The Universe of Discourse
Tue, 17 Feb 2009

Second-largest cities
A while back I was in the local coffee shop and mentioned that my wife had been born in Rochester, New York. "Ah," said the server. "The third-largest city in New York." Really? I would not have guessed that. (She was right, by the way.) As a native of the first-largest city in New York, the one they named the state after, I have spent very little time thinking about the lesser cities of New York. I have, of course, heard that there are some. But I have hardly any idea what they are called, or where they are.

It appears that the second-largest city in New York state is some place called (get this) "Buffalo". Okay, whatever. But that got me wondering if New York was the state with the greatest disparity between its largest and second-largest city. Since I had the census data lying around from a related project (and a good thing too, since the Census Bureau website moved the file) I decided to find out.

The answer is no. New York state has only one major city, since its next-largest settlement is Buffalo, with 1.1 million people. (Estimated, as of 2006.) But the second-largest city in Illinois is Peoria, which is actually the punchline of jokes. (Not merely because of its small size; compare Dubuque, Iowa, a joke, with Davenport, Iowa, not a joke.) The population of Peoria is around 370,000, less than one twenty-fifth that of Chicago.

But if you want to count weird exceptions, Rhode Island has everyone else beat. You cannot compare the sizes of the largest and second-largest cities in Rhode Island at all. Rhode Island is so small that it has only one city, Seriously. No, stop laughing! Rhode Island is no laughing matter.

The Articles of Confederation required unanimous consent to amend, and Rhode Island kept screwing everyone else up, by withholding consent, so the rest of the states had to junk the Articles in favor of the current United States Constitution. Rhode Island refused to ratify the new Constitution, insisting to the very end that the other states had no right to secede from the Confederation, until well after all of the other twelve had done it, and they finally realized that the future of their teeny one-state Confederation as an enclave of the United States of America was rather iffy. Even then, their vote to join the United States went 34–32.

But I digress.

Actually, for many years I have said that you can impress a Rhode Islander by asking where they live, and then—regardless of what they say—remarking "Oh, that's near Providence, isn't it?" They are always pleased. "Yes, that's right!" The census data proves that this is guaranteed to work. (Unless they live in Providence, of course.)

Here's a joke for mathematicians. Q: What is Rhode Island? A: The topological closure of Providence.

Okay, I am finally done ragging on Rhode Island.

Here is the complete data, ordered by size disparity. I wasn't sure whether to put Rhode Island at the top or the bottom, so I listed it twice, just like in the Senate.

