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Michael Hardy's Profile
Customer Reviews: 26
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Classic Reviewer Rank: 14,500
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Reviews Written by
Michael Hardy (Minneapolis, MN, USA, for the Time Being)
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68 of 72 people found the following review helpful:
Brilliant (but mostly not so _newly_ known), February 9, 2007
Again I feel I must post a review to counter misleading
information in an earlier review. The author of the
previous review seems to think these works were _not_
available to scholars during the Renaisance. In fact,
the famous "Archimedes Palimpsest" that resurfaced in
the 1990s is only a small part of the works of Archimedes
found in this book. Moreover, this book is a reprint of
the translation published in 1897 by Thomas L. Heath.
Heath _did_ have access to the Palimpsest (or maybe to
a translation into German or to a copy--of this I am
unsure) and did include a translation in this book in
1897. It is true that after the Palimpsest resurfaced
in the 1990s and began to be examined by modern methods,
some lacunae were filled in. But that's not even most
of the Palimpsest, let alone most of the contents of
this book. Moreover, the newly discovered material is
not in this book (but Heath's translation of the Palimpsest
is). The previous reviewer is _extremely_ confused about
the history.
Now to the contents of the book. The famous Palimpsest
actually is my favorite part. Prepare to be dazzled.
Many 20th-century calculus texts, saying that integral
calculus was anticipated by Archimedes in the 3rd century
BC, are so phrased that they may give their readers
the impression that Archimedes worked with something similar
to Riemann sums, or similar nonsense. The truth is far more
interesting. Archimedes used infinitesimals explicitly.
His proofs were amazingly efficient. If you think that a
brilliant proof by an ancient mathematician having only
relatively primitive methods at his disposal must be longer
and more complicated than a proof by modern methods, think
again. Modern methods are indeed more efficient, but not
because one writes _shorter_ proofs; rather it is because
(at least in the present case) one writes _fewer_ proofs.
Archimedes introduced the concept of center of gravity.
In the Palimpsest, he finds not only areas and volumes,
but centers of gravity (that of a solid hemisphere of
uniform volume is 5/8 of the way from the "north pole" to
the center of the sphere, Archimdes shows in one of his
startlingly efficient proofs--just one example).
It was not only by the use of infinitesimals that Archimedes
solved problems that would now be treated by integral calculus.
For example, one of the methods (just one of them) by which
Archimedes found the area between a parabola and one of its
secant lines involved dividing that area into an infinite
sequence of triangles, the sum of the areas of which is a
geometric series. Many other examples are in these pages.
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A Personal Odyssey
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by Thomas Sowell
Edition: Paperback |
| Price: $17.12 |
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| Availability: In Stock |
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3 of 4 people found the following review helpful:
Not profound but enticing, January 10, 2007
Perhaps nothing profound is in this book, but it
can lead the reader to suspect that Thomas Sowell
has written other, deeper things. It is full of
stories about various sorts of irrational bureaucrats
in academia, in government, and in the military,
maybe not _quite_ as extreme as the pointy-haired
boss in _Dilbert_, but definitely the sort who could
have inspired that character. Thomas Sowell could be
considered a sort of minor patron saint (or "patron
hero" if such a thing exists) of the virtues of
sticking to one's guns, calling the shots as one
sees them despite heavy pressure from those who
don't understand, refusing to follow any party
doctrine as if it were infallible dogma, and caring
about one's students.
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Limitations
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by Scott Turow
Edition: Paperback |
| Price: $10.14 |
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| Availability: In Stock |
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1 of 5 people found the following review helpful:
Ingenious and engaging, December 13, 2006
Scott Turow and I may have one philosophical disagreement
(a comment he wrote in an op-ed piece once), but who cares?
He writes beautifully and his plots are ingenious and engaging.
In my review of Robert Heinlein's _Starman_Jones_, I wrote
that the book has various readily identifiable flaws that
it would be easy for me to list, and that those don't matter
at all. In particular, I gave it five stars despite those
imperfections. Now I see a few reviewers here pointing out
flaws in this book (one of them cites a debatably run-on
sentence). Hey, I can do that too.
After finishing this book, I went back and read some
passages a second time, and I find that some of the clues
to the identity of the culprit are absolutely brilliantly
subtle. I understand that they were clues only because
after finishing the book, I know who the culprit is, and
they're subtle enough that I didn't notice them until the
incomplete second reading.
