‘Stuff that you long ago forgot isn’t general public knowledge’

What do Christian fundamentalists have against set theory?” asks Maggie Koerth-Baker at BoingBoing.

She goes on to answer why — basically for the same reason that Christian fundamentalists do everything: Us-vs.-Them tribalism. But don’t let me spoil the ending, go read the whole thing (the kicker is terrific).

What I want to highlight here, though, is her introduction, which I may plagiarize if I ever decide to write my own memoirs because it so closely parallels my own experience:

I’ve mentioned here before that I went to fundamentalist Christian schools from grade 8 through grade 11. I learned high school biology from a Bob Jones University textbook, watched videos of Ken Ham talking about cryptozoology as extra credit assignments, and my mental database of American history probably includes way more information about great revival movements than yours does. In my experience, when the schools I went to followed actual facts, they did a good job in education. Small class sizes, lots of hands-on, lots of writing, and lots of time spent teaching to learn rather than teaching to a standardized test. But when they decided that the facts were ungodly, things went to crazytown pretty damn quick.

All of this is to say that I usually take a fairly blasé attitude towards the “OMG LOOK WHAT THE FUNDIES TEACH KIDS” sort of expose that pops up occasionally on the Internet. It’s hard to be shocked by stuff that you long ago forgot isn’t general public knowledge. You say A Beka and Bob Jones University Press are still freaked about Communism, take big detours into slavery/KKK apologetics, and claim the Depression was mostly just propaganda? Yeah, they’ll do that. Oh, the Life Science textbook says humans and dinosaurs totally hung out and remains weirdly obsessed with bombardier beetles? What else is new?

For me it was grade 3 through grade 12. And neither classroom video nor Ken Ham had yet surfaced, but we did watch those Moody Science movies and read books by Dr. Henry Morris — so I know quite a bit about bombardier beetles, too. We didn’t use the BJU textbook in biology, but one of the textbooks for my Bible class was Hal Lindsey’s The Late Great Planet Earth. (Yes, in high school, I took a final exam on Hal Lindsey. Aced it.)

But I also share Koerth-Baker’s sense that, much of the time, my school “did a good job in education.” The tricky thing, for years afterward, was figuring out the difference between that much of the time and the time we spent galloping off to crazytown.

I also know just what Koerth-Baker means by “it’s hard to be shocked by stuff that you long ago forgot isn’t general public knowledge.” I’ve gotten better at remembering that some of that stuff from fundie-world should be shocking, though. It helps to have a wife who finds it all hilarious. I can usually crack her up just by reciting the Pledge of Allegiance to the Christian Flag, or the Pledge of Allegiance to the Bible, or by singing a few bars of “Bright and keen for Christ our savior. …”

Big-time extra credit to anyone who recognizes that last reference.

(Via Jeremy Yoder’s always cool “science online” roundups at Denim and Tweed.)

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  • http://mordicai.livejournal.com Mordicai

    I in fact still own one of those Creationist books about dinosaurs that mention bombardier beetles.  In it, it is strongly implied that dinosaurs– especially duckbilled dinosaurs– mixed chemicals in their body that allowed them to breathe fire.  This is how Saint George, & others of his ilk, where able to actually fight actual firebreathing dragons.  Another similiar one that I still own has lots of backflips to do to explain how Tyrannosaurus Rex was a vegetarian in the Garden of Eden.

  • Lori

    I’m so thankful that I made it through school before the culture wars got really ugly, and therefore have no real personal experience with A Beka and BJU’s ideas about education. When I was growing up the only Christian schools in our area were Catholic or Lutheran. At that time doctrinal differences trumped being anti-everything-in-modern-culture, so my folks weren’t about to send me there and homeschooling wasn’t the Thing that it is now. I doubt it ever occurred to my parents that my mom should basically be in sole charge of my education*. A couple decades on and I suspect they would have looked at things differently.

    *Thank FSM, because I love her but she & I would not have done well as teacher & student.

  • GDwarf

    I still don’t get the objection to set theory. I mean, really? Set theory? It’s such a basic idea that I don’t know how one could really be against it.

    I do wonder if there isn’t also some opposition because set theory lead to the conclusion that it is possible for some things to be impossible to prove true or false. Also that it’s impossible to have a set that contains everything. Those both seem like ideas that they’d be opposed to them.

    It’s yet another example of supporting or opposing basic facts because of conclusions they lead one to, rather than any actual rational thought or assessments of them.

  • AnonymousSam

    Set theory allows for the discussion of there being common ground between two otherwise distinct groups. Tribalism can’t acknowledge that by any costs.

  • Majromax


    I still don’t get the objection to set theory. I mean, really? Set theory? It’s such a basic idea that I don’t know how one could really be against it.

    — “Beware, you who seek first and final principles, for you are trampling the garden of an angry God and he awaits you just beyond the last theorem.”
    Sister Miriam Godwinson, Sid Meier’s Alpha Centauri

  • http://twitter.com/FearlessSon FearlessSon

    “Beware, you who seek first and final principles, for you are trampling the garden of an angry God and he awaits you just beyond the last theorem.”
    Sister Miriam Godwinson, Sid Meier’s Alpha Centauri

    — “Man’s unfailing capacity to believe what he prefers to be true rather than what the evidence shows to be likely and possible has always astounded me. We long for a caring Universe which will save us from our childish mistakes, and in the face of mountains of evidence to the contrary we will pin all our hopes on the slimmest of doubts. God has not been proven not to exist, therefore he must exist.”
    Academician Prokhor Zakharov, Sid Meier’s Alpha Centauri

  • Pat B

    I can believe it.

    I remember I had a babysitter when I was a little kid who my mom had hired from a nearby missionary college*. She was sweet, but I remember the exact point when I lost all respect for her at ~10 years old. 

    I was reading one of those little laminated “Science for Kids” books about ice age megafauna, and it had a wooly mammoth on the cover. She came over and said something like “What’s that?” and I spent the next 30mins explaining what a mammoth was to a grown-ass (~22) woman. She admitted she had never heard of them, nor sabre-toothed tigers or wooly rhinos.

    It wasn’t like a “oh what are you reading there? Want to talk about it?” thing, she legitimately did not know. She admitted she had been home-schooled and that was probably why. It blew my mind, and I’m still in shock about it. Between that and the talk about how women have to be subservient to men she gave me, it was one of the weirdest experiences of my life at the time.

    *I was raised by two soft-atheist parents, but they didn’t have any problem interacting with very religious (and often very disrespectful) christians. I’m a little less tolerant; I start to see red when people start telling me how I’m going to hell or “have a God-shaped hole” in my soul or question why I’m not a murderer since I don’t believe in hell.

  • Wingedwyrm

    And, I have to ask now, how did she respond to being given an indepth lesson in biology and history from someone 12 years her senior?

  • Wingedwyrm

    I mean 12 years her junior.

  • D. Potter

    And what is the business about bombardier beetles?

  • vsm

     Apparently, creationists think their defence mechanism is too complicated to have developed on its own. http://en.wikipedia.org/wiki/Irreducible_complexity

  • The_L1985

     That is only half of the story.  See my reply to the same comment.

  • The_L1985

     Mainly, it’s an attempt to reconcile several ideas:  the existence of dinosaur fossils, the YEC idea that dinosaurs and humans must have coexisted, and the fact that so many cultures have dragon legends.

    They try to mesh these apparently-unconnected ideas by positing that legends of “fire-breathing dragons” may have been dinosaurs (coeval with humans, mind you) who, like bombardier beetles, could shoot out superheated gasses in self-defense.  They often use Biblical beasties like Leviathan and Behemoth as examples of “dinosaurs” that man knew about and interacted with.

    As a child, I wanted to believe all this, because the idea of real live fire-breathing dinosaurs is even more awesome than the truth about dinosaurs.  But it seemed a little too simple to be right, and as soon as I learned about evolution in college, the chain reaction began.

  • http://twitter.com/FearlessSon FearlessSon

    Mainly, it’s an attempt to reconcile several ideas:  the existence of dinosaur fossils, the YEC idea that dinosaurs and humans must have coexisted, and the fact that so many cultures have dragon legends.

    To be fair, there is some scholarly speculation that dinosaurs had a role in the formation of wide ranging myths about dragons.  But that is not due to living dinosaurs, just due to finding their bones in the ground and making some crude guesswork as to what kind of a beast might have left bones like that.  It is only in the last few hundred years that we have begun to piece together such bones into a more complete picture of what the dinosaurs might actually have been like.  

  • Eric

    Koerth-Baker actually misses the real explanation here.  Teaching set theory in grade school was the central plank of the 1960s curriculum experiment we call “The New Math.”  The Birchers and their like were firmly against the New Math in the ’60s, and so A Beka still makes clear that they don’t include set theory in their textbooks.  They’re still fighting a battle they won 40 years ago.

    References: The New Math: http://en.wikipedia.org/wiki/New_Math
    The Birchers and the United Republicans of California make opposition to the new math a central plank of their platform: http://news.google.com/newspapers?nid=1948&dat=19660508&id=TPpJAAAAIBAJ&sjid=-h0NAAAAIBAJ&pg=4301,1527224

  • We Must Dissent

     

    Koerth-Baker actually misses the real explanation here.  Teaching set
    theory in grade school was the central plank of the 1960s curriculum
    experiment we call “The New Math.”

