Maggie Koerth-Baker is science editor at BoingBoing, author of a must-read book on how energy works…and a former fundamentalist. Having met her and interviewed her, I still had no idea about that last part. However, it came in very handy for a post from her yesterday.

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?

Well, for me,

thisis new:“Unlike the “modern math” theorists, who believe that mathematics is a creation of man and thus arbitrary and relative, A Beka Book teaches that the laws of mathematics are a creation of God and thus absolute….A Beka Book provides attractive, legible, and workable traditional mathematics texts that are not burdened with modern theories such as set theory.” — ABeka.com

Wait? What?

That was my response too. I understand why fundamentalists don’t like evolution. It threatens special creation. I get that they don’t like history. It undermines their Christian nation. I had no idea why they would object to set theory.

Now I know, thanks to Maggie. And you can too.

ericJust a guess, but its probably because set theory includes (most of?) the work of Cantor and Godel.

Just reading other math blogs, it appears lots of cranks object to the work of Cantor, though I am not sure why. Godel is easier to understand: his incompleteness theorems could be seen as challenging the notion that God could be be omniscent.

MyaRWeird. I couldn’t do my job without set theory, and I’m not even in a mathematical (or really, science-y) field. I’ll have to go do some searching to see what that’s about.

Francisco BacopaI really don’t understand the objection to set theory. And does it really even come up that much in the kind of math you learn in K-12?

What theology is really undermined by the diagonal argument? How does knowing that the elements of some infinite sets cannot be set into one to one correspondence with the elements of some other infinite set undermine God, morals, or society?

Sometimes I think fundies pick a fight with something just as a mark of group identity.

steve84I heard that before. This was the first time I saw someone explain why

aleph squared@eric #1 — but Godel was a theist…..so it seems they should appreciate having an ally there, right?

A lot of cranks object to Cantor because he was the first (well, not exactly, but certainly best known as “the first”) person to develop a transfinite set theory, which means he was one of the first people to prove such counter-intuitive things as the fact that there are different (an infinite number, in fact) sizes of infinites, that infinite sets are the same size as proper subsets of them, etc. etc.

As soon as math proves something that nonmathematicians don’t intuitively grasp, cue a whole bunch of cranks claiming it is nonsense. Like how .999…=1

smrndaThe typical objection to Set Theory is that it concerns things that are ‘infinite’ and proves that there exist infinite sets of different sizes. Apparently this is some blow to religion for some reason. Perhaps the objection is that Cantor sought to quantify ‘the infinite’ rather than wax incoherently poetic about it.

I’m sure that “Bekabooks” stops long before issues like set theory would come up.

Pierce R. ButlerAlso, we must remember how Cantor pronounced his first name: fundies think they have every reason to oppose an Org of Gays.

RiptideMathematics without set theory is like architecture without I-beams–sure, you can still make some semblance of civilization, but you’ll have nothing like the modern world. Set theory is the language in which practically every kind of noteworthy mathematics is expressed.

Corvus illustrisI’m not sure where these guys are coming from. One possibility is that they just object to their own notion of “set theory” because of bad experiences back when they were in K-12. Recommendations by various groups of professional mathematicans were implemented by teachers who taught “set theory” by rote, didn’t understand what the point was, and have convinced a generation of students that “set theory–bad”. Or they might just dislike Cantor (Jewish-sounding name). On the other hand, it is possible that their objections are based on some knowledge of model theory–e.g., the existence of nonstandard models of the real numbers like those popularized by Luxemburg, Robinson and their successors. If they reach even that level of sophistication, they might feel threatened by such constructions, which appear to replace “God’s numbers” by somebody else’s (as if even the rationals, let alone the reals, weren’t human constructs).

BTW, in his later years Goedel seems to have become a mathematical “Platonist” in the sense of feeling that “somewhere out there” was a really-existent set of “counting numbers.” IIRC he started life as a Protestant, even though he was an Austrian; a Catholic Thomist could have told him all about the putative locus of these objects.

