Immigration Reform -- Is there a Right Way to Do It?

I don't think so.

There are two sites at which immigration occurs: the border with Mexico, and everywhere else.  The southern border is essentially a semi-permeable membrane, and the trickle of people through it is virtually inevitable.

There are two kinds of smuggling, too: drugs entering the USA from Latin America, and everything else.  The demand for drugs in the USA is so great that the customs barriers are also semi-permeable, and the flow of drugs is inevitable.

It seems clear to me that the economic realities of Mexico and the USA are difficult or impossible to change, given the vested interests of all the parties involved.  So the economic pressure to keep illicit immigrants out can only do so much to stem the flow.

On the other hand, the demand for drugs --essentially recreational drugs, even if the term seems hardly appropriate for the vast majority of users-- has little or nothing to do with the massive economy of the USA.  This demand certainly can be changed.  I would like to see all those who are supportive of the new Arizona Immigration Law try to persuade any of their friends who are part of the drug culture to give them up for a year!  Ha ha, just kidding; druggies can't give up anything for a year.  The puzzle, for American drug lovers, is how to keep the drugs in and the Mexicans out!  We've come to think of Mexicans not as thinking, feeling human beings, but as mere obstacles to the American Way of Life, or AWL.  (In actual fact, they make a good deal of the AWL possible.)

How many of these drug users are there, anyway?  Are there just about 15 people in the USA who buy and snort all the cocaine, or are there millions who do little bits of it every day?  How many people will we be upsetting if we make use of illegal drugs a capital offense?  Now there's a lovely thought! How many people will we make happy if we make all (recreational) drugs legal?

But in Better Mousetrap Land, there just has to be a way of shutting the borders to illicit immigrants, while keeping them open to the drugs, for those who want them.  I've given up getting all upset about the contradictory desires of my neighbors.  (Huge cars AND great mileage.  Easy job, requiring practically no education AND big paycheck.  Big meals AND slim figure!  Small Government AND powerful military!  Huge polluting trucks that haul cheap food AND clean air!  Lots of unprotected sex AND no pregnancy!  Lots of yummy drugs from across the Mexican border, BUT no actual Mexicans.  Tons of garbage AND not in my back yard!  Luckily we have Pennsylvania.) 

Still, it seems silly for Mexico to complain about the USA Immigration policy, when theirs is so draconian.  A guest-worker program would make sense, though there are sure to be some disadvantages to it.  The one thing that it makes no sense to demand of the Mexican government is that they should improve the economy of their country.  That's as silly as telling Washington to just stop our own Economic Recession.

Arch.

An Interesting Project for Everybody

At the risk of repeating advice you might have heard elsewhere:

Write your autobiography.

Writing is a good thing to do.  I don't mean sending text messages or quick e-mails in code.  I mean considered writing, where you have a chance to go back and fix what you need to fix, add, change around, clarify.  Writing, said the man, clarifies your thinking.  Not that I'm saying your thinking needs to be clarified; it's just that all of us have ideas that could be useful to our friends and our colleagues, and setting them out clearly could just be a service to everyone.  If you were to keep a blog, such as this one, you're not going to force anyone to read the thing, and anyone who took something away from it would come back eventually to check it out.

Writing fiction is an interesting thing: why write fiction?  I began to write fiction just for my own amusement, and very soon it became a hobby that I took a lot of delight in.  But an enormous first step was writing my own autobiography.

I started one day some 15 years ago, typing it into one of the computers where I work.  Back then, they only had what we now call mainframes: computers with wires going to many offices, and each person could maintain his or her own files in the computer, until every once in a while someone came round telling you to get rid of any files you did not want!

For various reasons, having typed in close to 15 years' worth of reminiscences into the project (just an enormous text file, really), I went away one summer, and came back to find that they had moved the files into a newer mainframe, and my de-crypting routine was now useless.  I could not read my own autobiography, because I had encrypted it with a computer-specific procedure.

Anyone who starts such a project today, of course, will never have the same problem.  Encryption is no longer really necessary, because very few people have others fooling with their files, in the first place, and security is fairly uniformly well understood.

A very good reason for writing your autobiography is that you're probably not going to get stuck for material.

You start out with a brief biography of each of your parents.  Make these brief, because you can always expand them later.
Describe your older siblings, if any. Describe the time and place of your birth.  Alter the facts, if you're nervous about privacy.
Fill in year after year, as much as you remember.  To help you remember: always record where you spent the important feasts in your family: Thanksgiving, Christmas, Easter, etc, and any antics you, your siblings or your friends got into.  Record acquisitions of things important to your family, e.g. bicycles, yachts, automobiles, skates, etc; even private jets are good.  Record the arrival of younger siblings, and marriages and any other catastrophes visited on your older siblings.

Make sure you pay homage to any good teachers you have had.  Teachers get very little credit in this society, and make sure you do your part to correct this defect.  Big political events are natural milestones in an autobiography, especially your reaction to them at the time, and your thoughts looking back.  Students you admired in school, big victories in high school that you remember; your driver's license.  High school sweethearts, the ones that got away, and the ones you could not escape.

My own autobiography was centered around Christmases.  Music was big in our family, and I wrote as much as I remembered of each Christmas.  Our mother was often a resource-person for the musical and dramatic events wherever we happened to be, so that we were swept along with the general enthusiasm of our neighbors.

You can stop it anywhere.  Keep it ready, if you ever want to do something with it, or just leave it to your descendants, or just delete it when you think might forget how to do it pretty soon.

Good writing!

Arch

Oil Spill

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I'm beginning to think that this oil spill might be the true disaster of the decade.  It could easily happen that British Petroleum cannot, and will not, contain the leak.  Because of the precarious state of the national economic situation, the federal government cannot ask the oil company to step aside, and get the big engineering companies and the universities to work on the problem; one has to think that the cost-conscious oil company is going to be very cautious in spending money on the gusher.

The more everyone delays and takes a cautious approach towards the containment problem, the more destruction there will be before things get better.  The political opposition is licking its lips in anticipation of some serious finger-pointing.  This could easily be worse than Katrina.

One also sees the incredible richness of this particular well.  BP would have raked in the dollars on this one for years.  As it is, they might be completely destroyed by the cost of the clean-up, if the rest of the country has the guts to insist that it should be done right, and done quickly.

It is stunning to think that the downfall of the Obama government might just be not a war, but a stupid oil spill.  We can speculate that BP is forced to pull out their biggest clean-up guns sometime at the end of, say, 2011, after the oil has had a chance to work its magic on the gulf coast, and after more than a year of miserable mop-up efforts, the executives of BP will probably be rewarded with the biggest bonuses in history!

A

Bottled Water

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I had forgotten just how furious this phenomenon of bottled water makes me.

It has become a multi-million-dollar business that simply generates tons of used plastic waste for the landfills, and gives very little in return.  In a recent (agonizingly slow-moving) article, Peter Gleich describes the history, the politics and the economics of the bottled water phenomenon.

