humor, language, philosophy, science

Writing Well – Part 4

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Why is English Spelling Such a Mess?

Here are links to all posts in this project of reviewing and supplementing the splendid book

The Lexicographer’s Dilemma by Jack Lynch.

  1. Introduction
    What does the rise of “proper” English have in common with a physics conundrum about gravity?
  2. Babies, Names, and Snobs
    We name words by wrapping them in square brackets to avoid overloading more common conventions.
  3. Descriptivism, Prescriptivism, and ????
    We add a new ISM to the familiar duo of attitudes toward English language usage: readabilism.
  4. Why is English Spelling Such a Mess?
    An insight into the difficulty of spelling reform has wide-ranging significance, far beyond spelling.
  5. Ambiguity Sucks!
    Ambiguity is almost always at least a little harmful to clear communication. It can be disastrous.
  6. What is the Point of Punctuation?
    Careful punctuation helps avoid unwanted ambiguity.
  7. Yogi Berra’s Paradox
    Sometimes bad English is good English that’s good because it’s bad.
  8. Blood & Gold End This Series
    Apart from a concern about the examples on 2 late pages in the book, I could applaud those pages until my hands bleed.

This post’s subtitle is a quote from the book’s Chapter 8, which considers 2 versions of the question.  How did English spelling become such a mess?  Why is it still such a mess, despite various reform efforts?  A major insight into why reform is extremely difficult is also applicable to a wide range of otherwise very different activities (digging in rocky soil; making software run faster; philosophizing; …), so I will devote this post to it.  That devotion will make this post a little off-topic for the project, but the general insight is worth the detour and the length.  If U trust me about the wide range, U can skim or skip some examples to make it a much shorter read.

There is a tweetable (but crude and cryptic) way to formulate the general insight:

The word [the] is the most misleading word in English.

Huh?  My tweetable formulation uses the word [the] twice, with a mention of it in between.  The first use (in “The word”) is OK.  The second use (in “the most misleading”) is extremely misleading because it presupposes that there is a single word more misleading than any of the other words.  Be alert for bullshit whenever U see [the] followed by a superlative.  Sadly, the same kind of bullshit lurks in many phrases that start with [the] but have no superlative to raise a red flag.  A lot of effort can be wasted on questions of the form [What is the … ?] that cannot be answered at all well w/o refuting an implicit uniqueness assumption smuggled in by [the].

In particular, consider the ultimate goal of spelling reform:

The way we spell a word should match the way we pronounce it.

Oops.  Aiming at “the” way we pronounce a word is aiming at multiple moving targets, as Lynch notes.  As the author of the play Pygmalion (and thus the godfather of the musical My Fair Lady), spelling reformer George Bernard Shaw was aware that various pronunciations were out there.  But he lived at a time when educated Brits like Henry Higgins could be proud of their own pronunciations, disparage those of uneducated Brits like Eliza Doolittle, and ignore those of educated Yanks.

Now that Brittania no longer rules the waves but English has become a global language that plays roles formerly played by Latin and then French, the multiplicity of pronunciations is a bigger obstacle than it was in Shaw’s time (and a much bigger obstacle than it seemed to him).

Isn’t it obvious that multiplicity of pronunciations is a major obstacle to spelling reform?  It is now that Lynch has made it item #2 in his list of 7 obstacles.  Unless U can rattle off most them w/o peeking at pages 180 to 184 (hardcover edition), please do not dismiss the insight as obvious.

While organized efforts at sweeping reform are unlikely to succeed, minor word-by-word improvements in spelling do happen spontaneously now and then.  Lynch notes a few that have already happened.  In the examples to follow, I will note a few more that may be happening now.  I will also give examples of the wide scope of the insight about the perils of [the].

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Example 4.1: Realizing That Superfluous Letters Can Be Dropped

Dropping the superfluous [u] in various words that formerly ended with [o][u][r] (like [color], [honor], [humor], and [valor]) has already happened on my side of The Pond.

There are other minor improvements that do not presuppose mastery of the International Phonetic Alphabet.  For example, words whose last 2 sounds are like [eyes] can be spelled somewhat more phonetically with [z] rather than [s], as in [realize] vs [realise].  It is no surprize that prigs will object in some cases, as in [surprize] vs [surprise].  I have stopped caring about which version of each such word is more common on which side of The Pond.  Some of the wavy red underlines from spell-checkers can be ignored w/o harming readability.

Example 4.2: Common Shortcuts

While many of the shortcuts used in texting and tweeting are puzzling to outsiders like me, others are self-explanatory, improve the fit with pronunciation, and saw some use before 140 became a magic number.  Wish I could be as confident that civilization will persist for another century as I am that (assuming it does persist) spelling changes like

[you] —> [U]    &    [through] —> [thru]    &    [though] —> [tho]

will spread to formal prose.  W/o making a big fuss about it, I do my part in promoting these changes.

