Archive for July, 2019
A Bayesian folly of J Richard Gott
Posted by Bill Storage in Philosophy of Science, Probability and Risk on July 30, 2019
Don’t get me wrong. J Richard Gott is one of the coolest people alive. Gott does astrophysics at Princeton and makes a good argument that time travel is indeed possible via cosmic strings. He’s likely way smarter than I, and he’s from down home. But I find big holes in his Copernicus Method, for which he first achieved fame.
Gott conceived his Copernuicus Method for estimating the lifetime of any phenomenon when he visited the Berlin wall in 1969. Wondering how long it would stand, Gott figured that, assuming there was nothing special about his visit, a best guess was that he happened upon the wall 50% of the way through its lifetime. Gott saw this as an application of the Copernican principle: nothing is special about our particular place (or time) in the universe. As Gott saw it, the wall would likely come down eight years later (1977), since it had been standing for eight years in 1969. That’s not exactly how Gott did the math, but it’s the gist of it.
I have my doubts about the Copernican principle – in applications from cosmology to social theory – but that’s not my beef with Gott’s judgment of the wall. Had Gott thrown a blindfolded dart at a world map to select his travel destination I’d buy it. But anyone who woke up at the Berlin Wall in 1969 did not arrive there by a random process. The wall was certainly in the top 1000 interesting spots on earth in 1969. Chance alone didn’t lead him there. The wall was still news. Gott should have concluded that he saw the wall near in the first half of its life, not at its midpoint.
Finding yourself at the grand opening of Brooklyn pizza shop, it’s downright cruel to predict that it will last one more day. That’s a misapplication of the Copernican principle, unless you ended up there by rolling dice to pick the time you’d parachute in from the space station. More likely you saw Vini’s post on Facebook last night.
Gott’s calculation boils down to Bayes Theorem applied to a power-law distribution with an uninformative prior expectation. I.e., you have zero relevant knowledge. But from a Bayesian perspective, few situations warrant an uninformative prior. Surely he knew something of the wall and its peer group. Walls erected by totalitarian world powers tend to endure (Great Wall of China, Hadrian’s Wall, the Aurelian Wall), but mean wall age isn’t the key piece of information. The distribution of wall ages is. And though I don’t think he stated it explicitly, Gott clearly judged wall longevity to be scale-invariant. So the math is good, provided he had no knowledge of this particular wall in Berlin.
But he did. He knew its provenance; it was Soviet. Believing the wall would last eight more years was the same as believing the Soviet Union would last eight more years. So without any prior expectation about the Soviet Union, Gott should have judged the wall would come down when the USSR came down. Running that question through the Copernican Method would have yielded the wall falling in the year 2016, not 1977 (i.e., 1969 + 47, the age of the USSR in 1969). But unless Gott was less informed than most, his prior expectation about the Soviet Union wasn’t uninformative either. The regime showed no signs of weakening in 1969 and no one, including George Kennan, Richard Pipes, and Gorbachev’s pals, saw it coming. Given the power-law distribution, some time well after 2016 would have been a proper Bayesian credence.
With any prior knowledge at all, the Copernican principle does not apply. Gott’s prediction was off by only 14 years. He got lucky.
Physics for Frisco motorheads
Posted by Bill Storage in Engineering & Applied Physics on July 28, 2019
San Francisco police are highly tolerant. A few are tolerant in the way giant sloths are tolerant. Most are tolerant because SF ties their hands from all but babysitting the homeless. Excellent at tolerating heroin use on Market Street, they’re also proficient at tolerating vehicular crime, from sailing through red lights (23 fatalities downtown last year) to minor stuff like illegal – oops, undocumented – car mods.
For a progressive burg, SF has a lot of muscle cars, Oddly, many of the car nuts in San Francisco use the term “Frisco,” against local norms.