JacMy hunch was that it would involve non-intuitive concepts like infinite sets and the empty set, but I didn’t really know why. MK-B posits that the counter-intuitive stuff smacks of modernism, which is a threat to everything they stand for. Moreover, God is supposed to be the one infinity, inviolable. So having multiple sizes of infinity, being able to subtract an infinite set from an infinite set of the same size and still have an infinite set, etc, is an affront to their concept of God.

aleph squaredThis is what confuses me. After the abject failure of New Math in the USA, at least, set theory is only rarely introduced formally (in the sense that A Beka is objecting to) before college level, and then typically only at particularly good schools.

left0ver1underWhen christians say, “You can’t get to heaven unless you accept jesus christ,” what they’re really saying is,

“You don’t get the benefits of christianity unless you accept the basis of christianity.”Yes, it’s a load of bunk, but that’s what they think, that they’re “in the club” and anyone who is atheist, LGBT, not white or some other group isn’t.Turnabout is fair play. Let’s write and enact a law that says the same thing:

You don’t get the benefits of science unless you accept the basis of science.The religious reject infinity? Fine. Let them use Roman numerals so they never have to deal with numbers larger than a few thousand. After all, they believe the Earth and universe are only 6000 years old. Let them use only computers that go up that high, like the Apple II with its Integer Basic. That should be sufficient for them.

The religious reject set theory? Fine. They have to give up things based on set theory, like GPS systems or economic systems. Let them use roadmaps and compasses. Hey, the fictional characters in the bible didn’t have compasses, and they found their way around. And since their bible says they have to give their money away, let’s take it away and give it to the poor.

The religious reject evolution? Fine. They have to give up modern medicine, give up antibiotics, give up gene therapy, give up anaesthetic and surgery. Let them pray for healing if they’re such strong believers.

Of course they’ll never go for it and it would never pass, but I can dream. At least it’s within the realm of the possible, not a fairy tale.

Corvus illusrisInteger BASIC won’t quite cut it, seeing that various groups of the Saved have 144,000 members. (That’s in the Book of Revelation, particularly beloved of the fundies for its Rapture, ability to prove both Pre- and Postmillenarian stuff, and other good things. Kind of like set theory.)

BecomingJulieIt’s to be hoped that they didn’t use computers in the preparation of these textbooks.

Boolean algebra (you know, the stuff that makes computers work at the lowest-but-one level: AND, OR, NOT, NAND, NOR, EOR and BUN logic gates) is derived via set theory.

Also, that whole “Dogs have four legs, Fido is a dog, therefore Fido has four legs” deductive reasoning thing is pure set theory: Fido ∈ {dogs}, {dogs} ⊂ {things with four legs}, therefore Fido ∈ {things with four legs}.

Oh ….. maybe that’s why they don’t like it.

ericAh, should’ve read the link before replying. Good article.

smhllI had the kiddie version of set theory in my 6th Grade math textbook around 1970. I remember Venn diagrams and using operators for

unionU, andintersectionupside down U.One of the other parts of New Math was to try to get students to understand what they are doing when dividing (even dividing fractions), rather than just copying the arithmetic steps performed by the teacher. We can all imagine why fundamentalists would hate that.

cottonneroThis is like finding out that Andy “Conservapedia” Schlafly doesn’t believe in imaginary numbers.

I suspect it’s a combination of:

1) Ignorance/misunderstanding of a non-intuitive topic,

2) Pride in that ignorance, and

3) The need for ingroup markers.

robertmcclellanYou have to understand the fundamentalist mindset they genuinely believe the world is either black or white. To have the academic view that something that is thought to be true today may not be true tomorrow is to them absolutely unacceptable. They think you are just lying to prove a point.

smhllI found a Mother Jones article on the same topic.

D. C. SessionsIf set theory is too “modernist” for them, I truly wonder how they would deal with quantum mechanics. And if quantum mechanics is actually Lie of Satan, then what are these things we’re using to communicate?

Obviously, witchcraft.