Turow's ability as a fiction writer seems to result not
only from the conjunction of his first-hand experience
as a lawyer and his mastery of language, but also of what
seems like a thorough knowledge of the Dark Side of human
nature. (My one possible philosophical disagreement with
him is that his knowledge of the Bright Side may have a
piece missing.)
But gratuitous nitpicking can be a lot of fun, so let's
try a few (those who don't like English usage discussions
are hereby ordered to skip this paragraph):
(1) On page 17, he says "forebearer" where I would say
"forebear". Google bears me out: "forebearer" gets only
20,200 hits; "forebear" gets 289,000. So there.
(2) Page 91: "to revenge himself". Should that say
"to avenge himself"?
(3) Page 191: "Now he trips downstairs..." Was he
injured when he tripped on the steps? No---the verb
"trip" is being used here as a verbed noun; he made a
trip downstairs to the office of the court's chief
file clerk. The verbing of nouns in English has a
venerable history of many centuries of use by the
best writers, but intelligent people express horror
at every novel instance. It seems only old well-established
verbed nouns are respectable (e.g. "verbed" is a shady
usage permitted only because of my Censorious Grammarian's
license and then only when I'm at least a little bit
sarcastic).
(4) p. 188: "It is a long rule of law that defendants
must take their victims as they find them." I'd have
guessed that a _long_ rule of law would require more
words than that---maybe even a run-on sentence of the
kind that some lawyers might pride themselves on.
Perhaps unbeknownst to me it has long been a rule of
law that lawyers use the word "long" in that way, in
which case the reader is hereby ordered to skip item (4)
of the present list.
(5) p. 42: The terms "parking structure" and "parking garage"
appear. I wonder how many Americans realize how much
geographic variation there is in the meanings of these and
related terms in this country. What the British denote by
the self-explanatory term "multi-storey car park" is in the
western USA a "parking structure", in some parts of Canada
a "parkade", in Boston a "parking garage" (but in Minneapolis
that term is strictly reserved for _indoor_ parking facilities,
and an outdoor multi-level parking facility is a "parking ramp"),
and in some parts of the eastern seaboard a "parking deck".
I suppose we have to take these usages on that page as
infallible and give them their proper weight as evidence of just
where Kindle County is. The title "People of the state vs.
Jacob I. Warnovits" doesn't give us much information about that.
(6) "Parietal hours". I guess I'm too young to have heard that term.
Now the cute locutions department:
(1) p. 23: Our protagonist is a "standard-issue white guy."
(2) p. 60: "a Mid-Ten University". S'posed to sound like
"Big Ten", I guess, but different.
(3) p. 181: Someone's words inadvertently "emerge with a
steely undertone of accusation".
(4) Harrison Oakey is a minor character. I wonder if his
first name might have been taken from the actor who starred
in a movie based on one of Turow's novels?
Geography:
I sometimes wonder how much of Kindle County was inspired
by the Minneapolis/St. Paul area. "Tri-Cities" is a bit
reminiscent of "Twin Cities". Both Kindle County and the
Twin Cities area of Minnesota have about 3 million inhabitants.
Not overwhelming evidence there. The only thing that beyond
all doubt came from Minnesota is the political party called
the DFU. Let's see---p. 94 "hooks a right onto Washburn".
Naming a street "Washburn" won't make it past the reasonable
doubt standard, if being inspired by Minnesota is a crime.
How 'bout this: pp. 24-5. The hospital is "West Bank
Lutheran-Sinai". The West Bank is also mentioned in at least
one other place in the book. In Minneapolis the area just before
you cross the Mississippi heading eastward from the downtown
area is the West Bank, and "Lutheran" fits very very well indeed.
The big hospital near there was formerly St. Mary's and had a
Catholic affiliation (it's now under a different, secular,
management). The big state university in Kindle County is
colloquially called "the U", but I'm not sure there's not more
than one geographic locale that that fits. So what state is
Kindle County in? In _one_ of Turow's novels, a two-letter
abbreviation for it is given. "As a matter of friendly
torment [p.197]" I won't say which one.
"Who are we to judge?" (p. 75)
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Podkayne of Mars
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by Robert A. Heinlein
Edition: Mass Market Paperback |
| Availability: Out of Print--Limited Availability |
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Pre-feminist. Contains one superb insight., July 20, 2006
This book was written just before the feminist
movement's 2nd-half-of-20th-century phase got
underway. Heinlein had not yet broken free of
traditional gender roles (as he certainly did
shortly thereafter), although it is perfectly
obvious that he not only values, but always enjoys,
intelligence as a personality trait in women. So
you have to forgive him for certain things in order
to enjoy this book.
