I received an email earlier to day trying to promote some sort of a boycott of Exxon/Mobile Mobil gasoline stations in an effort to force them to lower their gas prices. Recognizing that there are few around my neck of the woods, I didn’t pay much attention to the email. Plus, I pretty much disregard those kinds of efforts anyway.

A follow up email attempted to make the point that we aren’t paying that much more for gasoline considering a significant increase in fuel efficiency over the last 20 - 30 years. The examples cited were anecdotal and encouraged me to do a little research on my own.

I was surprised to see that the increase in fuel economy is a lot less than one might have expected over the last 30 years. According to the National Highway Traffic Safety Administration (NHTSA) the average gas mileage for new vehicles sold in the United States has gone from 23.1 miles per gallon (mpg) in 1980 to 26.7 mpg in 2007. This represents a paltry increase of 15% over the 27 year period. Even if you limit yourself to domestic passenger cars the increase is from 22.6 mpg in 1980 to 31.3 mpg in 2007.

Even more interesting to me is the fact that we have benefited from a relatively low cost of gasoline for an extended period of time. (see here) Adjusting for inflation we see a steady decline in the cost of gasoline dating all the way back to the 1920s. The only exception is the late 70s, early 80s and the last 5 years. Prices are at their upper limit even with inflation considered. When considering only yearly averages, the highest cost occurred during 1981 at $3.17 (adjusted to 2008 dollars). Through March of 2008, this year’s annual average has been $3.08.

Now back to the original point, on average the cost (in 2008 valuation) per mile was 12.8 cents in 1981 (when gas averaged $3.17 per gallon in 2008 dollars and the average fuel economy was 24.6 miles per gallon) . The average cost per mile, currently, is 13.6 cents (with a current national average of $3.63 per gallon and average fuel economy of 26.7 mpg). In the end, while it seems that we are paying a ghastly amount at the pump we aren’t that far above the historical high, nevertheless we are, in fact, paying more than ever.

written by SplineGuy

Professor Andrew Watson of the University of East Anglia has recently published a paper in the February issue of Astrobiology entitled Implications of an anthropic model of evolution for emergence of complex life and intelligence. In this article he argues that a number of limitations must be overcome in order for evolution to progress to the point to leading to intelligent live.

Watson postulates that for intelligent observers to evolve, a small number (n) of very difficult evolutionary steps must be passed. Once passed, evolution occurs quickly until the next stage is reached. Complex and intelligent life evolved quite late on Earth and Watson suggests that this may be because of the difficulty in passing these stages. He suggests that n is less than 10 and most likely equal to 4. These stages include the emergence of single-celled bacteria, bacteria with complex cells, cells allowing complex life forms, and intelligent life.

Professor Watson uses the Earth’s fossil records to establish upper bounds on the probability for each state.

The work supports the Rare Earth hypothesis which postulates that the emergence of complex multicellular life (metazoa) on Earth required an improbable combination of astrophysical and geological events and circumstances.

Read more about his paper at Plus Magazine.  At the time I am writing this entry, the article is freely available at the Astrobiology Journal site.

written by SplineGuy

Philip Stark, a statistician at UC Berkeley, has been able to provide a more reliable technique for performing recounts of close elections.  As technology has entered into the voting realm, different kinds of errors have crept into the election system.  Based on election results, certain forms of recounts will undoubtedly need to be performed.  Hand counting is not necessarily any more accurate than the electronic count, each recount technique suffers from its own batch of problems.

Statistical methods have been developed to help provide an accurate recount procedure that takes into account the election results to verify that a sampling recount is 99% likely to be the same as a full hand recount.

The story below appeared on MathTrek.

By Julie J. Rehmeyer

Counting is hard. Neither people nor machines seem to be able to do it reliably. And that’s a nightmare for election officials who need an accurate ballot count to decide elections.

Eighteen states require officials to double-check the machine counts by hand for a portion of the ballots. But election officials have had little guidance on what to do with the recount results. If the election is close and the recount finds a few errors, should a registrar call for a larger recount or go ahead and certify the result? Most laws left it to their discretion.

