Manipulatives for Everyone

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Many years ago, it was discovered that far too many elementary students were being taught mathematics by giving them rules.  Some teachers motivated the rules with examples (See?  It really works!), others just insisted that the kids learn the rules, and use them.

Presently, it was decided by at least some authorities (and all backed up with research), that it was better for a child to learn a method slowly, using materials that worked like money, for instance, than to simply teach the child rules of addition.

In the case of place value, the big idea in representing numbers, this works as follows.  You first explain that all numbers must be represented by dollars, dimes, and pennies.  Ten pennies are worth one dime, and ten dimes are worth a dollar.  Okay; that certainly is a rule, but it is a definition, from the real world, so it isn't too illogical.

The next step is to convert every number of one, two, or three digits, into the least possible number of dollars, dimes and pennies; e.g. 123 = 1 dollar, 2 dimes, and 3 pennies.

Now you teach addition. 123 + 456 = 5 dollars, 7 dimes, and 9 pennies.

Next you teach carrying, which is merely trading 10 pennies for a dime, etc.

Base-Ten Blocks.  Units are represented
by the little cubes (yellow, in this set),
Tens by the rods (green, in this set),
and Hundreds by the slabs (blue, here),
and thousands by the big (red) block.

Teachers who are adept at this can diagnose which part of the procedure a kid has failed to get.  For instance, if a student gives a response to the problem 99+43=1312, you can tell that there is difficulty with the concept of carrying, but the actual addition is proceeding moderately well.

People outside the teaching profession take the concept of "Carrying" for granted.  A student taught with Base Ten Blocks, which is the classroom equivalent of money, knows exactly what carrying is.  It is more important for an elementary student to understand how what we call place-value notation works (an Arab invention, we believe), than to be able to use rules fast.

Calculators

Some "experts" are of the opinion that if kids can use calculators from the start, they will figure it all out someday.  I don't think this is either true or false; the big question is whether it will actually serve the child better in the long run.

What got me started on this harangue is a recent blog criticizing how students in some states were being tested for the so-called Common Core.  Some of the questions were undeniably bad, but a large part of the criticism was based on the critic completely missing the point of the question.  Unfortunately, some of the teachers inventing creative questions were also a little off the mark.

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Bach's Birthday: March 21, 1685

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For those who haven't read my previous years' posts about Bach's birthday: the short story is that in the part of Germany (Saxony, which was for some decades, behind the Iron Curtain) was so defiantly Protestant that they refused to reset their Calendar according to Pope Gregory's astronomers.  Over the years, because the Leap Year adjustments were not strong enough (or really too strong; they overcompensated) the seasons had crept, so that March 21st, for instance, was in late spring, early summer.  But poor Bach, and all his neighbors, were accustomed to this state of affairs: March was  early summer for all parts of the world that refused to reset their calendars in such a way that March 21st was the Spring Equinox.  Due to the intervention of various persons (notably one Ole Rømer, according to Wikipedia), the calendars in Prussia and, presumably Saxony (but I could be wrong) were adjusted to be in synchrony with the Gregorian Calendar in late 1700, when Johann Sebastian Bach would have been about 15 years old.  Apparently it involved a loss of only 11 days: October 4th was followed by October 15th.  I seem to remember reading somewhere that people got very upset over this; rents, for instance, were due eleven days earlier than expected.

I always celebrate Bach's birthday on March 21st, even if that day was really April 1st, or maybe even a different date, in Rome.  It is probable that Bach was aware that his birthdate would be different in other calendars, and he might even have known what it was.  But the baptismal registry in his church says March 21, 1685, so that's when I celebrate him.

I usually write about some work of Bach, and this year I have chosen the slow movement of the Concerto for Flute, Violin and Harpsichord, S. 1044 (or BWV 1044).

Bach wrote at least two triple concertos for this particular combination of instruments: Flute, Violin and Harpsichord: the most famous is probably Brandenburg Concerto No. 5, followed by this one: BWV 1044 in A minor.  Here is a clip on YouTube, played beautifully, in the pre-Original Instruments style, which I'm finding more attractive recently.