I love the playful style of language in which this
book is written -- it is unique among Heinlein's many
books.
When the seemingly amiable and undistinguished old
Mrs. Grew turns out to be in reality a mercenary
terrorist, the protagonist's brilliant but anti-social
younger brother Clark is unsurprised, because once,
when she hadn't known he was watching, he had seen
her cheating at solitaire!! How do you like that!
(A similar insight occurs elsewhere in Heinlein's
fiction, in the short story _Gulf_, when Kettle-Belly
Baldwin says "Evil is essentially stupid.")
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6 of 6 people found the following review helpful:
Pre-feminist. Contains one superb insight., July 18, 2006
This book was written just before the feminist
movement's 2nd-half-of-20th-century phase got
underway. Heinlein had not yet broken free of
traditional gender roles (as he certainly did
shortly thereafter), although it is perfectly
obvious that he not only values, but always enjoys,
intelligence as a personality trait in women. So
you have to forgive him for certain things in order
to enjoy this book.
I love the playful style of language in which this
book is written -- it is unique among Heinlein's many
books.
When the seemingly amiable and undistinguished old
Mrs. Grew turns out to be in reality a mercenary
terrorist, the protagonist's brilliant but anti-social
younger brother Clark is unsurprised, because once,
when she hadn't known he was watching, he had seen
her cheating at solitaire!! How do you like that!
(A similar insight occurs elsewhere in Heinlein's
fiction, in the short story _Gulf_, when Kettle-Belly
Baldwin says "Evil is essentially stupid.")
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10 of 10 people found the following review helpful:
You may have to soak this book up slowly, May 24, 2006
I've read some parts of this book and not others,
so I suppose I need to reserve the right to revise
this opinion from time to time.
Many good things in probability theory are not in
this book. That is not a fault of this book; it only
means you'll need others as well. It has an extremely
notation-intensive style, and at first I thought that
could slow down the reading a lot. But with the help
of the notation table on pages 525 - 528 it actually
moves along rather smoothly. If you just wanted to
read through a section, carefully checking and
understanding the correctness of everything, it wouldn't
be that hard, but you'd be wasting the book. You have
to go over things until you understand Stroock's point
of view---the aspects of it that he's not very explicit
about. Maybe it's a bit like learning a language; you
have to soak it up and integrate it.
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10 of 11 people found the following review helpful:
Not really a textbook, May 11, 2006
I feel I have to write this just to answer the previous
reviewer's assertion that there's nothing here that's not
in a modern textbook. Perhaps there's nothing here that's
not in any modern treatise on this subject written for an
audience of mathematicians, if such a book exists. But a
textbook is different from a treatise readable by
mathematicians. The latter is what this is. The table on
page 74 is amazing, and I challenge anyone to find it in a
textbook. It expresses the sine of each multiple of 3 degrees
in terms of rational numbers and square roots---expressions
involving nested radicals and fractions. Few if any textbooks
on trigonmetry would contain Euler's infinite product
expansion, found here near the top of page 128. Later there
is a whole chapter on infinite products. There is also a
proof of the irrationality of pi, using continued fractions.
Definitely it's too dense to be a textbook (but maybe an
exceptionally bright student could use it to learn this
material for the first time).
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18 of 21 people found the following review helpful:
Trigonometry is simpler when divorced from cyclometry, April 17, 2006
One of Wildberger's claims is that his approach to
trigonometry is both simpler and easier that the
traditional one ("simpler" is not synonymous with
"easier", but sometimes "simpler" entails "easier").
WARNING: This book will NOT make trigonometry easier
for non-mathematicians of the sort who are learning
trigonometry for the first time, since they are not
its intended audience. This is not a textbook. Wildberger
has said he will write that later. This book explains
his approach to mathematicians, who will find it easy to
read.
It would be very unfair to Wildberger and to this book to
judge it harshly for not making trigonometry easier to
those learning it for the first time. Wait until his
textbook is published and then judge THAT by that criterion.
Judge this book by its appeal to mathematicians and others
who are its intended audience.
Etymologically, trigonometry is "measurement of triangles".
Students learning trigonometry also spend a lot of time on
measurement of circles. An etymologically parallel term for
measurement of circles is "cyclometry", a seldom seen word
occasionally taken to refer to circle-squaring. Wildberger
"measures triangles" without "measuring circles", without what
are usually called trigonometric functions or any other
"transcendental functions", without talking about angles or
rotations. The angle at which two lines meet is determined
by what Wildberger calls the "spread", which is a rational
function of their slopes (this is a glimpse of the reason for
the word "rational" in the title), and in the language of
conventional trigonometry is the square of the sine.
