
Algebra in Wonderland - robg
http://www.nytimes.com/2010/03/07/opinion/07bayley.html?hp=&pagewanted=all
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georgecmu
Her exposition of math concepts is ridiculous.

"De Morgan had proposed a more modern approach to algebra, which held that any
procedure was valid as long as it followed an internal logic. This allowed for
results like the square root of a negative number"

Imaginary numbers were introduced by Descartes in 17th century and were widely
accepted by the middle of 18th (think Euler: e^(i \pi) + 1 = 0).

"This principle (now an important aspect of modern topology) involves the idea
that one shape can bend and stretch into another, provided it retains the same
basic properties — a circle is the same as an ellipse or a parabola (the curve
of the Cheshire cat’s grin)."

Huh? You can bend or stretch a circle into a parabola?

~~~
cperciva
_Huh? You can bend or stretch a circle into a parabola?_

In a sense, yes. A parabola is simply an ellipse with one of the foci at
infinity.

~~~
dmvaldman
you cannot stretch a parabola into a circle because a circle is a closed loop,
while a parabola is not. any stretching would necessarily have to tear the
circle. a topologist would say they have different fundamental groups.

the author of this article should stick to what she knows...english
literature, not algebra.

~~~
cperciva
_a topologist would say they have different fundamental groups_

In the affine real plane, yes. In the projective real plane, all (non-
degenerate) conics have the same fundamental group.

~~~
gambling8nt
To elaborate on cperciva's (correct) point:

On a projective plane a parabola contains a single point at infinity,
connected (both figuratively and topologically) to the two open ends. A
hyperbola contains two distinct points at infinity each connected to one end
of each of the two usual components.

------
anatoly
I read this argument before, in a paper by the author I think. I thought it
was nonsense then and this article doesn't change my opinion about it. The
purported explanations are really unconvincing, the analogies very strained.

~~~
hga
Agreed, the author just doesn't supply any strong evidence for her thesis.

Would it be impolite to point out that she's an "English Major"? Then again,
her A Levels might have given her a far better grounding in math than is the
norm in the US.

~~~
tsally
_Would it be impolite to point out that she's an "English Major"?_

You already know the answer to this question. Also note that she's not an
"English Major" in the sense you imply, she's getting a PhD in English Lit
from Oxford.

If indeed her arguments are incorrect, you should be able to frame a
refutation on ideas alone instead of resorting to an ad hominem argument.
Ironically, this is a basic skill even "English Majors" possess.

~~~
hga
Impolite does not mean irrelevant.

What I'm trying to point out is that there is no sign in what little we know
of her biography _or_ in this article that she knows math at this level, the
modern math she thinks Carroll is skewering.

Let's put it this way: how certain is anyone here that she understands how
quaternions are non-commutative and how that was such a leap from all previous
algebra? Such a leap that it took Hamilton years before he made it, such that
it is commemorated on the bridge where he first wrote (carved) a solution?

Something I impolitely point out is that all too often I've seen people from
"the humanities" make incorrect claims about "us" without any understanding of
our work _or_ our culture, which they don't realize is a superset of their's.
(And I'm annoyed about all the attention they get in doing this, but I suppose
that's obvious.)

~~~
tsally
I'll join you in being annoying that she got published in the Times and I'll
agree there are blatant inaccuracies in the article, but there are more
effective arguments than insulting the author or the humanities at large.
There's plenty to disagree with in the article without resorting to that.

As for mathematics being a superset of the humanities, that is just patently
false. Here are a few counter examples [1,2,3]. I always find it interesting
when fellow engineers/scientists argue for the superiority of their discipline
when compared to the humanities. Personally I find the hard sciences awe
inspiring enough to stand by themselves.

[1]
[http://upload.wikimedia.org/wikipedia/commons/e/e1/Brueghel-...](http://upload.wikimedia.org/wikipedia/commons/e/e1/Brueghel-
tower-of-babel.jpg)

