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A few weeks ago, my wife told me about a fairy door that appeared in Golden Gate Park in San Francisco. It was handmade and fitted perfectly in a notch between roots. It had a hinge and you could pull on the knob and it opened.

Park visitors had discovered the whimsical creation and started leaving things inside the door. Nuts. Treats. Notes. One, for instance, said, "I like cheesecake."

This makes sense to me. If you confine yourself to eating only desserts delivered by fairies, you stand a better chance of losing weight.

At the time the story broke, park officials said they had no plans to remove the fairy door.

I thought at the time that this was an astonishing attitude from a government bureaucracy, and indeed it was too good to be true. Soon the door was removed -- and replaced with a different, not-as-well-made door.

Is there a Department of Fairy Doors which found that the original fairy door did not meet the regulations and had to be replaced?

No doubt the door is doomed. There almost certainly is a regulation that nothing can be attached to a living tree in the park -- not even with teeny-tiny screws.

The possibility of deciding to ignore the rule for one exceptional situation is vanishingly small. That's because people can lose their jobs for making exceptions to the rules.

Besides, the kind of person who thrives in a regulatory job is the kind of person who loves regulation and is deeply, deeply disturbed by any rule violation.

No doubt this person spent many sleepless nights before weeping as he (or she) ordered the removal of the fairy door.

"I know everybody loves it, and the anonymous creator of the door made something whimsical and sweet that has increased the pleasure of park visitors. But it is bolted to the tree."

People have missed the point about the fairy door. Fairy doors have been around for years. We had a couple, bought from Toscano's catalogue, if I remember aright, attached to the bases of trees in our back yard, until tree growth and/or raccoons pried them loose.

We still have tiny fairy doors attached to the baseboard in a couple of rooms in our house. Why? Because my wife and I are extremely immature, or at least I am, and my wife is tolerant. And it's our house. Get over it.

What made the Golden Gate Park fairy door so wonderful was that it was so individual. It was handmade, finely finished, and it fit exactly in place.

It was genuine public art.

It was not going to advance the craftsman's career -- we still don't know who made it. Nobody was going to charge money for it. No doubt the maker of the door expected it to be removed as soon as the park officials found out about it.

But as long as it lasted, it brought delight to park visitors who happened to notice it. It was a generous thing to do.

And the fact that government, by its nature, had to destroy it is simply a fact of life. Government is destructive of some things, protective of others.

Losing the fairy door is the price we pay for also not having yard sale, lost dog, and we-buy-houses signs nailed to every tree in the park.

Yet because that one fairy door did exist, and was so creative and well-made, we will walk through all parks now, keeping our eyes open for the possibility that the next tree just might have a fairy door, too, which will only exist for a few moments before the ogres whisk it away.

The book Galileo, by J.L. Heilbron, is a thick biography that promises, in the preface, to spend plenty of time putting Galileo in his intellectual context. Most writers about Galileo, said Heilbron, plunge straight into his conflict with the Catholic Church; my book, though, will give you a much clearer perspective by showing what issues were already in contention in the Italian Renaissance.

Since Heilbron has written about the conflict between church and science before, and seems to have a distinguished resume, I was optimistic. This is exactly the kind of biography and history I thrive on.

Maybe I should have paid more attention to the "emeritus" in Heilbron's backflap bio. But I've known plenty of professors whose retirement from active teaching meant they had more time to write -- they could finally get to the projects that have been stewing in their minds and now are ready to serve.

So "emeritus" is not a code word for "too old to write well." "Old" doesn't necessarily mean "gaga." Some scholars' best work comes after they retire.

But I realized something was wrong with this book by page 7. As Heilbron is explaining why mathematics was regarded as a lower field of study than philosophy, he writes:

"In Aristotelian logic, the strongest demonstration (demonstratio potissima) is the perfect syllogism, of which the form 'all B are A, all B are C, therefore all A are C' is the exemplar."

Yes, yes, I know, this is needlessly thick writing, but unglaze your eyes and look at that syllogism. It has to be a typo, right? The A and B were accidentally swapped in the first premise, right?

No. Here's the very next sentence:

"In practice, the premises of a physical proposition (all B are A, all B are C) were agreements among philosophers based on the repeated and confirmed experiences of rational animals."

There it is -- he repeats "all B are A."

I read this aloud to my wife, whose brief section on logic in a college class was hundreds of months ago. "What?" she said. "That's not right."

Indeed it's not. From those premises, all you could derive about the relationship between A and C are the two statements "Some A are C" and "some C are A." There is no valid "all" statement you can make, period.

Let's get rid of the letters and put it in the traditional terms. A valid syllogism takes this form: "All Greeks are human. Socrates is a Greek. Therefore Socrates is human."

That's a valid syllogism.

But Heilbron's example is the equivalent of saying, "Socrates is a Greek. (All B are A.) Socrates is human. (All B are C.) Therefore all Greeks are human. (All A are C.)" Utter nonsense!