Here's a more recent, 'Original Instrument"-type performance, by I Barrochisti.

[To be continued]

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Classic Dad-ly Advice

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This was amazing —well, mostly!  A post going round on Facebook is remarkable, at least to me, because some of these were actually said to me by various older men: my Dad, sundry uncles, and other great guys who pretty much had it together.

Some of these sorts of pieces of advice are sort of dogmatic, but I think I want to look behind them, to see whether there is some underlying principle that might be worth discovering.

[I checked up on Google, and found that there are at least 4 variations on this list, and it appears that it's in the form of an image just to make it harder to copy.  But remember, when you're talking about advice, or teaching materials: steal all you see, keep all you steal, use all you keep.]

First and foremost: these are intended to be "father-son" advice, so the items having to do with relationships with women are particularly poignant.  Inter-gender dynamics have evolved over the years, and these tips reveal a sensibility that could still make sense.

(A)  So let's look at Dad's advice on dealing with women:

1.    Go for women you perceive to be “out of your league.”  You’ll surprise yourself.
2.    Never have sex with anyone who doesn’t want it as much as you do.
5.    Never take her to the movies on the first date.
7.    Nothing looks more badass than a well-tailored suit.
17.    Compliment her shoes.
39.    Always go out into public dressed like you’re about to meet the love of your life.
43.    Women find confidence sexy as hell.

That first one is a gem.  Generally speaking, from a man's point of view, women tend to present themselves as if to intimidate men who might be interested.  But they get stuck in a rut, and continue to act distant or reserved indiscriminately.  It is probably a good idea to ignore class implications if you're looking for a relationship; a classy woman will be polite enough that you can have a fair shot at presenting yourself.  This whole business of presenting oneself as higher-class than one really is has to be dealt with each person for himself; there are pluses and minuses in faking how classy you really are.  Anyway, if your ambit fails after a while, well, move along.

Having sex with a reluctant partner is just silly; there's always time for sex on a later occasion.  There are too many problems with being the one who wants the sex more.

Movies?  That does kinda make sense; you want to talk on those early dates.  So: a meal, dancing, some sort of activity--a concert, a game, places where you can study each other without being too obvious.  In a dark movie theater, guys have all the wrong instincts ready to go!

Shoes?  That one doesn't compute; compliments are always welcome if they're sincere, but why shoes?  Perhaps other items of clothing are a little too ... dangerous?

Confidence is good.  Generally, presenting yourself as just as confident as you really are is a good plan, but when going out on a date, overstating your confidence makes it easier on your lady friend.  Imagine how awkward it is for her, if she has to be your Mom!  Be confident; never mind about being sexy.

The well-tailored suit: unfortunately, this is still true, in many cases, and this is not just an observation about inter-gender strategy.  Dressing in a suit for an important occasion is still a good plan: it says that you respect all the other parties involved, including waiters, performers, everyone, and not least your date.  And well-tailored is something not to be taken for granted.  As long as it is possible to get a tailored suit, this advice stands.

(B)  This set has to do with personal style, the things that young women will find strange, but more mature women, who have observed men with both approval and disapproval, will notice with interest.

4.    Every hat should serve a purpose.
6.    Learn to wet shave.
8.    Shave with the grain on the first go-around.
9.    Always look a person in the eye when you talk to them.
12.    Brush your teeth before you put on your tie.
14.    Call your parents every week.
15.    Never wear a clip-on tie.
16.    Give a firm handshake.
18.    Never leave a pint unfinished.
19.    If you aren’t confident, fake it.  It will come.
21.    Be conscious of your body language.
23.    Always stand to shake someone’s hand.
26.    Keep a change of clothes at the office.
30.    When you walk, look straight ahead, not at your feet.
31.    Nice guys don’t finish last.  Boring guys do.
34.    No matter their job or status in life, everyone deserves your respect.