Back in the ’70s, in my small Ohio town, the losers drove muscle cars to high school. A very few of these cars had amazing acceleration ability. A variant of ’65 Pontiac Catalina could do zero to 60 in 4 1/2 seconds. A Tesla might leave it in the dust, but that was something back then. While the Catalina’s handling was awful, it could admirably smoke the starting line. Unlike the Catalina, most muscle cars of the ’60s and ’70s – including the curvaceous ’75 Corvette – were total crap, even for accelerating. My witless schoolmates lacked any grasp of the simple physics that could explain how and why their cars were crap. I longed to leave those barbarians and move to someplace civilized. I ended up in San Francisco.
Those Ohio simpletons strutted their beaters’ ability to squeal tires from a dead stop. They did this often, in case any of us might forget just how fast their foot could pound the pedal. Wimpy crates couldn’t burn rubber like that. So their cars must be pretty badass, they thought. Their tires would squeal with the tenderest touch of the pedal. Awesome power, right?
Actually, it meant a badly unbalanced vehicle design combined with a gas-pedal-position vs. fuel-delivery curve yielding a nonlinear relationship between pedal position and throttle plate position. This abomination of engineering attracted 17-year-old bubbas cocksure that hot chicks dig the smell of burning rubber. See figure A.

Fig. A
This hypothetical, badly-designed car has a feeble but weighty 100 hp engine and rear-wheel drive. Its rear tires will squeal at the drop of a hat even though the car is gutless. Its center of gravity, where its weight would be if you concentrated all its weight into a point, is too far forward. Too little load on the rear wheels.
Friction, which allows you to accelerate, is proportional to the normal force, i.e. the force of the ground pushing up on the tires. That is, the traction capacity of a tire contacting the road is proportional to the weight on the tire. With a better distribution of weight, the torque resulting from the frictional force at the rear wheels would increase the normal force there, resulting in the tendency to do a wheelie. This car will never do a wheelie. It lacks the torque, even if the meathead driving it floors it before dumping the clutch.
Figure A is an exaggeration of what was going on in the heaps driven by my classmates.
Above, I noted that the traction capacity of a tire contacting the road is proportional to the weight on the tire. The constant of proportionality is called the coefficient of friction. From this we get F = uN, meaning frictional force equals the coefficient of friction (“u”) times the normal force, which is, roughly speaking, the weight pushing on the tire.
The maximum possible coefficient of friction on smooth surfaces is 1.0. That means a car’s maximum possible acceleration would be 1g: 32 feet per second per second. Calculating a 0-60 time based on 1g yields 2.73 seconds. Hot cars can momentarily exceed that acceleration, because tires sink into small depressions in pavement, like a pinion engaging a rack (round gear on a linear gear).
Here’s how Isaac Newton, who was into hot cars, viewed the 0-60-at-1-g problem:
- Acceleration is change in speed over time. a = dv/t.
- Acceleration due to gravity (body falling in a vacuum) is 32.2 feet per second.
- 5280 feet in a mile. 60 seconds in a minute.
- 60 mph = 5280/60 ft/sec = 88 ft/sec .
- a = delta v/t . Solve for t: t = dv/a. dv = 88 ft/sec. a = 32.2 ft/sec/sec. t = dv/a = 88/32.2 (ft/sec) / (ft/sec squared) = 2.73 sec. Voila.
The early 428 Shelby Mustangs were amazing, even by today’s acceleration standards, though they were likely still awful to steer. In contrast to the noble Shelbys, some late ’60s – early ’70s Mustangs with inline-six 3-liter engines topped out at just over 100 hp. Ford even sold a V8 version of the Mustang with a pitiful 140 hp engine. Shame, Lee Iacocca. It could do zero to 60 in around 13 seconds. Really.
Those cars had terrible handling because their suspensions were lousy and because of subtle aspects of weight distribution (extra credit: see polar moment of inertia).
If you can’t have power, at least have noise. To make your car or bike really loud, do this simple trick. Insert a stack of washers or some nuts between the muffler and exhaust pipe to leave a big gap, thereby effectively disconnecting the muffler. This worked back in 1974 and, despite civic awareness and modern sensitivity to air and noise pollution, it still works great today. For more hearing damage, custom “exhaust” systems, especially for bikes (cops have deep chopper envy and will look they other way when your hog sets off car alarms), can help you exceed 105 db SPL. Every girl’s eye will be on you, bud. Hubba hubba. See figure B.