Basically, the bottled water industry has capitalized on the suspicions that people have about the cleanness of their drinking water.  The purity of water is a local thing, but a news story about a breakdown in water quality in, say, Boston, sends people in, say, Los Angeles, into a panic, all carefully orchestrated by the water interests.  As Consumer Reports reported back in the eighties, out of the twenty or so bottle water sources they sampled both in the lab and by tasting, plain old NYC tap water was second best, right after some mineral spring water that cost an enormous amount of money (and I remember had slight traces of lead in it).

Of course, the bottled water people keep about a few thousand workers employed across the USA, but let's be frank: it is spectacularly unproductive work.  The executives of this sector of the business world must be among the most cynical in the entire world.  One of these days they're going to be selling clean air out of bottles, and goodness knows that in certain parts of the country it is needed, because of the determination of citizens to cling to the most polluting variety of personal transportation that's available.  When that day comes, I will simply break down and cry, because the combination of gullibility on the part of consumers and cynicism on the part of the marketers will just make me so furious.

Firstly, public water sources in the US are among the best in the world.  Local laws usually require that the water authority supplies a quality report periodically, and of course their accuracy has to be verified carefully, and the reports have to be read carefully, and corrective steps taken when needed.  But you can drink water right out of your tap most of the time.  Ask your local high-school chemistry teacher whether there is any objective reason to believe otherwise.  I would expect him or her to assure you that the water is essentially safe.

Secondly, bottled water quality is highly variable.  The Consumer Reports article on the subject that I read decades ago reported that levels of lead and rare earth ions present was startlingly high in certain brands of bottled water.  Federal standards for bottle water are very relaxed for mineral spring water, since such kinds of water, drunk for centuries as medicinal aids, often contained certain minerals that we would not tolerate in regular tap water.  At one time, bottled water companies circumvented the stricter limits for plain bottled drinking water by claiming their product was "mineral water", which it wasn't.  There have been a few reports that certain companies were selling plain tap water as water out of mountain springs.  In a sense, it is not wrong to say that tap water is from a spring: all water that is drunk, unless it is from desalinated sea water, is ultimately from a spring somewhere.  But obviously tap water is not what a consumer expects when a bottle of water is purchased.  This degree of cynicism would incite me to violence, if it wasn't so amusing.

Thirdly, as Peter Gleich points out, buildings such as stadiums are often built without sufficient access to water fountains.  This helps the stadium authorities make money from water vendors (and soft drink vendors).  Such situations must be fought relentlessly.  The claim that stadium authorities have a fundamental right to exploit their customers for profit at the cost of depriving them of a simple, free source of plain drinking water is American Consumerism gone mad.  How long will it be before kids in elementary school have to bring money to school to buy bottled water?

Fourthly, the containers, be they plastic or glass, must form a huge proportion of the waste of most urban areas.  I don't know where to look for statistics, but most of the plastic containers I see blowing around in the wind are discarded water containers.  There must be reports from State Parks, for instance, that set out what proportion of their waste disposal efforts are due to dealing with water containers.

This means war.  I declare war on this ceaseless onslaught of bottled water propaganda that people are subject to all the time.  This is one industry that we must never bail out: bottled water.

P.S.
1.  Wikipedia supplies an annoyingly even-handed article on the bottled water phenomenon.

2.  The National Resources Defense Council reports that Aquafina, which is Pepsi's brand of bottled water, is entirely from municipal tap water.
3.  The NRDC also has done a survey of why people drink bottled water, and the results are on their website.  At right is a cleaned-up version of their chart.
4.  Consumers' Union is essentially a private organization that exists to provide reports of consumer products for its members, and those who buy their magazine, Consumer Reports.  Frequently, though, they provide public-service reports, alerting the public to situations that need some degree of public mobilization.  Here is a report on the safety of bottled water.  Evidently municipal tap water must satisfy stricter standards than bottle water.

Performing a Google search on bottled water resulted in a host of web articles, most of them critical of the bottled water industry.

Arch

Camping!

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[I would like to dedicate this post to two friends who first took our little family out camping: Lise and Mark.  These two wonderful people changed our lives in lots of ways, and we have never been able to communicate adequately to them that this was so.]

There seem to be two kinds of people: those who camp, and those who do not!  Of those who camp, too, there are two types: those who use campers, or cabins, and those who tent.  Finally, all campers are split into two additional types: those who like to rough it out at state and federal park campsites, and those who like comfortable commercial campsites.

There really is no need to grab onto one particular style of camping; I think a mix of several types is likely to provide variety, which is good.  No matter what your choice, it's probably a good thing to keep an eye on how much pollution you're indulging in; after all, pollution impacts campers very directly; if the air, or the water, or the campsites were polluted with chemical fumes, or water-borne pollution, or just litter, camping is pretty disgusting.  No matter what their political affiliation and ideological positions, experienced campers are usually considerate people.  Camping in a camper, which means you don't use a tent, is actually a quite different undertaking, since you have to either drive your camper around, or haul it around, and it limits the places you can go.  Camping is fun without investing in a camper (several thousands of dollars).

So let's assume that you're going to be tenting.  The following could cost up to around $150 per person, but is equipment you would use for several years.

Equipment:

1. A tent big enough, or a couple of tents.  The tent packaging usually indicates its capacity, e.g. 4 adults (a biggish tent) or 2 children (a tiny tent).   Read the set-up instructions if you can, to make sure that you can handle them!  (A dry run in your back yard is worth every minute you spend on it, and also teaches you how to fold the tent up at the end.)
2. A camp stove.  There are tiny little stoves that you hook up to little propane gas cylinders (under $25), or more elaborate stoves with two or three burners (under $75) which burn white gas, which seems to be something like kerosene.  I'd make sure I knew what I was doing with the latter; the propane stoves are all you need, if you're not particular about your food all being piping hot. 
3. Sleeping bags for everyone (anything from $30 and up), and if you're very delicate, a sleeping pad on which to lay each sleeping bag.  These are around $15 each at present, but who knows.  If you don't plan to camp in ultra-cold locations --and I wouldn't, if I were you-- all you need is to select a reputable manufacturer, and get the cheapest bags they offer.  [Consider getting sleeping bags whether you camp or not.  It is a lot of fun for younger people to camp out on the living room floor (after it has been carefully vacuumed).  Most kids eagerly welcome any change of routine, but there are a few odd types who are already, at age seven, creatures of habit.  The characteristics of the kids you have usually reflect your own!]
4. A moderate-sized cooler in which to store your food supplies.
5. Cooking equipment: a fry-pan, a 2-quart pot, knives and cutting-board, a bowl, a little trash can, which you can improvise, really; sturdy cutlery for everyone (don't use disposable stuff; it adds to the burden of the campground, and these are marginal operations, really), potato peeler, maybe a wooden spoon and a spatula for cooking.  Cups and plates.  A scrunge and dish detergent for cleanup.

[Avoid paper towels if you can, but I know this is asking a lot in these days.]  In addition, you need to bring along such things as toothbrushes, etc, and if you absolutely must, a roll of your favorite toilet paper, just in case you're picky.  There usually is usable toilet paper available, your tax dollars at work.

