The Universe of Discourse

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		Quotient
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:

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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.

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Stupid crap, presented by Plato
Yesterday I posted:

"She is not 'your' girlfriend," said this knucklehead. "She does not belong to you."

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.

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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.

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 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.

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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.

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.

"Huh."

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."

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.

Addendum 20150513: I have several times heard an argument against hate speech laws on the grounds that no other law punishes a person not for what they did but for what was in their mind. There may be good arguments against hate speech laws, this is not one. If you are the lookout for a failed bank robbery, you will be charged with bank robbery, despite having done nothing but stand on a public streetcorner; if you were the getaway driver you will be charged with bank robbery even if you paid the parking meter. Honest mistakes are distinguished from from fraud based on state of mind: fraud requires an intent to deceive. Assault, battery, and even homicide can be defensible if you are acting in self-defense, which requires a belief that one is in imminent danger. Identical behavior can result in a charge of criminal negligence, manslaughter, second-degree murder, or first-degree murder depending only on the perpetrator's state of mind. Criminal conspiracy is just two people talking in a room, nothing illegal about that, they might have been discussing a mystery novel, except they weren't, they were planning a crime. And so on.

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.

[ See also: radioactive potassium and "Crappiest literary theory this month". ]

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

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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...

    ...
    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;
                }
            }
        }
    }
    ...

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

                    citation.setCitationType(fields[0]);
                    setAuthors(citation,fields[1],personHome,false);
                    citation.setPublishYear(Integer.parseInt(fields[2]));
                    citation.setTitle(fields[3]);
                    ...
                    citation.setURL(fields[19]);
                    citation.setDoi(fields[20]);

		    if (! isEmpty(fields[13])) warn("Empty field expected...");

                    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]);

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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.

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