    After this was pointed out in the comments over at BoingBoing, I realized that both set theory and non-base-10 arithmetic are nowhere in the Common Core for math.  Which is sad, because both are conceptually simple, important, and fun in a weird way.

  • http://jamoche.dreamwidth.org/ Jamoche

     Which is sad, because both are conceptually simple, important, and fun in a weird way.

    And the foundation needed for future computer scientists. This may explain why the current crop of CS grads keep failing our Boolean-logic heavy phone screen question.

  • The_L1985

     It doesn’t help that logic has been removed from HS geometry classes, because it’s “too hard” or some such nonsense.  Gee, maybe if you’d teach kids some of the basics of logic in elementary and middle school, it wouldn’t be too hard!

  • Lori

    But why were Bircher’s against the New Math? Wasn’t it just tribalism, like most of the Bircher nonsense? If so that would make Koerth-Baker’s explanation essentially correct, it just needed to be moved back a step.

  • arcseconds

     I heard about the anti-set theory, anti-new math stuff several years back. 

    I always assumed the objection largely came about that the parents prided themselves at already knowing mathematics, maybe even prided themselves at being ‘good at math’  (and this may mean knowing their multiplication tables really well) and their kids started coming home from school talking about abstract nonsense like supersets.

    I can see this being a problem for a few reasons: it undermines the parents knowledge and authority, as their kids know things they don’t; they already take themselves to know what mathematics is, and they’ve never heard of this rot before, so whatever it is it isn’t maths; and finally their kids aren’t learning hard, objective facts and hard, objective, occassionally useful skills like arithmetic.

    I think there’s a widespread tendency to be protective of one’s own schooling (look at this furore over Pluto!) and to suppose Johnny isn’t being taught properly because his education isn’t like yours.  One could expect fundamentalists to turn this up to 11.

  • Wednesday

     Some people just object to any method of teaching elementary school mathematics that isn’t purely “skill & drill”. I had to explain to my aunt that reform* curricula like Everyday Math may not look like they’re teaching things, since they don’t focus on speed drills and rote memorization, but some of them actually are informed by what we know about how most children learn. She still seemed skeptical but stopped saying “they don’t teach math in elementary school” anymore, at least in my hearing. Maybe I should’ve also pointed out that I was terrible at speed drills as a kid but somehow I still managed to get a PhD in math.

    *Reform, in the context of math teaching, really just means anything other than the traditional skill & drill approach.

  • http://jamoche.dreamwidth.org/ Jamoche

    She still seemed skeptical but stopped saying “they don’t teach math in elementary school” anymore

    They weren’t teaching math. They were teaching arithmetic. Not the same thing.

  • http://twitter.com/FearlessSon FearlessSon

    They weren’t teaching math. They were teaching arithmetic. Not the same thing.

    Quoth my father, “I love math, I hate arithmetic.”  

  • Daughter

     This argument (skill & drill vs. concepts) is similar to the phonics vs. whole language debate of language arts teaching. I think the answer should always be, kids need both. In part that’s because kids learn differently–some grasp better when you move from part to whole, and some grasp better when it’s presented whole to part.  But it’s also because while not understanding concepts limits understanding, not having a strong mastery of basic skills slows you down.

  • arcseconds

    Some people just object to any method of teaching elementary school
    mathematics that isn’t purely “skill & drill”. I had to explain to
    my aunt

    Yeah, exactly, I’ve encountered that kind of thing myself — forgot to mention that earlier when I was discussing it.   Not from fundamentalists, though (don’t meet too many of them), but I can’t really see why they wouldn’t have a similar reaction.  

    I don’t really know what to say about learning multiplication tables, or mental arithmetic more generally (or even pen-and-paper arithmetic for that matter).  On the one hand it’s boring and tedious, and it’s not really necessary to be able to do mental arithmetic accurately and well in today’s society (I’m not all that good at it).   There are far more important mathematical skills to learn, and I think boring rote learning and mechanical procedures help put people off mathematics,  and having people put off mathematics is a big problem.  

    On the other hand,  it is a useful skill, and it’s good not to be utterly dependent on machines for arithmetic.  For one thing, it’s too easy to make fundamental errors if you really got no idea what’s going on.

    What I would say is that being able to do reasonable estimates is easier and more important than being able to do 4-digit multiplications in your head.   Order of magnitude is useful enough.   Forgetting to carry the ‘1’ is one thing, but forgetting where the decimal place is is quite another.

     

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    What I would say is that being able to do reasonable estimates is easier
    and more important than being able to do 4-digit multiplications in
    your head.   Order of magnitude is useful enough.   Forgetting to carry
    the ‘1’ is one thing, but forgetting where the decimal place is is quite
    another.

    That said, I find in science, multiplication is used a lot more than addition, so I’ve become very practiced at recovering from “off by 10” type multiplication errors, by just multiplying or dividing by the extra power of 10 I accidentally took.

    On the other hand, forgetting to add or carry a number? Basically I have to scrap the problem and rework it from scratch, because trying to offset the error I’ve made in an addition or subtraction is actually harder.

  • PJ Evans

     SMSG:
    http://en.wikipedia.org/wiki/School_Mathematics_Study_Group

    Funny thing: at least the kids I knew who had it are pretty good at math. Or at least have a mental toolkit that can handle stuff pretty well.

  • http://blog.trenchcoatsoft.com Ross

     I remember about a dozen sitcoms doing episodes touching on “The New Math”. They all followed the same plot: kid comes home, excited about the New Math, parent flips out and gets very angry about how they’re not teaching goo, old-fashioned god-fearing old-math, tries to prove the old math is better, kid runs circles around them at arithmatic. Parent is chagrinned.

    Seems like there was a period when *every* sitcom had to do an episode where this happened.

    That was in the 1980s.

    TV Writers have no perception of the passage of time.

  • Laodicean36
  • walden

    I took a final exam on Hal Lindsey. Aced it.

    NOW it’s clear why you’re so good at this Left Behind Stuff.  You’ve been training for decades.

  • Amaryllis

      It helps to have a wife who finds it all hilarious. I can usually crack
    her up just by reciting the Pledge of Allegiance to the Christian Flag,
    or the Pledge of Allegiance to the Bible, or by singing a few bars of
    “Bright and keen for Christ our savior. …”

    And now I’m picturing the Slacktivixen responding with a few rousing renditions of “Hail Holy Queen” (to thee do we send up our sighs, poor banished children of Eve, mourning and weeping in this valley of tears) or “Bring Flowers of the Rarest” (our full hearts are swelling, our glad voices telling the praise of the loveliest Rose of the dale!)… fun times.

  • JayemGriffin

    Turn then, most gracious Advocate, thine eyes of mercy towards us, and after this our exile- *cough*

    As noted above, you can take the kid out of the Church, but it takes a while to get the Church out of the kid. 

  • The_L1985

     Show unto us the blessed fruit of….oh gods, now you’ve got me doing it!

    Did your school have you do the little call-and-response addendum?  “Pray for us, Holy Mother of God.  “That we may be worthy of the promises of Christ.”

  • TheDarkArtist

    I didn’t see anyone address this, but part of the reason that fundies may be against Set Theory is Godel’s Incompleteness Theorem. If mathematics is something handed down by the hand of God and not in any way fallible in it’s purest state, then having a theorem that shows that mathematics cannot be entirely consistent, because it relies on truths that are not capable of being proven within the rules of the system itself, could seemingly be problematic.

    That’s kind of a mind bending thought for anyone who’s interested in mathematics or philosophy. As we all know, fundies need to bend their minds just a little too much already to believe in goofy things like the Earth being 6,000 years old, so they have no more dimensions in which to bend said minds.

    The whole “there’s only one infinity and that’s GOD” retort is the kind of thing that you’d hear a particularly zealous 10-year-old say. It’s actually really pathetic and sad. I’m not saying that everyone should enjoy mathematics, but that’s a really really silly response to a problem.

  • arcseconds

    Be careful here :]

    What it actually states is that a formal system that can express arithmetic cannot be both consistent and complete. Another way of saying this is that it can only generate every true statement of number theory if it can generate any statement whatsoever, whether it be true or false.  Obviously a theory in which every statement is ‘true’ is neither useful nor especially interesting.

    So it doesn’t say ‘mathematics is not entirely consistent’.  Your theory may well be consistent (although as per the second incompleteness theorem, if you can do arithmetic with it, you can’t use it to prove it’s own consistency (again, unless it is actually inconsistent)), it’s just that if it’s consistent, it’s not complete.

    Also,  it’s not correct to say that it’s because the system ‘relies on’ truths it can’t prove.   It’s true that an axiomatic system rests on axioms that it doesn’t prove in any meaningful way (they are ‘proven’ in the theory by trivially re-stating them), but this has nothing to do with incompleteness: every axiomatic system (even ones that are simple enough to be proven complete and consistent) is like that.