Now Philip Stark, a statistician at the University of California, Berkeley, has developed a recount method that guarantees a 99 percent chance that the result is the same as it would be with a full hand count. Several counties in California plan to try out the method on ballot measures during the presidential primaries this year. If this trial and others go smoothly, California could adopt the method statewide.

…

MathTrek: Checking It Twice

written by SplineGuy

Mathematicians at the University of Exeter in England model traffic jams based on the cascading effect of driver responses to the brake lights in front of them.  Not only does the mathematical model answer questions about why traffic can creep to a stop without any accident or obstruction, but it may also lead to better strategies for traffic management.

The story below appeared on KHOU.com:

The Math Behind Houston’s Traffic.

By Lee McGuire / 11 News

It doesn’t take a genius to know that accidents cause traffic jams. But it did take a genius to figure out why sometimes rush-hour traffic slows to a bewildering stop for no apparent reason at all.

In the last few months, two mathematicians at the University of Exeter in England came up with this equation, which has become something of a validation for engineers urging new approaches to traffic management. It’s changing things in Houston already.

Rice University’s Rolf Ryham explains the man.

He said for the first time, this equation takes driver “reaction time” into account. What’s revealed here could hold the key to solving Houston’s traffic problems.

Basically it’s mathematical proof that on a crowded freeway, when one driver just taps on his brakes, the driver behind him reacts and brakes a little more. The driver behind him brakes even more, and so on until drivers actually stop moving. It’s the kind of jam that happens on 290 every day.

“Slowing traffic down a little bit during peak periods is OK,” Highway 290 Expansion spokesman Stephen Hrncir said. “It’s the near-stop conditions we need to avoid.”

It’s called “cascading.” You can see it by speeding up video of 290 at rush hour. There are waves of congestion moving backward. The ripples start when someone up front does something that causes drivers behind him to brake, starting a cascade of slowing traffic.

…

The math behind Houston’s traffic | TOP STORIES | Breaking Houston News, Weather, Sports, Traffic, Video from KHOU.com | 11 News

written by SplineGuy

Are you flush with free time or procrastinating on some big important project?

Try out the Bulbous Blob Puzzle.

Professor Albert von Braun, noted food researcher and author of the Chinese Laundromat Cookbook, has just made a major breakthrough on his long sought after Grand Unified Meal Theory. Working in his laboratory late into the night he has, at long last, proved the mathematical link between the five foundation sauces of French cuisine and the thirty-one basic flavors of ice cream.

Your job is to free the reb blob from the laboratory. Can you accomplish this task before the tasty blobs of death make a meal out of you?

Plus, if you really enjoy yourself you can order the low-tech version that you can play without a computer!

written by SplineGuy

Did you know that 95% of all statistics reported on blogs are made up?

Not only that, but you have to be particularly careful when reading reports coming out from the media that interpret poll results. Here’s a perfect example.

Two stories came out from the Associated Press in the last two days. The first story was out on December 30,
AP Poll: Americans Optimistic for 2007.

Apparently, this was a little too upbeat and positive so the next day they offered this story,
Poll: Americans see gloom, doom in 2007.

Here’s the irony: They’re reporting on the same poll!

HT: Little Green Footballs

written by SplineGuy

There are currently a few bugs still to be worked out but, as I mentioned in yesterday’s post, the transition to the new server has gone fairly smoothly. You might’ve noticed my weather plugin on the sidebar is on the fritz.

The primary reason for the switch was that the previous server was a borrowed machine. It was here only until I found a suitable and affordable replacement. The $75 computer mentioned in yesterday’s entry was a perfect solution since it allowed me to toy with LINUX and do so cheaply.

I have some familiarity with LINUX and UNIX through my research that I did at the HPCC at TTU. The SGI Origin 2000 multiprocessor ran IRIX, the SGI version of UNIX. I can still remember my first few days learning it. It had been years and years since my experience in command line environments, even then it was either the Applesoft BASIC environment or booting MSDOS from the floppy. I wasn’t even in High School yet. Still, it helped quite a bit to have had that experience and to have developed a sense of “tinkering”.

