Archive for the ‘ Analysis’ Category

Tessellations in concrete

10 November 2017

A tessellation is a set of polygons that fills a plane without gaps or overlaps. Pavement makers often draw grooves in patterns like this example from Piedmont; I think one reason is to help the concrete break unobtrusively, along the grooves, rather than spiderwebbing all over a nice clean driveway. Another reason would be to help out the next worker who has to patch or repair the job by enabling them to cut the old concrete neatly. But mainly I think it’s just to show artisanship and decorate something utilitarian.

As a geologist, I look at this and infer a sequence of events. First came the sidewalk, installed by the developer. Then came the main part of the driveway, where the concrete worker tried to tie the tessellation to the divisions in the sidewalk and also tried to match the sidewalk’s color. Then came the worker who widened the driveway. He exercised less care in matching the colors, and less creativity in drawing grooves.

I also like the pattern of stones in the wall behind the driveway. Wallmaking is a whole nother expert art.

Mathematicians don’t care about haphazard tessellations like these. They’re fascinated by more challenging tessellations with some degree of order, or tessellations that can extend to infinity or wrap around curved surfaces and so on. You can get a dizzying taste of the subject at Wikipedia.

Polygons, by definition, have straight sides. Many sidewalk makers cover their work with curved grooves, and some time I’ll post a few examples. Those might conceivably be called tessellations, but I think I’ll just call them space-filling exercises.

Union concrete masters IV

2 June 2017

Since posting my last set of OPCFIA union bugs from Local 594, I’ve found another.

This one, you’ll know by the horseshoe and date, is from Ensor H. Buel. I’ll put together his story soon. But this shows what happens to so many marks as the years pass. When the parking-meter post at upper left was installed the workers smeared mortar on Buel’s mark, then more damage occurred when it was cut down, and sawcuts on the right were the latest insult.

After years of observing our sidewalk stamps, I notice when they disappear. Some are wiped out entirely as a whole lot is resurfaced, and others die gradually by a thousand cuts.

Odds and ends

15 July 2016

Here are a few add-ons for some previous posts on Oakland Underfoot.

I found a second variation of the utility-hole covers used by The Pacific Telephone and Telegraph Company, predecessor of Pacific Bell, featured in my post of June 17. I’m quite taken with it.


I found another concrete master number used by a member of OPCFIA local 594. As of now that makes 16 different numbers, but I’m sure there are a few more out there. Previous posts are here and here and here.


Finally, I located a fourth sidewalk maker who was a member of the Cement Contractors Association of Alameda County. The other three are here.


My impression is that like the others, this mark dates from the late 1920s.

Human errors

27 May 2016

A sidewalk stamp is a proclamation of the maker’s skill, an inscription literally made in (artificial) stone. But as every copy editor knows, mistakes can escape the most stringent quality checks. I’ve found misspellings on the very spine of a book. Here are some I’ve found on Oakland’s sidewalks.

Some concrete workers set their marks a letter at a time. I know this from the errors they made, like this one by T. A. Ryan.


Or this anonymous mark by the fire station on Martin Luther King at 17th Street.


More typically, a concrete contractor would have a stamp cast in bronze; see Louis Lambretti’s original stamp over on the Sidewalk Secrets blog. Having a stamp made was an important business decision that must have been a pricey deal, one that involved appointments with a metalsmith to settle on the design and text. I assume that if the contractor or the fabricator was fooled by the reversed text, the stamp sometimes came back from the foundry with a harmless mistake.

The earliest example I have is the pair of reversed letters on the Oakland Paving Company’s first stamp.


Patrick Ryan put up with this particularly sloppy stamp that included an inverted “A”.


Laurits Rasmussen never did have the reversed “N” on his stamp fixed, but it’s rarely even visible.


The error in James B. Lee’s stamp was more glaring, but he kept using it.


And it didn’t seem to bother A. Rodrigues that his city was spelled wrong.


But Lazzero Banchero had no choice but to reject his fabricator’s cockup. It’s conceivable that he didn’t notice until the first job he tried to stamp. All I know is that there’s only this one example in Oakland.


Some people just have trouble seeing letters. In earlier times we used to call them slow or stupid. As we all know today, you can be dyslexic and still be smart and successful, doing jobs like metalsmithing and concrete finishing that usually let you finesse your weakness. But you do have to take extra care to get things right. And if there are two dyslexics in the chain of fabrication, all bets are off.

Fortunately, today stamps are made cheaply of silicone rubber, and concrete is very predictable allowing mistakes to be troweled over. Both factors have made errors very rare . . .


but not impossible.

Union concrete masters III

13 May 2016

I’ve rustled up a few more numbers in the OPCFIA union bug since the last batch I posted.




Not much to say about these. Hal Bennett’s marks (very few of which are dated) run from 1930 to 1950. L. B. Duffin marks run from 1944 to 1947. And the Fitzmaurice mark II runs from 1926 to 1941.

Sidewalk makers of Fruitvale

1 April 2016

I count eleven different firms or practitioners who used “Fruitvale” in their sidewalk stamps. Here they are.


One dated example from 1915.


One example from 1927.


One example from 1926.


No dated examples.


No dated examples.


Examples from 1912 and 1914-1919.


No dated examples.


Examples from 1918, 1920, 1922, 1928, 1929, 1931, 1932 and 1936.


Examples from 1911 and 1922-24.


Examples from 1913-18, 1920, 1922, 1924 and 1927.


One example from 1912.

Conceivably there are others whose work survives only outside Oakland. I doubt it, though.

Union concrete masters II

25 March 2016

In the last few weeks I’ve spotted five more numbers in the OPCFIA union bug. The last three are interesting to me in a new way.






What’s interesting about the last three? First, J. H. Fitzmaurice employed several master craftsmen, although that’s not a surprise. It was a big firm, probably accounting for more Oakland pavement than any other. Second, students of Fitzmaurice marks will note that the first is the fourth configuration used by this longtime Oakland company, and the other two are the fifth and last. The older mark was made by an earlier registered master, as indicated by the lower number.

The master number ought to be a secondary clue to the ages of marks, like Fitzmaurice’s, that rarely bear dates. Paleontologists will be familiar with this problem because fossils never bear dates — all we know is their position on the stratigraphic column. That’s an idealized stack of sedimentary rocks built by noting what rocks overlie or underlie other rocks. The stratigraphic position obviously corresponds to some true age, measured in years, but the only way to estimate it, even partially, is to find a secondary clue, like a bed of fresh volcanic ash that yields an absolute date with isotopic (radiometric) methods, like the uranium-lead or potassium-argon or carbon-14 techniques. If we have that, then we can say that a nearby fossil has a comparable age.

In the case of sidewalk stamps, we can safely assume that the numbers of the master concrete workers were assigned in numerical order. But those numbers aren’t dates. We need marks that have both a date and a master number to help establish the timeline of masters. And that won’t tell us much. A single example will only tell us that the master was active that year, not the year he earned his number or the year he retired. With enough data, we can zero in on those years but never know them for sure. I’ll see what comes up as I look around. Because as the saying goes, “What songs the Syrens sang, or what name Achilles assumed when he hid himself among women, although puzzling questions are not beyond all conjecture.”