The disaster in Houston is partly Mother Nature — natural disasters will happen sometimes whatever we did — but with a powerful assist from human action. Climate change definitely made such an event more likely; beyond that, Houston’s total lack of zoning, complete failure to limit the amount of land paved over, made it much more vulnerable than sheer geography required.
But this isn’t a simple parable where hostility to government intervention is the villain. In general, I have contempt for “both sides” arguments; given the corruption of modern American conservatism, on most issues there is a huge asymmetry between left and right. When it comes to land use policies, it really is true that both sides get it wrong.
Having no zoning, no control, can be disastrous — which is what we’re seeing in Houston now. But all too many blue states end up, in practice, letting zoning be a tool, not of good land use, but of NIMBYism, preventing the construction of new housing.
In fact, liberal (in the non-political sense) land use policy is probably the secret behind Texas economic growth: the state doesn’t offer high wages, but it does offer cheap housing even in huge metro areas. Compare real housing price evolution over the decades in Houston and San Francisco (sorry, the blue state is the red line and vice versa):
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What we need is effective land-use regulation that doesn’t strangle housing construction. But how do we get there politically? No idea.
Donkeys and cattle were herded by Trey Holladay, a civilian search and rescue worker, through a neighborhood west of Houston.CreditAndrew Burton for The New York Times
HOUSTON — Five days after the pummeling began — a time when big storms have usually blown through, the sun has come out, and evacuees have returned home — Tropical Storm Harvey refused to go away, battering southeast Texas even more on Tuesday, spreading the destruction into Louisiana and shattering records for rainfall and flooding.
Along 300 miles of Gulf Coast, people poured into shelters by the thousands, straining their capacity; as heavy rain kept falling, some rivers were still rising and floodwater in some areas had not crested yet; and with whole neighborhoods flooded, others were covered in water for the first time. Officials cautioned that the full-fledged rescue-and-escape phase of the crisis, usually finished by now, would continue, and that they still had no way to gauge the scale of the catastrophe — how many dead, how many survivors taking shelter inland or still hunkered down in flooded communities, and how many homes destroyed.
For everybody, it was another head-shaking day:
• Local officials in Texas said at least 30 deaths were believed to have been caused by the storm through Tuesday, up from eight a day earlier. The dead included a Houston police officer, Sgt. Steve Perez, 60, who was caught in flooding on Sunday while trying to report for duty. “I expect that number to be significantly higher once the roads become passable,” said Erin Barnhart, the chief medical examiner for Galveston County.
• The city of Houston imposed a curfew from midnight to 5 a.m., starting Tuesday night and continuing until further notice. The curfew was requested by the Houston Police Department, partly in response to reports of “small-scale looting” and other crimes, Chief Art Acevedo said at a news conference Tuesday evening. He added that the curfew would help search and rescue teams get around without interference.
• Parts of the Houston area broke the record for rainfall from a single storm anywhere in the continental United States, with a top reading on Tuesday afternoon, since the storm began, of 51.88 inches in Cedar Bayou, east of Houston, the National Weather Service reported. The previous record was 48 inches in Medina, Tex., from Tropical Storm Amelia in 1978, and with the rain still falling along the Gulf Coast, Harvey could top the 52 inches recorded in Kauai, Hawaii in 1950 from Hurricane Hiki.
• Houston officials had at first limited the city’s main shelter, the George R. Brown Convention Center, to 5,000 evacuees, but by Tuesday morning it had swelled to more than 9,000, with more arriving by the hour, Mayor Sylvester Turner said. By the evening, evacuated residents were setting up cots in corridors because they said the main dormitories were uncomfortably crowded.
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National Guard soldiers slept at Gallery Furniture in the Houston suburb of Richmond.CreditAlyssa Schukar for The New York Times
One of the people bunking at the convention center, Keimaine Percel, a mechanic, had not seen his home since it flooded, but he was trying not to think about it. “I heard it was real bad,” said Mr. Percel, 35. “I don’t know unless I get back.”
The Red Cross said that in Houston alone, 17,000 people began their day Tuesday in shelters, and the numbers were rising there and in inland cities that had taken evacuees such as Dallas, San Antonio and Austin. Mr. Turner said Houston would create new shelters, Dallas opened its convention center on Tuesday as a shelter for 5,000 people, and Fort Worth said it would open shelters, as well.
