Content by Mary P. Campbell
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Reviews Written by
Mary P. Campbell "math geek" (Flushing, NY USA)
3.0 out of 5 stars
The Mystery of the Missing Words, Feb. 25 2003
Most of the "proofs" in this book will be of more
use and interest to math teachers -- how many
people want to see 10 different diagrams showing
trigonometric identities? Still, much is of great
use to teachers; the standard textbooks are often
redundant in their figures and thus bore students
in their predictability. As well, students are in
need of stretching their mathematical intuitions
and understanding -- when all right triangles are
shown with the legs parallel to the pages' sides,
when all variables are either x or y, people think
that math is a matter of grinding through standard
procedures. PROOFS WITHOUT WORDS II links
subjects that are usually treated disparately:
geometry is connected to combinatorics (a fancy
name for counting), calculus, and linear algebra.
Many of the most technical figures are accompanied
by equations and words explaining the use. The
back cover blurb does admit that many of the
proofs aren't actually wordless, but I'm sure no
one will sue them for false advertising -- these
problems would be difficult to interpret
However, the math enthusiast will be most rewarded
by the figures with the least amount of words, for
they provide mini-mysteries to be solved. The
book starts with six different figures proving the
Pythagorean Theorem -- and only one has any kind
of "language" on it (a few variables and their
products). These examples' author range from a
10th century Arab mathematician, a 3rd century
Chinese mathematician, and Leonardo da Vinci to
current contributors to the journals from the
Mathematical Association of America. A few of
these proofs are easier to interpret, as they
involve cutting up squares into various pieces and
rearranging them (but how to prove these
various pieces are congruent?), one uses similar
triangles, and the da Vinci one still has me in a
fog. The Arabic proof was very elegant and
involves a tiling pattern that looks like it would
work well on a modern kitchen floor. The most
elegant of all the proofs in the book is the one
on the front cover: a geometric series represented
by stacked equilateral triangles, fitting inside a
larger triangle. The combinatorics proofs are
also very elegant ways to visualize special sums
None of these figures would be considered proofs
by most people because one needs to have various
parts explained; however, all crucial parts of the
proofs are in the figures. As the editor writes,
what makes these proofs good is that they show
=why= a statement is true. Many
mathematicians discover new theorems by playing
around with figures representing already known
objects -- some of these figures can show how
certain relations were discovered. Unfortunately,
we are usually shown a cleaned-up, perfectly
deductive version of theorems in school, making it
difficult for us to make the leap to new
mathematical discoveries and understandings. The
figures in this book make for a good course of
mental calisthenics, and they provide inspiration
to one to find one's own visualizations.
I recommend this book for high school and college
math teachers, particularly those who teach
trigonometry, calculus, and discrete math. If you
know a student gifted in math, this book is
appropriate for any student who is familiar with
some basic geometry (Pythagorean Theorem, area of
triangles and rectangles, similar triangles); they
will be able to figure out a few of the counting
and geometry proofs, and will grow into the other
figures in time. For the intelligent child who
enjoys math, this provides an extra challenge, and
as they learn the math various proofs refer to,
the pieces will fall into place.
5.0 out of 5 stars
A Crystal Bead, Aug. 27 2001
In honor of the 20th anniversary, I put up a review I wrote 11 years
ago, for a school assignment:
When I am feeling that life is pointless
or unwondrous, I read Douglas Hofstadter's =Godel, Escher, Bach=; time
and time again, this book leaves me in awe over the interconnectedness
of several "unrelated" subjects, over order arising from
apparent chaos. This book made me regain my faith in and admiration of
the beauty of math, art, music, and the universe -- the beauty that is
almost never shown in a class or revealed in a "scholarly"
work; after reading it, the isolation of those subjects from the rest
of the conceptual world seems simply ludicrous. Each time in reading I
am challenged to discover more connections, more self-references, more
meaning in the several subjects presented. In short, reading this book
is like a religious experience for me -- I love it.
