Geometric Growth & the City

I’m convinced that humans aren’t wired to understand geometric growth. Linear growth – the notion that you get x more of something each time period – makes total sense to us as the math is easy to do in your head.

But geometric growth – you get x percent more of something each time period – is something that we struggle with (and have forever). Hence the apocryphal story of the origins of chess. As an aside, I once had a professor who said that the only thing that investment bankers understand better than anyone else is compound interest.

Geometric growth is so cunning because for a long time it seems like nothing is happening. You’re growing consistently but overall the numbers are small. After all, 10% growth on a base of 100 is just 10 more.

But over time, the base gets bigger. 100 becomes 1,000 and now 10% is all of what you were just a few periods before. The absolute numbers get big faster and at this point things feel like they’re exploding – but the growth rate is exactly the same as it was before.

This process also works in reverse. I’m reminded of Hemingway’s The Sun Also Rises:

How did you go bankrupt?” Bill asked. “Two ways,” Mike said. “Graduallythen suddenly.” 

Enough digressions.

What’s interesting is when geometric growth happens in our physical world on short timescales. One place where this occurs is in cities. They start small and then sprawl. Here are some shots of Vegas over the years:

Las Vegas, 1972 Source
Las Vegas, 2021

But what if you don’t have space to expand?

This isn’t an issue in the vast majority of US cities. But it absolutely was an issue in America’s ur-city, New York. For years, New Yorkers have tried to create more land in Manhattan but unless you want to fill in the Hudson, you’re out of luck.

And New York City went through a period of geometric growth from basically the founding of America until the Great Depression (geometric growth always plateaus in an s-curve…). The first phase of this growth was focused on Manhattan; it’s population peaked in 1910 or so:

NYC & Manhattan’s population (& share) over time. Source

This begs the question of what happened to Manhattan during this period of hyper growth when the absolute numbers started to add up? What was it like to be there?

No one alive on earth remembers this time but it turns out that there are actually photos of this timer period. The New York Historical Society recently published the Robert L. Bracklow Collection online.

Bracklow was a stationer and an amateur photographer who snapped photos of Manhattan between 1890 and 1919. Luckily for us, this corresponds to the exact time Manhattan was undergoing massive growth and gives us a unique portrait of what the city looked like during this transition.

Let’s explore.

Empty Spaces

One theme that comes across in Bracklow’s photos is that despite it’s size, Manhattan still had a lot of open space and places could appear eerily quiet at times. (And this isn’t due to long exposures; if you inspect some photos you can see a bit of motion blur but there are truly no people in many of the photos).

Perhaps he was only shooting early in the morning but the photos are consistently empty.

Watts Street, 1890-1910
Overin’s Stables at W. 42nd Street and Seventh Avenue, New York City, 1889
Tobacco companies at the corner of Water Street and Burling Slip, New York City, undated (ca. 1910-1919)
Entrance to the Liverpool and London and Globe Insurance Company, corner of Maiden Lane and William Street, New York City, 1913


This is a period of transition from “low” to “tall”. There are entire city blocks where buildings snake around corners, starting low to the ground and climbing to new heights.

The Hotel Albemarle and Hoffman House, Broadway, Fifth Avenue and 24th Street, New York City, undated (ca. 1888-1907)
The corner of Broadway and Fulton Street, New York City, 1902
View of Battery Place from Greenwich Street to the Battery, New York City, 1902
Intersection of Grand Street and Centre Street, New York City, undated (ca. 1890-1910)
Intersection of Broadway and 42nd Street, New York City, undated (ca. 1910-1911)

Views appear and disappear quickly. Here’s the Waldorf-Astoria in a rapidly changing landscape:

Rooftop view of the Waldorf-Astoria Hotel from W. 31st Street, New York City, 1905
High-angle view of the Waldorf-Astoria Hotel (?) on W. 33rd Street, New York City, undated (ca. 1897-1919)

I particularly love this photo of Dutch St (a one block lane in lower Manhattan; I believe Bracklow lived or worked near there) where we see dramatically the destruction of the old low-rise Manhattan and its skyward growth.