    A system that grounds arithmetic does imply the existence of true but unproveable (in that system) statements, but it doesn’t ‘rely’ on those statements for anything.  They’re just hanging around somewhere, probably wearing leather jackets and smoking.

    (The second incompleteness theorem does make consistency a somewhat elusive property though.  You can potentially prove your system’s consistency by using another system, but that system can’t prove its own consistency. )

    But I imagine actually the anti-set theory crowd knows nothing of Gödel.   At most, they have heard of the incompleteness theorem, and they just don’t like the word ‘incomplete’ because it sounds ‘postmodern’.

  • Janet Aydelott

    Thus a solid understanding of incompleteness would make it difficult to accept circular arguments about Biblical truth based on truths found in the Bible.  There lies the wedge of uncertainty, and set theory is the mallet of logic.

  • arcseconds

     FearlessSon made a similar point.  

    Some fundamentalists do have natural ideological defenses against logic,
    I’ve seen evidence of that.  Can’t actually remember how it goes now,
    perhaps someone else can help?  It can be very explicit, though, almost
    ‘logic is a tool of the devil! God wants you to use feeling & the
    bible.’.

    They may be intuitively shying away from set theory for that reason. 

    But I’m thinking they don’t understand enough about it to really make a call here.  They’re really unlikely to be explicitly going “well, set theory is basically logic, and we all know that logic leads to atheism and baby-killing!”   I think Koerth-Baker’s take that they think it’s a filthy modernist indoctrination trick of some kind sounds plausible to me (and she’s got personal experience here).  I still think my curmudgeon explanation has got something going for it i.e. “you need to get the same hard schooling I did son and learn some ‘rithmetic, not this new math rubbish.  you’ll never be able to run a business if you don’t know your 13 times table inside out!”.  

    I’m going to add to that something that I think is implicit in both Koerth-Baker’s account and my curmudgoen idea, and that’s that everyone likes a basic undeniable fact that they thoroughly understand.  Fundamentalists (of all stripes, not just Christian ones) really like them, and really don’t like ambiguity and possibility and confusion.  They don’t understand set theory, and they’d rather their kids got ‘real facts’ that they do understand (or think they do) .  If they have any inkling that set theory can be used to ‘justify’ arithmetic, they’d like it even less, because they’re not going to want any suggestion that clear facts require further justification.

    (I’m pretty sure that they can’t know anything at all about the incompleteness theorems apart from at the very most the name)

  • Daughter

     I suspect that some of the originators of these anti-set theory beliefs may understand what they’re all about. I remember reading somewhere that one of the founding “moms” of the Quiverful movement had been a computer scientist before her conversion. Some fundie leaders are well-educated; because many of their followers aren’t, they can be easily led.

  • arcseconds

    Yeah, a lot of Camping’s followers were engineers, too. 

    However, I have a lot of difficulty even entertaining the idea that the rejection of New Math on broadly religious grounds originated with people who understand set theory.    I really can’t see how anyone who actually understands it could possibly believe that it’s somehow anti-Christian.  I suppose one could imagine a set theory adept cynically manipulating the ignorant by creating propaganda about New Math, but in this scenario the understanding of set theory is not doing any work.  Someone could develop cynical, manipulative propaganda about New Math without understanding set theory just as well.

    (There would be reason to believe someone had some understanding of set theory if the propaganda showed any signs of understanding it, but I’ve never seen anything that indicates this.  Not that I’ve looked very far, just when it’s come up from time to time, so if anyone knows any better do tell.)

    While there are quite well educated people amongst fundamentalists, and fundamentalists can be easily led given the right circumstances, I don’t think it’s good to assume that it’s the well-educated that are always doing the leading.   The rank and file are quite capable of applying their paranoia of contemporary culture and coming up with craziness all on their own.

    (also, it’s not as if set theory is a sine qua non for being educated, or for that matter getting a computer science degree. )  

  • http://twitter.com/FearlessSon FearlessSon

    Some fundamentalists do have natural ideological defenses against logic, I’ve seen evidence of that.

    THOUGHT FOR THE DAY:  
    A logical argument must be dismissed with absolute conviction!

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

     Reason begets doubt; Doubt begets heresy.

  • http://jamoche.dreamwidth.org/ Jamoche

    A logical argument must be dismissed with absolute conviction!

    “We demand rigidly defined areas of doubt and uncertainty!”

  • http://nwrickert.wordpress.com/ Neil Rickert

    If you start with nothing, you can have the set containing nothing (or the empty set).
    Next, starting with the empty set, you can have a set whose only member is the empty set.  This is a set with 1 member.

    Foundations of mathematics builds up the whole of traditional arithmetic in this way.

    In other words, you can get something from nothing.  That must be a big problem for fundamentalist apologetics.  It’s no wonder that they don’t like set theory.

  • http://tobascodagama.com Tobasco da Gama

    My partner all but refuses to believe that we used to sing “Onward, Christian Soldiers” in school.

  • Lori

    Public school? Srsly?

  • http://www.facebook.com/jon.maki Jon Maki

    From K-8th grade we had to say Grace before eating lunch at my school.

  • Lori

    Out loud? Holy crap. We went to school in the same state and yet apparently totally different worlds. It would be one thing if you were older than I am, but you’re not.

  • http://www.facebook.com/jon.maki Jon Maki

    Out loud?

    Yep, in unison.  We would all have to stand around and wait until everyone had gotten his or her serving and taken a spot at the tables, then we would say it.   Fortunately, given how few of us there were we didn’t have to wait too long.  (Even so, many of us would get in a few surreptitious bites first when no one was looking.)

    Several years ago while I was home visiting my family there was a celebration held in honor of the school’s centennial.   At the reunion dinner, a former Principal made a comment about how taken aback he was on his first day when he saw this happen – “Separation of Church and What?” –  but he wasn’t prepared to make any waves.

    Beyond that – and the fact that we sang actual hymns in our Christmas progams – the rest of the school’s approach wasn’t particularly sectarian.  We worked from standard textbooks and so on.

    Growing up in isolation as I did, it wasn’t until around 6th grade that it occurred to me that there was anything unusual about engaging in this ritual.  In fact, when the Principal made that reference at the reunion dinner, there were plenty of people to whom it still  didn’t seem especially unusual. 

    As I came to have a better understandng of how things are supposed to work, I became increasingly bothered by the fact that we did this every day, but, like the former Principal, I wasn’t prepared to make waves.  I did, however, stop joining in eventually.   I didn’t ever say anything about it, and I don’t think that anyone ever noticed.

    Anyway, while the UP is part of Michigan, it really is rather distinct from the rest of the state, especially in the tiny, backwater part of it that I grew up in…

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    I remember in grade 5 our teacher led us through the Lord’s Prayer. In retrospect I should have used that to get him fired ‘cos he was a jackass anyway.

  • http://tobascodagama.com Tobasco da Gama

    No, no, a private Baptist school.

  • fraser

    The New Math, from what I remember reading about it, triggered a lot of opposition because it relied on something other than doing endless sums and memorizing the times table. So it wasn’t rigorous or serious. Part of the problem was that it was initially going to be an experimental program but in the post-Sputnik Is Our Children Learning Science and Math? panic, it was rolled out to lots of teachers who hadn’t learned how to teach it.

  • http://lliira.dreamwidth.org/ Lliira

    Seriously, what’s the bombardier beetle thing about?

  • Jenny Islander

    Something about how a mechanism like the bombardier beetle’s defensive spray couldn’t possibly be the result of evolution, IIRC.  The shop guy who got moved into the science slot when I was in 7th grade preached that once and the kids heckled him into getting back to the stuff that was actually in the book because we wanted to pass our semester final.

  • Lori

    Some people insist that the bombardier beetle would never have evolved and therefore must have been created, which obviously proves God is true and evolution is a lie. I’m not sure why they’re so focused on the bombardier beetle instead of one of the, doubtless myriad, other creatures whose evolution they can’t imagine.

    I always want to reply to things like that by pointing out that if the human eye was a first semester design project the designer would flunk the course and likely  be on the receiving end of some pointed advice about other fields of study to pursue.

  • cjmr

    I think they focus on the bombardier beetle because kids think explosions are cool.

  • vsm

    Most people are also unlikely to know just how its defence system works, which makes you seem knowledgeable in comparison. If you tried the same with the human body, it would be much easier for your opponent to counter with examples of several well-known and perhaps self-observed “design flaws”, like the eye’s blind spot or male nipples.

    I find this creationists’ talking point debate technique interesting. Learning about evolution in a mainstream school doesn’t really prepare you to answer highly specific questions like these, so it’s easy to create a cadre who can win informal debates on evolution vs. creationism simply by reciting the list. Apparently, the training starts pretty early.

  • Lori

    The eye’s blind spot and things like the fact that keeping it clean enough to work properly involves being temporarily blind, IOW having it cease to do its job, something like 17k times a day. I saw a display at a science museum (can’t remember which one, I’ve been to several) that demonstrated that if something about a scene changes during a blink we simply don’t perceive that the change happened. Even when we’re told that it happened we can’t see it. It’s as if the change is the way things always were.

    That is not good design.