"The Buddhist allegory of 'Indra's Net' tells of an endless net
of threads throughout the universe...At every crossing of threads is
an individual and every individual is a crystal bead. The great light
of 'Absolute Being' illuminates and penetrates every crystal bead;
moreover, every crystal bead reflects not only the light from every
other crystal in the net -- but also every reflection of every
reflection throughout the universe."
Hofstadter's book is the
perfect example of one of those crystal beads; Hofstadter portrays (or
"reflects") several subjects in his work, e.g., formal
systems, Zen, moplecular biology, the art of fugues and canons, model
of the brain, various geometries, number theory, Holism
vs. Reductionism, and much more, and then shows the
"reflections" of the subjects in one another -- truly a
large task. For the most part, he comes across quite well; his
dialogues which encapsulate and discuss ideas to be presented, his
"dogmaps" which outline parallel ideas and "map"
them onto one another, and his relatively simple language enable him
to communicate his ideas quite easily. However, this book is quite
weighty -- almost 800 pages long, full of digressions and
perspective-blowing ideas; many ideas and underlying themes must be
sought out within the dialogues, many open-ended questions are left
for the reader to ponder. If you aren't used to flexible or abstract
thinking, and you don't want to work very hard in reading, this book
isn't for you.
GEB is an unique "nonfiction" book -- it does
not address one subject, or even several "closely related"
subjects. Even though published in 1979, many parts deal with research
still going on today [this is still true in 2001, as it was in
1990]. For example, Hofstadter presents a possible model for a brain
to be used in artificial intelligence in computers -- one of many
models being studied today in that field. In one short section, he
presents recursive graphs that were generated in theoretical
experiments -- graphs that bear some similarity to the modern study of
fractals. Especially in the area of computer science, Hofstadter
leaves several goals for people to attain -- goals that may never be
realized, but perhaps goals that will enlighten us as we seek to
The ideas in this book shall live long past its authorr;
I can say no more but that the people who awarded the Pulitzer Prize
to this book made no mistake.
| by Orson S Card|
Edition: Mass Market Paperback
|Price: CDN$ 9.89||
3.0 out of 5 stars
Mormons, computers, and bugs, oh my!, Aug. 25 2001
This novel was expanded from a short story by Card, and it shows; the
plot, at its core, is simply this: a Mormon family moves to central
North Carolina, has some troubles and makes enemies, all the while
boys are going missing in the neighborhood. They find out what has
happened to the boys. That's it in a nutshell, and as my husband
remarked, this novel is obviously taking the background of a short
story and pushing it into the foreground. That does =not= mean it's
boring or lagging; Card uses this opportunity to create a
fully-fleshed family, enmeshed in various communities (the Mormon
Church, a computer software company, a medium-sized southern town), so
that the plot has overall personal meaning.
On a personal note of my
own, having grown up in medium-sized southern towns with a father who
worked for IBM when the IBM PC came out, I was brought back to my
childhood, when my favorite fast food place in the Savannah Mall was
Der Weinerschnitzel, when I was disappointed in my Commodore VIC-20
and its tape drive, when I had to battle through swarms of bugs just
to get to my backyard swingset. Card nails the details perfectly,
especially the kind of resentment one can get as a gifted child
growing up in "advantaged" circumstances; I had no
Mrs. Jones in my past, but I very well could have. I've seen other
children treated as Stevie was, and there's little a child can do
about a teacher who hates children. On another detail note, I'm sure
the episodes with the bugs were intended to be creepy, and I'm sure
Card thought the armies of bugs that greeted him in Greensboro were
daunting, but I just had to laugh about it. My lord, I used to eat
South Carolina =dirt= as a child, which is full of dead bugs. I'm
supposed to be scared by a bunch of crickets pouring through a rotten
Seriously though, there are so many moral triumphs in this
book, in which parents under extreme pressure try their best to
protect their family, in many cases succeeding and in many cases and
in a few, not being able to do much about the external world, but
achieving a moral victory nonetheless. It also gave me ideas in how to
deal with certain people, so literature can actually be useful now and
then! Card has always presented one of the most accurate pictures of
how religion acts in people's lives, especially from the point of view
of a person of faith. In particular, I enjoyed learning a little more
about how the Mormon social structure actually works, which of the
duties people actually follow up on, and which they let slide (Sunday
services and classes seem well-attended, but things like home teaching
were given short shrift). Being a Catholic, I know how comforting a
Church with an international structure can be -- instant community
whereever you go -- but some of the duties can be shortchanged
depending on local attitudes.