When our friends first took us out camping, we started with the most rigorous kind of camping first, in our case in the Blue Ridge of Virginia in the Shenandoah Valley.  This is a state campground, which meant at one time that there were no hot showers.  One thing that I'm ashamed of is that I have to have a hot shower at least every other night, so camping under non-hot-shower conditions was not an option for three nights running!

Selecting a tent site

Get to your site early, so that you have plenty of daylight.

When you drive up to the office area of a campground --bear in mind that camping is a laid-back sort of business, and the staff are not highly driven, suspicious motel types, but usually casually energetic folk who get bored waiting at the check-in counter-- you tell them what nights you want to camp, that you will be using only a tent, and then select a camping site.  These sites are shown on a sort of map, or you get taken round to look at the sites, or you get sent off to scout out the campsites, and come back with the number of the campsite you like.  (There are usually numbers on little posts at each campsite, so they can identify the one you're interested in.)  They tell you how much it will cost per night, and what they're giving you: e.g. electricity, water, and so on.

The important thing is to select a campsite on a slight rise.  Ideally, you should pick a dry spot on a slight mound, so that if there happens to be a shower in the night, the water will flow away from your tent.  Either a sandy spot or a grassy spot would be fine; a gravelly or stony spot will be impossible.  If a slight rise isn't available, a dry flat area is ok.  (The fact that it's dry would suggest that water hasn't collected there, which is good.)  Or you can hope that it will not rain...

Once you've paid for at least one night, drive round to the camping spot, park your vehicle carefully so that it isn't in the way for other campers, and you have easy access to it.  Then you go to the selected tent spot, and carefully pick out any large stones or debris, and put it aside.  Then you put up your tent, following the instructions.  (Kids are usually very sharp at figuring out tents, but adult supervision will usually be required.  Watch out for fingers, if sharp edges are involved.)

Tents are usually structured to be held up by poles or rods that hold up the fabric, and guy-ropes or stays that keep the poles/rods in position.  Make absolutely sure that the guy-ropes and stays are firmly anchored.  Guy-ropes should be at roughly 45 degrees, for a good compromise between pulling down and pulling over.  Tent pegs should be pushed or pounded in as deep as they will go, given that of course you have to pull them out at the end of your stay.  Again, 45 degrees.

While you're doing other things, keep the food locked up in the trunk of your car, in the cooler; otherwise, little critters (e.g. raccoons) will come looking for it, and they chew through your tent fabric to get at the food.  Even as we speak, evolution is creating new raccoons who can chew through your car trunk! 

Food!!

This could easily be the fun part of camping.  Everybody should join in, because it is something to do, since you don't have TV!  Quite good food is possible to fix in camp; for instance, if you have a fry pan, you could fry a little bit of sliced onion in a tiny bit of oil, cube a potato, cube some beef, cut up some vegetables, e.g. beans, carrots, turnips, and make a stew.  Everyone should help, and after the stew is on the stove, you need to have something to do for about half an hour.  You should not put the stew on and leave the campsite; this is just asking for trouble.  Apart from fire disasters, there could be wild critter disasters.  (You could half-cook the stew at home, and finish cooking it at camp, as your first meal.)

Washing up!

You have to wash up after the meal, of course.  It's less work for when you're ready to eat again, and smells a lot better.  First, you scrape off as much of the food as possible, and put it in a trash bag.  [Often campsites ask you to sort your trash into Dry Trash (goes in the land fill, oh dear), Food and Organic (goes in a compost heap, hopefully), Recyclable (glass, aluminum, plastic); please cooperate as much as you possibly can.]  There is usually a faucet near the campsites to do some preliminary rinsing.  In our family, we usually took the pre-rinsed utensils to the bathrooms to wash out with the minimum of detergent.   Other campers occasionally frowned at this.

Amusement

State and Federal campgrounds have become adept at providing good entertainment for easily bored youngsters (who would otherwise get into trouble): there is often talks by rangers about the surroundings of the camp, e.g. the geology, the forestry, the wildlife, and the history.  There are often sing-songs and performances, usually with quiet guitars and folk instruments; occasionally a movie, and in the larger campgrounds, hikes and tours.  Yellowstone, for instance, has museums and other very elaborate features.

At commercial campgrounds, there are often many of the above: definitely music, and often a pool and sunbathing facilities.  But there's nothing to prevent you from alternating camp-style entertainment with books and Ipods.  Anything you want to do that doesn't annoy your fellow-campers is fine; so coloring with crayons: thumbs up; subsequently cutting up your drawing into a thousand pieces and scattering the pieces around: thumbs down!

Breakfast!

After a night's sleep --usually the adult in charge worries too much to relax, but everyone else sleep like logs-- a good breakfast simply puts the crown on a successful camp night.  Most campers are big breakfast people, and with a little practice, it is possible to make the usual delightfully cholesterol-filled bacon or sausage and eggs, and maybe pancakes, too.  Whoever is fixing breakfast has to start early, because you usually only have one burner.  You have to decide whether you prefer to have eggs cold, or pancakes cold... I used to know clever ways of heating them up at the end, but I have forgotten.  (I never learned a decent way of dealing with leftover bacon grease; there has to be one...)

The cold cereal people are usually easy to please; a small amount of milk could have been brought in the cooler; milk is usually available at campgrounds.  It used to be interesting to taste milk from campgrounds across the country; now it probably all comes from Big Milk, as it is called, and probably mixed so that it has no taste whatever.  Cold cereal, of course, is easy to transport.  All the dry goods should be stored in a box or container that is easy to haul from the car to the camp table and back.  Again, wash the containers and bowls before putting away, to make your daytime exploring pleasant.

Hot cereal and oatmeal is a natural at camp; there is no special trick to it.  Cooking oats at camp is a bad idea, just because you're often left with a layer of oatmeal lining the pot, which has to be thrown away.

Lunch

should ideally be cold cuts, or pasta salad, or something you buy on your exploring trips.  Campgrounds will usually sell you prepared lunch-type food, but it is usually easy to get cold cut supplies from a neighborhood deli, and make your own sandwiches.  Sandwiches, too, can be eaten in the car (if you don't mind doing that), so that you can eat while you're headed back to camp, or while you drive from one attraction to the next.  If the whole group doesn't share responsibility for serving the food and clearing up, some person usually doesn't get to enjoy the camping trip very much!  On a first trip, every effort should be make not to get so fancy that you find yourself in trouble, nor so basic that you don't enjoy yourself.

Coffee and Tea

Most adults like one or the other; in cold weather, young people like hot chocolate.  So a billy can in which a quart or so of water can be heated up is useful.  Most people know how to improvise hot chocolate from dry packets.  Tea is prepared exactly the way you do it at home: boil the water, pour into a cup in which the tea has been put (bag or loose), let it steep covered, wait until the leaves sink to the bottom (if it was loose tea) and drink.