Hats: I guess this advice was given at the point in time when hats were beginning to go out of fashion.  It says: don't wear a hat just for show.  You have to figure this one out for yourself.  Wet shaving; shaving with the grain: well, okay.  Maybe some folks have an opinion on this.  (Shaving against the direction of your beard results in scraped skin; it's something I only do on special occasions, and using as little force as possible.)

Some of these, such as not wearing clip-on ties are, as I said, matters of personal style.  A clip-on tie looks pretty silly, especially if it comes off, by accident.  I don't know about leaving a pint unfinished; there must be some deep meaning there that eludes me.

Standing to shake hands is something I stand behind.  It is very refreshing to anyone to be given this degree of automatic, minimal respect.  It goes with no. 34: give respect as a matter of principle.  As a young man, I was often rude, and now I regret having been that way.

(C)   Another group of these pieces of advice are about planning, thinking ahead.

3.    Never hit anyone unless they are an immediate threat.
10.    Buy a plunger before you need one.
11.    Exercise makes you happy.  Run, lift, and play sports.
13.    A small amount of your paycheck should go directly into your savings account every month.
22.    The only reason to ever point a gun at someone is if you intend to shoot them.
24.    Never lend anything you can’t afford to lose.
27.    Buy high quality tools, so you only have to buy them once.
29.    Go with the decision that will make for a good story.
32.    Find your passion and figure out how to get paid for it.
37.    Do what needs to be done without complaining.  Complaining won’t help speed things up.
38.    Never stop learning.
42.    Luck favors the prepared.
44.    Do whatever you want to do in life, but be the best at it.
45.    No one lies on their deathbed wishing they had spent more time at work.  Enjoy your life.

It's all about thinking ahead, and having some decisions made beforehand.  Buying a plunger; deciding to fight, keeping your body in shape.  Saving.  Carrying firearms.  Lending and borrowing.  Investing in quality tools and equipment.  Deciding on an occupation.  Education and training.  Keeping a balance between work and recreation.  Some of this advice is trivial, but easy to forget.  Other pieces are really priceless suggestions.
[Added later: No. 24 is particularly good advice.  An aunt of mine once said: never lend to a good friend.  Just give them whatever it is; otherwise, the loan will stand between you, and you will end up valuing the loan higher than your friendship.  Often, the friend will return the item--hopefully in fair shape.  If you never get it back, you have to weigh its value; if it is one of the most valuable things you own, politely ask for it back.  Your friends might have actually forgotten that they had borrowed it.]  

Finally, (D) we have several suggestions about personal attitude.  Attitude, those mental adjustments that really pave the way for quick thinking and decisions, are very important to have thought out beforehand, and kept ready.  It is a different sort of thinking ahead: these are patterns of thought that make decisions easier:

20.    You can tell the size of a man by the size of things that bother him.
25.    Ask more than you answer.  Everybody likes to talk about themselves.
28.    Manliness is not only being able to take care of yourself, but others as well.
33.    Don’t let the little head do the thinking for the big head.
35.    The most important thing you can learn is personal responsibility.  Bad things happen; it’s your job to overcome them.
36.    The first one to get angry loses.
40.    Don’t change yourself just to make someone happy, unless that someone is you.
41.    If you’re the smartest person in the room, you’re in the wrong room.

A big man isn't bothered by trivialities.  No. 20 makes you realize that being petty reveals more about you than you might want people to know.  25 is about trying to make yourself interested in whomever you're having a conversation with.  It is a priceless gift, to make yourself interested in someone.  On the face of it, the advice is just to make it appear as if you're interested.  But it is better to be interested.

The advice about responsibility, of not losing your temper, of not making decisions based on your libido, these are all difficult.  About changing yourself: to do it for someone else is a terrible thing.  Because, if you don't like how it goes, you would blame the other party.  Change must come from within, and you have to be on board with it, and do it for yourself.  (Don't expect change from your significant other; you've got to take them the way they come.)