I spent much of the book wondering how
much autobiography was in this story, as the actual origin of this
book was a bedtime story Card made up for his son, Charlie Ben, who is
echoed in the birth of the Fletchers' son Zap. Card had grown up in
the west, done mission work in Brazil, and moved to Greensboro, NC
which looks (to me, a Raleighite) alot like the fictional Steuben,
NC. Card has been one of my favorite authors for so long, I was
somewhat distracted by so much I could tell came directly from his own
life. I can tell what a personal book this was, and anyone reading it
for the human story will be well-rewarded.
5.0 out of 5 stars
Yes! We have the cultural history of bananas!, Aug. 25 2001
Who would have thought there was so much to say about the modern
love affair between America and bananas? I should have known it,
though, for at Mathcamp the staff had entire wars based on bananas and
the pilfering thereof. We snuck extras out of the cafeteria, hid them
in refrigerators, even wrote our names on the peels in a feeble
attempt to secure a personal, steady supply. Alas, it was not to
be. How did this miracle fruit go from being an exotic food iteam for
the rich to the universal snack? Jenkins tells us how, in this very
thoroughly researched book. Pretty much anything you want to know
about bananas in the 20th century is here: medical attitudes, recipes,
social status, trade wars, banana jokes ("I'm sorry, I can't hear
you -- I've got a banana in my ear.") - you name it, it's in
here, which is surprising for such a relatively trim book. She's got a
slew of references in the back, should you ever wish to check her
sources; for the less academic of us, there's also an extensive list
of banana songs.
Bananas are such a workaday fruit, we
forget how important they have been in reflecting society. With each
new medical fad, bananas reinvent themselves as a perfect food; during
the period where dirty fruit was a concern, the thick peel of the
banana was a boon; when vitamins, minerals, and proteins were seen as
important, bananas were found to have such things in abundance; when
high-calories and high-fat were a concern, bananas were found to be an
energy-full, low-fat snack. Even stranger, at one point in history,
bananas were considered a treatment for celiac disease (an extreme
form of gluten-intolerance - so basically all breads and grains are
inedible to such children, and many died due to malnutrition); during
World War II, during which much of the banana supply was cut off,
there were stories of frantic parents mobilizing entire towns to round
up banana supplies for their sick children, sure that their children
would die without bananas. And yet, in just a generation previous,
parents had been warned against giving =any= raw fruits or vegetables
to children under the age of 7. The chapter in which this fascinating
material resides is called "Peril and Panacea", which
provides a prismatic view of the changing medical atmosphere in
America in the 20th century. A few other details which I found
interesting: there were banana cookbooks, one of the recipes being for
"Bananas and Bacon" - I kid you not. There's even a picture
of it in the book. As well, much of the editorial cartoons and jokes
involving banana peels reflected anti-immigrant sentiment, once
bananas had become so cheap even the newly arrived poor could afford
to eat them. Of course, there are a couple of obligatory "banana
as phallus" remarks (explaining why proper young women were to
use a knife and fork to eat the offending fruit), but they do not
overwhelm. Sometimes a banana is just a banana.