  • vsm

     Oh, I didn’t meant to imply they worked optimally or anything. I put “bad design” in quotations because no one actually designed the human body, well or badly.

  • Lori

    I understood. I was just ranting a little about how ridiculous I find it that anyone would think the human eye was made the way it is on purpose.

    I’ve never met a creationist who can actually justify the human eye as a designed thing, and in fact most of them have never thought about it at all. I guess because it’s not on the talking point list they were taught. I’ve found it to be a very effective counter to things like the bombardier beetle nonsense, with the advantage that it doesn’t require me to remember a lot of detail about bombardier beetles.

  • vsm

     Good. I often fail spectacularly at communication and just wanted to make sure.

    Your tactic is quite clever. Bombardier beetles are relatively unimportant in the grand scheme of things, so your opponent could just move on to argument #327. The human body, however, is something you’d think the great designer (as ID is obviously completely agnostic on the question of who the designer was) would have spent some time on and gotten rid of the most obvious bugs.

    Incidentally, my sister’s boyfriend’s father apparently justifies his belief in creationism precisely because of the eye’s “irreducible complexity”, and he’s an MD. I’d be curious to know just how he feels about its design flaws, but he can barely speak because of a hereditary illness that will one day kill him and probably at least one of his children. I feel kind of bad for noticing the irony.

  • http://profiles.google.com/marc.k.mielke Marc Mielke

    I used to play gun games such as airsoft or paintball and quit only after finding out other people could actually see their weapon fire. I think that might have had something to do with it. 

  • http://lliira.dreamwidth.org/ Lliira

    I always want to reply to things like that by pointing out that if the human eye was a first semester design project the designer would flunk the course and likely be on the receiving end of some pointed advice about other fields of study to pursue.

    Not to mention the human spine. Any clue how they explain appendixes?

  • http://dpolicar.livejournal.com/ Dave

    After my stroke, I was reading a book about strokes that said, in passing, “…and because blood is toxic to neurons, yadda yadda yadda…” and I just stopped.

    Seriously?

    Blood is toxic to neurons?

    Blood.
    Is toxic.
    To neurons.

    What is this I don’t even.

  • Pat B

    It’s a titch more complex than that, but basically the cerebro-spinal fluid is an entirely separate medium to protect the neurons from diseases and toxins in the blood. Hence the Blood-Brain barrier and the brain’s ventricular system which is very different from the normal circulatory system.

    Of course it comes down to the same point; no intelligent designer capable of making an organism as complex as a human being would think it was a good idea, rather than giving us a full-on brain liver or making the brain less fragile.

  • http://dpolicar.livejournal.com/ Dave

    Oh?

    But hemorrhagic strokes are the result of blood leaking into the brain, no?
    That is, not cerebrospinal fluid, but blood.
    At least, so I thought.

    Which, as I understood it, has decay products which are toxic to neurons, independent of whatever diseases and toxins it might or might not be carrying.

    But perhaps I’m confused.

  • Turcano

    Hemorrhages are a problem because of the sudden increase in pressure on brain matter, which is very bad for it.

  • PJ Evans

     I don’t know if blood is actually toxic to neurons, but if you have blood escaping into the brain tissue, the pressure it produces is going to do a lot of damage.

  • http://dpolicar.livejournal.com/ Dave

     Yup. This is also true when you get swelling for other reasons.

  • Lori

     

    Any clue how they explain appendixes?  

    IME, much the way God responded to Job’s questions—-Look, a hippo! Now stop asking about stuff for which I have no reasonable explanation.

  • Azraelmacool

    If I’m not mistaken, its that bombadier beetles can shoot acid or whatever it is they shoot, so therefore dinosaurs could breathe fire. Something like that. I only got the Christian indoctrination at camp, and although I generally believed it, I did realise that it could not be taught in schools, and therefore had no problems compqrtmentalizing my brain for religious facts and non-religious facts. Or as I call them now, lies and facts.

  • We Must Dissent

     

    And the foundation needed for future computer scientists.

    That was part of “important”, but not all of it.

    Reading about this, I had a minor epiphany about some of my struggles to teach geometry. I don’t think I got full-blown New Math in elementary school as I was about a decade too late for that, but I still learned basic set theory pretty early on and modular arithmetic, arithmetic in bases other than 10, and several other topics that were part of New Math before leaving high school. Anyway, I realized today that when I learn something new, I automatically invoke concepts from set-theory. I start building categories and groups in my mind and making relationships between them. So when I know that squares are both rhombuses and rectangles, I thoughtlessly assign everything I know about the latter two types of quadrilaterals to squares. For most of my students, they can know that squares are both rhombuses and rectangles but not realize that everything they know rhombuses and everything they know about rectangles applies to squares and need to have each property pointed out to them.

    Many of them think of everything as a vast collection of particulars, instead of as groups and subgroups.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    I learned geometry totally differently. I ended up being able to visualize vectors in physics, which was how I finally kind of grokked geo as well.

  • GDwarf

     

    Many of them think of everything as a vast collection of particulars, instead of as groups and subgroups.

    That’s because that’s how math is taught. Or, at least, was taught to me.

    I can still remember when I realized that fractions and division were the same thing. I was in grade 10. I had been taught rules to do division, and rules on how to handle fractions, and they were never combined. Never explained. Suddenly fractions made sense. Before they were just these weird, arbitrary, numbers that you sometimes got and had to use weird, arbitrary, operations on.

    Now, obviously, much of math can’t be explained to students as they learn it. It’s a field where justifying the basics requires you know very advanced stuff (it takes a whole book to prove that 1+1=2, for example). But it’s also always taught as a bunch of completely unrelated concepts. I was taught powers of 10 as being separate from exponents, for example, so I was confused for a year about how you knew if you were multiplying a number by 10 or itself.

    It isn’t until high school that classes started to explain various relationships and had you using old ideas in new ways and so-on. My sister, who avoided math as much as she could, still doesn’t believe me when I explain how certain concepts are related (such as division and fractions) because she was taught them separately and doesn’t want to have to re-build her understanding if she doesn’t have to.

    I would’ve loved learning “New Math”, because it’s all about learning how this stuff works and putting it all together, instead of rote memorization.

  • http://lliira.dreamwidth.org/ Lliira

    But it’s also always taught as a bunch of completely unrelated concepts.

    Not always. I was taught that fractions and division were the same thing expressed differently, that exponents and powers were the same thing, etc. I can’t think of anything in math I was taught as you describe it until algebra 2 in 10th grade, which preceded trigonometry. Probably not coincidentally, that’s also the year I became utterly uninterested in math, and started only taking it because it looked good on my transcript. 

  • The_L1985

    Then you are damned lucky.  I am a math teacher, and I did not know how to do word problems until I was taking college physics, because it wasn’t until then that I was finally able to figure out how to set up a problem in symbolic (math) form based on the words therein.

    Until then, I had to have someone else set up the equation for me, because I didn’t know how to tell which numbers went where, or how you knew which operation to use, unless it was something like D = rt where you have a specific formula given to you to use.

    I now teach remedial courses to adults, in essence undoing whatever poor practices my students were put through, and apparently good elementary-school math teachers are depressingly rare.

  • Lori

     

    I took AP Calculus in high school, while still being unable to set up the average word problem.  

    I’m simultaneously horrified on your behalf and seriously impressed.

  • PJ Evans

     ‘Old math’ was heavy on word problems. It didn’t really teach how to set them up either.

  • Lori

    I don’t know if the story problems I got were part of New or Old Math, but I was definitely taught how to set them up. I really don’t get not being taught that since it’s the entire point of story problems. When the equations are the point you don’t need the “story” part.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    I must have been lucky, then, since my teachers tried to cover some of the basic principles in word problem solving (such as identifying the quantities, etc).

  • http://twitter.com/FearlessSon FearlessSon

    I learned much the same way, and hated it.  I did terrible in math because there were so many discrete components to keep in my head, and inevitably some of those tiny components kept falling through my mental fingers every time I grabbed them for a test.  

    It makes so much more sense when I can see the singular relationship between all this stuff.  I would tell the teachers “The hard stuff is easy and the easy stuff is hard,” because I could only “get it” once my knowledge about the subject reached a critical mass such that I could finally see the big picture and how everything connected.  Lead to a lot of plateaus in my learning.  

    When you get down to it, all arithmetic is addition, mixed in various ways, and even that is just a kind of Boolean logic, built out of a few true/false gates sorting numbers by value.  

  • http://jamoche.dreamwidth.org/ Jamoche

    When I took Calculus 1 in high school, I felt like I was the only one who didn’t care how it worked, just that it did. Then I took Calc 2 and suddenly Calc 1 made sense – but Calc 2 didn’t, and the same thing happened in Calc 3.

  • http://twitter.com/FearlessSon FearlessSon

    When I first took Calc 1, it made me think, “Hey, I know this!  This is a function!  I can write those!”  

    … unfortunately, my solving exam problems by writing pseudo-code involving looping and Boolean tests proved to be not acceptable as demonstrated understanding of the math.  :(  

  • arcseconds

     

    When you get down to it, all arithmetic is addition, mixed in various
    ways, and even that is just a kind of Boolean logic, built out of a few
    true/false gates sorting numbers by value. 