State Largest city and
its Population
Second-largest city
and its population
Rhode Island Providence-New Bedford-Fall River 1,612,989
Illinois Chicago-Naperville-Joliet 9,505,748 Peoria 370,194 25.68
New York New York-Northern New Jersey-Long Island 18,818,536 Buffalo-Niagara Falls 1,137,520 16.54
Minnesota Minneapolis-St. Paul-Bloomington 3,175,041 Duluth 274,244 11.58
Maryland Baltimore-Towson 2,658,405 Hagerstown-Martinsburg 257,619 10.32
Georgia Atlanta-Sandy Springs-Marietta 5,138,223 Augusta-Richmond County 523,249 9.82
Washington Seattle-Tacoma-Bellevue 3,263,497 Spokane 446,706 7.31
Michigan Detroit-Warren-Livonia 4,468,966 Grand Rapids-Wyoming 774,084 5.77
Massachusetts Boston-Cambridge-Quincy 4,455,217 Worcester 784,992 5.68
Oregon Portland-Vancouver-Beaverton 2,137,565 Salem 384,600 5.56
Hawaii Honolulu 909,863 Hilo 171,191 5.31
Nevada Las Vegas-Paradise 1,777,539 Reno-Sparks 400,560 4.44
Idaho Boise City-Nampa 567,640 Coeur d'Alene 131,507 4.32
Arizona Phoenix-Mesa-Scottsdale 4,039,182 Tucson 946,362 4.27
New Mexico Albuquerque 816,811 Las Cruces 193,888 4.21
Alaska Anchorage 359,180 Fairbanks 86,754 4.14
Indiana Indianapolis-Carmel 1,666,032 Fort Wayne 408,071 4.08
Colorado Denver-Aurora 2,408,750 Colorado Springs 599,127 4.02
Maine Portland-South Portland-Biddeford 513,667 Bangor 147,180 3.49
Vermont Burlington-South Burlington 206,007 Rutland 63,641 3.24
California Los Angeles-Long Beach-Santa Ana 12,950,129 San Francisco-Oakland-Fremont 4,180,027 3.10
Nebraska Omaha-Council Bluffs 822,549 Lincoln 283,970 2.90
Kentucky Louisville-Jefferson County 1,222,216 Lexington-Fayette 436,684 2.80
Wisconsin Milwaukee-Waukesha-West Allis 1,509,981 Madison 543,022 2.78
Alabama Birmingham-Hoover 1,100,019 Mobile 404,157 2.72
Kansas Wichita 592,126 Topeka 228,894 2.59
Pennsylvania Philadelphia-Camden-Wilmington 5,826,742 Pittsburgh 2,370,776 2.46
New Hampshire Manchester-Nashua 402,789 Lebanon 172,429 2.34
Mississippi Jackson 529,456 Gulfport-Biloxi 227,904 2.32
Utah Salt Lake City 1,067,722 Ogden-Clearfield 497,640 2.15
Florida Miami-Fort Lauderdale-Miami Beach 5,463,857 Tampa-St. Petersburg-Clearwater 2,697,731 2.03
North Dakota Fargo 187,001 Bismarck 101,138 1.85
South Dakota Sioux Falls 212,911 Rapid City 118,763 1.79
North Carolina Charlotte-Gastonia-Concord 1,583,016 Raleigh-Cary 994,551 1.59
Arkansas Little Rock-North Little Rock 652,834 Fayetteville-Springdale-Rogers 420,876 1.55
Montana Billings 148,116 Missoula 101,417 1.46
Missouri St. Louis 2,796,368 Kansas City 1,967,405 1.42
Iowa Des Moines-West Des Moines 534,230 Davenport-Moline-Rock Island 377,291 1.42
Virginia Virginia Beach-Norfolk-Newport News 1,649,457 Richmond 1,194,008 1.38
New Jersey Trenton-Ewing 367,605 Atlantic City 271,620 1.35
Louisiana New Orleans-Metairie-Kenner 1,024,678 Baton Rouge 766,514 1.34
Connecticut Hartford-West Hartford-East Hartford 1,188,841 Bridgeport-Stamford-Norwalk 900,440 1.32
Oklahoma Oklahoma City 1,172,339 Tulsa 897,752 1.31
Delaware Seaford 180,288 Dover 147,601 1.22
Wyoming Cheyenne 85,384 Casper 70,401 1.21
South Carolina Columbia 703,771 Charleston-North Charleston 603,178 1.17
Tennessee Nashville-Davidson--Murfreesboro 1,455,097 Memphis 1,274,704 1.14
Texas Dallas-Fort Worth-Arlington 6,003,967 Houston-Sugar Land-Baytown 5,539,949 1.08
West Virginia Charleston 305,526 Huntington-Ashland 285,475 1.07
Ohio Cleveland-Elyria-Mentor 2,114,155 Cincinnati-Middletown 2,104,218 1.00
Rhode Island Providence-New Bedford-Fall River 1,612,989

Some of this data is rather odd because of the way the census bureau aggregates cities. For example, the largest city in New Jersey is Newark. But Newark is counted as part of the New York City metropolitan area, so doesn't count separately. If it did, New Jersey's quotient would be 5.86 instead of 1.35. I should probably rerun the data without the aggregation. But you get oddities that way also.

I also made a scatter plot. The x-axis is the population of the largest city, and the y-axis is the population of the second-largest city. Both axes are log-scale:

Nothing weird jumps out here. I probably should have plotted population against quotient. The data and programs are online if you would like to mess around with them.