other fruit that could possibly have had as much impact on the
American psyche is the apple (well, maybe the orange). Though this is
a history book, it is far from dry, and Jenkins lets off a couple
zingers of her own. If you've ever eaten a banana or know someone who
has, this book is for you; so I guess that means about everyone. I
have no idea, then, why this isn't at the top of the bestseller
3.0 out of 5 stars
Regency mystery, with fewer historical distractions, July 18 2001
Barron's fictional Jane continues her surprisingly dangerous career by stumbling upon a particularly grisly corpse -- a young man, she thinks, shot in the head and eviscerated. As it comes out that the deceased was a stillroom maid, in charge of remedies and preserves, and a vicious rumor implicating the Freemasons spreads throughout the village, Jane once again becomes enmeshed with a murder investigation. There are plenty of false leads to follow, plenty of scandals to uncover, and all in the company of Lord Harold Trowbridge, who is in Derbyshire to pay a visit of morning for the Duchess of Devonshire.
Of the Jane Austen Mystery series so far, this is the one most distilled - fewer side issues for Jane to consider, fewer forays into the politics and the culture of the day. There is, of course, the aristocratic name-dropping; we are treated to the leading people of the Whig movement in Parliament. Also, there is a small mention of Freemasonry, but it passes quickly. The chapters are interspersed with recipes for folk remedies, in sure opposition to the "more modern" apothecary and doctor, who prefer their bleeding cures to tinctures and poultices (Warning: do not try these remedies at home. Stick to our "modern" remedies of St. John's Wort and saw palmetto). However, there are far fewer footnotes in this book than the previous novels and far fewer reveries on Jane's part. Barron seems to have decided to make this a murder mystery, with few distracting elements. Once again, an enjoyable read, like the rest of the series, but no tedious bits as some of the previous novels suffered from.
| by Orson Card|
Edition: Mass Market Paperback
|Price: CDN$ 9.89||
3.0 out of 5 stars
A living and dying house, July 17 2001
This book is standard Orson Scott Card fare -- people with very concrete, contemporary problems, people with mysterious pasts, a protagonist a little too good, and a little bit of folk magic thrown in. I wasn't surprised to find that the "house come alive" (a horror subgenre, perhaps born of authors building homes and realizing the way these things suck up time, money, and spirit) wasn't exactly malevolent, but it wasn't benevolent either. Above all, there's a consistent atmosphere of haunting throughout this book - Don Lark, the main character, is haunted by the death of his daughter in a car accident caused by his ex-wife, haunted by a situation which he had tried everything he legally could and yet still unable to prevent. The trio of elderly neighbors next door (one unseen upstairs, consuming an unbelievable amount of food) are haunted by the house, trying to get Don to at the very least let the house decay instead of renovating it.
The harking on the past of the house, repeatedly back to the Bellamy's - the original builders and happy owners of this now seemingly ominous decaying hulk, back to the impotent choices or horrible compulsions of various characters - made me feel like this was a ghost story without an actual ghost. I found I was wrong. However, when the ghost did finally show, it was barely a surprise; this house =had= to have a ghost.
An interesting characteristic of all Card novels is that he does give peeks of truly evil people, but he never exposes the reader to them for long. That's a good idea on his part, for when an oily, insinuating character appears, my blood pressure shoots up as I wish to throttle the nonexistent person. Card prefers to linger on those who are essentially good, but who have gone through extremely harrowing trials and who are left in mental and emotional confusion in the wake of evil results.
So, no, this isn't a horror novel, and not exactly a fantasy book, for all the animistic forces at work in this novel. It's a story of people trying to escape their pasts, but unable to for many years, and then coming together to, as a group, conquer the spirits holding them prisoners. It's a quick read (I finished it in one evening) and it has a satisfying ending. I would recommend this book for a rainy summer Sunday, a book for one of those days in which one would otherwise be living in one's own mind.
| by Orson Scott Card|
|Price: CDN$ 18.17||
4.0 out of 5 stars
A shadow which overtakes the original, July 16 2001
If you ever intend to read =Ender's Game=, make sure you do before reading this book. First of all, the "secrets" of the first novel are given away, and thus lessen the impact of surprise one gets on first reading =Ender's Game=. Secondly, the characterization and plotting in =Ender's Shadow= surpasses the original novel; a lot of time has passed since Card wrote his wildly popular book, and he has used his intervening time well in improving his craft as a storyteller.