Finally, another piece of advice about people who might be superior to you.  It is a companion exhortation to the very first one: don't be put off by smart people unduly.  I mean, it is pretty miserable to be surrounded by a bunch of snooty geniuses.  But it is just as silly to seek out the company of people of lower intellectual ability just for the sake of being comfortable with them.  It is not very different from pursuing a woman who might be your superior, at least in attitude, if not fact!

In conclusion, some of this advice is less than genius grade, but a lot of it is very good advice indeed.  Incidentally, going for women who are out of your league: you're not going to surprise yourself--after all, it is a deliberate plan.  But, I think the author meant that you just might be surprised at how the woman responds.

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Mystery tune again!

Come on, check this out on YouTube!!!



[Added later:

For those who missed the Memo the first time: this is a tune that is stuck in my head; it sounds like Haydn, but as we know, lots of non-Haydn tunes sound very Haydnesque.   (We speak, of course, of Joseph Haydn, the composer of the Creation, which anyone who hasn't heard it must listen to very soon.  Haydn also wrote the National Anthem of Germany, arguably one of the most stirring entries in the National Anthem genre.)

I just happened to speed the playback up a little, and it sounded like a very convincing march.  Also, quite by accident, I tried fading the sounds that the MIDI player which produced the video (Music Animation Machine, by Stephen Malinowski, basically just a piano playing the notes,) into the orchestral MIDI sounds, and it came out brilliantly!  So here it is, with slightly improved graphics, if I may be permitted to use the word "improved" in connection with Mr Malinowski's wonderful piece of software!

Flash Mob: Mr. Blue Sky in County Cork in Ireland

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Just re-posting this :)




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A “Leaderless” World? Hmm... Leadership and Trust

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In a recent article in the New York Times, David Brooks puts forward the view that political opinion in the US regarding leadership has significantly changed.  This is hardly news, but Brooks is talking about a very specific kind of leadership: US leadership in international politics, and our participation in it.

In his article he cites a recent (2014-3-7)  Pew Center survey report (Milennials in Adulthood) which reveals that in contrast to the Baby Boomer generation, of whom 40% responded that ‘most people can be trusted’, of Millennials (the folks just approaching adulthood at present) less than 20% responded this way.  Brooks’s theory is that this makes the younger generation less comfortable with entrusting international affairs to high-stakes diplomacy, or military intervention.

You need to read the entire article to get the subtleties, all of which are fascinating, of Brooks’s op-ed, but it all seems to depend on exactly why the Millennials --anyway, young people, let’s say-- responded this way.

The actual statement --see at right-- was: ‘Most people can be trusted, vs. You can’t be too careful in dealing with people.’

This is an unfortunately vague statement, whose interpretation is almost too broad to be useful.  If you mean:  “Can you trust a counter clerk to return a wallet to the Lost and Found?” the mistrust of a person means one thing, while if you mean “Can you trust the Rebels to hold off hostilities until the Convention is over?” it means something entirely different.  In both cases, however, a Millennial is likely to be less trusting than a Baby Boomer.

Why?

Because Baby Boomers started out being naive about the world, and even a long cold war and the missteps of the Vietnam War only adjusted their habits of thinking in specific ways.  Their mistrust was saved for “people over 35”, or people in politics, or whatever, whereas Millennials —and I might be generalizing where angels fear to tread— have been brought up to mistrust even Uncle Ed.  Millennials might think that Mom’s cautioning is a little over the top, but the steady diet of a certain kind of news in the media has had its results: There are people out there who are very . . .  different.

How does that fit in with the increase in diversity, the rise of women in politics, the significant presence of Latinos, Chinese and Vietnamese and Japanese in American Colleges, even Canadians!  A far greater proportion of American citizens come into contact with people of different ethnicity, both US nationals, and visitors or immigrants, in ways that are positive, in this century than in the last.  This must support a young person’s belief that people are differenter than their parents thought.  But, I suggest, they are probably comfortable with differences.

