Today's NYT Science Section.

http://www.nytimes.com/2008/07/06/bo...lenberg-t.html

Numerology

By JORDAN ELLENBERG
Published: July 6, 2008

My cousin, bound for a top liberal arts college in the fall, was
amused when I told her I was reviewing a book about big ideas in
mathematics, from the classical to the contemporary. “Don’t they
already know everything about math?” she asked. “You know, there’s
algebra ... and then calculus ... and that’s it, right?

Andrew Hodges, a fellow at Oxford and the author of the lively new
book “One to Nine,” would have been horrified, but not surprised. My
cousin, in his view, is a victim of the pedagogical tradition that
presents math as an eternally fixed array of computations, to be
memorized and repeatedly executed without motivation or explanation.
The result, he writes, is a “legacy of fear and anxiety generated by
schools, which leaves most of their victims with a lifetime of
mumbling apologetically about ‘my worst subject.’”

“One to Nine” offers a different model for teaching math — discursive
rather than linear, topical rather than abstract and remote, and,
above all, manically energetic rather than repetitive and plodding.
The book is composed of nine chapters, each focused — very, very
softly focused — on one of the first nine natural numbers. Chapter
Four, for instance, starts out with the observation that four is a
perfect square, and from there skips along to the construction of
Latin squares, the irrationality of the square root of two, the
definition of the logarithm (whose relation to “four” never comes
entirely clear), complex numbers, and the even more exotic quaternions
(a number system in which “numbers” are actually strings of four
integers, and the product of two numbers depends on the order in which
you multiply them!), the theory of four-dimensional spacetime and
Einstein’s equation E=mc2 (squares again) before finishing with a
short and speculative account of the theory of twistors, one of many
competing candidates for the universe’s underlying geometry.

Catch all that? Hodges’ lightning pace allows him to cover in one
little book the greatest hits of the last 3,000 years of math and
physics, leaving plenty of room for jabs at the Bush administration
and quotes from the Pet Shop Boys (these so frequent as to be
tabulated in the index).

The overall effect is like that of a lecture by the type of professor
who paces back and forth in front of the blackboard, with insistent
voice and waving arms, and has trouble adhering to the ostensible
syllabus for any extended period. Being this type of professor myself,
I can attest that the style is popular with students. But it requires
discipline to convey real information as well as enthusiasm.

Hodges often manages that trick. He ably explains the subtly distinct
shadings of the word “probability” in statements like “There’s a 90
percent probability I’ll get a six in the next 12 rolls of this die,”
“There’s a 90 percent probability of a catastrophic climate change in
the next 50 years” and “There’s a 90 percent probability that the
current warming of the earth is a result of human activity.” This is
the kind of tacit knowledge about mathematical practice that’s
unrelated to computations and hard to test, so it doesn’t show up in
school math classes. But it’s crucial for arguing sensibly about the
planet’s uncertain future. Hodges is also excellent at describing the
ways in which mathematical thinking winds its way into every aspect of
human life, from fashion to politics to finance, whether we’re aware
of it or not. Like Molière’s Monsieur Jourdain, most people have been
speaking math their whole lives.

The hyperactive style of “One to Nine” is less well suited to more
conventional mathematical material. Georg Cantor’s notoriously
mind-boggling hierarchy of infinities is covered in just three pages;
the proof of the irrationality of the square root of two, a theorem so
profound and startling in its time that its discoverer is
traditionally held to have been drowned in the sea by his scandalized
Pythagorean colleagues, gets just one. And it’s hard to imagine a
novice reader getting much from exposition this compressed:

“Latin squares can be used for devising a duty roster for n dirty jobs
in a houseshare of n people. Or, for comparing the effect of n drugs
on n animals in some doubtless vital trial. Who said mathematics
wasn’t useful? Similar ideas lead to the error-correcting codes which
make it possible for computers to communicate reliably. Or, for that
matter, to football leagues, speed-dating nights and the plot lines
for ‘Desperate Housewives.’”

Too much of the book is like this passage, which is not exactly math,
but what Stephen Colbert might call “mathiness”: a series of fervent
gestures that gives the impression that mathematical ideas are being
expressed, but doesn’t actually deliver the goods. Readers will enjoy
sprinting through “One to Nine,” and they’ll certainly learn that
there’s much more to the subject than the algebra and calculus taught
in high school. But they might not be able to explain exactly what.

On Sun, 06 Jul 2008 11:44:08 GMT, Short Wave Sportfishing
wrote:

Today's NYT Science Section.

http://www.nytimes.com/2008/07/06/bo...lenberg-t.html

Numerology

By JORDAN ELLENBERG
Published: July 6, 2008

My cousin, bound for a top liberal arts college in the fall, was
amused when I told her I was reviewing a book about big ideas in
mathematics, from the classical to the contemporary. “Don’t they
already know everything about math?” she asked. “You know, there’s
algebra ... and then calculus ... and that’s it, right?