Conceivably, this could still be a typo, or a case where an editor, faced with two versions of the premise, chose the wrong one to keep.

Except that Heilbron goes on to explain that philosophers were regarded as superior to mathematicians because syllogisms were based on a consensus about the real world, and geometry was about pure abstractions that could not exist in reality -- a line without width or breadth, perfectly straight, etc.

But this is absurd. Consensus about the real world is a part of inductive logic, in which repeated experience leads to generalized, but perpetually questionable, conclusions.

Syllogisms, on the other hand, are loved precisely because they are abstract -- like geometry. They deal with validity, not factuality.

"All ducks are geese. Donald is a duck. Therefore Donald is a goose."

This statement happens not to be true because ducks are not geese at all.

But the syllogism is valid because if both premises were true, the conclusion would be inescapable. Syllogisms are about validity; truth is a separate discussion.

Then there's this syllogism: "All bucks are deer. One dollar is a buck. Therefore one dollar is a deer."

In this case, both premises are accurate enough. But that "buck" in one proposition is not even remotely the same thing as "buck" in the other. The coincidence of sounds ("buck" and "buck") is meaningless.

In fact this "syllogism" says, "All A is B. All X is Y. Therefore all A is Y." Silly. A pun, not logic. The syllogism is invalid regardless of whether the premises are true or not.

This is all elementary logic. But Heilbron writes as if he has no comprehension of the difference between syllogism, which is demonstratio potissima precisely because it is independent of reality and does not depend on consensus among philosophers, and induction, which derives conclusions from repeated, uncontradicted experience.

Induction says, "So far every living mammal we've found has a sequence of vertebrae enclosing a bundle of nerves. We therefore predict that all future mammals we find will also be vertebrates."

So then a naturalist in some obscure location reports (complete with photographs, videos, and X-rays) that he has found a furry creature that gave birth to living offspring and suckled its young, yet whose nervous system is not enclosed in a column of articulated bones.

The arguments that would ensue might be definitional: "Obviously, it's not a mammal." "No, it's not a vertebrate mammal." And so on.

Or they might be observational: "This specimen he used merely has a birth defect. It's a miracle that it lived to reproduce, but notice that its babies do have spinal columns, so the species is a vertebrate mammal, and this is merely a deformed specimen."

That is how inductive reasoning works: It relies on an assumption of universality, which is always tentative; there is always the unspoken "so far."

This is what science depends on to determine the truth value of a proposition; syllogisms are only to determine the validity of a conclusion drawn from two premises.

I know, how boring is all this? My point is that by page 7, in the first instance where Heilbron does what he promises his whole book will do -- attempt to explain the intellectual context in which Galileo was developing his thoughts and methods -- his writing is flat wrong and a hopeless muddle.

On pages 10 and 11, Heilbron writes about how Galileo returns to music, another "inferior" science but one which was pretty much the family business, since Galileo's father was an accomplished lutanist (lute player; early guitarist).

Heilbron carefully explains that Ptolemy's theory of music deals with the mathematical relationship between tones coming from divided strings. That is, the tone produced by a taut string of a certain length will be exactly one octave lower than that produced by an identical string of half that length.

Then Heilbron, after an incoherent couple of paragraphs in which he makes a complete muddle, using the terms "temperament" and "mode" without the slightest explanation of either, says:

"Referring to a 'simple-minded assertion of Zarlino,' father or son [Galileo or his dad] points out that to get a tone and its octave simultaneously from a single string, it must be stopped at a third, not a half, of its length...."

Heilbron presents this as if it were a contradiction of Ptolemy, but it is not. It is an affirmation, since the two-thirds of the string is exactly twice the length of the one-third, and therefore Ptolemy would have predicted that their tones would be an octave apart.

The argument about tempered pitch versus mathematical pitch was an important one at that time, and in one form or another it still goes on. But tempered pitch won in practical usage because it is so much simpler to work with.

That's why pianos are even possible. If the pitches were mathematically pure, the piano could play accurately in only one key, and any change of "key" would actually be a change of mode.

That is, you would only have the white keys, and the pitches would not be the distance apart that they are now.

But instead of that single true seven-tone scale, we use the "tempered" twelve-tone scale, each note exactly evenly spaced (in pitch) from the notes before and after. Thus you can begin a seven-tone scale from any of the twelve tones and it will sound "the same" as long as you skip notes in the right proportion.

The same piano can thus play in any key -- but all the keys are slightly off from mathematical purity. We simply adapt our hearing to accept the "wrong" notes (or at least a certain group of musical purists would say so).

Have I made it clear? Only to people who are already musicians, and probably not even then. But I have done a far, far better job than Heilbron does. In fact, Heilbron doesn't even try.

He just throws around words, and it quickly becomes clear to anyone who does know what the musical argument was about that Heilbron is completely clueless.