One must wonder what it is, in the vast arrays of assumptions that support the thinking of an idealist such as David Brooks, that leads him to interpolate between what he sees in world affairs and US responses to them, and the Pew Report, and his knowledge of the people around him, to arrive at the conclusions he does.  Clearly some of his conclusions are straightforward: Millennials are probably suspicious of military action, certainly more suspicious than older Americans.  The causes could be many, but I suspect that among them is the huge suspicion that neither Congress nor the Pentagon can be trusted to oversee a military action of any sort.

Millennials are probably —and I’m alarmed at how smoothly the term Millennials slides off my fingers— cautious about whether political conversations between foreign leaders, especially those who are non-Western educated, and American diplomats, are understood correctly by Our Side.  It is not just that the foreign leaders are being deceitful; leaders are invariably deceitful, including our own.  It is that deceit is less well understood today than it has been in the past; and you know what?  I wouldn’t be surprised that brighter Millennials are well aware of that.

[And here’s something else to think about, completely unrelated to David Brooks’s article.  Whatever deceit is involved in international diplomacy, the intolerant Christian Conservative Right can be trusted to make a big fuss about it, further muddying the waters.  One wonders what the Millennials think about that.  A pox on the Christian Conservative Right: may rabid dogs . . .  Sorry.]

One thing is certain: it is fascinating to analyze how the younger generation will approach political leadership and its problems.  I still see energetic and enthusiastic young undergraduates rushing to declare double majors in Business and Political Science, and I shudder.  I sincerely doubt whether we can continue to be guided by the received wisdom of those pseudo-disciplines.

Appendix: A summary of Brooks’s Article

The main thrust of the article is that there appears to be a trend towards less engagement in world affairs: military, political, business and economic.  This is not isolationism, says Brooks; he argues that while the younger generation distrust big actions by individuals, large corporations, or star diplomats, they do look favorably on person-to-person conversation and persuasion.  “The power is in the swarm,” he quotes.

The conclusion is that individuals tend to be less comfortable delegating power to others, simply because they don’t “have enough trust” in political leaders.  (I wonder whether Mr. Brooks has lost trust in the President over the years? Hmm.)

Do please read the article yourself; it is worth reading, not least because of the additional information there which I have not passed on to you.  There are a few deplorable lapses in clarity due to unclear uses of tense; something about which I am hardly in a position to complain.

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The Long Assault on Intuition

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To anyone who has been paying attention, it has to be clear that what we call intuition has been under a steady attack.

Let's take law enforcement, for example.  It used to be that a policeman could accost anyone who looked suspicious, and subject him or her to an on-the-spot questioning.  Over the years, as the police force grew, and money grew tight, and for various reasons employment in the police force became attractive to people of questionable talent, it became possible to correlate the tendency of a policeman to think someone suspicious with the ethnicity of the suspect.  Meanwhile, of course, many more dollars were stolen by white middle-class males, I'm ashamed to say, than by any minority group, so the harassment of minorities was given a name: profiling.  What had happened was that the intuition of a law officer had become replaced by an objectionable rule of thumb: "Immigrants are suspicious, just because," and of course that would not be allowed to continue.

Mathematics is an area where intuition is very important and useful.  When I was a lad, my classmates and I were taught how to solve mathematical problems using at least 50% intuition.  But, as mathematics was seen to be important, teaching mathematics was an area that saw an influx of people who needed to teach more than they wanted to teach.  Furthermore, mathematicians became classified into categories such as pure mathematician and applied mathematician.  All mathematicians solved problems, of course, but while applied problems came from outside mathematics, pure problems came from withing mathematics: how could you find a such-and-such that did such-and-such?  I remember when I discovered the fascination of pure mathematical problems.  There was none of this dirtying your hands with principles of chemistry or physics; you looked at a problem just in order to perfect your technique.  Unfortunately, though, as pure mathematicians began to edge out the applied mathematicians from the calculus-teaching cadre, they systematically replaced the intuition with theorems, and mechanical rules of thumb.  Textbooks began to fill up with theorems (which were readily converted into rules of thumb), and proofs began to replace intuition.