Coffee is made like tea.  Bring a small amount of your best coffee.  Boil the sweetest water you can get --you might need to buy a bottle of water if you're a coffee connoisseur.  Now you need a coffee-pot (or a tea pot; just a heavy container with a spout) into which you pour a teaspoon of coffee per person.  Pour in the hot water, wait for 3 minutes (or longer, if you must, but not so long that the coffee loses heat), and pour out.  The weight of the coffee-pot should keep it warm.

Practice at home, if you're motivated enough.  I often put less water into the coffee than I think I need, because if it's too strong, you can always dilute it with the leftover hot water.  If it is too weak, you can't do nothing.

Take as little as possible with you

The charm of camping is to improvise entertainment for yourself.  Kids tend to think of entertainment as flowing from toys and other objects.  In camp, though, the best entertainment for kids flows from adults, and the best entertainment for adults flows from the kids.  Older kids often make friends in the camp, and could be left to themselves, after a quiet check that they're not hooking up with kids who look frighteningly suspicious, or young adults of the same description.  Some guidelines such as be back by eleven, or play where we can see you go a long way towards making everyone comfortable with the situation.  Constant vigilance is probably good advice; you need to gradually find out just how much you can rely on the kids to stay out of trouble.  (You don't want your kids to get the kids of other campers in any sort of danger, either.)  It is usually a lot of fun when junior drags in a friend from a site across the way!  He or she will talk about this friend for days.  And she's probably going to be called Courtney, and is probably going to be from Florida, and you're going to wonder why the heck they have to come so far north, while you would give anything to live in Florida.

Leave your campground better and cleaner than you found it.  You may hate everyone outside your own family with a passion, but when camping one usually sets aside one's prejudices and makes sure that one doesn't sabotage the camping experience for other campers.  Consider transporting dry trash back home, e.g. paper, aluminum, plastic, etc, since you know how to recycle it at home, and must find out at camp.

Take sunscreen, anti-histamines, pain-killers, band-aids with you.  A small bottle of generic shampoo taken with you would save you a little money; baby shampoo will do for everybody.  Most places you would go on vacation will have the usual things you have at home, even if in an unfamiliar form; for instance, in Canada, Sweet and Low has slightly different ingredients and tastes different, and is, of course, labeled in both English and French!  Gasoline, of course, is sold in Liters (more or less the same as quarts) and costs a little more.

A.

How to construct a regular Pentagon using only circles and lines

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We first need to practice doing easy things such as making a perpendicular to a given line at a given point.  This is not too hard:

A perpendicular to a line at a point

Suppose our line is l  and our point is P. Here we go.

1. Obtain any point on the line other than P. [This is a more common request than you might think.] Call this point A.
2. Make a circle centered at P, radius PA. This circle will cross the line l again at another point, call it B.
3. Make the perpendicular bisector of AB! This will go through P, as desired, and be perpendicular to l.

Next, let's create a line of length √5.  For this purpose, we first note that 2² + 1² = 5.   So if we make a right triangle with its two shorter sides of length 1 and 2 respectively, its longest side (its hypotenuse, that is) will be the length we want.  This is not too hard.  In what follows, let's denote the length of a line segment AB as |AB|.  The notation AB will continue to represent the line segment itself.

Segment of length √5

[Actually, given a segment AB, we're going to construct a segment of length √5|AB|.]

1. Given: segment AB.
2. Construct the line AB.  In other words, extend AB in both directions.
3. Make a circle center at B, radius BA, and let it cross the line again at C.  At this point, |AC| = 2|AB|.
4. Draw another circle, center C, radius CB.
5. Draw a perpendicular at C.  This will cross the last circle at two points; just pick one of them, and call it D.  CD, of course, is the same length as AB.

Let's give you a picture to look at here.  If all has gone well, the triangle ACD is a right triangle, one side has length 2|AB|, and the perpendicular side has length |AB|.  The hypotenuse (the third and longest side) will have length √5|AB|, so the construction will be complete.

The next step is to construct a segment whose length is ½(1+√5).  If you think about it, this is just the average of the numbers 1 and √5.  There's an easy way of doing this generally.  If you want to find a segment whose length is the average of the lengths of PQ and RS, it's easy:

1. Base the construction right at PQ.  Extend the line PQ past Q.
2. At Q, construct a segment QT whose length is equal to RS.
3. Now PT has length equal to the two given segments combined.  But you want the average.  So, find the midpoint of PT; call it M.
4. PM has the length you want.

Construct a Pentagon!

We're going to build a regular Pentagon on a given side AB.

1. Construct AZ along the line BA so that |ZA| = √5|AB|.  (All we have to do is, working with the previous figure, draw a (large) circle, center A, radius AD.  This circle should cut the line AB on the far left of A at some point Z.  That's the point we want.
2. Construct a point Y on ZB so that YB is ½(1+√5)|AB|.  To do this, let Y be the midpoint of ZB.  (Why does this work?  ZA has length √5|AB|, AB has length |AB|, so put them together, they have length (√5+1)|AB|.  When you find the midpoint, the right half should have length as desired.  We show you a picture up to this point, and from here on, we will make these early construction lines very light and grey.)
3. Draw a circle of radius YB centered at B.  Why?  Because the third point from A (oh dear; I could have called it D, but I've used it up...), call it E, has to be on this circle, because the radius of this circle is the length of the diagonal!
4. Draw the perpendicular bisector of AB.  Why?  Because the third point from A, which we have called E, must lie on this perpendicular bisector, just from common sense.
5. The next steps might be a little surprising at first: construct the circle passing through A, B and E, and using circles in the obvious way, find the two last points of the pentagon, which must both lie on this circle.

Well, there you have it.  It is sometimes useful to look at a process in large stages:
First, construct a line whose length is √5|AB|.
Secondly, use this segment to construct another segment whose length is the average of the one above, and AB itself.  This is the length of the diagonals of the Pentagon.
Thirdly, draw a circle with radius equal to the diagonals at B (or at A; doesn't really matter), and construct the "highest" point on the Pentagon where this circle hits the perpendicular bisector of AB.
Finally, construct the circumcircle of the three points of the Pentagon you've got so far, and using circles of radius AB, mark on the circumcircle the remaining two points of the Pentagon.

This is a quite complex construction, even if it is short.  It is algebraic in inspiration, since we base it on the theoretical length of the diagonals.  The various alternative constructions of Pentagons are all extremely informative about the properties of pentagons, and the concepts of geometric rule-and-compass constructions generally.

A.

The Pentagon!

For more than 2500 years, the regular Pentagon has held a special place among the favorite shapes of mathematicians.  Pythagoras practically invented the idea of mathematician back around 500 BC (when he should have been spending his time trying to prove his famous theorem; actually there are almost-proofs, or demonstrations, that are attributed to him).  He and his friends organized the very earliest known secret society of math geeks, called the Pythagorean Society.  Back then people were very conservative, and would have killed you if you told them that numbers other than simple fractions existed, like, say Pi.  (There are stories that Pythagoreans were pushed off ferries once they were discovered.  At least today they would have merely prayed for your death.)  So what's the punchline?  The Pythagoreans used the regular Pentagon as their secret symbol.  To this day, many of the mathematics societies have a pentagon somewhere in their insignia, or at least a 5-pointed star.  (At left is the logo of the MAA.)