Example 4.3: Digging in Rocky Soil

Suppose we need to dig a hole in rocky soil with hand tools.  A pick and a shovel are in the tool shed.  Which is “the” better tool for the job?  A few minutes of digging experience reveals that neither is much good w/o the other.  Using one creates an opportunity to use the other.  Tho often debased as a euphemism for layoffs in announcements of corporate mergers, [synergy] is an honorable word for the way a pick and shovel complement each other.  Similar synergies are important elsewhere, as the next example sketches.

Example 4.4: Making Software Run Faster

The instructions followed directly by a computer are mincing little steps for tiny little feet.  Writing out the long sequence of steps needed to do anything interesting is a tedious and error-prone job, so computer software is usually written in artificial “high-level” languages that are closer to how people would tell each other about an algorithm to compute whatever needs to be computed.  The computer programs that translate software from the relatively intelligible high-level languages down to the mincing little “low-level” steps are called “compilers” (despite the fact that compiling is not what they do).

Early compilers had a bigger problem than a misleading name.  They produced code (sequences of low-level instructions) that ran much slower than the code skilled people could eventually produce, after agonies of debugging.  How do we build compilers that can translate an algorithm written in a high-level language into correct code that runs roughly as fast as hand-crafted code for the same algorithm?  That was among the hot topics when I started my career in computer science.

Very broadly, the strategy for producing fast code was (and still is) to start with slow code that is presumed to be correct because it is a straightforward translation of a high-level algorithm to low-level code, w/o trying to be clever.  (Whether the algorithm itself is correct and whether there are better algorithms were also hot topics.  They still are.)  The slow code is tweaked here and there, so as to do whatever it has been doing but do it a little faster.  While no single tweak accomplishes much, there are many places to tweak.  A tweak here can reveal a previously hidden opportunity for another tweak there.  Synergy!

Alas, the opportunities for synergy struck me as so obvious that I never figured out how to persuade other compiler researchers.  There was a subculture working on one bag of tricks and a subculture working on another bag of tricks.  The debates over which bag was “the” one to use struck me as more like medieval theology than science, and I was explicit about the “Pick and Shovel Principle” in a few of the papers I wrote.  Did not help.  Cutting classes in the school of hard knocks is harder than ignoring sometimes tactless writing by the brash new guy, so the lesson was eventually learned the hard way.

Example 4.5: Philosophizing

Have U noticed a big omission in this post so far?  Not a word about writing well after the title.  Let’s fix that omission to end this post.  I promise to be more on-topic in the next part.

Some philosophers have shown that it is possible to write serious thoughts about deep stuff in a way that is also clear and good-humored.  Really.  (As other philosophers have shown, it does not just happen.)  To keep it short, I will point to just one well-written book (by D.C. Dennett):

Intuition Pumps and Other Tools for Thinking

Apart from the clunky title, Dennett’s book can be highly recommended, for both what it says and how it says it.  Indeed, some of the 77 chapters deserve to be required reading in any college curriculum.  Having been a young nerd who was hassled by his elders about getting a “well-rounded liberal education” supposedly obtainable before any serious study of STEM, I do not use the phrase [required reading] lightly.

Dennett’s chapter 43 is among those that deserve to be required.  It starts with a variant of a familiar infinite regress:

Which came first, the chicken or the egg?

A careful look at what is flaky about trying to identify “the first mammal” leads to a thoughtful objection to the Socratic quest to nail down things like “the essence” of virtue.

While not so requirement-worthy as chapter 43, Dennett’s chapter 30 provides another good read about [the].  Pick any problem U like and consider the phrase [the solution].  Depending on which problem U pick, there are many possibilities.  Maybe there are no solutions at all.  Maybe there is a unique solution.  (Both provably-none and provably-just-one do happen in pure math.)  Maybe there is just one known solution and so many constraints that looking for another is a bad bet.  Maybe there are 2 or more known solutions and fretting about which is “the” real solution would be silly.  Dennett concocts an amusing quibble-proof example of this last possibility.  With a lot less trouble, the way English imports words from other languages provides a quibble-resistant example.

As a word in English, [concerto] has 2 plurals.  A minute with Google shows that both [concerti] and [concertos] are widely used by people who know what a concerto is.  Asking for “the” plural of [concerto] as a question about an Italian word makes sense; asking for “the” plural of [concerto] as a question about an English word imported from Italian does not.  Be wary of [the]!

education, grammar, history, humor, language, philosophy, politics

Writing Well – Part 2

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Babies, Names, and Snobs

Here are links to all posts in this project of reviewing and supplementing the splendid book

The Lexicographer’s Dilemma by Jack Lynch.

