OP.

  72. says

    I find it sort of amusing — and all too typical — that even the meaning of “mathematics” can’t be agreed upon. Some posters above think that “mathematics” is only the purity of, say, the Pythagorean Theorem (query: how does one teach the Parallel Postulate to students who have become aware that they live on a globe and not in Flatland without bringing in cultural context… even by omission?). Some posters are looking not at mathematics qua mathematics, but at the consequences of (purported) ignorance thereof, especially concerning bridges of all kinds (man-made and Tasmanian).

    That’s the entire point of alternate curricula and instructor-level inquiries: That the boundary conditions we impose on topic definitions to determine what is acceptable teaching/discussion on that topic have cultural elements worth examination. Sometimes those boundary conditions make sense, and are well-tested, and are not inherently problematic; other times… not so much. One of the key, unstated subplots in the material PZ cited to is that no matter how seemingly neutral a tool is, it can be used for many purposes — often with consequences. Beating swords into plowshares sometimes results in Dust Bowls…

  73. says

    I, too, am going to vote for Republican to say free speech. Sure, they might be ok with calling the press ‘enemies of the people.” Sure, they are ok with using secret police to unlawfully detain protestors. Sure they want to save statues that were erected to glorify white supremcy, but throw a shit fit if satanists want to erect a monument. Sure they want to use public funds to force their brand of Christianity on people, while at the same time trying to surpress all other religious idea. And maybe they arre no long even pretending not to be racists. And they might throw kids into cages. Sure that might be bad. But last week, I called a chick a broad, and now human resources is making me take a thrity minute sensitive training. And if that is not threat to the fundalment nature of our democracy, I don’t know what is.

  74. mailliw says

    Jaws @86

    I find it sort of amusing — and all too typical — that even the meaning of “mathematics” can’t be agreed upon.

    As the British mathematician Ian Stewart once said, the relationship between pure and applied mathematicians is based on trust and understanding. The pure mathematicians don’t trust the applied mathematicians and the applied mathematicians don’t understand the pure mathematicians.

  75. consciousness razor says

    KG, #81:
    That’s nonsense. Suppose I vote for Biden in a few months (on a secret ballot of course, but suppose I tell you about it). Will that mean I’m not “ignoring” some group of people who voted in the primaries? Nope. What if you had the impression that I’m very enthusiastic about the Biden/Harris ticket and offered nothing but praise for them? Still no, and on the contrary, that seems a lot like ignoring some people who have legitimate criticisms which ought to be heard, since there are quite a few people like that.

    So where does that leave us? I think it’s problematic how much Biden has been ignoring some voters: especially leftists/progressives, younger people, poorer people, Latinos….

    Meanwhile, John Kasich (former governor of Ohio and Republican presidential candidate in 2016) has been invited to speak at the Democratic convention this year. And for a little while, I thought poor old Michael Bloomberg would have to resign himself to quietly draining blood from corpses while no one pays attention, but he’s been invited to speak at the convention too. So that’s something. At least we know that not everybody is being ignored.

  76. logicalcat says

    @CR

    Except for all the concessions and work done by Biden and Sanders/AOC working together? Yea other than that they ignore leftists/progressives.

    This fact was even used by right wingers as a negative actually lol.

    As for ignoring latinos. I dont speak for the rest of my people, but I want to get rid of the guy with concentration camps.

  77. leerudolph says

    raven@17: “He can go back to painting in caves or whatever else the Europeans invented.”

    Check out this story (the one with the most recent date that I could find quickly; I learned about it somewhat earlier).

    A STUNNING cave painting discovered in Indonesia may be the earliest evidence of storytelling. The artwork is at least 43,900 years old, and shows that humans were depicting scenes tens of thousands of years earlier than previously thought.

    The painting is a 4.5-metre-wide hunting scene, discovered in the limestone cave of Leang Bulu’ Sipong 4 in Sulawesi in 2017 by Maxime Aubert of Griffith University, Australia, and his colleagues. Painted in a dark red pigment, it depicts at least eight small human-like figures hunting two pigs

    That date is somewhat earlier than any such paintings in European caves.

  78. KG says

    consciousness razor@90,
    Here’s the sort of whining I’m talking about:

    But wouldn’t it be nice if we had standards? I think that would be nice. That’s apparently the sort of bad thought that makes me a bad person. I think I’m okay with that — just a bit of thoughtcrime, in very moderate amounts. There are far more catastrophic mistakes I could’ve made in my life, which probably has to count for something. And I hear that in some places, they still let you get away with that sort of thing. I assume that they’re not all hopeless shitholes, like this fucking country is.

    All about how fucking put-upon poor consciousness razor is. Made me want to puke.

  79. consciousness razor says

    What it made you do is lie about me, KG. Then you didn’t retract it when I called bullshit. And you still won’t do that now.

    You’re certainly not the only one here who has lied in response to criticisms of Biden, but I do take it personally when the lies are personal. You probably shouldn’t expect anything else. And if that’s what makes you feel sick, then my suggestion is to not lie in the first place.

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