[Added later:  I just realized that the MAA logo has little or nothing to do with a pentagon!  It is a so-called Icosahedron, a polygon with 20 faces.  But, as it happens, if you join the centers of every neighboring pair of triangular faces together, you get a companion figure, called a dodecahedron, which has all pentagonal faces.  Even in the figure at right, you can discern a number of pentagonal caps; in fact, every point is the center of a pentagonal cap.  Anyway, I still feel silly about that mistake.]

Incidentally, Pythagoras’s Theorem does play a part in the celebration of the Pentagon below:  If you have a right triangle (one of its angles must be 90 degrees; in other words, it must look like a rectangle cut down its diagonal), if you build three squares on the triangle, one on each side, the area of the largest one will be equal to the areas of the two smaller squares added together.  Above right you see a well-known instance of this:  There is a right-triangle, and squares on each of its sides.  The two smaller squares have area 9 little squares and sixteen little squares, and the large square has area 25.  Note that 9+16=25.


Let's look at a regular Pentagon a little closely.  A regular polygon always has all its sides congruent to each other, and all its angles congruent to each other; if you were to rotate it carefully, we could never tell the difference.  A little arithmetic, and the fact that the angles of any triangle have to add up to 180 degrees, tell us how much each of the inside angles are.  Here's how:

1.  There are 5 angles at the center (one from each of the little triangles I made by joining the sides to the center).  Those five angles must all be equal to each other, and add up to 360 degrees.  So each one must be 360/5 = 72 degrees.

2.  Now, all the five little triangles are identical, and because each of them has two equal sides (the spokes from the center), the remaining two angles must be equal.   This is a basic fact about so-called isosceles triangles.  Consider one of the triangles; one angle is 72, all three must add up to 180, and the two unknown angles have to be equal.  That makes each of them 54 degrees.  So the inside angles --the wide, shallow angles of the pentagon itself, without the radial lines-- are 108 degrees each.


3.  Now, we look at diagonals.  The diagonals of a Pentagon are fascinating, for a reason that will emerge shortly (but will perhaps not impress everyone equally).  Let's name the points of the Pentagon A, B, C, D, E, starting at the top, and consider the diagonals AD and EC.  It seems reasonable that all the diagonals must be the same length.  Now look at triangle EDC.  We can do the same trick as before: all three angles must add up to 180; angle D is 108, we know, the other two must split the remaining 72 degrees between them equally, so they must each be 36.  Looking carefully at triangle CXD, we discover that angle XDC is 108 − 36 = 72.  The remaining angle must also be 72, so triangle CXD is isosceles!  The side CD is a, which is what I'm going to call the length of one side of the Pentagon.  So the segment CX must also be a.

The little triangle EXD is a scale model of EDC --we call them similar triangles.  Similar triangles have proportional sides; so CD/EX should equal CE/ED.

Now EX = EC - CX, which is the same as EC − a, since CX and CD are equal in length.  So our similar triangles equation can be re-written
a/(EC−a) = EC/a
which can be simplified by multiplying through by a(EC−a) to get a² = EC² − a·EC.

This is a fascinating equation, as promised.  Suppose we represent the unknown length of the diagonal EC by x; the equation becomes x² − ax − a² = 0. This is what we call a quadratic equation in x, since a is unknown but fixed.

Now, most of my readers are probably thinking: hey, we didn't escape from Algebra 2 just to have to come to your blog and solve quadratic equations for you.  So I will graciously solve the equation for you: the answer is .

What in the heck is that?  It turns out that this is the fabulous Golden Ratio.  It is the ratio of the longer dimension to the smaller dimension of a kind of rectangle which the renaissance Italians thought was perfect.  Why is it perfect?  Because the part of it which needs to be trimmed off to make it a square is itself a perfect rectangle.  The ratio between a diagonal of a Pentagon and its side is the same as the Golden Ratio.  (For those of you who are of an algebraic disposition: if you take the fraction above, duplicate it with a minus sign instead of the plus sign, and multiply it into the original Golden Ratio, you should get something interesting! Heh heh heh ...)

4.  Now that we know the length of the diagonal, we can actually build a Pentagon, using only ruler and compasses, if only, given a line segment of length a, we can build another line segment of length .

It is not too difficult, merely long and drawn out. To practice, we could start with trying to construct a segment whose length is the square-root of two times a.  We'll do that another time...

A.

My Own Funeral

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Let us be absolutely clear about this: I'm not planning to hand in my slide rule in the immediate future; I have quite a lot of mileage left in me.  But I did get to thinking that, when I die, being an atheist, my family would be at a loss as to what to do with me.

1.  Well, I would certainly like to be buried, without embalming.  Cremation is an elegant idea, but what the world needs right now is not elegance, but practicality.  This is just one place where the Muslims are way ahead of us; they bury their dead wrapped in unbleached vegetable-fiber cloth, enclosed within five boards (four sides and top; the bottom is left open to the earth) of untreated lumber.  Treated lumber contains insect repellent, whereas what we want here is to let the insect (and other sub-surface critters) to have at the body, in the natural order of things.  Cremation, in contrast, pollutes the air rather fiercely.  There is heat pollution, and not least, release of a number of gases that mess up the air and contribute to the greenhouse effect.  The Ozone Layer alone is probably left unaffected.  So I urge everyone to consider popularizing the Islamic burial traditions, which really do not even require a coffin.

2.  Afterwards, the friends of the deceased (which means "the lately dead" or "recently departed", rather than "the sick person", which would be spelled "diseased") traditionally gather for a funeral, or a memorial ceremony.  (Actually, now I remember, the funeral is before burying, and the memorial is roughly a month after.  A wake is, er, I don't know.  It is an Irish thing, and I'm not Irish at time of writing.)

In a religious funeral ceremony, the ostensible purpose is to commit the soul of the absent friend to the care of God.  In actual fact, it is for a ritual comfort to the bereaved.  It is hard to have someone die on you, and then suddenly find oneself all alone; at least at a funeral you get fussed over, until you're finally ready to be by yourself.

In Christian rituals and ceremonies, make no mistake, there is always an element of education.  Propaganda is hurled at the audience at every opportunity; this is not what is bad about it, but that it is propaganda about unworthy and unnecessary beliefs that actually hinder society and individuals.  So it seems reasonable that when an atheist dies, even if propaganda is not indulged in, it is an opportunity for reflection and education.

3.  I would dearly like some music.  At the very least, (or even in addition to other things that might go down,) a musical concert with the favorite music of the late departed would make enormous sense.  Play a lot of Bach, Brahms, Mozart, maybe even Beethoven, heck, even Rachmaninov's Vocalise.  (Stay away from Barber's Adagio, because that was used for an Agnus Dei for choir by Barber himself.  Not that I would object to Christian music, but that I was so decidedly an atheist, and from such a young age, that Christians would probably object to having their music sullied by association with me!!!)