  1. Introduction
    What does the rise of “proper” English have in common with a physics conundrum about gravity?
  2. Babies, Names, and Snobs
    We name words by wrapping them in square brackets to avoid overloading more common conventions.
  3. Descriptivism, Prescriptivism, and ????
    We add a new ISM to the familiar duo of attitudes toward English language usage: readabilism.
  4. Why is English Spelling Such a Mess?
    An insight into the difficulty of spelling reform has wide-ranging significance, far beyond spelling.
  5. Ambiguity Sucks!
    Ambiguity is almost always at least a little harmful to clear communication. It can be disastrous.
  6. What is the Point of Punctuation?
    Careful punctuation helps avoid unwanted ambiguity.
  7. Yogi Berra’s Paradox
    Sometimes bad English is good English that’s good because it’s bad.
  8. Blood & Gold End This Series
    Apart from a concern about the examples on 2 late pages in the book, I could applaud those pages until my hands bleed.

Sorry, but we need a short digression on ways to name a word so we can talk about it.  Some details here will also contribute later to the overall project.

Failure to distinguish using a word from talking about it can lead to confusion, as in the following dialog:

Mother :         What did you learn in school today?
Small Child :  Teacher showed us how to make babies.
Mother :         What?  WHAT?
Small Child :  Drop the Y and add IES.

In casual speech, we can insert “the word” in a few places.  That is clunky in extended writing.  There are 2 common ways to do the job in writing: quote marks and italics.  Using quote marks works well in short documents, but it can be confusing in longer ones that also use quote marks for actual quotations and/or for sarcasm, as in

After an ad blitz from the National Rifle Association rescued his failing campaign, Senator Schmaltz “bravely” defended the right of crazy people to buy assault weapons.

Maybe we should follow Lynch and use the convention popular among those who are most fastidious about the difference between using a word and discussing it: those who often call it the “use/mention distinction” and put words being mentioned (rather than used) in italics.  I do not mind doing w/o italics for emphasis because I prefer bold anyway, but italics are also used for titles and for foreign words temporarily imported into English.  I want those uses, and I found that Lynch’s use of italics for multiple purposes in quick succession invited confusion.

There is a simple way to give any word or phrase a name that works well here and in many other contexts, tho not universally.  Wrap it in square brackets (or curly braces).  Choose the wrapper U never (well, hardly ever) use for some other purpose in the current document and run with it.  If both wrappers are OK, use square brackets and give the Shift key a rest.

Now I can avoid confusion, even if I want to be emphatic, be sarcastic, and mention words (marking some as foreign), all in the same sentence:

Some snobs flaunt their “education” by saying [Weltanshauung] when [worldview] is all they need.

While not so disgusting as Senator Schmaltz, the flaunting snobs are enemies of clarity.  An enemy of my friend is my enemy too, and clarity is both a very dear friend and a concept crucial to amicable resolution of some of the tensions that Lynch explores so ably.  So I want to be especially clear and hope U will forgive the digression into metametalanguage.  Will put a quick reminder of the square brackets convention early in each subsequent post.  The next one will get down to business.


baseball, enlightenment, humor, philosophy, politics, quote, riff

Riff on a Yogi Berra Quote

Some of the many humorous quotes (mis)attributed to Yogi Berra may be trenchant expressions of genuine wisdom, not just funny malapropisms.  Consider Yogi Berra’s Law.
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In Yogi Berra’s Washington Post obituary, the subtitle “American philosopher” is well-chosen.  While some of the quotes attributed (or misattributed) to Yogi Berra may just be funny malapropisms, some strike me as quirky ways to say something important, akin to Zen koans.  One of his gems is widely applicable and especially relevant to a world on the brink of ecological and/or political collapse.  It deserves a special name.  It is also so widely quoted that 2 versions are common, as indicated below:

Yogi Berra’s Law
The game ain’t over til it’s over.
It ain’t over til it’s over.

Yes, the original context was baseball.  With 2 outs in the bottom of the 9-th inning, the home team may be trailing.  Yogi rightly admonishes both the home team (to resist despair) and the visitors (to resist complacency).  A lot can still happen with 2 outs in the bottom of the 9-th inning.  I prefer the shorter version of the law because it is more explicit about the law’s generality.  “It” could be almost anyhthing.

My current context for heeding Yogi Berra’s Law is the imminent inauguration of Donald Trump as POTUS.  At best, this event marks the start of 4 long and nasty years in the US.  At worst, this event might combine with trends elsewhere (in China, Europe, and Russia) to start a new Dark Age.  To consider the worst case is prudent, not alarmist.

Mindless repetition of platitudes like

  • It can’t happen here.
  • Every cloud has a silver lining.
  • It is always darkest just before the dawn.

is no substitute for the eternal vigilance that Jefferson said is the price of liberty.  (There are other prices.)  I resist the complacency of those platitudes; I also resist despair and continue (in my own small way) to be a citizen rather than just a complainer.