Maybe they should move to farms where they can live without all of that Satanist modern electronics.

christophburschkaMust be predeterminists. How can you have free will without the Axiom of Choice? 😛

D. C. SessionsI forgot to mention that branch of set theory called “number theory.” Which is the basis for all of those Satanist communications devices like cell phones and … computers. And DVD players.

Alan(UK)Are you all not making this all too complicated? Surely the objection to ‘Set Theory’ is that it contains the word ‘Theory’. If you want to insist that ‘the laws of mathematics are a creation of God and thus absolute’, then anything containing the word ‘Theory’ implies a guess, and consequently is of human origin, whereas anything containing the word ‘Law’ implies authority and consequently is of divine origin.

christophburschkaThe fun part is there really are multiple seemingly contradictory set theories, none of them are more or less true than the other, and the very concept of empirical evidence is meaningless here.

In a way, the creationist types should feel right at home.

In another way, of course, they are frightened by the idea that axioms are arbitrary. As well they should, since that calls all unreasoning belief into question.

shocknaI recall reading a “disproof” of the existence of god that was based on set theory; I always figured this was why it was universally hated.

And to anyone asking about how creationists deal with modern physics, behold, Conservapedia and physics:

http://rationalwiki.org/wiki/Conservapedia:Conservapedian_relativity

aleph squaredBwahahaha.

So they should just teach ZF, not ZFC 🙂

geekadooMath teacher perspective…I think that traditionalists get “New Math” and the current approach to teaching math mixed up.

Traditionalist approach to math: one expert tells you what to do, you don’t ask why, just trust the expert. No calculator, just do all arithmetic with pencil and paper.

As others have said, New Math was an attempt to teach math from first principles, building everything from set theory. (Might make more sense to a mathematician, but doesn’t work as an approach to education. It has been discredited, and no one really uses it anymore.)

Current approach to teaching math: Teach critical thinking, creative problem solving and never use procedures unless you know why they work and make sense. Use calculators for large messy numbers and to make it possible to do more realistic calculations. There is more than one right answer. Being able to communicate how you got your answer and why it is right are key.

The name New Math is offensive to someone that thinks that Truth is given from on high and can’t be “NEW.” Here, the name is more the problem than the approach. The more substantial arguments I hear are for the traditionalist approach and against the crazy touchy-feely, no-right-answers, question authority approach. You can’t teach someone to think critically in math class but not to think critically in life.

RobertI seem to remember reading somewhere that in 12th century Europe, merchants were forbidden to do calculations in arabic numerals because the church objected to the concept of ‘zero’. Seems there is some progress after all, even though they still seem to be lagging by a few centuries.

Steve RThere are a lot of people who are afraid of any math beyond the four-function arithmetic they learned in elementary school, because they learned their arithmetic as a set of rituals that they didn’t really understand. These are the people who can’t add sales tax to a price with a calculator unless the calculator has a percent key, the people who are utterly baffled by the concept of arithmetic in any base but ten.

BecomingJulieAny idea what their thoughts are on fractions? Negative numbers? Complex numbers?

Zinc Avenger (Sarcasm Tags 3.0 Compliant)Well, Statistics

isthe Devil’s work.smhllThe name New Math is offensive to someone that thinks that Truth is given from on high and can’t be “NEW.”I think you nailed it. Only

traditional, Biblicalmath is acceptable to that group.bradcWilliam Lane Craig uses an argument about the contradictions inherent in the concept of infinity in his Kalam Cosmological argument (From this blog post:

Which is all, I think, a profound missing of the entire point of Hilbert’s Hotel. To me, Hilbert’s Hotel is simply an illustration of why “normal arithmetic” with infinite sets is non-intuitive, and why we need to come up with new ways of determining whether infinities are equal (namely, putting infinite sets into one-to-one correspondence).

Anyway, I’m not convinced that this has anything to do with A Beka Books’ problem with set theory, since WLC’s book on this wasn’t published until 1979. Still, I wonder if it comes from the same kind of thinking.