In the Kingwood neighborhood of Houston, people waved towels from apartment windows and yelled “we’re here” and “family of three needs help,” hoping to draw one of the volunteers piloting fishing boats, inflatable rafts and kayaks. Seeming shellshocked, evacuees climbed into boats clutching plastic bags of clothes, cat carriers and children; Kyle Hawthorne of Baton Rouge, La., at the helm of his fishing boat, said he and his friends had pulled three people from a tree, and transported a 6-year-old who was separated from his parents.
Bennie Hooper, 20, and his dog sat on a curb, both shivering, as he searched for a sign of his husband, Cody Cress-Likes, who was left behind in their apartment by the boat that rescued Mr. Hooper. “I’m waiting for him,” he said.
Dan Diaz, 84, was rescued from his girlfriend’s house, which normally sits 30 feet above Buffalo Bayou in Houston. On Tuesday morning, water was approaching the front door, and on the other side of the house, Memorial Drive was a raging river.
“I used to worry about fire,” he said. “I’ve never seen anything like this.”
Two flood control basins on the western edge of Houston, Addicks and Barker reservoirs, reached their capacity on Tuesday, and spilled into adjoining neighborhoods that had not previously been under water, flooding more than 3,000 homes. Water also began pouring over Addicks Reservoir’s emergency spillway, a flow that will increase to 4,500 cubic feet per second by Thursday, flooding streets in another neighborhood, said Edmond Russo Jr., deputy district engineer for the Army Corps of Engineers.
Engineers did a controlled release of 8,000 cubic feet of water per second through the dams that hold back the reservoirs, but it was not enough to keep up with the rainfall and runoff pouring in. The reservoirs are intended to prevent flooding on the Buffalo Bayou, which runs through central Houston, but the bayou has spread far above and beyond its banks, and the discharge from the reservoirs will add to that flooding.
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Lt. Zach West, center, and Specialist Jaxen Halicke evacuated Frank Weido, 69, from his home in Katy, Tex. “I’ve been watching the front stoop,” Mr. Weido said. “The rain just kept coming and coming and coming.”CreditAlyssa Schukar for The New York Times
The Houston police and fire departments, and the Harris County Sheriff’s Office, reported that they had rescued about 7,000 people since the storm began, many of them from the tops of houses and cars, in addition to those taken by volunteer boaters.
President Trump visited the southern edge of the storm-affected area, arriving at a Corpus Christi firehouse and then traveling to Austin for a meeting with officials involved in the disaster response.
“It’s a real team, and we want to do it better than ever before,” Mr. Trump said to state and federal officials in Corpus Christi. “We want to be looked at in five years, in 10 years from now as, this is the way to do it.”
The severity and scope of the emergency daunted aid efforts. Houston’s fire chief, Samuel Peña, said Tuesday that the water was so high around some fire stations that firefighters had been unable to leave for days, either to go home or to help others. Federal Emergency Management Agency trucks full of supplies and provisions left from a staging area near San Antonio, but some of the hardest-hit areas remained unreachable, their roads under water, washed-out, or blocked by abandoned vehicles.
“Normally we plan response for that first 72 hours, 96 hours,” Maj. Gen. James C. Witham, director of domestic operations for the federal National Guard Bureau, said at a news conference. But because of the rare intensity and duration of Harvey, “we will be doing lifesaving, life-support efforts for a much longer period,” he said, and it will be “days, if not weeks, before we’re into the recovery mode.”
Gov. Greg Abbott has mobilized Texas’ entire available National Guard force, some 12,000 people, for storm response, and General Witham said that with help from other states, the Guard strength involved could reach 30,000 troops.
Harvey made landfall on Friday near Corpus Christi as a Category 4 hurricane, the most powerful storm to strike the United States in over a decade, then weakened to a tropical storm and headed back out to sea. Late Tuesday, it was centered about 30 miles east-southeast of Galveston, with sustained winds of 50 miles per hour, and heading north.
The storm was projected to make a second landfall, in the region of Beaumont, Texas, and Lake Charles, Louisiana, on Wednesday. The National Weather Service said late Tuesday that Harvey would hit that area with an additional six to 12 inches of rain and a storm surge along the coast.
Suppose that a ramp leading to the top of a ziggurat wall is 56 cubits long, and the vertical height of the ziggurat is 45 cubits. What is the distance x from the outside base of the ramp to the point directly below the top? (Ziggurats were terraced pyramids built in the ancient Middle East; a cubit is a length of measure equal to about 18 inches or 44 centimeters.)
Could the Babylonians who lived in what is now Iraq more than 3,700 years ago solve a word problem like this?