I gratefully acknowledge the gift of Tim McKenzie. Thank you!

[Other articles in category /misc] permanent link

Sun, 15 Feb 2009

Milo of Croton and the sometimes failure of inductive proofs
Ranjit Bhatnagar once told me the following story: A young boy, upon hearing the legend of Milo of Croton, determined to do the same. There was a calf in the barn, born that very morning, and the boy resolved to lift up the calf each day. As the calf grew, so would his strength, day by day, until the calf was grown and he was able to lift a bull.

"Did it work?" I asked.

"No," said Ranjit. "A newborn calf already weighs like a hundred pounds."

Usually you expect the induction step to fail, but sometimes it's the base case that gets you.

[Other articles in category /misc] permanent link

Stupid crap, presented by Plato
Yesterday I posted:

"She is not 'your' girlfriend," said this knucklehead. "She does not belong to you."
Through pure happenstance, I discovered last night that there is an account of this same bit of equivocation in Plato's Euthydemus. In this dialogue, Socrates tells of a sophist named Dionysodorus, who is so clever that he can refute any proposition, whether true or false. Here Dionysodorus demonstrates that Ctesippus's father is a dog:

You say that you have a dog.

Yes, a villain of a one, said Ctesippus.

And he has puppies?

Yes, and they are very like himself.

And the dog is the father of them?

Yes, he said, I certainly saw him and the mother of the puppies come together.

And is he not yours?

To be sure he is.

Then he is a father, and he is yours; ergo, he is your father, and the puppies are your brothers.

So my knuckleheaded interlocutor was not even being original.

I gratefully acknowledge the gift of Thomas Guest. Thank you very much!

[Other articles in category /lang] permanent link

Sat, 14 Feb 2009

The junk heap of (blog) history
A couple of years ago, I said:

I have an idea that I might inaugurate a new section of the blog, called "junkheap", where unfinished articles would appear after aging in the cellar for three years, regardless what sort of crappy condition they are in.
Some of the stuff in the cellar is in pretty good shape. Some is really trash. I don't want to publish any of it on the main blog, for various reasons; if I did, I would have already. But some of it might have some interest for someone, or I wouldn't be revisiting it at all.

Here's a summary of the cellared items from February-April 2006, with the reasons why each was abandoned:

  1. Two different ways to find a number n so that if you remove the final digit of n and append it to the front, the resulting numeral represents 2n. (Nothing wrong with this one; I just don't care for it for some reason.)

  2. The first part in a series on Perl's little-used features: single-argument bless (Introduction too long, I couldn't figure out what my point was, I never finished writing the article, and the problems with single-argument bless are well-publicized anyway.)

  3. A version of my article about Baroque writing style, but with all the s's replaced by ſ's. (Do I need to explain?)

  4. Frequently-asked questions about my blog. (Too self-indulgent.)

  5. The use of mercury in acoustic-delay computer memories of the 1950's. (Interesting, but needs more research. I pulled a lot of details out of my butt, intending to follow them up later. But didn't.)

  6. Thoughts on the purpose and motivation for the set of real numbers. Putatively article #2 in a series explaining topology. (Unfinished; I just couldn't quite get it together, although I tried repeatedly.)

I would say that the aggregate value of these six articles is around 2.5 articles-worth. In all, there are 23 items on the junkheap of calendar year 2006.

I invite your suggestions for what to do with this stuff. Mailing list? Post brief descriptions in the blog and let people request them by mail? Post them on a wiki and let people hack on them? Stop pretending that my every passing thought is so fascinating that even my failures are worth reading?

The last one is the default, and I apologize for taking up your valuable time with this nonsense.

[Other articles in category /meta] permanent link

Fri, 13 Feb 2009

Stupid crap
This is a short compendium of some of the dumbest arguments I've ever heard. Why? I think it's because they were so egregiously stupid that they've been bugging me ever since.

