Cities in Los Angeles County fit together like jigsaw puzzle pieces. Often - but not always - the division is in the middle of the street, the double yellow lines bracketing where jurisdictions simultaneously end and start.

Often, Los Angeles is on one side of a street and not-Los Angeles is on the other.

The side you live on can still determine what fire truck pulls up to your door, what paramedic comes to your aid, or what police officer writes up the crime report. Forty feet of roadway width is the reason.

The city of Torrance, southwesterly of downtown, is one of those puzzle pieces. Where Los Angeles ends and Torrance begins along Western Avenue, Torrance is putting up a fence in the center of a bleak, concrete-and-asphalt median. The median is being landscaped, and shrubs will cover much of the five-foot-high, steel fence.

When council members in Torrance discussed putting up the fence, it was described as a beautification project. By the time Mayor Frank Scotto was asked by the Daily Breeze what the project was for, beautifying had been replaced by safety. For Mayor Scotto, the project meant preventing people from jaywalking across Western Avenue.

Western is, in fact, wide open from 190th Street to Carson Street, with relatively long blocks in a warehouse district and with residential streets that make T-intersections along another stretch. Pedestrian safety almost makes sense.

But the fence also puts a barrier down a once permeable divide, visibly separating Western Avenue into a Los Angeles side and a Torrance side, with modern, low-rise industrial and office buildings on the Torrance side and small houses and apartment buildings on the Los Angeles side.

The reason is history. Torrance boomed in the first half of the 20th century as an oil town and industrial center. It was a model working-class city, too, laid out by the celebrated landscape architect Frederick Law Olmstead, Jr. Across Western Avenue, Los Angeles was the unplanned alternative to planned Torrance, with a relaxed view of what a property owner might build.

When industrial L.A. declined in the 1990s, Torrance began to turn the brownfields of vanished industries into neat rows of commercial buildings behind wide setbacks of landscaping and employee parking.

Los Angeles didn't change much. Areas zoned manufacturing and commercial along Western stayed industrial. Neighborhoods zoned residential became denser with ding-bat apartments and informal "accessory" units. These neighborhoods became African-American and Latino in the last 50 years, as did much of working-class Los Angeles - and neither better nor worse than similar neighborhoods.

Some who live along Western wonder why their side of the jigsaw puzzle piece looks worn in comparison to the Torrance side, as if there was a rule somewhere that dividing lines didn't matter, that history didn't matter (or that history didn't exist at all). As if Los Angeles should have been built better a hundred years ago or Torrance in the 1990s built worse.

The mayor of Torrance refused to frame the issue as racial anxiety. Safety demanded a fence, he said, not a desire to keep outsiders out. It depended on which side of the uncompleted fence you stood if you regarded this tap dance as convincing.

Like a lot of L.A. - to the frustration of urban planners and believers in regional government - what isn't Los Angeles and what is stares across the width of a boulevard, separated more by history than by a fence.

D. J. Waldie, author, historian, and as the New York Times said in 2007, "a gorgeous distiller of architectural and social history," writes about Los Angeles every Monday and Friday at 2 p.m. on KCET's SoCal Focus blog.