Fig. B
I get a bit of nostalgia when I hear those marvels of engineering from the ’60s and ’70s on Market Street nightly, at Fisherman’s Wharf, and even in my neighborhood. Our police can endure that kind of racket because they’re well-paid to tolerate it. Wish I were similarly compensated. I sometimes think of this at 4 am on Sunday morning even if my windows are closed.
I visited the old country, Ohio, last year. There were no squealing tires and few painfully loud motors on the street. Maybe the motorheads evolved. Maybe the cops aren’t paid enough to tolerate them. Ohio was nice to visit, but the deplorable intolerance was stifling.
Representative Omar’s arithmetic
Posted by Bill Storage in Probability and Risk on July 28, 2019
Women can’t do math. Hypatia of Alexandria and Émilie du Châtelet notwithstanding, this was asserted for thousands of years by men who controlled access to education. With men in charge it was a self-fulfilling prophecy. Women now represent the majority of college students and about 40% of math degrees. That’s progress.
Last week Marcio Rubio caught hell for taking Ilhan Omar’s statement about double standards and unfair terrorism risk assessment out of context. The quoted fragment was: “I would say our country should be more fearful of white men across our country because they are actually causing most of the deaths within this country…”
Most news coverage of the Rubio story (e.g. Vox) note that Omar did not mean that everyone should be afraid of white men as a group, but that, e.g., “violence by right-wing extremists, who are overwhelmingly white and male, really is a bigger problem in the United States today than jihadism.”
Let’s look at the numbers. Wikipedia, following the curious date-range choice of the US GAO, notes: “of the 85 violent extremist incidents that resulted in death since September 12, 2001, far-right politics violent extremist groups were responsible for 62 (73 percent) while radical Islamist violent extremists were responsible for 23 (27 percent).” Note that those are incident counts, not death counts. The fatality counts were 106 (47%) for white extremists and 119 (53%) for jihadists. Counting fatalities instead of incidents reverses the sense of the numbers.
Pushing the terminus post quem back one day adds the 2,977 9-11 fatalities to the category of deaths from jihadists. That makes 3% of fatalities from right wing extremists and 97% from radical Islamist extremists. Pushing the start date further back to 1/1/1990, again using Wikipedia numbers, would include the Oklahoma City bombing (white extremists, 168 dead), nine deaths from jihadists, and 14 other deaths from white wackos, including two radical Christian antisemites and professor Ted Kaczynski. So the numbers since 1990 show 92% of US terrorism deaths from jihadists and 8% from white extremists.
Barring any ridiculous adverse selection of date range (in the 3rd week of April, 1995, 100% of US terrorism deaths involved white extremists), Omar is very, very wrong in her data. The jihadist death toll dwarfs that from white extremists.
But that’s not the most egregious error in her logic – and that of most politicians armed with numbers and a cause. The flagrant abuse of data is what Kahneman and Tversky termed base-rate neglect. Omar, in discussing profiling (sampling a population subset) is arguing about frequencies while citing raw incident counts. The base rate (an informative prior, to Bayesians) is crucial. Even if white extremists caused most – as she claimed – terrorism deaths, there would have to be about one hundred times more deaths from white men (terrorists of all flavors are overwhelmingly male) than from Muslims for her profiling argument to hold. That is, the base rate of being Muslim in the US is about one percent.
The press overwhelmingly worked Rubio over for his vicious smear. 38 of the first 40 Google search results on “Omar Rubio” favored Omar. One favored Rubio and one was an IMDb link to an actor named Omar Rubio. None of the news pieces, including the one friendly to Rubio, mentioned Omar’s bad facts (bad data) or her bad analysis thereof (bad math). Even if she were right about the data – and she is terribly wrong – she’d still be wrong about the statistics.
I disagree with Trump about Omar. She should not go back to Somalia. She should go back to school.