In a late inning in the biggest game of my lifetime, the Enlightenment is trailing.  That sucks.  But 2+3 is still 5 and Yogi Berra’s Law is still true.

ethics, humor, oversimplify, philosophy, politics

Green Grass and Golden Rules

Like overeating, oversimplifying is something we should always try to avoid.  Oops, that’s an oversimplification.  Sometimes it is harmless (or even helpful, for certain purposes or as a temporary expedient) to oversimplify; sometimes it is hardly better than lying.
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Is grass green?  Not if it’s Japanese blood grass in autumn.  Does a bear shit in the woods? Not if it’s a polar bear.  Is the sky blue?  Not at 1:00 AM.  Something important is hiding in plain sight here.  Everybody and their uncle have always known counterexamples to the claim that the sky is blue, and some of them have been celebrated with striking photos.  On the other hand, when cartoonist Garry Trudeau wanted to poke fun at reflexive Republican opposition to anything proposed by President Obama, he used this same claim in the Doonesbury strip that appeared 2015-05-24 in my local paper.  Clinging to his tattered hope for bipartisanship, Obama responds to an aide’s disillusionment by announcing something he thinks will be utterly uncontroversial: that the sky is blue.  The last panel shows a subsequent press conference held by the Senate’s Republican majority leader.

Leader McConnell, is the sky blue?
I am not a meteorologist.

Whether or not U agree with Trudeau’s take on the attitudes of those who pass for Republicans nowadays (and whether or not U found the strip funny), I trust that U did recognize the question about the sky’s color as a more polite version of the question about ursine defecation.  Even tho U know about sunsets.  Even tho U know that everybody else knows about them too. What is going on here?

1. Everything Is Oversimplified

Well, not everything.  The black and white cattle living on the farm near my house are not oversimplified.  They just are what they are.  Much of what I might say about them is oversimplified.  Indeed, it is hard to find anything nontrivial to say about them that is just plain true (like 2+3 = 5), w/o any qualifications or exceptions.  From a distance, they are black and white cattle, lounging on green grass under a partly blue sky.  Look more closely, and a few of them have brown instead of black.  Does it matter? Not to me.  Maybe it would matter to somebody who breeds Belted Galway cattle.  I just admire the bu-cow-lic scene and stay upwind.  Does a cow shit in the pasture?

Overeating is something people often do.  They should always try not to, and many of us can succeed most of the time.  Oversimplifying is more complicated.  Sometimes it is harmless (or even helpful, for certain purposes or as a temporary expedient); sometimes it is hardly better than lying.  Trying not to oversimplify is generally good, but the cure can be worse than the disease.  It may be better to oversimplify, be honest about it, and remain open to working on a more accurate formulation as the the need arises.  A more accurate formulation may well be good enough for a long time, but not forever.  Scientific theories and engineering calculations are like that.  Guess what?  So are ethical principles.

2. Why Is “Golden Rules” Plural in the Title?

What we call “the” Golden Rule has been formulated in various ways by various cultures.  A nice discussion appears on pages 83-86 in the book Plato and a Platypus Walk into a Bar by Cathcart and Klein.  (The book is a great read, even if U aced Philosophy 101 and have already heard many of the jokes.)  They use an old joke to illustrate how seriously oversimplified the rule is:

A sadist is a masochist who follows the Golden Rule.

It gets worse.  Even when how people like to be treated is pretty much the same thruout a group, the Golden Rule stumbles.  I was both amused and disturbed when cartoonist Scott Adams showed how badly it stumbles in a Dilbert strip I should have saved.  The boss proclaims that company policy will henceforth be to follow the Golden Rule.  Dilbert objects; the boss asks why.  The resulting exchange goes something like this:

Would U like me to give U $100?
Um, yes.
OK, follow the Golden Rule and give me $100.

The boss is reduced to sputtering indignation.  Dilbert is clearly taking the rule too literally and ignoring an implicit consensus about exceptions.  But what are they?  I could not say where Dilbert errs.

Most of the formulations discussed by Cathcart and Klein are somewhat clunkier than our culture’s usual

Do unto others as U would have others do unto U.

They amount to saying

Do not do unto others as U would not have others do unto U.

Maybe people thought of the Dilbert objection and tried to get avoid it by prohibiting X rather than mandating Y.  This does help, but there is still a problem.

Would U be disappointed if I refused your request to give U $100?
Um, yes.
Please give me $100.
 I see.  U are just as hypocritical about the Confucian version of the Golden Rule as U are about our usual version.

If U fall off a boat and I hear U shout a request to be thrown a life preserver, I will try to do just that.  Just don’t walk up to me and request to be given $100.  What is the difference?  People can start with our usual formulation of the Golden Rule, admit that it is grossly oversimplified, consider what seems reasonable in thought experiments like this, try for a more explicit consensus about exceptions, and remain open to considering more adjustments as more situations arise, either in practice or in thought experiments.  Can we do better?

Immanuel Kant tried valiantly to do better with his Supreme Categorical Imperative, which is a fun read if U like reading tax laws or patents.  Cathcart and Klein have the details.