Andrew Hodges, a fellow at Oxford and the author of the lively new
book “One to Nine,” would have been horrified, but not surprised. My
cousin, in his view, is a victim of the pedagogical tradition that
presents math as an eternally fixed array of computations, to be
memorized and repeatedly executed without motivation or explanation.
The result, he writes, is a “legacy of fear and anxiety generated by
schools, which leaves most of their victims with a lifetime of
mumbling apologetically about ‘my worst subject.’”

Haven't seen it, but it sounds interesting. I probably won't read it
though. It sounds like it would make a good textbook for, "Intro to Math
for the Liberal Arts Student", especially with the anti-Bush rhetoric.

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime number after
two is either one more or one less than four.

Another good book, which I *have* enjoyed is, "Nature's Numbers" by Ian
Stewart.

On Jul 6, 9:52*am, John H. wrote:
On Sun, 06 Jul 2008 11:44:08 GMT, Short Wave Sportfishing





wrote:
Today's NYT Science Section.

http://www.nytimes.com/2008/07/06/bo...lenberg-t.html

Numerology

By JORDAN ELLENBERG
Published: July 6, 2008

My cousin, bound for a top liberal arts college in the fall, was
amused when I told her I was reviewing a book about big ideas in
mathematics, from the classical to the contemporary. “Don’t they
already know everything about math?” she asked. “You know, there’s
algebra ... and then calculus ... and that’s it, right?

Andrew Hodges, a fellow at Oxford and the author of the lively new
book “One to Nine,” would have been horrified, but not surprised. My
cousin, in his view, is a victim of the pedagogical tradition that
presents math as an eternally fixed array of computations, to be
memorized and repeatedly executed without motivation or explanation.
The result, he writes, is a “legacy of fear and anxiety generated by
schools, which leaves most of their victims with a lifetime of
mumbling apologetically about ‘my worst subject.’”

Haven't seen it, but it sounds interesting. I probably won't read it
though. It sounds like it would make a good textbook for, "Intro to Math
for the Liberal Arts Student", especially with the anti-Bush rhetoric.

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime number after
two is either one more or one less than four.

Another good book, which I *have* enjoyed is, "Nature's Numbers" by Ian
Stewart.- Hide quoted text -

- Show quoted text -

I'll give you guy till the count of three to STFU If I can just
remember what comes after 4 :O

"John H." wrote in message
...

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime number after
two is either one more or one less than four.

Mind explaining this. The way it reads is that 5 is the most significant
prime number.

On Sun, 6 Jul 2008 10:26:51 -0400, "Jim" wrote:


"John H." wrote in message
.. .

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime number after
two is either one more or one less than four.

Mind explaining this. The way it reads is that 5 is the most significant
prime number.

My bad. "...every prime number after two is one more or less than a
*multiple* of four.

"John H." wrote in message
...
On Sun, 6 Jul 2008 10:26:51 -0400, "Jim" wrote:


"John H." wrote in message
. ..

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime number
after
two is either one more or one less than four.

Mind explaining this. The way it reads is that 5 is the most significant
prime number.

My bad. "...every prime number after two is one more or less than a
*multiple* of four.

I'm going to take a leap of faith and trust you on that one.

BTW:
I think they miss you over at Chucks. They seem to be clamming up either in
support of you of fear of the axe man.

"Jim" wrote in message
...

"John H." wrote in message
...
On Sun, 6 Jul 2008 10:26:51 -0400, "Jim" wrote:


"John H." wrote in message
...

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime number
after
two is either one more or one less than four.

Mind explaining this. The way it reads is that 5 is the most significant
prime number.

My bad. "...every prime number after two is one more or less than a
*multiple* of four.

I'm going to take a leap of faith and trust you on that one.

BTW:
I think they miss you over at Chucks. They seem to be clamming up either
in support of you of fear of the axe man.
PS I'll bet it's driving JIM H crazy trying to find out how I'm able to get
information on Chuck's place.

Jim wrote:

"Jim" wrote in message
...

"John H." wrote in message
...
On Sun, 6 Jul 2008 10:26:51 -0400, "Jim" wrote:


"John H." wrote in message
...

But, four is an interesting number, as Hodges points out. One other
interesting factoid about the number four is that every prime
number after
two is either one more or one less than four.

Mind explaining this. The way it reads is that 5 is the most
significant
prime number.

My bad. "...every prime number after two is one more or less than a
*multiple* of four.

I'm going to take a leap of faith and trust you on that one.

BTW:
I think they miss you over at Chucks. They seem to be clamming up
either in support of you of fear of the axe man.
PS I'll bet it's driving JIM H crazy trying to find out how I'm able to
get information on Chuck's place.


Doubtful.