    Well, that’s how we build adding machines these days, with logic gates.  I don’t think that shows us anything fundamental about the nature of arithmetic, though.  A few years ago addition was done mechanically with cogs, and before that with beads on wires, and we don’t think addition is really just a kind of mechanical action or movement of beads, do we?

  • http://twitter.com/mattmcirvin Matt McIrvin

    There are several different models of computation that mathematicians use to study things like the universe of computable functions, and it’s possible to prove that all of the strongest ones we know are equivalent to one another.

    So, for instance, Alan Turing had his Turing machines, in which a device with a finite number of internal states trundles along an infinite tape reading and writing symbols, and Alonzo Church had his lambda calculus, which is a kind of language for defining arbitrarily complex functions without having to give them names.

    It wasn’t immediately obvious that anything you can calculate with a Turing machine you can compute with the lambda calculus and vice versa, but it turns out to be true. So this doesn’t do anything to tell us that arithmetic is “really” the working of some cosmic Turing machine, or some Platonic lambda calculus. But the fact turns out to be useful anyway: the lambda calculus is the basis of functional programming languages, which are used to program computers, which are basically glorified Turing machines.

    So arithmetic isn’t necessarily “really” the working of some logic gates. But that is one of the many equivalent ways you can approach it, and a very useful one.

  • arcseconds

    How strange.  I got an email saying you’d replied to me, but the webpage doesn’t indicate it…  disqus being coy?

    If arithemetic is anything essentially, it’s the Peano axioms.

    There are several different models of computation that mathematicians
    use to study things like the universe of computable functions, and it’s
    possible to prove that all of the strongest ones we know are equivalent
    to one another.

    There’s an entire field called ‘hypercomputation’ dedicated to studying models of computation that are stronger than Turing computation: Zeus machines, oracle machines, analogue neural nets, etc.

    (some dispute that what these machines do is computation. it’s true that it isn’t Turing computation, but that seems a bit question-begging to me.  others complain that the machines aren’t possible, but that’s merely an empirical matter :]  (besides, Turing machines aren’t possible either…) )

  • arcseconds

     Oh, yeah, the other thing that’s interesting about your post is that you talk as if arithmetic is fundamentally a matter of computation.   It could also be seen as being a matter of relations. 

    That is to say, you appear to be thinking  that 2 + 3 = 5 means something like ‘once I have applied the addition-operation to 2 and 3, I get 5’, and a further investigation (or modelling) involved detailing what the addition-operation is (a bunch of logic gates, a set of instructions carried out by a universal Turing machine, or whatever).

    But it could also be read as ‘2 and 3 stand in the addition-relation to 5’.  And that’s generally how mainstream mathematics has conceived of mathematical entities.  You can see this most strongly with set theory, which is also capable of modelling arithmetic, by treating numbers as sets, and an arithmetic equation would tell you about what relationships pertain amongst sets.

    And set theory was very much in vogue throughout much of the 20th century, so much so that there were those that thought that set theory was mathematics, and therefore 2 is a particular set (either {{}.{{}}} or {{{}}} depending on which school you went to).

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

     And set theory was very much in vogue throughout much of the 20th
    century, so much so that there were those that thought that set theory was mathematics, and therefore 2 is a particular set (either {{}.{{}}} or {{{}}} depending on which school you went to).

    As a result, I’ve become allergic to overprecise math professors who insist on postfixing all equations with something like (x e R) or refusing to refer to 3-dimensional space as 3D but instead “as all vectors in R^3” or the like.

  • The_L1985

    The only reason I did even halfway decent in math is because I memorize things quickly and easily.  I was memorizing formulas and rules instead of understanding how everything fits together.

  • Turcano

     Useless fact of the day: music was taught as an aspect of math in medieval universities.

  • The_L1985

     Sounds like a very useful fact to me.  If schools did it like that today, we would have a much higher percentage of students doing very well in math.

  • http://twitter.com/FearlessSon FearlessSon

    The only reason I did even halfway decent in math is because I memorize things quickly and easily.  I was memorizing formulas and rules instead of understanding how everything fits together.

    I was good at memorization.  My math and physics professors would joke that they would swear the class notes I took were so precise that they must have come from a computer printer if it were not for the fact that they were written in graphite.  Other students would ask to photocopy my notes because they were that good.  But that did not really help me much.  

    While I might have had the formulas, actually applying them was a different matter.  The teachers observed that I tended to blunt-force my way through every problem, running through each formula I knew, trying to find one that applied and gave me a plausible answer, wasting a lot of time doing it, and not necessarily getting it right anyway.  Other times I would just go with as much calculator-driven arithmetic as possible to get an approximate answer, then retroactively apply the formulas until I got the one that closest resembled the approximate arithmetic answer.  I longed to be able to solve everything with a clearly defined procedure that could be looped through repeatedly until the solution resembled what it was supposed to and it could be looped no further.  But math was not taught that way.  

    Ultimately, the people who studied from the notes that I took did better on the exams than I did.  :(

  • The_L1985

     The only reason I was able to work with fractions is because I took piano for 12 years.  Math education is woefully fragmented as it is, and I hate this idea that the old-guard seems to have that lessons should be discrete and separate, instead of blending concepts from different levels and disciplines in order to help kids make sense of things.

  • http://guy-who-reads.blogspot.com/ Mike Timonin

    As I understand it, having talked with a teacher from the immediate post-Sputnik era, there were several problems with the New Math, and, indeed, the New Pedagogy. 

    After the Russians launched Sputnik, the US government panicked, and there was a whole “Math and Science, we must teach them!” thing (which hasn’t really ended, see the whole “Math and Science” component to standardized testing. In order to ensure that Math and Science were taught, two things happened:

    1) Nice men approached anyone who was studying towards a degree in Math and/or Science and asked them if they would be interested in becoming a teacher, without grasping the idea that teachers need to know more than just the material they are supposed to be teaching – they also need to know how to be a teacher.
    2) Nice men approached anyone who was studying towards a teaching degree, and asked if they would be interested in teaching Math and/or Science, without grasping the idea that someone who would be a good English teacher will not necessarily be a good Math and/or Science teacher (and that you need good English, History, Art, Music, Gym, etc teachers to teach students properly)

    Then, there was the development of New Math, which (as many have said) actually creates a good foundation for learning Mathematics (and, when I read stuff about sets and such, actually makes sense to my History degree brain, AND, what is more important, makes math beautiful in a way that it never was in school), but which requires that the teacher understand the material properly. Here, several things happened:

    1) Some teachers were not properly trained, or not properly equipped – teaching the New Math with the Old Textbooks simply didn’t work.
    2) Some teachers refused to use the New Math, but were forced to adopt the new textbooks – teaching the Old Math with the New Textbooks didn’t work either.
    3) Parents didn’t understand their children’s homework and thus couldn’t (or didn’t think they could) help, which resulted in a range of emotions, from frustration to anger, and a range of responses, up to insisting that the New Math be abandoned.

    All of that means that you end up with a a very spotty roll out of the program, with inconsistent implementation, and thus some kids who really grok Math, and some kids who really don’t.

    None of that has anything to do with the Fundie resistance to set theory, but I think the video that Koerth-Baker includes in her article is really helpful in that regard. The implication that Math is, itself, uncontainable (multiple infinities), and also full of unanswerable questions (it is impossible to prove the Continuum Hypothesis either false or true) makes Math godlike. I can see how a Fundie might have a problem with that.

  • PJ Evans

     The school district we lived in while I was in ‘new math’ put about 30 percent of the junior-high students in it, but we didn’t get special teachers. Fortunately it was also a school district where many of the students had at least one parent who was an engineer or a scientist, so help was generally available.
    (I remember having trouble with an exercise where everything was there except the parentheses, and we were supposed to add them to the left side in a way that would produce the number on the right.)

  • AnonymousSam

    The arguments for Creationism always make me remember the point someone made about how the banana is an atheist’s nightmare:

    Is shaped for the human hand
    Has a non-slip surface
    Has outward indicators of inward content:
    Green – not ripe enough
    Yellow – just right for eating
    Black – too ripe

    Has a tab for easy removal of its wrapper
    Is perforated on the wrapper for easy peeling
    Has a biodegradable wrapper
    Is shaped for the human mouth
    Is pleasing to the taste buds
    Is curved towards the face to make the eating process easy

    The conclusion: obviously the banana was designed by “Almighty God” for the benefit of human beings.

    … To which the atheist replies that the banana we eat today was brought about by artificial selection and now the lack of natural reproduction prevents genetic diversity, making the banana vulnerable to pests and diseases… and suggests that the appreciation for the banana more likely stems from its phallic shape. Just right for the mouth indeed.

  • Lori

    Ah yes, Kirk Cameron’s favorite food.

    Has a tab for easy removal of its wrapper 

    It’s actually easier to open from the other end. I guess they didn’t get the memo on that.

    http://www.youtube.com/watch?v=nBJV56WUDng

    Or maybe they simple refuse to acknowledge it because folks figured it out by watching monkeys peel bananas. Can’t admit to learning from monkeys.