Dutch Street, New York City, undated (ca. 1890-1919)

From this angle, the city almost looks like a pyramid rising up from the Hudson:

View of West Street showing Washington Market and the Lackawanna Hotel, New York City, 1909
The Hotel Manhattan, E. 42nd Street and Madison Avenue, New York City, undated (ca. 1895-1919)
Two unidentified Greek revival houses, New York City, undated (ca. 1882-1919)

Freestanding Buildings

This was the time period when Manhattan lost all of its freestanding buildings. They simply did not make economic sense and almost every freestanding building – whether Gilded Age mansion or a more pedestrian affair – disappeared:

Cyrus Clark mansion on Riverside Drive at W. 90th Street, New York City, 1890.
Charles M. Schwab House, Riverside Drive between W. 73rd Street and W. 74th Street, New York City, September 19, 1909
Unidentified building on the northwest corner of E. 93rd Street and Park Avenue, New York City, undated (ca. 1882-1919)
W. 81st St. & the Boulevard (now Broadway), New York City, 1898
Smith House (now the Mount Vernon Hotel), E. 61st Street between First Avenue and Avenue A (York Avenue), New York City, undated (ca. 1897)

Actually, I lied. The Mt Vernon Hotel (above) is still there, but it’s nestled amongst towers now.

Wooden Buildings

Freestanding buildings weren’t the only type of construction to disappear. The growth also meant the end of the wooden building. Not only was it a fire hazard, it also simply couldn’t be made tall.

And it turns out that there were a lot of wooden buildings in Manhattan. They didn’t come down all at once, rather they slowly were turned out as the neighborhood grew too expensive:

Old house on the site of the Metropolitan Hotel, New York City, 1897
21-23 Pearl Street, New York City, undated (ca. 1890-1919)
Bruno’s Garret, Washington Square, New York City, 1914
O.K. Bottling Company, 45 W. 62nd or 64th Street near Boulevard (Broadway), New York City, 1896
Houses at Lexington Avenue and E. 83rd Street, Yorkville, New York City, 1900
Old Grapevine Tavern at Sixth Avenue and Eleventh Street, New York City, 1913
Unidentified old wooden building, New York City, undated (ca. 1890-1919)

I love the photo below because that is the Met in the background! You could have lived in a two story wooden house next to Central Park just over a century ago!

Unidentified frame house on East 83rd Street between Fifth Avenue and Madison Avenue, New York City, 1909
Old wooden building, possibly at Central Park West and W. 70th Street, New York City, undated (ca. 1890-1910)


Part of the reason for Manhattan’s growth was people leaving the poverty of Europe. And unfortunately sometimes they ended up trading European poverty for American. This was the time of tenements and How the Other Half Lives.

Out houses behind unidentified tenements, New York City, 1889

While I’d heard of the downtown slums, I had no idea that there were wooden shanties elsewhere in the city:

Houses and fields at W. 115th Street and Amsterdam Avenue, Manhattanville, New York City, 1890
Shanties on W. 62nd Street near Boulevard (now Broadway), New York City, 1896

Flatiron Building

While economics dictated that buildings would go up, it was a combination of a building code change in 1892 (masonry was no longer needed for fireproofing) and new technology (steel frame construction) that enabled the city to race to new heights.

The embodiment of this is the Flatiron (nee Fuller) building. Here is the view south from Madison Park at the turn of last century:

Broadway and Fifth Avenue at 23rd Street, prior to the construction of the Flatiron Building, New York City, 1900

Just a few years later the Flatiron was under construction…

The Fuller Building (Flatiron Building) under construction, New York City, April 6, 1902

…and the view and the city haven’t been the same since. The Flatiron literally towered over its neighbors. It must have felt like a vision for a future New York:

The Flatiron Building, looking south down Fifth Avenue, New York City, undated (ca. 1900-1910)
View looking north on Fifth Avenue from between 19th Street and 20th Street to the Flatiron Building (Fuller Building), New York City, October 26, 1902
View looking up Broadway from E. 20th Street at the back of Flatiron Building (Fuller Building), New York City, August 24, 1902
The Fuller Building (Flatiron Building) seen from the Camera Club of New York, New York City, 1902