Pure mathematicians had a ready defense of the gradual replacement of intuition with theorems: intuition is fallible, theorems are (if correctly proved) never wrong.  So, in theory, a class that survived the more theoretically oriented calculus course could do a few things perfectly.  They might not understand, in intuitive terms, the heuristic behind the logic, but they know the facts.

In the mid Eighties, the applied mathematicians rebelled.  They labeled the proof-based calculus approach as sterile and unintuitive, and pleaded to be allowed to teach calculus intuitively, so that their students would understand why --in intuitive ways; we know that logically everything is supposed to work as advertized-- why the methods make sense.  This was partially successful.  The compromise was that the subject should be presented (1) logically, (2) intuitively, (3) geometrically, (4) numerically, and (5) using technology, e.g. computers.  This was a tall order, but everyone bought into it, for a while.  But, over the years, instructors taught calculus any way they wanted to.  Quietly, the computer lab periods that used to accompany calculus were dropped, (hey, I did it, too) and calculus became highly theoretical again.  Now, the emphasis is on learning calculus via YouTube.  Online calculus teaching enthusiasts emphasize the intuitive approach; they can show lots of graphics, and the classroom instructor can only do that through a lot of work with software and PowerPoint; some instructors do it, others do not.

Along with the opening up of mathematics teaching opportunities, I also observed the power of students to challenge grades.  Why have I lost three points here?  Oh, I just thought your work was not up to standard.  But in exactly what way?  You see where you did B instead of A?  You do know that that's the wrong thing to do, don't you?  Oh, I see.  But why three points, and not two, for instance?

It became convenient --nay, necessary-- to invent rules for everything, so that everything was done mechanically.  There were rules about when a state trooper could pull over a car.  Rules about how many points you could deduct, because, of course, deducting points had to be defensible.  To every occupation rules were required.  On the one hand, this eliminated wayward and fanciful ways of doing things.  On the other hand, the rules empowered no-talent hacks to do the work of people with intuition and insight.  But, as we observe around us today, it is convenient to hire no-talent hacks  in preference to talented people because:
(1) No-talent hacks are predictable, and obey orders.
(2) No-talent hacks can be made to be consistent.
(3) No-talent hacks are not temperamental.
(4) No-talent hacks are (usually) happy with lower pay.  They cost less.
(5) No-talent hacks do not think for themselves.
(6) No-talent hacks don't usually ask troublesome questions, because they're really not interested in what they're doing.  They just do it for the nickel.

Consider music.  For centuries, music was an art, which is to say, you did it by ear.  But then, some clever fellow decided that he would actually make rules by which music could be written, enabling, famously, any idiot to be able to write correct harmony, or what have you.  And, many idiots did.  Mozart railed against inspiredly bad correct music.  Bach lost his temper against an idiot bassoonist, and drew his sword on him.  (Actually, we don't really know how the bassoonist had offended Bach.)

Around the time of Leonardo Da Vinci, and Albrecht Durer, artists were beginning to discover mathematical and geometrical rules for drawing representative art.  But it appears that artists were among the first to abandon the rules, because too many people were drawing according to the rules, and in a field crowded with paint-to-rule hacks, artists felt the need to jettison rules in favor of individualism.  Similar things happened in literature.  Musicians held onto rules longer than most others, and every time they tossed out one category of rules, they seemed to adopt an alternative set.  Because of the peculiar problems that a musician faces, there must be rules.  Communication through music is fragile, and a composer must be "commercial" to at least some degree, or he or she has no livelihood.