As a former wannabe mathematician, I would very much like to see a nice crisp formulation of the Golden Rule (or of any other important general principle) that just nails it, w/o exceptions or vagueness.  Nice work if U can get it.  If I ever get stuck with trying to help socialize a child, I will give the kid our usual version of the Golden Rule, say that it is a great starting point for thinking about how to behave, admit that real life is messier, and offer to talk about it more as the need arises.  I will not mention Kant.

engineering, humor, philosophy

How My Blog Became Phone-Friendly

The tweetable answer is that I switched to the Satellite theme.  U can get a wry take on the sometimes quirky path of progress by reading the rest of this post.
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The tweetable answer is that I switched to the Satellite theme.  There are more things in heaven and earth than are dreamt of in Twitter’s philosophy (and I don’t tweet anyway), so U can get a wry take on the sometimes quirky path of progress by reading the rest of this post.

When I started blogging, I wanted a genuinely uncluttered theme that would leave me free to concentrate on content and decide whether I wanted to continue, w/o paying upfront with $ (for a premium membership) and with time (spent customizing).  I wanted black text in a sans serif font on a white background, with lines long enough and vertically separated enough for a readable brief essay w/o too much scrolling.  I also wanted something that was (and still is?) rare among uncustomized themes: I can print out a preview of a draft, get hard copy that looks very much like what the browser displays, and scribble notes about revisions.  Yes, I am that old.

Browsing the theme catalog was a dreary experience, and I found that the only good way to see what my own stuff would really look like was to adopt a theme temporarily and hope nobody was turned off by how ugly my blog was before I found and switched to something better.  After several false starts, I settled on Academica.

A post on Horizon Feedback on 2015-09-14 asked users to beta test changes to “the” editor (the “Beep-beep-boop” editor reached from the WordPress interface with a blue top bar).  Tho I usually used the other editor (the “Classic” editor reached from the WordPress interface with a black top bar), I decided to help out a little.  Improvements in “the” editor might lead me to use it more and enjoy the nice colors.

I started drafting a post, observed the result of clicking the [Preview] button, and submitted a comment including the complaint that

What comes up … is horizontally truncated, with the 1st letter of each line flush against a sky blue border on the left and the last few letters of each line hidden under a vertical scroll bar for the frame containing the draft purportedly being previewed.

Sheri at WordPress looked into the problem promptly and found that it was 2-fold.

  1. The preview was coming up in tablet mode, with no provision for changing the mode to either desktop/laptop or phone.
  2. My theme was not responsive to the kind of device (desktop/laptop, tablet, or phone?) in use.

Sheri and friends fixed #1 soon after, adding buttons that would let a blogger working at (say) a desktop/laptop see how the previewed post would look on (say) a phone:


Fixing #2 by switching to a responsive theme would of course be my responsibility, and now I could see how utterly unreadable my posts were to anybody browsing on a phone rather than a real computer.  Remembering how dreary theme shopping was, my initial reaction was curmudgeonly.  I was writing for people who use real computers, not people who surf while standing in line at Starbucks, so I would stay with Academica.

On the other hand, I can remember when the only real computers filled rooms with refrigerator-sized boxes and ran up huge electric bills for power and cooling.  I have also been a frequent visitor to a nursing home and noticed that the aides could sometimes get a brief respite from their jobs by enjoying things like cat videos on their phones.  However unlikely it was that an aide might want to read my blog on a quick break, they should not be forced to look elsewhere just because I am an old fart with an unresponsive theme.  So I resolved to fix #2.  Someday.

When someday finally came in 2016-04, I found that theme shopping is easier now, with a preview capability that lets me see how one of my own posts would look on a phone rather than just how a demo would look on a computer.  I also had plenty of my own posts to play with.  With some experience in blogging, I was willing to forego printed previews.  I could tolerate crappy printing and be content with a theme whose perversities in displayed pages either were minor enough to ignore or could be worked around by adding attributes to a few HTML tags.  (As a frugal Yankee, I still wanted to avoid paying for extensive customization unless I actually needed it.)  Several themes looked OK until I saw what they did to block quotes: they maimed them with an ugly distracting decoration.  I was a big user of block quotes and did not know how to work around this sin.  I did know how to work around Satellite’s sin of using an absurdly light font color for block quotes, and I can bypass the use of a similar font color for my tag line by not having a tag line.

So I switched to Satellite and went over all my posts, retrofitting them with a few workarounds, a few small unrelated updates I had been intending to do someday, and a few small wording changes to make the flow of text around narrow images look good on all devices.  Only 1 post required nontrivial rearranging to look good on a phone.  The whole process took roughly 4 times longer than I had expected, as is common in software engineering.


There is a great virtue of Satellite that should be mentioned: the retractable sidebar.  Apart from the click-me-for-a-menu button at the top, the retracted sidebar is an unobtrusive black band along the left side of the post.  Clicking that button reveals widgets like the [Follow] button and the Search box.