     

    Is curved towards the face to make the eating process easy 

    Or is it curved away from the face to result in banana smeared all over one’s chin  & nose in order to amuse one’s friends and family? Who’s to say which way it’s supposed to go?

     

    The conclusion: obviously the banana was designed by “Almighty God” for the benefit of human beings.  

    So why didn’t “Almighty God” make all fruit edible by humans to the same basic specifications? For that matter, if the banana is perfectly designed for humans why do other fruits exist at all?

    The whole banana thing really is just so dumb I’m embarrassed for people who actually recite it in public. I mean that literally. As I’ve mentioned, I have really serious secondary embarrassment. Watching that stupid video with Kirk was physically painful for me.

  • The_L1985

     Ray Comfort, and that is exactly why he doesn’t do the banana thing anymore.

  • AnonymousSam

    Others have started doing it since, though. Apparently they didn’t get the memo about it being thoroughly refuted. Then again, considering where I first read the proposition and its rebuttle, “facts” are never a priority of theirs.

  • http://dpolicar.livejournal.com/ Dave

    I remember when I was in grammar school, it really puzzled me that every year, we would start the math portion of what we were doing with an introduction to set theory. It never really connected to anything else we were doing, and I never really understood what it was supposed to have to do with math, but it was interesting enough the first couple of years. But it was always the same discussion of set theory, which by fourth or fifth grade got a little tedious.

    I took to referring to it as “Everything I ever wanted to know about sets but was afraid to ask.”

    Meanwhile, my mom is visiting, and we’re having conversations about how Israel is important to her so she’s going to vote for Romney (because Obama can’t really be pro-Israel because, being Muslim, he’s of course pro-Arab, and to be pro-Israel, one must of course be anti-Arab.)

  • Emcee, cubed

     My sympathies. One of the many things I thank Barrowman for every day is that my mother is a bleeding-heart liberal and always will be, and my dad tends to think republican, but knows that me and mom actually get our facts right, so if we tell him that some right-wing talking point is baloney, he knows it’s true. (And as far as my dad goes – mom too, but she’d think this way anyway – he would never vote for an anti-SSM candidate, because he knows it would hurt me directly. Gotta love him for that.)

  • http://dpolicar.livejournal.com/ Dave

    My mom’s basic attitude seems to be that knowing the real facts is just too difficult, so she can basically only go with the facts as they’re presented to her, and since she lives in a predominantly Republican area she gets her facts filtered through that lens, so what can she do?

    My own approach is that when I know that the facts I’m being presented with are cherry-picked, and I don’t know enough to get the real complete picture across the board, the best I can do is decide what areas I value the most and pay attention to whether the facts I’m being presented with seem to provide a full picture of my choices in those specific areas, and reject pictures that seem importantly incomplete.

    To my mom, U.S. support for Israel is really important, so it should be worthwhile for her to look at U.S. support for Israel over the last four years, and over the eight years before that, and ask whether Israel is getting less support now than it was before. Because if it isn’t, that should at least make her wonder whether the narrative she’s been hearing reflects reality. For me, maintaining the government’s status as a regulatory agent on industry rather than exclusively as an enabler of industry is really important, and I should similarly look at that.

    The SSM thing was kind of interesting. Her own position was that she felt marriage equality really had no business being part of a Presidential campaign, ditto abortion. People, says she, should be able to choose who to have in their families, and that isn’t the government’s business. Which I actually agree with. But the fact is that absurd as it is, right now one party actively endorses preventing by law certain choices I believe people should be able to make.

    And while ultimately that isn’t as important to me as preserving a viable balance between the power of citizens and the power of businesses, it’s still important to me and I make choices accordingly.

    And I recognize that isn’t especially important to her, which saddens me personally, but it is what it is.

    And I don’t really know why I’m talking about this here.

  • Lori

     

    Meanwhile, my mom is visiting, and we’re having conversations about how
    Israel is important to her so she’s going to vote for Romney (because
    Obama can’t really be pro-Israel because, being Muslim, he’s of course
    pro-Arab, and to be pro-Israel, one must of course be anti-Arab.)   

    Oy vey.

    You could maybe try a slightly different Jewish perspective on her:

    http://www.samefacts.com/2012/08/campaigns/campaign-2012/are-you-still-an-atheist/

  • Dmoore970

    Reading Maggie Koerth-Baker’s post, I think she has a pretty good answer.  Set theory, as taught at the elementary or secondary level is innocuous.  Higher level set theory is highly esoteric and counter-intuitive.  Fundies tend to evaluate everything through the lens of, is it a challenge to our religion.  If it is simple an easily understood, they can at least evaluate it.  If it is too esoteric and counter-intuitive to be understood, it is presumed to be a menace.  In fact, it comes under strong suspicion of being a rival religion.

    Try reading Andrew Schlafly in Conservapedia.  You see exactly the same reaction to everything he doesn’t understand, from e=mc2 to complex numbers.

  • MaryKaye

    It’s also true that eyes with genuine color vision–not our three-pigment approximation–are biologically possible.  Octopuses have eyes with (a) no blind spot and (b) full-color vision obtained by a kind of spectroscopy.  It’s speculated  that accurate color vision is particularly important for a creature that can change color, but it’s also quite possible that the octopus lineage just got lucky and hit on a better solution than we did.

    Color TV and color pictures in magazines would puzzle and disappoint an octopus, because to it, a mix of red and yellow is *not* orange, it’s just a mix of red and yellow.  Orange has a quite distinct wavelength, but humans are not equipped to sense that directly–all we get is pings on our three color receptors, and we have to infer colors indirectly from that.

    Anyway, the view that, as a colleague of mine said, “Evolution created the bacterium but the flagellum is too complex so God had to stick it on directly” lacks elegance.  Surely something capable of creating the world could create it evolutionarily (which is, I think, the predominant Christian view worldwide–just not in the US).

    I can’t resist one more color vision story, courtesy of another colleague who works on color-vision genetics.  Red water penetrates the ocean rather poorly, so below a certain depth most fishes lack red receptor genes.  But they found one, very deep down, which had them.  Why?

    They finally caught a live specimen and discovered the answer:  the fish has a red light on its head.  It red-lights its hapless prey, just like a human poacher!  Biology is so cool.  The saddest thing about creationism is that it gets in the way of people being able to appreciate how cool it really is.

  • arcseconds

    There actually isn’t much in either set theory or Gödel’s incompleteness theorems that prevents one from being a theist of quite a traditional sort.  Indeed, Cantor and Gödel were both theists.  Cantor had a concept of the ‘absolute infinite’ going beyond any infinity which is tractable in mathematics, and identified it with the magnitude of the system of all ordinal numbers Ω, and also with God.

    Incompleteness spells the death of formalism, not platonism.  In fact, it kind of suggests a kind of platonism – arithmetic is a structure that can’t be captured fully by any axiomatic system, as there will always be truths that the axiomatic system can’t prove (or else the system can prove everything, including false things).  So if you thought that the numbers exist in the mind of God, then you’ve got more reason to think that post Gödel, not less.

  • arcseconds

    I forgot to say in my earlier remark that set theory does kind of mean you have to go for a ‘passeth all understanding’ bit of mysticism about God, though, because there can’t be a set of things known by God, because then there will be something God doesn’t know (namely the power set of the things known by God).

    But that kind of understanding of God is also plenty traditional.

  • http://twitter.com/FearlessSon FearlessSon

    I have to wonder if they deliberately want to obfuscate things like set theory because understanding sets can undermine positions that they promote.  

    For example, remember SherryLevine from this thread?  Assuming that her position was genuine, she felt that letting gay people get married would lead to an increase in social acceptance of statutory rape because there are some gay people who are also pedophiles.  The thing is, pedophiles is a set that does not correlate with sexual orientation.  Sure, it is a set that intersects with the set of people who are homosexual, but it also interacts with the set of people who are non-homosexual, and has more items in that set to boot.  

    If Sherry understood better the way these sets intersect, the kind of bad data she was arguing from would render her position unsustainable.  Not that it makes it any better of a position, just that she would not be able to sustain it even in her own mind.

  • http://jamoche.dreamwidth.org/ Jamoche

    I’m not sure what I find more depressing: that the Discovery channel is running a faux-documentary on mermaids with a “blink and you missed it” disclaimer(*) when they could be running Mythbusters (or just about anything else), or that when I went web-searching to find out just why this was on the Discovery channel of all places, I found a lot of people who believed there really is a mermaid conspiracy coverup.

    (*) I only discovered there *was* a disclaimer when I did the web search.

  • http://twitter.com/IndigoCeleste Indigo Celeste

    Grades 8-12, I was homeschooled using Pensacola Christian Academy’s materials. Those A Beka books are crazy. It took me about a semester of college to undo everything & start realizing that nearly everything I’d been taught was complete and utter BS.

  • The_L1985

    That’s actually better than getting it in a private-school setting from grades K-8, though.  Imagine having misinformation reinforced by everyone in your elementary-school class and by lots of grownups at the school.

    It actually makes it harder to admit later on that A Beka was wrong about stuff.