Two Australian mathematicians assert that an ancient clay tablet was a tool for working out trigonometry problems, possibly adding to the many techniques that Babylonian mathematicians had mastered.
“It’s a trigonometric table, which is 3,000 years ahead of its time,” said Daniel F. Mansfield of the University of New South Wales. Dr. Mansfield and his colleague Norman J. Wildberger reported their findings last week in the journal Historia Mathematica.
(If you need help to solve the problem, the answer is explained below.)
The tablet, known as Plimpton 322, was discovered in the early 1900s in southern Iraq and has long been of interest to scholars. It contains 60 numbers organized into 15 rows and four columns inscribed on a piece of clay about 5 inches wide and 3.5 inches tall. It eventually entered the collection of George Arthur Plimpton, an American publisher, who later donated his collection to Columbia University. With all the publicity, the tablet has been put on display at the university’s Rare Book & Manuscript Library.
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Dr. Daniel Mansfield of the University of New South Wales holding the Plimpton 322 tablet at the Rare Book and Manuscript Library at Columbia University.Credit
Andrew Kelly/University of New South Wales
Based on the style of cuneiform script used for the numbers, Plimpton 322 has been dated to between 1822 and 1762 B.C.
One of the columns on Plimpton 322 is just a numbering of the rows from 1 to 15.
The other three columns are much more intriguing. In the 1940s, Otto E. Neugebauer and Abraham J. Sachs, mathematics historians, pointed out that the other three columns were essentially Pythagorean triples — sets of integers, or whole numbers, that satisfy the equation a2 + b2 = c2.
This equation also represents a fundamental property of right triangles — that the square of the longest side, or hypotenuse, is the sum of the squares of the other two shorter sides.
That by itself was remarkable given that the Greek mathematician Pythagoras, for whom the triples were named, would not be born for another thousand years.
Why the Babylonians compiled the triples and wrote them down has remained a matter of debate. One interpretation was that it helped teachers generate and check problems for students.
More Reporting on Mathematics
Dr. Mansfield, who was searching for examples of ancient mathematics to intrigue his students, came across Plimpton 322 and found the previous explanations unsatisfying. “None of them really seemed to nail it,” he said.
Other researchers have postulated that the tablet originally had additional columns listing ratios of the sides. (There’s a break along the left side of the tablet.)
But what is conspicuously missing is the notion of angle, the central concept impressed upon students learning trigonometry today. Dr. Wildberger, down the hall from Dr. Mansfield, had a decade earlier proposed teaching trigonometry in terms of ratios rather than angles, and the two wondered that Babylonians took a similar angle-less approach to trigonometry.
“I think the interpretation is possible,” said Alexander R. Jones, director of the Institute for the Study of the Ancient World at New York University, who was not involved with the research, “but we don’t have much in the way of contexts of use from any Babylonian tablets that would confirm such an intention, so it remains rather speculative.”
Eleanor Robson, a Mesopotamia expert now at University College London who proposed the idea of the tablet as a teacher’s guide, is not convinced. Although she declined interviews, she wrote on Twitter that the trigonometry interpretation ignores the historical context.
But that doesn't stop mathematicians with no cuneiform, no Akkadian, no ancient history, from treating it like modern maths. Tediously wrong
Perhaps the strongest argument in favor of the hypothesis of Dr. Mansfield and Dr. Wildberger is that the table works for trigonometric calculations, that someone had put in the effort to generate Pythagorean triples to describe right triangles at roughly one-degree increments.
“You
don’t make a trigonometric table by accident,” Dr. Mansfield said.
“Just having a list of Pythagorean triples doesn’t help you much. That’s
just a list of numbers. But when you arrange it in such a way so that
you can use any known ratio of a triangle to find the other sides of a
triangle, then it becomes trigonometry. That’s what we can use this
fragment for.”
A
Babylonian faced with the ziggurat word problem may have found it easy
to set up: a right triangle with the long side, or hypotenuse, 56 cubits
long, and one of the shorter sides 45 cubits. Next, the problem solver
could have calculated the ratio 56/45, or about 1.244 and then looked up
the closest entry on the table, which is line 11, which lists the ratio
1.25.
From
that line, it is then a straightforward calculation to produce an
answer of 33.6 cubits. In their paper, Dr. Mansfield and Dr. Wildberger
show that this is better than what would be calculated using a trigonometric table from the Indian mathematician Madhava 3,000 years later.
These days, someone with a calculator can quickly come up with a bit more accurate answer: 33.3317.
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