Like =Ender's Game=, =Ender's Shadow= is a story about an execeptional child trying to fit in and succeed, in which the child has a nemesis who haunts his thoughts, and an advocate who seems to betray him. Upon multiple readings of both novels, more and more parallels pop out; however, I find the characters of Ender and Bean to be extremely different. Ender seems to sink further and further inside himself, as he tries to protect himself from the dangers which threaten him from outside; Bean starts as a cold, survival machine, remnant of his battles to stay alive on the streets of Rotterdam as a toddler, but as he moves on he reaches out to protect himself from his own external dangers. As Ender becomes more obsessed with the Buggers, Bean keeps thinking about the wider world, and the inevitable wars on Earth that would result from defeating the Buggers. At the end of the novel, Ender is about to leave Earth forever, to start on his long journey away from humanity as =Speaker for the Dead=; Bean returns to Earth to a new family and a new sense of purpose and humanity.
It does not matter that one knows what happens in =Ender's Game=; Card realized that Ender's point of view on Battle School and the world as a whole was extremely myopic. One finds new significance to dialogues between Ender and Bean, knowing the limitations both have in knowledge of the other. I'm glad Card revisited the story of Ender and has extended it to the period on Earth right after the Bugger War, which was glossed over in the Ender series. Bean's series continues with =Shadow of the Hegemon=, and the parallel stories have ended. If nothing else, one can note the maturation of Card as an author in the time between =Ender's Game= and =Ender's Shadow=, with more complex characterization and a sharper contrast of good vs. evil, =Ender's Shadow= definitely comes out on top.
3.0 out of 5 stars
A little less than genius, but still fun, July 16 2001
In this, the fourth of the Jane Austen Mystery series by Stephanie Barron, we are once again drawn into a tale more sordid than the ones we are used to from Jane Austen. Jane attends Canterbury Race Day with some of the Austen clan, witnessing the excitement over straining horses, and being shocked by Mrs. Grey, a rich Frenchwoman with a good taste in racehorses, a genius at shocking the populace, and the bad fate to end up brutally strangled by Race Day's end. Once again, our fictional Jane is close to the investigative action -- this time, it's her brother Neddie, local magistrate, who is in charge of discovering the murderer. There is an obvious suspect, the man who owned the carriage in which Mrs. Grey's body was found (scandalously undressed!), but Mrs. Grey had made enemies of much of the people of the Kentish neighborhood.
As is usual, Stephanie Barron weaves in cultural information of the day -- one starts with some knowledge of the low pursuits of cock-fighting, high-stakes card parties, and speculation on horseracing, but by novel's end one has learned of the new perspectives in landscaping "improvement", a bit on current women's fashions, British troop movements in holding off Napolean's armies, and the financial ramifications of the Napoleanic wars in general. Not all of the historical information is pleasant to learn; Barron reminds us a little bit too often of the August heat making it a necessity for quick inquests and burials. I'm sure the coroners of England were happy when the inquest jury no longer had to examine the corpse for themselves.
As an avid reader of Agatha Christie, I figured out a few of the mystery's puzzles early on, but though I could tell =how= the murder was done, I couldn't tell =who= did it. There are some odd, distracting bits of plot, I believe; however, I do appreciate the little bit of =Emma= that was stolen for the use of this book. It makes for interesting pitfalls; a devoted Janeite will be able to recognize phrases, dialogue, and plot taken from Austen's works, but Barron uses them for her own end and the unwary reader can be caught in surprise twists to the Austen originals. I found the ending of the novel somewhat unsatisfying, but the novel as a whole is entertaining.