I think we must make room for intuition in today's world, even at the cost of alienating the critics.  On one hand, having rules makes the work of critics easier, because they merely have to assess to what extent the rules have been satisfied.  On the other hand, having no rules makes it easy for critics, too, because they can simply claim that a work has "no soul", for instance.  Whether you do have or don't have rules, there are winners and losers.  But if someone has an intuitive approach or skill about something, it seems to me that it is a capability that we must, in most cases, encourage.  It would be a terrible world if everyone dealt with everything according to rules alone.

Because of various missteps, I find myself teaching all my classes without the support of printed textbooks.  This means that I'm not at the mercy of the numerous rules that typical mathematics texts are full of, and can encourage my students to proceed using their intuition a lot of the time.  But, on the other hand, there are going to be numerous complaints that I did not provide rules for the students.  While I think that developing their intuition is the greatest service I can render my students, some of them think that this is all very well for students who have some intuition to start with, but what about the rest of them?  How are they going to go out into the schools and teach, if I don't supply them with all the rules they need?  Yes; it seems that teaching today proceeds on the wheels of rules, rather than intuition and understanding.  Schools, colleges and universities are full of people wanting to be taught without appeal to intuition.  Wanting to be taught things that they have absolutely no interest in, too.

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Libraries: Do we really need them?

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Yes.  I certainly think we do need libraries, and now let's think of good reasons for keeping them.

First of all, what are they?  In the abstract, they're collections of books or documents in various forms (paper, microfilm, and today, electronic documents), but they're also buildings or rooms in which these materials are kept, and in which (or parts of which) there are places where a reader can sit and read, and also places where a reader can browse: the so-called stacks.  In today's libraries, there are also people who are adept at finding information: Librarians; and of course, there are other library users, and programs for younger people and special categories of people, such as those looking for work, or school kids researching a paper.

What strikes you right away is that Libraries take us in the direction opposite to that in which most other modern institutions and technology are pushing us, namely to pursue solitary activities, such as browsing the web, watching movies at home on our video monitors, or engaging in pseudo-social activities, such as FaceBook.  Information is certainly available, even on a mobile telephone ("cell phone"), but we don't have the opportunity to browse, to talk to others who are interested in the same information, to use more sophisticated channels to obtain more sophisticated information and analysis than just a query in a search engine.  In a library, you appear to be on your own, but you're really surrounded with people with whom you could interact spontaneously at any time, not least the Librarians, who are arguably the most peculiar people in our society, both eager to engage with you, but also longing to be left alone.

I think I can make a case for the idea that the browsing in a Library is quite different to browsing the Web.  In a browser, you look up something, and you may or may not find something relevant to what you're looking for, but each destination provides other links, which may take you in any number of other directions.  In a library, in contrast, you see things adjacent to whatever you're looking for, all of which might be interesting.  (On your browser, to mimic this, you have to retrace your steps to the original inquiry, and look at adjacent items; possible to do, but not somehow the same.)  In a library, a book that you might never actually look for may catch your eye; it hardly takes a second to pick it up, and look through it, or leave it aside.  You walk through the library, to the shelves in which new acquisitions are displayed, and you could pick up something you might never think of actually chasing down in an online resource.  Could this be the reason why older people, accustomed to using libraries, might have such a variety of reading experiences, in contrast to younger people who seem to know exactly what they're interested in, and nothing else?

Talking about Library buildings, though, we begin to see some of the problems.  They are typically old, beautiful buildings, whose upkeep is expensive.  I'm all in favor of maintaining old, beautiful buildings, but the question of public support for Libraries is certainly confused by the peculiar fact that so many of them need such great investment in maintenance.  Fiscal Conservatives want to eliminate as much routine spending as possible from the budgets of Government at all levels, which means that as soon as support for libraries is seen to be a mix of upkeep of an aging building and support for acquisition of new information technology and materials, their immediate reaction is to reduce or deny funding.  In other words, it is easy to view a Library as a Money Pit.  Obviously, funding sources for maintaining beautiful old buildings are going to be entirely different from funding sources for increasing literacy or for education and cultural extension.  The way things are, Libraries are at the mercy of having to find funding for both sorts of expenses.