Press the [Enter] key after entering a few words, and U will get a display of that search’s hits.  There is just 1 hit for the specific words illustrated here:


Clicking on the title of that search’s single hit will visit a whimsical introduction to one of the 20-th century’s epistemological earthquakes.  It’s OK if U don’t give a rat’s ass for epistemology; the secret revealed at the end is useful in daily life and does not depend on anything else in the post.  Even if U skip the post’s mental exercise, please do consider why I displayed a screen shot with the search words instead of putting them in the text of this post.  Extra credit for all who can explain how the answer to that question relates to the earthquake.

haiku, humor, math, philosophy, science

Could a Long Fly Ball Hit a Flying Horse?

This is one of the few times I need to put some fiction into my blog, so I will change font for a little while.


Sometimes it is hard to be fair to Plato.  He is basically a good guy, but his politics are bullshit.  That “philosopher-king” notion is so self-serving.  Then there is that cave shtick.  Most people know that philosophers can be a little klutzy in everyday life.  We give them some slack and don’t make a big deal of it.  But Plato says the wannabe king has been looking at ultimate reality and absolute truth (and maybe a pretty girl sunbathing?) in bright daylight, so he stumbles in the cave that passes for the real world among ordinary Joes.  After his eyes adapt to the dim light, he will govern just fine.  No way.

Feeling mellow enough to ignore Plato’s politics, I invited him over to watch a baseball game on TV.  He was surprised that the pitcher threw a ball rather than a discus or a javelin, and that nobody was naked.  But he is a smart guy and soon understood the duel between the pitcher and the batter.  He noticed the (4 balls or 3 strikes) rule for ending an at-bat and said something about the ratio 4:3 in music by The Pythagoreans.  Are they a band I don’t know about?  He broke into a big grin when a batter sent a long fly ball arcing high above the field.  Tho he knows zip about physics, he hangs out with Euclid and knows a parabola when he sees one.

To Plato, the path of the fly ball in the grungy everyday world is an imperfect realization of the timeless perfection of an ideal parabolic form.  To me, the description of the path as a parabola is a good approximation that ignores air resistance and wind.  Ignoring those things is OK in an introductory physics course.  It is not OK in a baseball game.


Using the parabola to describe the fly ball oversimplifies a staggeringly complex everyday world that emerges from a staggeringly weird tarantella of elementary particles.  Our use of the parabola is fundamentally a story we tell ourselves.  Unlike the story of Pegasus the flying horse, it has been corrected, refined, and integrated with many other stories by scientific processes.  The notion of a flying horse is appealing (to people who have not been hit by a bird splat).  The parabolic story is ultimately more satisfying, as part of something gloriously predictive and useful (despite not being much help to the outfielder running to catch the fly ball).

Pegasus himself is as limited in time and space as the Pegasus story: an idea created by some people at some time and place, elaborated and spread by other people at other times and places.  The Pegasus story will vanish and its starring horse will vanish with it, if we succeed in our current efforts to make the Earth uninhabitable long before we can go elsewhere.  Would the parabolic story vanish also?  That is a question for another time.  The mathematical cast of characters in the parabolic story, on the other hand, is special.  Very special.

Plato’s Challenge
|Three plus two was five
|before any mind could know.
|Where do numbers live?

My snapshots of Plato and of Pegasus could not get thru the time warp, but I did some cropping of public domain images with good likenesses.

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haiku, humor, philosophy

Games, Beauty, and Overreach

The list of games is long and diverse (peekaboo; scrabble; solitaire; …).  What do all those “games” have in common?  In defiance of centuries of tradition dating back to Plato and Aristotle, the philosopher Ludwig Wittgenstein proposed a radical answer in the 20-th century: not much.
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As readers of my previous post may have guessed, obeying the 5-7-5 Rule has become something of a game for me.  When I began writing this post, I had written about 50 haiku, all of them (5-7-5)-compliant.  I hoped to extend my streak to at least 56 because Joe DiMaggio’s epic hitting streak lasted for 56 consecutive baseball games in 1941.

Wait a minute.  My (5-7-5)-compliance is a game; DiMaggio’s profession was the game of baseball.  The list of games is long and diverse (peekaboo; scrabble; solitaire; …).  What do all those “games” have in common?  In defiance of centuries of tradition dating back to Plato and Aristotle, the philosopher Ludwig Wittgenstein proposed a radical answer in the 20-th century:


(We can leave some wiggle room for something bland and inconsequential about amusing activities, often but not necessarily competitive.)  Looking long and hard at the word “game” in all its sprawling diversity, Wittgenstein observed that there are many is-a-lot-like relationships among games, such as

Hockey is a lot like soccer.

To a nonfan like me, hockey and lacrosse and soccer are all essentially the same game, with obvious minor differences.  Remove the goalie and U get basketball.  Football is somewhat like such games and also somewhat like baseball.  Card games are like each other in various ways.  One may well be able to get from one game to another by several is-a-lot-like steps, but is-a-lot-like relationships are not transitive.  After more than a few of such steps, it is no surprise if nothing worth fussing about is shared.