[Added later: My friend Susan suggested Schubert, and I stumbled upon An die Musik: To Music, sung here by Kathleen Ferrier.  Schubert, who died young, did nevertheless re-invent German art-song.  His predecessors had brought the aria to great heights, but Schubert showed how the piano-accompanied Lied, or song, could be a vehicle for poetry, where the text was at least as important as the music.

Here is Elisabeth Schwartzkopf singing this powerful song: Im Abendrot, by the post-Wagnerian Richard Strauss.  The same song is sung by American Renee Fleming, if you care to look for it.  The long lines demand great breath control, and Ms Fleming does a great job, though she does breathe all over the place.  Her voice sounds lovely even in the lower register.]

4.  I would like some readings from rational and wise atheists.  I'm not into reading inspirational atheistic writings (or inspirational writings of any sort), but I wish there were some I was familiar with.  Part of what Christians do so well, is to give inspiration and encouragement to each other; if only they would do it for the right things!  The most inspirational things written by atheists [that I know of, anyway] have been to point out why atheism is good, rather than evil, but this has usually been done by pointing the unavoidable finger at religion, and one wishes to keep the tone nice and positive.  Bertrand Russel was great; he would not have prayed for anyone's soul.  [Note: he was ruthless at condemning religion.]  Now there's a guy who would have laughed at taking out a prayer contract on B. Obama!

5.  I would like some humor!  If my estate were large enough to fund hiring a comedian or humorist, that would be awesome!  That Jon Stewart is really funny, and evidently an alumnus of William and Mary.  I would have said that either William or Mary would have suited me fine.

6.  I would love some non-religious song, and this was going to be the central point of this post: is there inspirational song that does not invoke religious ideas?  I guess this is going to be a summer project for me!  It was never an issue for me personally, since I was perfectly happy to listen to Christian sacred music.  But it is a philosophical obligation to find out what is out there, and I should.  I will report if and when I find enough interesting stuff for you.  So there; you have lots of stuff to do when I'm ready to push up the daisies and dandelions, the privilege of anyone whose body is not embalmed.  (If you're embalmed, you're not going to be pushing up anything; your neighbors would have to do it.)

A.

The Twisted Prayers of the Fearful

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Recently one of my aunts died.  Her decline had taken a number of years, but she was so ill at the last, that to us who watched her husband suffer with her felt that death was a merciful release.  (I realize that this language is borrowed from Christians, and this is particularly ironic, because I want to write about the quandary in which an atheist finds him- or herself.)

My aunt's greatest joy and satisfaction was to be the librarian of her choir in Phoenix.  It was a large church, and it had an enormous organ, and vast quantities of choir music that it had accumulated over the decades, and my aunt was the one who painstakingly kept track of who had borrowed which items, and got them back with great persistence.

In her youth she had an incredibly high and accurate soprano.  I remember her singing an octave above everyone else, when we were all together on this pilgrimage to honor a team of missionaries who had traveled a great distance to bring The Gospel to the heathens.  To believers, such great endeavors are evidence that God Exists.  But we are all aware that a dream need not be real to inspire people to mighty things; false dreams continue to inspire individuals to both wonderful and horrible things.

Since my uncle was unfamiliar with church music, and in any case not in a fit state of mind to focus on a funeral service, and since, despite all my atheism, I was; and above all, since my aunt's life had been given a great deal of structure and (probably) meaning by her church, I found myself setting aside my determination to keep away from religious things, and undertaking to collaborate with the funeral music.

Rather than the dismal dirges that are common in funeral services (or whatever you want to call them!), I decided that we should open with a hymn of praise, a versification by the great hymnodist Joachim Neander of psalm 150 for which my hero, J. S. Bach had provided harmony.

It begins: Praise to the Lord, the Almighty, the King of creation!  It continues with noble and poetic sentiments; the CyberHymnal has all of the numerous verses, most of which I was familiar with, though I had chosen it primarily because I associated it with a generally uplifting mood.  But then, to my deep regret, we came to the following verse:

Praise to the Lord, who, when darkness of sin is abounding,
Who, when the godless do triumph, all virtue confounding,
Sheddeth His light, chaseth the horrors of night,
Saints with His mercy surrounding.

Though the psalmist here uses the word "godless" to refer to the enemies of Israel, modern congregations would surely take the word to mean atheists.  This prayer was saying, inadvertently or intentionally, "Praise the lord, because when atheists succeed making believers really upset, He shines his light, and gets rid of the Horrors of night (probably more atheists), and protects his Saints with his mercy."

Well, I had only myself to blame.  A regular hymn, such as "Abide with Me" would have focused on general misery and despair, and left us atheists out of it.  But noo, I had to be different.  Fortunately, the other hymns were OK (The Lord's my shepherd, and For all the Saints), and almost everyone, without exception, were glad that the dirges had been left out.  But they didn't know that I had endorsed a hymn that prayed for chasing me off, if indeed I were to be identified as one of the horrors of night.

Recently, most of you must know, a group was set up on FaceBook to pray for the death of Barack Obama.

On one hand, this is amusing.  But the implications of this prayer are interesting to list.

• If the group is serious (and I doubt that they are, really), they have made a mockery of what prayer is supposed to be for.  I'm by no means an expert, but prayer isn't intended to petition the Deity to kill off inconvenient people.
• If the group is an attempt at humor, it is interesting that the believing community tolerates it.  Evidently cynicism is alive and well in Christian America!
• It seems to suggest that Barack Obama alone is responsible for all that a particular sector of the population considers bad or undesirable --bad enough to take out a prayer contract on him.  This ascribes greater powers to the President than is warranted by the facts.

Finally, FaceBook appears not to regard this group as founded on Hate Speech, and refuses to shut the group down.  Meanwhile, a number of FaceBook members have started up a counter-group to petition FaceBook to shut down the Prayer group.

One of the most fascinating --and amusing-- features about this prayer business is that we atheists are puzzled over how to respond.  To take it too seriously, of course, would seem to suggest that despite our skepticism, we believe that prayer is efficacious.  (To the extent that it focuses the feelings of the person who offers one, it probably is efficacious, but that is far from the objective of a typical prayer.)  This is repugnant; if there is one single thing that is part of the agenda of all atheists, it is probably to wean The Faithful away from prayer, and towards positive and productive action.  So we're left wringing our hands in futile and ineffective dismay.  It is left to those among The Faithful with a conscience to point out the wrongness of it.  In the present case, such individuals seem very few.

If it is hate that inspires such a prayer, I can only feel sorry for the individuals concerned.  Those who support such Obama initiatives as overhaul of the health system and overhaul of the financial system cannot possibly have ulterior motives --unless it is perceived in certain quarters that success in these areas will result in certain political parties being seriously discredited.  (It is sad that all those who are outspoken about their dissatisfaction with  Congress take each of its success as a personal defeat.)

If it is fear that inspires this sort of prayer, just as it most definitely inspired the Psalmist, we must wonder why universal health care frightens people so.  How can anyone imagine that health care legislation is horrible enough to pray for a man's death?  It is both funny and alarming.  One has to wonder whether there's something in the water that makes people stupid.  Okay, taxes may go up, but people act as though the Dems are ruining the noble face of civilization!  I can't believe that the Insurance Industry alone is orchestrating this symphony of hate that is sweeping the nation.  What is going on?