3.0 out of 5 stars
Murder Amongst Actors and Artists, July 13 2001
The book opens on a masquerade in honor of an acting company, with our fictional Jane Austen in the guise of a Shepardess, and the scene ends with a murdered Harlequin, stabbed during a dramatic soliloquy from Macbeth (the "cursed play"). Harlequin turns out to be Richard Portal, manager of the troupe. A young man is standing over the body, knife in hand, but all is not as it seems, as is usual in mystery books.
It turns out this young man is a relative of Lord Harold, Jane's old nemesis-turned-ally from the first of the Jane Mysteries. Lord Harold and Miss Austen comb the worlds of acting, staging a scene of their own in order to rifle Mr. Portal's papers, and of artistry, as it turns out that the "Wandering Eye" of the title, a mysterious, expensively-made eye portrait had been found on the corpse. As is usual in Ms. Barron's Jane mysteries, one learns much of the cultural history of the Regency period -- the tumultuous politics of the time, the fashions in dress and affectation (Jane runs into some of the dandies of the day), and the ways in which people's reputations her broadcast (imagine, they had gossip columns -- one can't blame current media for starting the practice of nosing into people's private lives!)
I found the solution to the mystery a little disappointing, but the characters much more interesting than in the two previous books. Jane and her sister Cassandra's relationship strains with their increasing age and obvious spinsterhood, Jane reacts to the smearing of her own good name, and Jane loses a very close friend. Ms. Barron has done an excellent job of weaving Jane Austen's real biography (and actual words - I noted several phrases from Austen's own novels and letters inserted liberally into the text) into dramatic action. I think Jane herself would have found these books amusing; we now think of Austen as having a retired, uneventful life, and these books paint a portrait very different. The queen of irony would have smirked.
3 of 3 people found the following review helpful
5.0 out of 5 stars
Please Be Discrete, July 13 2001
What is "concrete" math, as opposed to other types of math? The authors explain that the title comes from the blending of CONtinuous and disCRETE math, two branches of math that many seem to like to keep asunder, though each occurs in the foundation of the other. The topics in the book, such as sums, generating functions, and number theory, are actually standard discrete math topics; however, the treatment in this text shows the inherent continuous (read: calculus) undergirding of the topics. Without calculus, generating functions would not have come to mind and their tremendous power could not be put to use in figuring out series.
The smart-aleck marginal notes notwithstanding, this is a serious math book for those who are willing to dot every i and cross every t. Unlike most math texts (esp. graduate math texts), nothing is omitted along the way. Notation is explained (=very= important), common pitfalls are pointed out (as opposed to the usual way students come across them -- by getting back bleeding exams), and what is important and what is =not= as important are indicated.
Still, I cannot leave the marginal notes unremarked; some are serious warnings to the reader. For example, in the introduction, one note remarks "I would advise the casual student to stay away from this course." Notes that advise one to skim, and there are a few, should be taken seriously. All the marginal notes come from the TAs who had to help with the text, and thus have a more nitty-gritty understanding of the difficulties students are likely to face. Still, there are plenty of puns and bad jokes to amuse the text-reader for hours: "The empty set is pointless," "But not Imbesselian," and "John .316" made me chuckle, but you have to find them for yourself.
To someone who has been through the rigors of math grad school, this book is a delight to read; to those who have not, they must keep in mind that this is a serious text and must be prepared to do some real work. Very bright high school students have gotten through this text with little difficulty. I want to note ahead of time - some of the questions in the book are serious research topics. They don't necessarily tell you that when they give you the problem; if you've worked on the problem for a week, you should turn to the answers in the back to check that there really is a solution.
That said, I would highly recommend this book to math-lovers who want some rigorous math outside of the usual fare. The formulas in here can actually come in handy "in real life", especially if one has to use math a lot.