Wittgenstein did not stop with games.  Philosophers have often sought to find and formulate what is common to all the activities or things that may rightly be called “good” or “beautiful” (or whatever uplifting adjective U want), with the presumption that something nontrivial and enlightening might be said.  Tho Wittgenstein did not actually prove that quest to be hopeless, he did show that the burden of proof is heavier on somebody who thinks

What is beauty?

makes sense than on somebody who just says

I can’t define it, but I know it when I see it.

Images of beautiful people and places abound.  Sculptors create beautiful objects; composers write beautiful music.  In math, a beautiful proof of the Pythagorean Theorem was created by replacing the usual picture (of 3 squares glued to the sides of 1 triangle) with a picture of 4 copies of the same triangle, arranged to form 2 squares:

4 · ( ½ · a · b) + c²

Intellectually, I agree with Wittgenstein.  Pachelbel’s canon and the 2-squares proof are both beautiful, we already knew that, and philosophy has nothing to add.  I just want to remark that the urge to understand the world in terms of general principles works rather well when science encourages sobriety, by testing predictions about little things before trusting grandiose pronouncements about big things.

Emotionally, I sense something more likable than mere hubris in those who overreach, something akin to the spirit of people in New Orleans who tough out hurricanes or return after them.

This is Not Apollo 13
|Is failure an option?
|No, it is a given.
|But we will still try.
No Pots of Gold
|Seek ends of rainbows.
|You will not find them? Okay.
|The quest is enough.
haiku, humor, music, philosophy

Wordless Wisdom

Can there be such a thing?  Tho unable to offer a strong argument, I believe so.  (There definitely can be wordless knowledge.)  The notion of wordless wisdom is not preposterous, despite the conditioning we inherited from Socrates.
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Let’s start with something easier than wisdom.  The canonical example of wordless knowledge is how to ride a bicycle.  There is much that can be said about riding a bike, but how to do it cannot be put into words and/or formulas.  Millions of children know how to ride their bikes w/o knowing anything about the underlying physics.  On the other hand, one can have the physics down cold and still not know how to ride.  Many kinds of knowledge can and should be written down, but definitely not all.

Verbal and nonverbal knowledge can work together, which is the main reason that baseball teams have hitting coaches and pitching coaches.  To keep this post simple, I will ignore that possibility for wisdom.  Sometimes it is better to be simplistic (with an understanding about wiggle room) rather than precise (but ponderous).

The notion of wordless wisdom is not preposterous, despite the conditioning we inherited from Socrates asking people to tell him what virtue is and then being dissatisfied when the only verbiage they can supply is a list of a few virtues, with or w/o “and so on” after the specifics.

I am among the many people whose response to some great pieces of music goes beyond ordinary enjoyment.  The last movement of Beethoven’s last piano sonata seems to hint at something important (as well as beautiful) that resists verbalization.  Maybe it is just subjective; other music lovers have differing lists of transcendent works.  Maybe putting “just” in front of “subjective” is unwise.

If the foregoing sounds addled, let me proclaim my (slightly qualified) devotion to Wittgenstein’s Laws:

  1. What can be said at all can be said clearly.
  2. Whereof one cannot speak, thereof one must be silent.

My only reservation about #1 is a request for a footnote remarking that clarity often does not come easily.  With #2, I see a little wiggle room in interpreting “be silent” (or “schweigen” in the original German text).  Does it rule out images?  Instrumental music?  Singing in a language the listener does not understand?  Fortunately for me, I do not understand enough Latin to get distracted by the words in sacred music and thereby risk misunderstanding the nonverbal wisdom it conveys.

Hildegard of Bingen, 1098-1179
|Mystic visions or
|migraine headaches? Whatever.
|Her music lives on!

Memo to Mystics
|Unless you can grab
|bubbles, you cannot put your
|wisdom into words.

haiku, humor, philosophy

Trojan Horse in Bagelology

Those who read this long post thru to the end will be rewarded with a secret for avoiding green fuzz.

Despite being bagel-deprived, ancient Greek philosophers posed deep questions and pondered partial answers in ways that still deserve attention.  In particular, one of them showed how slippery is the notion of truth by considering the Liar Paradox:

This statement is not true.

To give a short name to the statement just quoted, I will call it LP. If LP is true, then it is false, which implies that it is true, and so on.  It is like a puppy chasing its tail.  Very annoying to anybody who agrees with what another ancient Greek philosopher said about the excluded middle.  Yes, there many utterances that are not statements and so are neither true nor false.  But the duck test says that LP is a statement.

For millenia, the usual way to dodge the Liar Paradox has been to abstain from self-referential language.  Tho I may talk about myself, I never talk about myself talking about myself.  Except in previous sentence.  Avoiding LP-ish talk is harder than just avoiding the exact words of LP itself.  How much harder?  Apart from some temporary scares that I will ignore in this post, everybody thought it was only a little harder.  Until 1931.