Arch

Construction Strikes Again!

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Suppose you know the construction to find the midpoint of a line segment, as described in the previous post.  By now you realize that as a by-product, we also construct a line CD perpendicular to the original segment AB.  So, without making too much of a fuss, we know how to construct a perpendicular bisector of a given segment.

I was going to go on to the next construction, which was simply to construct a perpendicular to a given line, but wait; this is America, and we're not allowed to teach anything boring, just because it is good information.  (Oh sinful generation...)  Ok, so here's something a little jazzier, for instant gratification.  (Who knew we had that in geometry, eh?)

It turneth out (as King James might have said), that if you've got a line segment --call it, say, oh, I don't know ... how about AB?  Okay-- well, if you make the perpendicular bisector, every point on it (on the perpendicular bisector, that is, or bisectoris rectus, as Augustus Caesar would most certainly not have said, but I could be wrong) is equi-distant from A and B!

This brings us to an interesting result.  If you pick any triangle at random, it so happens that it is possible to draw a circle through the three points of the triangle!  Not everybody is as excited about this as we math folks are, but this is a fundamental fact of Euclidean Geometry (the geometry that seems to describe the world in which we live pretty accurately, and where the circumference of a circle of diameter 1 is Pi, and so on).

How one constructs this circle --called the circumcircle-- is interesting, and quite an easy application of perpendicular bisectors.  Why it happens to exist is another matter entirely, and at this moment I'm not totally feeling brave enough to embark on an explanation.  Maybe at a later time.

So, as indicated before, here at right (dextra) is a step-by-step diagram about how it's done: you just construct perpendicular bisectors of any two sides of your triangle; miraculously, if the third perpendicular bisector were to be drawn, all three of them would cross at the same point, and this is the center of the fabulous circle, which is all you really need.  Just for excitement, I show all the trillions of circles we draw to get the perpendicular bisectors; otherwise the sketch would look pretty dull.

Proof

Okay; it's tomorrow, and I've got a proof ready for you.  For this proof, we construct the first two perpendicular bisectors, mark where they intersect as O, and then, join O to the three vertices, A, B and C.

Since the two blue segments are perpendicular bisectors, the two yellow-filled triangles are congruent, so the big yellow triangle they form together is isosceles, which is what makes it possible to draw the circle in the first place, actually.

Similarly, the two green triangles are congruent, and the big green triangle is isosceles.

Now we have to show that if we were to make the third perpendicular bisector, it would go through O too.

How does one do such a thing?  We just mark the midpoint, M of BC, and join it to O.  Now if only OM turns out to be a perpendicular to BC, our point would have been proved.

But it is possible to show that the two purple triangles, OMB and OMC are congruent too (SSS, or "side-side-side", since we know already that OB and OC are congruent, from the earlier reasoning.)  So OM is in fact a perpendicular.  There can be only one perpendicular to a line at a given point, so OM is the perpendicular bisector of BC.  So that's how the whole thing works, QED.

Constructions!

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(I had a colleague --in Communications-- who objected to an exclamation point used in a poster for a mathematics colloquium.  He was of the opinion that exclamation points had absolutely no place in mathematics, and constituted a violation of the principle of truth in advertising!)

Anyway, constructions are a truly fun part of traditional geometry.  The idea is: how to build various geometric figures using only straight-lines and circles, or "ruler and compass," to quote the traditional phrase.

Here is a simple introduction to the subject.  It has the form of a game, with very stringent rules:

1.  Given a line segment, you can make a circle with its center at either end, passing through the other.  (In other words, your segment becomes one of the radii of the circle.)

2.  Given a line or circle, you can select any number of points on them.  (Actually, you can select any point that has not already been selected.)

3.  You can join any two points with a segment, a ray, or a whole line.


Well, that's it!  Obviously, you can also use a construction that you've described earlier, as part of a later construction.

Well, just to show you how this works, here's a simple example.

Midpoints
Given a line segment AB, it would seem that it is a simple matter to find its midpoint.  But the question is: can it be done using only rules 1, 2 and 3?  The diagram should make the following clearer.

Given:  The segment AB.

Step[1] Make a circle with center at A, going through B.

Step[2] Make a circle with center B, going through A.

Step[3] Name the points where the two circles cross C and D. 
(Does not matter which is which.)

Step[4] Join CD with a line.

Step[5] Name the point M where CD crosses AB. 
This is the required midpoint!

(Please excuse the gratuitous use of the exclamation mark above.  I shall feel free to use them at my discretion hereinafter.)

Once you get the hang of this and you realize that all that is happening is circles and lines, a simple diagram --or a sequence of diagrams-- is all you need to follow the construction.  Just click on the diagram (or double-click), and see whether the construction is clear.

The next two constructions: finding the bisector of an angle, and constructing a perpendicular both use this one.

Note: the constructions have very important geometric implications, but I'm not going to emphasize those.  I want it to be clear that this is just for fun, and there is no hidden educational agenda here, at least at present.

A.

Monetization: "Google Blogger" would like its bloggers to link to Amazon

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Generally speaking, the experience of blogging (for Google; yes, this is sponsored by Google) has been a rewarding and fruitful experience.  Google has raised to a fine art --and in most ways, an objective and non-intrusive one-- the technique of gathering information about those who browse pages.

Anyone who has uploaded videos to YouTube --another operation that is related to Google-- knows at least some aspects of the statistical information that Google collects.  They give you summary details about those who watch YouTube videos:

1. Their gender.  (Obviously YouTubers are not required to be honest when they give this information when they "join" YouTube.)
2. Their country of location.  (Again, YouTube must rely on their members to provide this information accurately.)
3. Their age.
4. At what point in the video they stopped watching.  This is a measure of how interesting the video is, and how interesting a particular point in the video is.
5. How they found your link; e.g. from an outside page (and when did this pattern start?), from another video, though their internal linking; through searching for a particular string using YouTube search, etc.

They also provide a graph of how many "hits" your video has received over time.

Other websites, e.g. the one that does the counter for this blog, also report (*) What operating system you're using [e.g. Windows, Unix, MacIntosh], (*) What browser you're using [e.g. Internet Explorer or Firefox or Safari, etc etc]; in short, things that would interest a software developer --which I'm not.

Lovely, though all this is, and despite the fact that I do review books and stuff on Amazon, thus far I have been an independent reviewer, not obliged to Amazon very much, except that a couple of years ago I consented to be a Vine Voice, which meant that I was permitted a few free books to review, in exchange for reviews of those books.  I have ordered a half dozen books (of which I really liked four) on that program, but now I have this blog, and Amazon is unhappy at losing their reviewer, and Google is eager to make some money out of my reviews for Amazon!  If I sign up for this program, I could get a portion of whatever money Amazon gives Google for sending customers their way via these blogs.  But readers would --justifiably-- suspect that the money I make out of the deal might bias my reviews.