Anyway, it's been on my to-do list for about three years, so what the hell.

Around 1986, I heard it claimed that Ronald Reagan did not have practical qualifications for the presidency, because he had not been a lawyer or a general or anything like that, but rather an actor. "An actor?" said this person. "How does being an actor prepare you to be President?"

I pointed out that he had also been the Governor of California.

"Oh, yeah."

But it doesn't even stop there. Who says some actor is qualified to govern California? Well, he had previously been president of the Screen Actors' Guild, which seems like a reasonable thing for the Governor of California to have done.

Around 1992, I was talking to a woman who claimed that the presidency was not open to the disabled, because the President was commander-in-chief of the army, he had to satisfy the army's physical criteria, and they got to disqualify him if he couldn't complete basic training, or something like that. I asked how her theory accommodated Ronald Reagan, who had been elected at the age of 68 or whatever. Then I asked how the theory accommodated Franklin Roosevelt, who could not walk, or even stand without assistance, and who traveled in a wheelchair.


I was once harangued by someone for using the phrase "my girlfriend." "She is not 'your' girlfriend," said this knucklehead. "She does not belong to you."

Sometimes you can't think of the right thing to say at the right time, but this time I did think of the right thing. "My father," I said. "My brother. My husband. My doctor. My boss. My congressman."

"Oh yeah."

My notes also suggest a long article about dumb theories in general. For example, I once read about someone who theorized that people were not actually smaller in the Middle Ages than they are today. We only think they were, says this theory, because we have a lot of leftover suits of armor around that are too small to fit on modern adults. But, according to the theory, the full-sized armor got chopped up in battles and fell apart, whereas the armor that's in good condition today is the armor of younger men, not full-grown, who outgrew their first suits, couldn't use them any more, and hung then on the wall as mementoes. (Or tossed them in the cellar.)

I asked my dad about this, and he wanted to know how that theory applied to the low doorways and small furniture. Heh.

I think Herbert Illig's theory is probably in this category, Herbert Illig, in case you missed it, believes that this is actually the year 1712, because the years 614–911 never actually occurred. Rather, they were created by an early 7th-century political conspiracy to rewrite history and tamper with the calendar. Unfortunately, most of the source material is in German, which I cannot read. But it would seem that cross-comparisons of astronomical and historical records should squash this theory pretty flat.

In high school I tried to promulgate the rumor that John Entwistle and Keith Moon were so disgusted by the poor quality of the album Odds & Sods that they refused to pose for the cover photograph. The rest of the band responded by finding two approximate lookalikes to stand in for Moon and Enwistle, and by adopting a cover design calculated to obscure the impostors' faces as much as possible.

This sort of thing was in some ways much harder to pull off successfully in 1985 than it is today. But if you have heard this story before, please forget it, because I made it up.

I would like to acknowledge the generous gift of Jack Kennedy. Thank you very much!

This acknowledgement is not intended to be apropos of this blog post. I just decided I should start acknowledging gifts, and this happened to be the first post since I made the decision.

[ Addendum 20090214: A similar equivocation of "your" is mentioned by Plato. ]

[Other articles in category /misc] permanent link

Thu, 12 Feb 2009

More Uzi-clubbing: a counterexample
Last year I wrote an article about iterating over a hash, searching for a certain key. Larry Wall called said this was like "clubbing someone to death with a loaded Uzi", because the whole point of a hash is that you don't have to scan all the keys to find the one you want.