This set off the skyscraper building boom and Bracklow catalogued a few of them. While not particularly tall, I thought it was worth including the Pabst Hotel because its as almost immediately torn down to build a new headquarters for the New York Times and led to the naming of Times Square:

The Pabst Hotel under construction, New York City, February 26, 1899
The Pabst Hotel, W. 42nd Street between Seventh Avenue and Broadway, New York City, 1899

The Woolworth building in 1911 showed just how tall the city could build:

The Woolworth Building viewed from Fulton Street, New York City, 1916
The Woolworth Building seen through an arch of the Municipal Building, New York City, undated (ca. 1912-1919)

I love the image below because it highlights how discontinuous it must have been to live in this era. The Woolworth Building occupies almost the entire sky and looms over everything around it, heralding the future:

View looking north on Broadway from Vesey Street, New York City, undated (ca. 1882-1913)
View looking down Broadway from Astor House to St. Paul’s Chapel, the City Investing Building (under construction), and the Singer Building, New York City, undated (ca. 1907-1908)

Horses & Cars

This is the time when horses gave way to cars. At first we see horses by themselves and the city has build infrastructure to support them:

Unidentified city street with horse cart and a man holding an advertising sign, New York City, undated (ca. 1890-1919)

Then the trains appear and there is an awkward juxtaposition of raw power and horse power:

Unidentified old house and the Steam Ship Hotel, West Broadway below Washington Square, New York City, undated (ca. 1890-1910)
Saks Department Store, 34th St. and Boulevard (Broadway), New York City, August 24, 1902

Later the car starts to appear. What’s interesting is how the streets are still empty. Cities before cars were truly pedestrian places.

View looking south on Broad Street from Nassau Street, New York City, 1904

A Different Context

Almost all of the buildings in these images have been destroyed. This is a bit mind-jarring as they weren’t destroyed in war, rather even though many were perfectly good they simply weren’t as valuable as they could be. Could this have been the greatest ever peacetime destruction of buildings?

Despite this, many of these buildings still exist and it is fascinating to see them in their original context and scale:

Engine Company 31 Firehouse, 87 Lafayette Street between Walker Street and White Street, New York City, 1897
View down Wall Street to Trinity Church, New York City, undated (ca. 1882-1919)
The Sub Treasury Building (later Federal Hall), New York City, 1897
The Riverside Drive Viaduct, New York City, January 19, 1902
James A. Farley Post Office, Eighth Avenue and W. 34th Street, New York City, 1915


There are many great photos that don’t fit into any of the above categories but still show us what life was like during this period of intense growth.

Mr. Ed Slater getting a shoeshine, New York City, 1911
Crowd watching baseball scores being posted on the Sun Building, New York City, 1914
Building construction, 78-88 Maiden Lane, New York City, undated (ca. 1890-1900)
Excavation for the New York Times Building, Times Square, New York City, 1902

The Croton Reservoir -now the public library – had 25 foot thick walls and used to be the primary water source for Manhattan:

View of Croton Reservoir looking southwest, Fifth Avenue and 42nd Street, New York City, 1899
West 14th Street, looking west from Fifth Avenue, New York City, 1902
Lower Manhattan skyline viewed from Brooklyn, New York City, 1902
Lower Manhattan skyline viewed from the South Street piers, New York City, 1915

And I’ve included a few extras because Bracklow developed a great sense of contrast and how to take full advantage of shooting black and white film:

Hague Street, New York City, 1913
Laundry strung on lines between unidentified buildings, New York City, undated (ca. 1890-1919)
The National Arts Club (Samuel J. Tilden House), 15 Gramercy Park, New York City, undated (ca. 1900-1919)
Police officers at the door of the A. J. Vetter Whalebone building, New York City, November 23, 1902

All in all, the Bracklow collection is a rabbit hole to disappear into and wonder what it was like to live in Manhattan during that period of heady growth. I also hope that in a few years some folks will publish similar collections but for Beijing, Shanghai, Lagos, Delhi and other cities. Onwards & upwards!