[2] <http://plagiarist.com/poetry/1760/>

[3]
[http://books.google.com/books?id=lZDCequ4E4kC&pg=PA170#v...](http://books.google.com/books?id=lZDCequ4E4kC&pg=PA170#v=onepage&q=&f=false)

~~~
hga
I think I was unclear WRT to your last point. I'm saying that "we", the STEM
types, live in a popular and to a certain degree also a higher culture that is
a superset of the culture that those in "the humanities" live in. It's a
_very_ broad generalization, perhaps colored by my being a part of a sub-group
that would go to the ballet, Shakespeare productions, Ring Cycles (and each of
us had at least one poet and painter we really liked, etc. etc.) ... but then
again those who didn't like attending "operas [that] last three or four days"
nonetheless had at least a minute appreciation, e.g. we weren't denigrated for
our particular interests.

I was told an anecdote by someone in a course by Sherry Turkle: he said that
one day there were many absences due to a Grateful Dead concert and that she
couldn't comprehend this. Unfortunately I can't remember the details of her
incomprehension, but at least as of the early 80s I didn't know anyone who
knew her who thought she had a clue about what she was studying.

Perhaps I should say that there was nothing in the culture (as construed
above) of those in "the humanities" that was out of bounds for us, whereas
e.g. they'd never get jokes like the ones about an Abelian Grape, or better, a
spherical cow ("Let us solve Schrodinger's equation for a cow. First
assume...").

~~~
anatoly
I don't really like where you're going with this.

For every lit-crit type who'll never understand what quaternions are, I'll
find you a math geek with a shelf full of Star Trek novels, who'll never
understand what real literature is.

(I once tried, and failed, to convince a mailing list chock full of some of
the most brilliant programmers I knew that there's more to fiction than
science fiction).

The humanities and the STEM fields (I didn't know this abbreviation) are not
exactly balanced in this way; there is something to what you're saying; but
the something that's there is not anything like a "superset" relationship, not
even close.

Once you restrict to people who both understand what quaternions are, and
prefer Kafka to Zelazny, you're talking about a superset of both sides, not a
STEM subgroup that also assimilated knowledge from the humanities, but
remained essentially STEM. I don't think it works that way.

~~~
hga
I agree that "superset" is too crude a term for what I'm trying to say, but as
you acknowledge, there is _something_ to what I'm saying.

E.g. the equivalence you draw in your second paragraph is not relevant to my
point, which is more like "while there are math geeks who understand what real
literature is, there are essentially _no_ lit-crits who will ever understand
what quaternions are".

(And Star Trek novels might be a bad choice, seeing as how Patrick Stewart
introduced a lot of Star Trek fans to Shakespeare. :-)

Let me take this further by discussing people who I'll call "bridges". In my
subgroup of "lit-geeks" there was one seriously into philosophy. and she got
some of us to appreciate some of it. Similarly, I was the one who dragged
people to the first showing of the Ring Cycle (although pretty quickly that
became a larger group thing as someone else e.g. dug up a fantastic Wagner
scholar, it's a _real_ shame he died as he was finished his commentary on _Die
Walküre_.)

Despite your lack of success with the members of that mailing list, what I'm
suggesting is that it's in theory possible to make that bridge and that it's
not so with lit-crits and quaternions (well, not without years of math study
they've essentially shown they won't or can't do).

~~~
anatoly
I agree that it's much more likely for a math geek to develop serious
knowledge of lit-crit than it is for a lit-crit type to develop serious
knowledge of math. That's the something that there is to what you're saying.

However, being that either scenario is astonishingly rare and unlikely, I just
don't see that as a good argument for asserting any kind of superiority of
STEM culture over humanities culture. And when, astonishingly rarely, that
does happen, I suspect the human in question doesn't see themselves as
primarily STEM or primarily humanities, but just, you know, curious about
stuff. Knowledge-hungry, culture-hungry, and screw the tags.

------
nazgulnarsil
19th century writing in general makes a mockery of today's level of education.
I believe this is due, in part, to the more limited availability of print at
the time. most of the people printing things in any sort of quantity that
ensured it would survive to our times was generally pretty worldly.

not that i'm arguing that such times were better. the diaspora of artistic
expression fueled by cheaper means has been a boon for humanity.

~~~
Groxx
I'd argue that the limited availability meant that only the extreme few who
could afford to print did so, and when they did they kept things to what their
elitist groups would find interesting. Meanings hidden within meanings not
because they were any more intelligent than others, simply because they needed
to do so to fit in with the elitist habits / aesthetics.

You see the same thing in art prior to the modern art shift. Art was _so_
elitist that it wasn't focused on being artistic any more, it was instead a
conglomeration of meanings that could be examined and critiqued by the social
elite. All social elite groups do this, it raises them above others who don't
know the language and gives them a feeling of superiority.

------
eitally
I think everyone who posted here would be well served reading Martin Gardner's
The Annotated Alice. Gardner, who was the puzzle editor for Scientific
American for decades, is also a Lewis Carroll scholar, and his annotated
versions of Alice in Wonderland and Through the Looking Glass are tremendous.

[http://www.amazon.com/Annotated-Alice-Definitive-Lewis-
Carro...](http://www.amazon.com/Annotated-Alice-Definitive-Lewis-
Carroll/dp/0393048470)

