In The Road to Clarity, the NY Times discusses how a new font ClearView was developed to make roadsigns more readable. I especially enjoyed the typographic blog typographica’s posting on the font, Clearview: A New Typeface for US Highways which visually highlights the differences between the old and new sign fonts. You can download a close copy of the new font over at Mike The Actuary’s Musings. Key quotes: “Signs that you’d be hard pressed to read at 700 feet were legible at 900 or 1,000 feet” “Clearview showed a 16 percent improvement in recognition over Highway Gothic, meaning drivers traveling at 60 miles per hour would have an extra one to two seconds to make a decision”
“”Representative Jerrold Nadler, whose district includes part of the Brooklyn Bridge, points out that the White House has so shortchanged repair work on roads and bridges, by some $90 billion, that it might make a list of structures it considers worth saving, and another list for what would have to be closed and abandoned for lack of money.” As Is: One Bridge, Needs Work I’m curious what he means. The House of Representatives has the power control the purses of government, so how is this Bush’s fault? If it was the fault of the Republicans, the Democrats have been in power for 6 months, so why haven’t they fixed it? Sure maybe it wouldn’t have been fixed in time, but where is the big ramp up after the change in power to suggest that the Democrats knew any better than the Republicans that infrastructure spending was being under- and miss-spent? Article 1 Section 7 All Bills for raising Revenue shall originate in the House of Representatives; but the Senate may propose or concur with Amendments as on other Bills.”
In answering this question in the simplest way, I don’t think it’s enough to say “complex numbers are important because they’re sometimes solutions to equations with real coefficients.” We need to find an example where the complex solutions yield real results. The simplest college-level example is probably the solution to the second-order differential equation that governs spring oscillation, but 7th-graders don’t know differential eqs. Difference equations, however, might be more understandable to a seventh-grader. For instance, consider the recursive system a(t+2) = a(t+1) + a(t), with a(0)=a(1)=1. This is just the Fibonacci sequence, which I think most grade-school kids can understand or might have been exposed to (I first saw it in third grade at a public school). Now supposed you want evaluate a(1000) without having to calculate a(999),…,a(1). You can derive a closed-form non-recursive solution to this system of the form a(t) = A*r1^t+B*r2^t where r1 and r2 are the irrational roots of the equation r^2=r+1, and A and B are determined by the initial conditions. What’s beautiful about this example is that though the equation involves irrational numbers, the solution yields integer results for integer initial conditions. From there, it’s not hard to leap to the example of the difference equation a(t+2) = a(t+1)-a(t) which exhibits oscillitory behavior, and it’s not too hard to think of a practical application for this equation. Here the solution is the same form as above, except the roots are now complex. Here even though the closed form solution involves all sorts of irrational and complex numbers, you still get integer results when you evaluate the equation given integer initial conditions. I think this is about the simplest application of complex roots leading to real results that you can get.
“What were the 10 hottest years in American history? From highest to lowest, “1934, 1998, 1921, 2006, 1931, 1999, 1953, 1990, 1938, 1939″ It isn’t only economic figures that are revised, recent records of US temperatures have been revised down considerably.”
I project has taken me out of town for two days and so posting will be light to nonexistant until Friday.
“With an eye toward the high shipping and handling costs, I was wondering if Snapfish, the photograph printing/developing service that I’ve used for the last 7 or 8 years was still deserving of my business. A recent (2007) review by Top 10 Reviews found that Snapfish was the second best. Given that the best was no cheaper in bulk, the photo quality was the same, and Snapfish has given me years of flawless customer service, I’m sticking with them. Take a look at how your preferred printer compares. Most of my friends use Snapfish or Kodak Easy Share, so I was surprised that Kodak came in dead last.”
“An amazing article on corn ethanol from the July 24 issue of Rolling Stone, Ethanol Scam: Ethanol Hurts the Environment And Is One of America’s Biggest Political Boondoggles, is fantastic and a must read for anyone interested in understanding American energy policy or who thinks that Ethanol should be a big part of America’s fight against anthropogenic climate change. A few quotes: “The most seductive myth about ethanol is that it will free us from our dependence on foreign oil. But even if ethanol producers manage to hit the mandate of 36 billion gallons of ethanol by 2022, that will replace a paltry 1.5 million barrels of oil per day — only seven percent of current oil needs. Even if the entire U.S. corn crop were used to make ethanol, the fuel would replace only twelve percent of current gasoline use.” “Nor is all ethanol created equal. In Brazil, ethanol made from sugar cane has an energy balance of 8-to-1 — that is, when you add up the fossil fuels used to irrigate, fertilize, grow, transport and refine sugar cane into ethanol, the energy output is eight times higher than the energy inputs. That’s a better deal than gasoline, which has an energy balance of 5-to-1. In contrast, the energy balance of corn ethanol is only 1.3-to-1 – making it practically worthless as an energy source. “Corn ethanol is essentially a way of recycling natural gas,” says Robert Rapier, an oil-industry engineer who runs the R-Squared Energy Blog.” “…The gas tank of an SUV with pure ethanol requires more than 450 pounds of the difference between ethanol from corn and ethanol from cellulose is “like the difference between traveling to the moon and traveling to Mars.”corn — roughly enough calories to feed one person for a year…In Mexico, tortilla prices have jumped sixty percent, leading to food riots. In Europe, butter prices have spiked forty percent, and pork prices in China are up twenty percent. By 2025, according to Runge and Senauer, rising food prices caused by the demand for ethanol and other biofuels could cause as many as 600 million more people to go hungry worldwide.” “…the difference between ethanol from corn and ethanol from cellulose is “like the difference between traveling to the moon and traveling to Mars.”””
“I am saddened to report that that Abigail Alliance for Better Access to Developmental Drugs that I mentioned in my posting Dying so that others may live lost their most recent appeals court ruling in the U.S. Court of Appeals for the D.C. Circuit. Now more people have to die so that they can be protected from the side effects of drugs. I know I feel safer already.”