It is probably the case that Libraries habitually inflate their budgets, to attempt to ensure that they have sufficient money even if the request is cut down.  On the other hand, those who control the funding expect the grant requests to be inflated, and so cut down the grants even more than they otherwise would.  Matters are aggravated by the need Libraries perceive to increase usage of their facilities, and so Libraries tend to spend even more just in order to establish that there is a need for them.  Library funding, in other words, tends to spiral into a game, in which it is the Libraries themselves that are the losers.

When a funding agency has to choose how to divide grant money between different libraries, there is a tendency to fund big, well-established Libraries with sophisticated services over small local libraries with only basic services.  On the face of it, from the point of view of objective bang for buck, it seems as though supporting large Libraries with big delivery engines is a better choice, in important but intangible ways, the decline of small libraries is a bigger tragedy than that of holding back on the spending of big libraries.  A small library in a rural town is a more important part of the quality of life of that place than an already established library in a big city.  Why, you say, is it important to enhance --or keep from eroding-- the quality of life in small communities?  If you've ever deplored the drift of population into the big cities, you know exactly why.  To remove resources from small communities is to encourage the crowding in big cities; it's a no-brainer.  People are going to move into the cities no matter what; what we need to do is to ensure that we do not help that trend along in senseless ways.

Libraries are, of course vulnerable to the inexorable decline of literacy.  They're one of the first defenses against illiteracy, and particularly badly hurt when general readership declines.  Ironically, if literacy in a given region is in rapid decline, it is both a strong argument for increasing library funding, as well as decreasing library funding.  Since there are fewer readers, they're not going to need the library as much.  But if the library curtails its operations, literacy will decline still further.  The library is one of the most acceptable instruments of social engineering, behind public eduction.  If you want a literate and knowledgeable workforce and electorate (well, perhaps an ignorant electorate is all to the good, as far as some people are concerned), you must support the libraries.

Let's talk about how Libraries keep their book collections up-to-date.  Libraries continually look to replace older, out of date books, older editions, book that do not circulate, with newer books.  This is the job of the Acquisitions Librarian and his or her staff, for which they have an Acquisitions Budget.  Unfortunately, of course, there are a million idiots out there, spewing out valueless books, alongside fascinating new books that deserve to be read.  The job of the Acquisitions Librarian is difficult, but of course there are numerous "authorities" who are only too willing to make the choices --or most of the choices-- on behalf of the Acquisitions Librarian.  It is probably hard to resist ready-made book lists that a library can order from, without going to the trouble of hand-picking the new acquisitions.  If a Librarian is reading this, they would furiously challenge me to select books from the trillion whose publication they are notified of each week.  "It is humanly impossible!" they're probably crying, even now.

This is probably true.  So the agencies that must support libraries (in the absence of government support) are doomed to have to support the acquisition of books and other materials that may or may not have been filtered carefully by the library staff.  No doubt there is a principle that librarians must abide by, that the selection process must be objective, somehow.  I'm curious to know whether there are inappropriate ways in which the lists that libraries are offered are influenced by the publishing-house equivalent of that most vicious category of criminals: Congressional Lobbyists.

In summary, while I am, in principle, very much in support of libraries for the usual cultural reasons --especially for medium-sized libraries in medium-sized town, as one of the repositories of local culture-- I am getting increasingly suspicious of how well this public money is spent by these institutions.  I know that some Libraries make brilliant use of the few dollars they're given.  But is this the rule or the exception?  Must we fund Libraries at any cost?  How can we push libraries towards modernizing their buildings so that they require less, and less expensive, maintenance, and use energy and technology more efficiently?  And above all, how can we evolve a new sort of library that is less of a burden on public funding, but which still provides the same sorts of physical resources that traditional libraries do, of paper books, and physical spaces for meeting, and browsing, and community activities?  There are benefits in multipurpose facilities such as libraries, in contrast to numerous single-purpose facilities.

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