Suppose we are willing to pause in our search for all the answers to all the questions; we restrict our attention to some narrow subject and restrict our language to statements about that subject.  We can agree to talk only about bagels for a while.  We want to use language expressive enough to say interesting things about bagels, but not so expressive that we blunder into LP land.  Maybe, if we are both careful and lucky, we can console ourselves for talking about so little by celebrating success in saying so much about it.  Maybe we can discover a Grand Unified Theory of Bagels that encompasses the truth, the whole truth, and nothing but the truth (so long as we speak in a restricted language that can still say a lot about bagels).  Welcome to bagelology.

Suppose we have already agreed on the syntax and semantics of statements in bagelology.  What next?  We might make a list of some important things we already know about bagels.  For now, it does not matter whether we got this knowledge from empirical observation or divine revelation.  I will call these statements the “axioms” of bagelology.  The axioms are all well and good, but we want new knowledge.  One way to get new knowledge is by logical deduction, which ancient Greeks also pioneered.  (No, they did not do it all.)  So we get up to speed about rules of inference and agree that whatever can deduced from the axioms is a “theorem” of bagelology.  Logic has its pros and cons; a big pro is the way we can keep adding to whatever we have.  We can toss yesterday’s theorems in with the axioms and bake (i.e., deduce) more theorems today, along with some bagels.

After baking a new batch of theorems every day for many days, we have a substantial body of knowledge.  Of course it is still incomplete.  Somebody writes down a statement about bagels and asks if it is true.  Dunno.  Neither the statement nor its negation appears in our growing inventory of theorems that have already been baked.  Maybe the next batch of theorems will answer the question.  Maybe not.  We can still hope that our Grand Unified Theory of Bagels is “complete” in the weaker sense that someday the answer will appear.  Just keep on baking.

There is not much to be said about bagels without talking about flour.  Come to think of it, we also need to count bagels and price them.  We need to talk about numbers.  Nothing fancy; just plain old integer arithmetic.  Throw it all in.  Bagels; flour; ovens; numbers — we still have a shot at a complete theory, which eventually decides whether any given bagelogical statement is true or false.

Oops.  The greatest logician in history was not an ancient Greek.  He was Kurt Gödel, who showed that bagelology (and anything else that uses the axiom/theorem paradigm) cannot be both complete and expressive enough to support arithmetic.  Yes, he dropped that bomb in 1931, long before we wrote down our axioms.  He did not need to know them.  He knew that we would be in trouble as soon as he knew that we would count and calculate.  Arithmetic is a Trojan horse.

There is still a trivial way to make every true bagelogical statement appear eventually in a batch of theorems.  An inconsistent theory that just asserts everything will do the job.  Every  statement appears eventually, and each true statement may appear either before or after the false one that denies it.  An inconsistent theory tells us nothing and is useless, except in politics.

No matter how cleverly we set up bagelology, there are true statements that are not theorems, unless bagelology is either inconsistent or too weak to support arithmetic.  Really.  Gödel proved this with a combination of deep insight, technical virtuousity, and a little help from an ancient Greek.  He showed how to seduce bagelology into talking about itself implicitly (despite that pledge of abstinence from self-reference) and then into saying something much like LP:

This statement is not a theorem in this system.

Having shed a few tears for completeness and saluted great thinkers (both ancient and modern), we can go on living.  If we do set up bagelology well, it may be consistent and informative, revealing much that is true (and maybe also good and beautiful) but not at all obvious from a glance at the axioms.  There will always be truths that are not theorems, and we may sometimes discover a few of them by other means.  We can advance bagelology by adding those discoveries to the older axioms; we should never declare victory and carve the current set of axioms in stone.

BTW, I know there is a difference between supporting arithmetic and just using some of it as a black box.  If U know enough mathematical logic to exploit that difference in a Houdini escape from incompleteness for bagelology, then I salute U and hope U still enjoyed my whimsical way of summarizing one of Gödel’s discoveries for those who do not already know and admire it.

Now it is time for something that really is about bagels.  If U believed what U read on package labels and in food columns, U can improve your own version of bagelology by replacing that old axiom about storing things at room temperature (or in a cool, dry place) with Rosen’s Rule:

It is OK to refrigerate bagels.  Likewise for bread.

Once a bagel is no longer warm from the oven, it needs to be toasted before being eaten.  A bagel pulled from the frige recently takes a little longer to toast; the result is ever so slightly chewier than with room temperature storage.  More than a week after purchase, a wrapped bagel or bagged loaf of bread in the frige is still good.  Tho it may not be quite so good as when first brought home, it does not sport the green fuzz that adorns the poor schmuck stored the conventional way for more than a few days.

A small household that dislikes green fuzz can still buy baked goods in convenient quantities w/o being forced to pig out or throw out.  While the toaster does its job, U can read a haiku that talks about itself:

Basho Meets Gödel

Haiku written on
a typewriter: ultimate