  • Andrew_Ryans_Caddy

    [quote]
    It red-lights its hapless prey, just like a human poacher!  [/quote] 

    Can you explain more about what red-lighting means?  The whole area of weird undersea creatures and the things they do is fascinating, and Google’s not helping much. 

  • GDwarf

     

    Can you explain more about what red-lighting means?  The whole area of
    weird undersea creatures and the things they do is fascinating, and
    Google’s not helping much.

    The idea with the fish is that it lights up its surroundings with red light. Since it’s the only fish down that deep that can see red light this lets it hunt visually without other fish being able to see it, or even know it’s there.

  • Andrew_Ryans_Caddy

    Thank you! Nature has some awesome sorts of genius. 

  • Tonio

    “Pledge of Allegiance to the Christian Flag, or the Pledge of Allegiance to the Bible” – I’ve heard of the former but not the latter. When I reached the line “life and liberty for all who believe,” I immediately imagined non-Christians being herded into camps. The fact that such pledges even exist illustrates the degree of danger that the US could become an outright theocracy.

  • AnonymousSam

    Wait, that’s a thing? *Websearch* …

    Yeah, that’s… that’s disturbing. It does, if indirectly, imply death to the rest of us.

  • http://mistformsquirrel.deviantart.com/ mistformsquirrel

    So glad my mom got me out of fundieschool when she did (x-x) it still took years to deprogram myself, but I don’t like to think of who I could have been.  I was NOT a good person when I was still in the bubble* – I said terrible things to people who didn’t deserve it, I thought horrible things about others… no I do not like that person I was and could still have been.

    I will however admit, like Fred and Maggie Koerth-Baker – when they weren’t trying to stuff my head full of BS, and stuck to genuine facts – there was some excellent education to be had there.  I was pretty far ahead of my classmates when I moved to public school** – and there is a part of me that wishes I could have stuck with the ‘just the facts’ side of that education while ditching the bullshit.

    *I don’t know that I’m a good person now; but I take some comfort in that uncertainty – at least I’m wise enough to know that I *don’t know*; and that helps me at least make an effort.  After all, if you’re absolutely certain you’re a good and righteous soul, you aren’t going to be doing too much careful reflection on what you’ve said and done.

    **This landed me in a ‘gifted’ course for awhile.  As I’ve gotten older I’ve started to wonder whether or not I was more intelligent than average… or if perhaps it was just a function of being several steps ahead.

  • Randall M

    I think it’s important, when criticizing the “design” of the human body or other parts of nature to remember to emphasize that while these things are bad design they are exactly what we would expect from evolution.

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

    Perhaps there’s some element of my education that I’m forgetting, but what exactly are “multiplication tables?” Are they just tables where you cross-reference two numbers to find their product? Children are taught to do arithmetic that way?

    (I don’t remember anything about the teaching process I went through, just that arithmetic has always been a more or less automatic process for me. Not sure if that’s genetic – my grandfather and two of my uncles have the same trait – or part of being non-neurotypical.)

  • http://dpolicar.livejournal.com/ Dave

     Children are taught to memorize the products of numbers from 1 to 10. When I was a kid, this was done by rote: “1×1=1, 1×2=2, … 4×4=16, 4×5=20, 4×6=24, … 7×8=56, 8×8=64, …, 9×9 =81”.

    “Knowing your multiplication tables” roughly means being able to recite that list.

  • PJ Evans

     Only to ten? They made us go to 12×12. Which is certainly useful with feet and dozens.
    My 8th grade math teacher had us learn the squares of the numbers up to 25 squared; this is occasionally useful.

  • Lori

     

    They made us go to 12×12. 

    Us too. School House Rock came in really handy for both my 11s & my 12s. If I tried really hard I could probably still remember the words to “Hey Little Twelve Toes”.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    Yep, I remember the 12s as well. I remember being rather daunted by that part of it.

  • EllieMurasaki

    https://en.wikipedia.org/wiki/Multiplication_table –yeah, pretty much. I don’t know how one would teach kids to multiply one- and small two-digit numbers that isn’t rote memorization, anyway.

  • http://jamoche.dreamwidth.org/ Jamoche

    Pre-computers a lot of arithmetic was done with tables. Some you memorized, some you looked up – my physics textbook had a section in the back full of trig tables. The Babbage engine’s purpose was to generate “difference tables” for printing presses because the ones built by hand tended to have transcription errors.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    I remember the rote multiplication thing m’self. I grew up before computers really took hold, so a lot of my math knowledge is from an era where you were still expected to do stuff without resorting to a calculator right away.

    As a result I learned how multiplication is repeated addition, and division is repeated subtraction. It took a while before I grasped that division is the multiplicative inverse, which is why dividing by a fraction means multiplying by the reciprocal.

    Seeing things as inverse operations to one another helps me understand relationships in mathematics a bit better, I think. It helps that it’s taught similarly in calculus: that differentiation is the exact opposite of integration, and vice versa.

  • The_L1985

     The multiplication table is a chart showing all the multiplication facts from 1×1 to 12×12, all lined up in neat little columns.  In my school, we spent much of 2nd-4th grade memorizing our multiplication tables, so we wouldn’t have to look things up or count on our fingers.

    I know a lot of people who “forgot their times tables,” and thus have to re-learn the basic multiplication facts before they can take any math classes as adults.  Thus, I’m pretty sure that forced memorization of times tables was pretty common.

  • http://blog.trenchcoatsoft.com Ross

     Yeah. As I understand it, the traditional way of teaching multiplication was not actually to teach the fundamental process of multiplication, but to simpyl drill the 144 squares of the 12×12 multiplication table into the students via rote memorization.

    The “New Math” was not a big thing at the time I was learning math in grade school, but one thing I do remember was my parents’ consternation and “What’s this hippie crap they’re teaching my kids?” reaction when they found out that I was taught how to multiply without having rote memorized a table through drilling with threat of a ruler across the knuckles if we missed one.

  • http://jamoche.dreamwidth.org/ Jamoche

    I did get a “you *could* add X+X+X+X+X+X+X, or you could memorize 7*X” lesson early on.

    My high school physics teacher started the school year out with Uncle Jerry’s Super Easy Rules for Solving Word Problems:

    In any problem there are one or more Givens and a To Find. You can identify them by certain key phrases (there was a list), and other key phrases tell you how to fit them into an equation.

    Simple, right? But not one of the elementary school classes that supposedly taught the things ever broke them down like that. I suspect anyone who found them intuitively obvious (hey, they’re in plain English!) felt the same way about Cobol (ADD X TO Y GIVING Z). But some of us think better in symbols.

  • PJ Evans

    But some of us think better in symbols.

    Some of us think in sounds and pictures. Doesn’t help in more advanced math.

  • http://blog.trenchcoatsoft.com Ross

    I knew a guy who was applying for a job at an elementary school a decade or so ago, and he was informed that the math teachers were forbidden from using the phrase “divided by”, as it was considered too math-y and offputting to students who weren’t mathematically inclined. THey were required to replace it with “share”, as in “Eight share four is two”. I believe there were other “friendlier” terms for “plus”, “minus” and “times”.

    A little part of me died when I heard this.

  • http://apocalypsereview.wordpress.com/ Invisible Neutrino

    You’re joking. That’s the kind of absurdity I would think only someone anti”Politically Correct” would make up, as oppsoed to a real thing which anti-PC people use to beat social liberals over the head with their alleged lack of common sense.

  • BaseDeltaZero

    Of course it comes down to the same point; no intelligent designer capable of making an organism as complex as a human being would think it was a good idea, rather than giving us a full-on brain liver or making the brain less fragile.

    Assuming that the designer could make the brain less fragile, without compromising other elements of the design (such as, say, not being incredibly expensive in terms of production time/materials).  Granted, if you’re working with a perfect designer, as creationism is…
    Mostly, a lot of the flaws in various beings could be explained as a flawed or compromised intelligent design – a lot of the things we make have similar flaws, after all.

    (which is, I think, the predominant Christian view worldwide–just not in the US).

    It’s the predominant Christian view in the US, I believe… the creationists are just loud.

  • http://dumas1.livejournal.com/ Winter

     

    Mostly, a lot of the flaws in various beings could be explained as a flawed or compromised intelligent design – a lot of the things we make have similar flaws, after all.

    If humans were designed at all, it was by a large number of lowest-bidders who weren’t talking to each other working from design specs drawn up by committee. And then production was farmed out to another lowest bidder who read the blueprints upside-down.

  • Mary Kaye

    I was very resistant to memorization as a child–the pain of teaching me to tell time is proverbial in my family, and it took some increasingly frustrating years of cursing (behind their backs) at people who would respond to “What time is it?” by showing me their analog watches to force me to finally learn it.  I was deeply offended, somehow, by the double use of the numbers as themselves and as multiples of five.

    As a result I am still pretty slow at multiplying, and there are parts of the table that I do not have memorized despite using them a lot (I play games that involve a lot of small-number multiplication on the fly).  What I have instead, after many decades of this, is very quick ways to work them out from table entries that I do know.  “Six times four must be two times twelve, twenty-four” goes by so quick I can barely perceive it, but it does go by every time.