I ended the article by saying:

I had already realized that you could, in principle, commit this error with a regular array instead of with a hash, but I had never seen an example until...
Just recently I saw another example, which I think is interesting because it seems to be a counterexample. It's part of a somewhat longer Java program. The crucial section is:

    LINE: while ( ( line = in.readLine()) != null ) {
        String[] fields = line.split("\t");  

        for ( int i = 0; i < fields.length; i++ ) {
            if ( ! isEmpty(fields[i]) ) {
                switch(i) {
                    case 0: citation.setCitationType(fields[i]); break;
                    case 1: setAuthors(citation,fields[i],personHome,false); break;
                    case 2: citation.setPublishYear(Integer.parseInt(fields[i])); break;
                    case 3: citation.setTitle(fields[i]); break;
                    case 19: citation.setURL(fields[i]); break;
                    case 20: citation.setDoi(fields[i]); break;
                    default: warn("Empty field expected, found: " + fields[i] + " for line: " + line); break;
The Perlishness of this Java code might lead you to think that I wrote it, but I did not.

My temptation here was to replace the loop and the switch with code like this:

We lost the warnings, but there were only 4 of those, so we can add them back explicitly:

		    if (! isEmpty(fields[13])) warn("Empty field expected...");
This might have been an improvement, except that we also lost the isEmpty tests on the nonempty fields. To get them back we must spend at least all our gains, possibly more:

                    if (! isEmpty(fields[0])) citation.setCitationType(fields[0]);
                    if (! isEmpty(fields[1])) setAuthors(citation,fields[1],personHome,false);
                    if (! isEmpty(fields[2])) citation.setPublishYear(Integer.parseInt(fields[2]));
                    if (! isEmpty(fields[3])) citation.setTitle(fields[3]);
		    if (! isEmpty(fields[13])) warn("Empty field expected...");
                    if (! isEmpty(fields[19])) citation.setURL(fields[19]);
                    if (! isEmpty(fields[20])) citation.setDoi(fields[20]);
So at least in this case, my instinct to eliminate the loop-switch was not helpful. There are plenty of Java-esque techniques for cutting up the complexity and sweeping each little piece underneath its own little carpet ("Replace fields with an object! Or with a series of 20 objects!") but nothing that actually reduces the entia multiplicantis. There may be ways to easily improve this code, but I have not been able to think of any.

[Other articles in category /prog] permanent link

Fri, 06 Feb 2009

Maybe energy is really real
About a year ago I dared to write down my crackpottish musings about whether energy is a real thing, or whether it is just a mistaken reification. I made what I thought was a good analogy with the center of gravity, a useful mathematical abstraction that nobody claims is actually real.

I call it crackpottish, but I do think I made a reasonable case, and of the many replies I got to that article, I don't think anyone said conclusively that I was a complete jackass. (Of course, it might be that none of the people who really know wanted to argue with a crackpot.) I have thought about it a lot before and since; it continues to bother me.

But I few months ago I did remember an argument that energy is a real thing. Specifically, I remembered Noether's theorem. Noether's theorem, if I understand correctly, claims that for every symmetry in the physical universe, there is a corresponding conservation law, and vice versa.

For example, let's suppose that space itself is uniform. That is, let's suppose that the laws of physics are invariant under a change of position that is a translation. In this special case, Noether's theorem says that the laws must include conservation of momentum: conservation of momentum is mathematically equivalent to the claim that physics is invariant unter a translation transformation.

Perhaps this is a good time to add that I do not (yet) understand Noether's theorem, that I am only parroting stuff that I have read elsewhere, and that my usual physics-related disclaimer applies: I understand just barely enough physics to spin a plausible-sounding line of bullshit.

Anyway, going on with my plausible-sounding bullshit about Noether's theorem, invariance of the laws under a spatial rotation is equivalent to the law of conservation of angular momentum. Actually I think I might have remembered that one wrong. But the crucial one for me I am sure I am not remembering wrong: invariance of physical law under a translation in time rather than in space is equivalent to conservation of energy. Aha.

If this is right, then perhaps there is a good basis for the concept of energy after all, because any physics that is time-invariant must have an equivalent concept of energy. Time-invariance might not be true, but I have no philosophical objection to it, nor do I claim that the notion is incoherent.

So it seems that if I am to understand this properly, I need to understand Noether's theorem. Maybe I'll make that a resolution for 2009. First stop, Wikipedia, to find out what the prerequisites are.

[Other articles in category /physics] permanent link