What I would like is a non-monetized relationship with Amazon.  If I happen to give a favorable review to some book or piece of equipment, I would like to provide an easy link to that item on Amazon (and there's really nothing to stop me, even now); if I happen to give an unfavorable review, there is no need to provide a link.  So I guess that answers my own question; just leave things the way they are.

Independent Bookstores : a dying breed
At this point, I would like to make a pitch for your friendly neighborhood bookstore.

The big lesson that Wall Street and its endless tentacles have taught entrepreneurs is that starting small is a mugs game if you're going to stay small.

I was addicted to a game on FaceBook called Cafe World.  You cooked meals, and little figures (who represented your fb friends whom you "hired" --quite unbeknownst to them, I should add) served the food, and you made money.  Unless you expanded your operation, you were stuck with a few boring dishes, e.g. cheeseburgers.  Furthermore, you had to constantly revisit Cafe World to keep cooking for your customers.  This pressure to keep expanding was an artificial echo of the real-world pressure to expand.

Oddly enough, expanding does not always make sense in the restaurant business.  Many restaurants are successful precisely because they're small.  For instance, I knew a couple of restaurants, essentially sports bars, that were highly profitable.  They expanded one of their locations by taking over several square feet from their neighbors, but their sales plummeted.  Is there a lesson here?  I think so.

All across the country, the small independent restaurant feels pressure to link up to some giant franchise.  The franchise provides standardized food offerings, in return for the franchise presence in that locality; e.g. a small hot-dog bar in a remote village becomes a new McDonald's.  Hamburgers and fries are trucked in at regular intervals, obviating the need to obtain them from local suppliers.

The same thing is happening to bookstores.  I can only speak to what is happening here in my town.  There were a couple of bookstores, but they've mostly all gone out of business, except for one that specializes in comics.  The sole survivor in town must now compete with the giant Border's out at the suburban mall.

Does Borders provide a service that the small independent bookseller cannot?  Yes.  They stock DVDs and CDs, both of which are tricky and specialized sorts of merchandise for a bookseller to sell.  Furthermore, teenagers and 20-somethings who buy such things do tend to shop at the mall, rather than downtown.  However, I like to support the smaller bookseller for several reasons.

• The downtown area needs support.  If most of the interesting retailers quit downtown, it becomes the stomping grounds of addicts and vandals, in turn discouraging ordinary people from occupying the area in the evenings.
• The smaller bookstore enables one to browse, in the original sense of the term.  You can easily find --at a reasonable price-- something you were not expecting at all.  Browsing in a large Book Mall requires you to decide what genre you're interested in, and then browse withing the several hundred square feet devoted to that genre.  You can also look at the stuff on the discount tables, I suppose.  But the discount tables at the big mall bookstore are pathetically limited both in variety and value.
• The local bookstore provides a living for adults supporting families, in contrast to the the mall bookstore that employs much younger workers.  In my stage of life, I sympathize more with the aging professional than the younger seasonal worker.
• The workers at the local bookstore are amazingly knowledgeable about the books in the store.  The workers at the mall store are hard put to know where particular items are, and how their software works in locating these things; knowing anything about the items themselves takes an understandable back seat, unless they're among the 20 or so top-selling items at any given time.
• The profits of the smaller bookstore stay in town, whereas the profits of the big mall bookstore are spread out among starving millionaires around the country.  (OK, many of these people barely scrape together an annual before-taxes income of $200,000, but as one who earns less than a third of that, my sympathies are with the locally owned bookstore.)

One can easily argue that I'm talking about sticking a finger in the dyke.  But this is not necessarily the case.  The economies of scale are not entirely what they are held up to be.  It is the economies of scale that require enormous trucks to be polluting our highways, causing traffic accidents.  It is the economies of scale that require small schools to be shut down, and school districts to be amalgamated.  Airlines merge; cellphone companies eat each other up, provide slightly better service at higher rates, and fire hundreds of workers.  Economies of scale allow banks to consolidate bad loans, and take unjustified risks on under-estimating just how bad the loans are.

Meanwhile, many franchise restaurants decide to give up their affiliations.  For instance you occasionally see a sign such as "king Donut", and you wonder whether those white spots to the left used to be "Dun".  Similarly for Perky's (formerly Perkins?), and so on.  For franchise restaurants, the issues are rather extreme: you surrender a lot of control when you align yourself to a franchise.  For bookstores, the issues are less clear cut.

In principle, it should be possible to create a bookstore chain that permits a lot of local control, in exchange for a relatively small share of their profits.  However, once a franchise goes public (or since franchises are usually public anyway), the insatiable stockholders keep demanding higher dividends, and workers and the customers become secondary players.

So support your local bookstore.  Amazon books are priced so low that they are irresistible.  But it is a scary thought that Amazon might become someday the only game in town.

Arch

What is Education?

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I read somewhere that the point of education is the imparting of knowledge and thinking without the pain of bitter experience.

Experience is definitely the greatest teacher.  But because of the size of our brains, our capacity to use knowledge and information has outstripped the rate at which we can teach ourselves (from experience alone), and so the species has this method of organizing vicarious experience, in the form of people who can summarize experience efficiently.  They're called teachers.

Teachers teach material that ranges from obvious and self-evident, to obscure and, on the surface, irrelevant and inapplicable.  Unfortunately, those who need the information most, are least in a position to make judgments about whether particular information being offered at a given moment is going to be useful.

Alarmingly, some education theorists who are looked up to to provide leadership and guidance about matters of curriculum and administration choose to consider student input as inordinately valuable.  We recently read about a school district in which teacher selection was done based on input from students.  This does make sense at the College level, but perhaps not with middle-school students.  While I don't dispute that some student input might help, we have to look hard at how this input is obtained, and how the interaction between prospective teacher and student representatives is orchestrated.

Curriculum --the choice of exactly what to offer in the classroom-- is a tricky issue.  Left to themselves, experienced teachers might be expected to avoid revisiting curricular issues, since the curriculum of a particular class or course is highly interconnected with other courses upstream and downstream from the course in question.  Students, in contrast, tend to want major changes in curriculum, since they feel that the less interesting and less exciting topics are largely irrelevant to their lives, which, they are quick to point out, will be significantly different from those of their teachers.  Life moves on, and is it possible that perhaps quadratic equations will be less important in the 21st century than they might have been in the 14th?  How much of the curriculum that they haven't seen yet hinges on understanding the humble quadratic equation?  Much of the difficulty with curriculum is based on uncertainty: uncertainty about what the future will bring, and ignorance of the true potential of a student.  The more potential there is, the less we want to gamble with leaving something out.

Finally, the desire to specialize too much, and too early, is something that young students must struggle against.  On the other hand, they must also struggle against the desire to understand everything only superficially.  This struggle against being the narrow specialist and being the perpetual dabbler will never go away; society needs every person to be widely- and well-informed and experienced, as well as to be knowledgeable in a number of fields at the insider level.  Only the exceptional individual can be all these things successfully, but we must all try.

A.