    I also have a kind of kinetic formalism, like drawing a little house out of dots, that allows me to add columns of numbers fairly well without being able to intuitively add two one-digit numbers.  But I’m slowly getting better at that.  Maybe by the time I’m 60 I will have it down.

    I work in computational biology and statistics, go figure….I was much happier about math when I realized that it wasn’t mostly arithmetic.

  • Will Hennessy

    Cheeses!, with the f***ing bombardier beetles! I went to public school and I don’t remember s*** about f***ing fruit flies! Except that we had to deal with masses of the little f***ers in Advanced Bio!

    But then, I am from the Entitlement Generation (I mean, the Millenials!), whose motto is “I showed up to class, teacher, give me an A+.”

    …I’ve said too much…

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

    Thanks for the info on multiplication tables. That may have been how I was taught, but not how I learned (if you follow me). Perils of being “gifted” and having a non-diagnosed autism spectrum disorder include learning the subject without learning the lesson.

    The idea of “forgetting times tables” seems bizarre to me. I don’t need to memorize the product of 18 and 13 because I can calculate it. That many people with similar educations can’t is one of those things I had great trouble understanding.

  • arcseconds

    The idea of “forgetting times tables” seems bizarre to me. I don’t need
    to memorize the product of 18 and 13 because I can calculate it.

    Why is it bizarre?   For most of us, it’s a lot easier to produce a rote-answer than it is to calculate something.

    Do you calculate multiplcation in all cases, even say 5 × 5?  Even if you’ve had the same equation several times in the last hour, would you still calculate it every single time?

    Is it ever faster for you to memorize something than it is to calculate?

    (if for some reason you can calculate all multiplication results where the factors are under 10 just as fast as you can recall them, then maybe it would help to think of another operation, like logarithms, that you can’t perform that quickly)

    or is it the forgetting you think is bizarre?

    I’m not all that great at my ‘times tables’, and I often have to do a bit of calculation even with two numbers under 10, although I’ll normally backtrack to a result I can remember and work it out from there.  e.g. if I can’t remember 6 × 7 I’ll remember back to 6 × 6 and add 6.   I think i did that as a kid, too, which is probably partly why I never memorized them properly in the first place.   My slowness at arithmetic annoys me, and it’d probably be to my advantage to drill multiplication more, but I really can’t be arsed.

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

     

    Why is it bizarre?   For most of us, it’s a lot easier to produce a rote-answer than it is to calculate something.

    This is another one of those areas where I have trouble understanding how neurotypical people think.

    Do you calculate multiplcation in all cases, even say 5 × 5?  Even if
    you’ve had the same equation several times in the last hour, would you
    still calculate it every single time?

    It’s more of an automatic process for me. If I stop to think about it, I do calculate each equation. I think in terms of discrete values rather than “A and B means C.”

    Is it ever faster for you to memorize something than it is to calculate?

    (if for some reason you can calculate all multiplication results
    where the factors are under 10 just as fast as you can recall them, then
    maybe it would help to think of another operation, like logarithms,
    that you can’t perform that quickly)

    Most daily arithmetic takes me less time to calculate than it would to remember a chart or to use a calculator. I’ve never been much good at mathematics outside of arithmetic, basic algebra and probability.

    or is it the forgetting you think is bizarre?

    While I certainly understand people forgetting something they’ve worked to memorize (I remember no calculus or trigonometry), I have trouble understanding how forgetting some specific equation requires sitting down and working it out, as I have seen people do. If you have the basic principles, rote memorization is not needed.

  • lowtechcyclist

     “The idea of “forgetting times tables” seems bizarre to me. I don’t need
    to memorize the product of 18 and 13 because I can calculate it.”

    Tru dat, but you are almost certainly ‘calculating’ it from some smaller times-table that you have memorized.  To actually calculate it without a multiplication table would be to compute any products by repeated addition, because that’s what multiplication is.

    Let’s make it just a little more challenging, because it’s plausible that you can certainly get this particular product by (a) going 18+18+18=54 for the 18*3 part, and (b) remembering the rule that you multiply by 10 by tacking a zero on the end, then (c) adding 54+180=234, all without thinking about it much.

    But if we’re talking, say, 37 x 59, then your ability to calculate the answer without the use of a mental times-table that involves at least the products of one-digit numbers is going to be sorely strained.  You’re going to remember 7 x 9, say, not compute it and all the similar pieces via repeated addition.  (I suppose you could add up one stack of five 37’s, and another stack of nine 37’s, put a zero on the first total, and add the results together, but those stacks are where most of our brains gum up, even the brains of those of us who have one of them PhD thingies in math.)

  • http://www.facebook.com/people/Patrick-McGraw/100001988854074 Patrick McGraw

    I suppose you could add up one stack of five 37’s, and another stack of nine 37’s, put a zero on the first total, and add the results together, but those stacks are where most of our brains gum up, even the brains of those of us who have one of them PhD thingies in math.

    Taking the time to think about it, that is pretty much what I do. My brain gums up on other things that neurotypical people’s brains perform with ease (such as multi-tasking).

  • lowtechcyclist

    I’ve never understood the point of having a “Christian Flag,” let alone having the hubris to call a flag by that name without the consent of the vast majority of those who consider themselves Christians.

    I mean, we have a cross.  What on earth do we need a flag for?

    I just don’t get it.  Unless we want one “such as all the other nations have”  (1 Samuel 8:5) which seems to be getting the point of that story completely backwards.

    And a Pledge of Allegiance to either the Bible or the ‘Christian Flag’ – maybe Revelation 22:8-9 isn’t in their Bibles.  Our allegiance as Christians is to God, and God only, not to any lesser thing.

  • Daughter

    I think this whole thread shows that people learn differently. What works for one, doesn’t work for another.

    Several have said that they hated arithmetic, times tables and the like. I loved arithmetic so much as a kid that I made up my own math games using it. But when we got to proofs in geometry, I was completely lost. (It didn’t help that my original teacher left early in the year and we had a string of substitutes for the remainder).  I managed to get a 4 on my AP Calculus test in high school, but that took more mental anguish that anything I’d ever done up to that point. When I took my first calculus class in college, I was again lost and totally bombed it, and that was it for higher level math for me. Yet I’ve gone on to teach SAT prep in math to students, because I scored well and basic algebra and geometry continue to be fun for me.

    ~~~~~~~~~~

    I’m not sure how math is taught around the U.S. these days, but I have to say, I’m impressed with how math was taught by my daughter’s first grade teacher. They spent some time on place value and telling time, but most was spent on “number facts” starting with the number 2 and advancing up to 10. So they learned, for example, how many ways can you make five? Can you count to 5? Can you add two numbers together to get 5? How about 3 numbers? How many ways can you add 2 numbers, or 3 numbers, and still get to 5? If you go over 5, how much did you go over? Can you look at that pile of blocks and tell if there are 5 of them? If there aren’t enough blocks in that pile, how many do you need to add to have 5? If there are too many, how many do you need to take away?

    They’d spend several weeks on say, “5 facts,” learning all kinds of different ways you could manipulate objects or numbers in your head and on paper to get 5, and then they’d move on to “6 facts” and do the same thing.

  • http://twitter.com/mattmcirvin Matt McIrvin

    This is amusing, because just a couple of days ago, I got into a conversation with my daughter (age 6) which somehow got into set theory. Simple sets, unions, intersections. I described the empty set, and she announced that she didn’t like the empty set, so no more about that.

    We’d already talked about the idea of infinity. So I asked her how many members the set of all counting numbers would have, and she pretty quickly twigged that it would be infinite.

    “Right. So you can have sets with ordinary numbers of elements, and you can have infinite sets.   Like the set of all numbers, the set of all even numbers…”

    And she shouted “The set of all sets!” Into the deep water so soon…

    She seemed a bit put out when I mentioned that mathematicians ran into some paradoxical trouble when they tried to go there, with “the set of all sets that do not contain themselves” and such.

  • http://twitter.com/mattmcirvin Matt McIrvin

    Anyway, I think Eric had it back at the beginning of the thread. The objection to set theory had nothing to do with Cantor and Godel; it was that set theory was part of the New Math, and New Math was one of the educational reforms of the 1960s, which were bitterly opposed by conservatives.

    I went to elementary school in the 1970s, and, sitcom plots notwithstanding, it had pretty much blown over by then, except for some aftereffects: they called carrying/borrowing in addition and subtraction “regrouping”, and explained it in terms of gathering ten objects into a bundle of ten and back again, which I think was a consequence of the New Math-inspired emphasis on conceptual fundamentals.

  • Headless Unicorn Guy

    We didn’t use the BJU textbook in biology, but one of the textbooks for my Bible class was Hal Lindsey’s The Late Great Planet Earth.

    Ah, yes.  Back when the Bible was 3 1/2 books — Daniel, Revelation, the “Nuclear War Chapter” of Ezekiel (the 1/2), and Late Great Planet Earth.  Been there, done that, still got the scars to prove it.

  • Consumer Unit 5012

    I can’t believe we’re this far into a discussion of New Math and nobody’s linked to Tom Lehrer’s song on the subject.


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