In other words, Heilbron has promised to explain the intellectual context in which Galileo was working, and by page 11 he has proven that he understands the root concepts of neither logic nor music.

If he lived in Galileo's time, and uttered these explanations (in Latin or Italian, of course), he would be sent out of the room while the grownups talked.

Heilbron then moves on to a discussion of Dante, and here again his handling of critical theory is just as muddled and unclear -- though since even when you understand exactly what was being argued about, the ideas are idiotic anyway, it doesn't matter as much.

So here I am with a book that has 365 pages of text, on a subject I care about, with glossaries and charts and footnotes galore, and before I get twenty pages in, I have reached the inescapable conclusion that the author does not understand his own subject matter.

He has come to the joust armed with a noodle.

How did the author of this incoherent, incompetent mess survive a long academic career and achieve his reputation? I will offer some logic here:

Premise 1. In the cutthroat academic world, someone would have noticed and pointed out such utter incompetence at many points in Heilbron's career, which would have destroyed his reputation.

Premise 2. He had a fine reputation.

Conclusion: During his academic career, Heilbron did not make the kind of mistake, or write with the kind of incoherency, that we see in this book.

The publishing company gave Heilbron a contract because they thought they were getting the Heilbron who earned that good reputation.

But surely someone in the editing process noticed that the manuscript was utter nonsense, completely useless and unpublishable. Surely that editor said to some executive, "Heilbron's lost it. I ask him about these incoherencies and obviously wrong statements, and he gets angry and tells me to print it as he wrote it."

Here's where a merciful publisher would have said, "All right, let's quietly let this one go. Return the manuscript to him and tell him we're canceling the project. We won't ask for the money back unless he sells it elsewhere -- which won't happen because once they read the manuscript, no one else will publish it, either. So we've lost the amount we gave him as an advance. But at least we won't lose any more money editing or printing it, and his reputation won't be hurt at the end of his career."

But no. Either there was no editor, or the editor was incredibly lazy or incompetent, or the publisher said, "We've already sunk a lot of money into the advance on this book, and it's too late for us to get another book out in time for the 2010 quadricentennial of Galileo's greatest discoveries. So clean it up as best you can, and we'll publish and promote this book as if it actually had value."

"But won't people read it and be angry with us? Won't the reviewers crucify us for such a fraud?"

"Most people who buy it will just put it on the coffee table or in the stack by their bed and never get around to it. Most reviewers are Heilbron's friends and they won't be mean to him. The few reviews that actually point out the flaws will be ignored, and anyway, the only way we'll make any of our money back is to publish a book and sell as many copies as we can, so get back to work."

I admit, I'm a fiction writer. But there must surely have been such a conversation, even if it was only inside the mind of the publisher who decided to go ahead and publish this embarrassing mess.

The flap copy says, "In this fresh and frank portrait, John Heilbron captures the hero and martyr of science with a wide-angle lens, which takes in the landscape of culture, learning, religion, science, theology, and politics of late Renaissance Italy."

Every phrase of that flap copy is a lie. But since it was probably written before the manuscript was turned in, the person who wrote it was not the liar. The liar was the person who went ahead and ordered the book printed, knowing that the Heilbron who earned his academic reputation was not the Heilbron who piled together this jumble of half-remembered, mostly-incomprehensible facts.

This book is actually an example of mental deterioration with aging. It's a tragic footnote to a distinguished career. The publisher should have had too much respect for the real John Heilbron to publish this book by the man who was by then using his body.

Galileo, by John Heilbron, is an evidentiary document in a discussion of publishing ethics. It is not a useful biography of Galileo or a reliable account of his times.

One more tragic entry in our long list of "lost products." A few years ago, Reynolds -- known for its aluminum products -- introduced a line of plastic wrap that was far superior to any other cling wrap on the market.

They also offered the best (i.e., longest-lasting, stain-free) plastic fridge-to-microwave containers we've ever used.

The containers were gone before we could stock up on them. We did stock up on the plastic wrap, though.

I wish I had bought twenty cases instead of one. Because we're finally running out of them, and yes, Reynolds is no longer making its wrap.

The most frustrating thing is that the Reynolds plastic wrap we loved came in a package with an "EZ Slide" dispenser. Instead of having to tear off a sheet on a serrated edge that is likely to cut your fingers, you simply slid a plastic glider along the rim of the box and get a perfect edge every time.

Of course we were throwing away these EZ Slide dispensers when they ran out of plastic wrap. But we realized our mistake, and now we have two left.

We will take the rolls of Glad Wrap that we're now using, and put them in the Reynolds EZ Slide boxes. Meanwhile, we will curse the fact that these brilliant Reynolds products have gone the way of the Scrunge -- the best product, lost forever as we are forced to make do with inferior competitors.

http://www.hatrack.com/osc/reviews/everything/2013-04-18.shtml