All of that portion of conventional trigonometry that is
concerned with measuring triangles, whether applied to physics,
geography, land surveying, navigation, etc., is simpler if
done by the methods introduced by Wildberger.
Wildberger also covers a considerable amount of interesting
geometry not usually treated when trigonometry is taught.
The sine and cosine functions used in Fourier series and
harmonic analysis do not appear. For Fourier series, it
is of course simpler to use "cis(x)" = cos(x) + i sin(x)
= e^{ix} than to use the sine and cosine functions. Since
the trigonometric identity cis(x + y) = cis(x)*cis(y) is
simpler than the formulas for sin(x + y) and cos(x + y),
should we expect that if Wildeberger's proposal to separate
trigonometry from what I called "cyclometry" above becomes
the norm, then all those complicated identities normally
worked with in trigonometry will be forgotten? I will
indulge in wild speculation for a moment. Another place
where those functions can appear is as generating functions
in combinatorics. The coefficients in the not-too-well-known
power series for tan(x) enumerate "alternating permutations"
of the set {1, ..., n} when n is odd; those of sec(x) do the
same when n is even. Conventional trigonometry tells us that
the sum of a tangent and a secant is a tangent, i.e.
tan(x) + sec(x) = tan(x/2 + pi/4); thus, that function
enumerates all "alternating permutations". Will things like
that someday be a reason for all those complicated identities
to be remembered? And will they somehow become simpler if
someone succeeds in separating their study both from the topics
relied on in Fourier series and from the measurement of
triangles?
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3 of 4 people found the following review helpful:
Good for math majors; perhaps annoying to graphics experts, July 19, 2005
As the preface says, this book approaches the subject from two different directions: analytic and synthetic. The synthetic approach seems to contain both (1) the parts of the subject best suited to students who know only high-school math, and (2) the parts ill-suited to those who are not "pure" mathematicians. An example of the former is a high-school-geometry-style proof that any three points on any line may be transformed to any three points on any other line via a composition of two perspectivities. An example of the latter is the projective plane that is freely generated by a configuration. The inclusion of things like this latter example is the reason why the word "foundations" is in the title; "foundations" does not mean that which should be learned before everything else; perhaps "foundations" should be defined as "that which will annoy those who want to apply projective geometry to computer graphics and which will delight `pure' mathematicians who want to know how the subject interacts with abstract algebra." The latter group will like this book and will find it very readable.
This book is short and omits some topics found in many books. Conics and polarities are not dealt with.
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Starman Jones
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by Robert A. Heinlein
Edition: Paperback |
| Availability: Currently unavailable |
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15 of 18 people found the following review helpful:
Excellent, June 28, 2005
It is unfortunate that Heinlein has received a lot of press for some of the worst things he wrote for an adult audience, such as _Stranger_in_a_Strange_Land_. His genius was in his "juvenile novels" -- the stories he wrote for serialization in boy scout magazines, later published as books.
Max Jones dropped out of high school to support his lazy irresponsible stepmother by working on their farm, which has only those amenities that would have been commonplace in 1850. But he dreams of becoming an astrogator aboard a starship like his late Uncle Chet, who instructed him in that profession. When his stepmother marries a man who is uneducated and cannot appreciate his ambition, Max leaves. The world being badly mismanaged, he must hitchhike to the city of Earthport to find out whether he has been appointed his uncle's professional heir.
I will not give away spoilers, but herewith I will tease you a little bit. Heinlein was a graduate of the Naval Academy, where he learned some of the laws in force aboard ships. While Max is serving aboard a ship that has become lost and set down on an unknown planet, with no realistic hope of finding its way home, the First Officer explains to the passengers and crew certain legal rights and obligations that apply in such an emergency. A passenger objects: "There are no laws HERE." The First Officer corrects him, saying the law goes where the ship goes. That sets the context for a climax several chapters later, involving legal, moral, political, and psychological aspects of leadership in an emergency.
The book dramatizes the role of intelligent purposefulness in human life. A scene occupying about the first four pages of the second chapter is a beautiful example: Max is alone facing difficulties and using his head.
The book has various readily identifiable flaws, which it would be easy for me to list. Those don't matter at all.
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(Minneapolis, MN, USA, for the Time Being)