As for my server, I went with the default configuration for the SUB-100, namely Xubuntu. As I understand it, this is probably the most ideal version of LINUX for an older machine. At any rate, I added Apache2, PHP, MySQL, ssh support, SAMBA (to share data on a recently purchased 160G hard drive with my windows machines on my home network), ftp support, an SMTP server (req. authentication), and I think that is about it.

Each step along the way took anywhere from a few minutes (Apache, PHP, MySQL) to 5 or 6 hours (SMTP, FTP). I am most proud to have successfully set up the webserver to point to my ext. hard drive and then also allow each of the other 3 computers that regularly use the home network to access it as a shared drive.

Some people fear change….

Not me, I fear stagnation. If something stays the same too long, I’ll break it, just to fix it. That is, as long as it relates to technology. I’ve had enough of that stupid swimming pool!

written by SplineGuy

Barry Bonds has surpassed Babe Ruth’s homerun record but a large contingent of basefall fans are less than thrilled at the news.  The likelihood of steroid use has tainted the achievement of Bonds prompting many to suggest either an asterisks beside the record or simply a denial of the record entirely.  David Young of Glenshaw, Pa.. has suggested that simple math could resolve the whole issue. Apparently, he believes any suspicious use of performance enhancers should require the actual number of home runs obtained by an individual be multiplied by a 0.9 weight factor. On the other hand, any performance inhibitors, such as the legendary obesity, beer guzzling and womanizing habits of the Babe, should require a weight factor of 1.1. When all is said and done, the single season record would still go to Roger Maris at 67, who survived crushing media scrutiny. Second place would be the Babe with 66, Bonds a close third with 65.7, then McGwire at 63 and Sosa at 60. By the way, actual totals are given by Bonds (73), McGwire (70), Sosa (66), Maris (61) and then Ruth (60). In should be noted, however, that exactly where Young’s numbers of 0.9 and 1.1 come from is a mystery. It likely was derived just to put the order as he would like it. We should be careful not to use math to simply artificially manipulate the decision process. After all, 95% of all statistics are made up, right?

By the way, I find it quite interesting that amidst all the controversy of Bonds, we are likely to see others join the exclusive club of Aaron-Bonds-Ruth in the fairly near future. Alex Rodriguez recently became the first player to top 400 homeruns before the age of 30. Others in the realm of possibility include Pujols and possibly even Manny Ramirez or Jim Thorne. Read more here.

written by SplineGuy

A worthwhile read:

Medical Guesswork

Modern medicine seems to have missed the usefullness of using mathematics as a decision making process.  This article is about Dr. David Eddy, a cardiac surgeon, who “discovered the beauty of mathematics and its promise of answering medical questions.”  After making it through a two-year math course in a couple of months, he persuaded Stanford to accept him as a PhD student in the mathematically intense field of Engineer-Economics Systems.  He has since spent his career promoting what he calls, “Evidence-based medicine.”

Apparently there is a truly alarming number of common practices, treatments and medicines that are utilized, not because of proven effectiveness, but merely as “cherished physician myths.”  As a couple of examples he showed that the annual chest X-ray is worthless, and he traced the general practice of preventing women from giving birth vaginally if they had previously had a cesarian to one lone doctor’s recommendation.

One of the more interesting portions of the article is where it describes Eddy’s development of a computer model that helped him crack the “diabetes puzzle.”

The human brain, Eddy explains, needs help to make sense of patients who have combinations of diseases, and of the complex probabilities involved in each. To provide that assistance, Eddy has spent the past 10 years leading a team to develop the computer model that helped him crack the diabetes puzzle. Dubbed Archimedes, this program seeks to mimic in equations the actual biology of the body, and make treatment recommendations as well as figure out what each approach costs. It is at least 10 times “better than the model we use now, which is called thinking,” says Dr. Richard Kahn, chief scientific officer at the American Diabetes Assn.

I strongly recommend this article as just another example of the many, many applications of mathematics that make a real difference in the world.

written by SplineGuy

I just finished reading an article in today’s paper that discussed a proposal before the Texas Transportation Commission whereby two interstate highways in West Texas would have their speed limits boosted to 80 mph. Wow. For most of my driving life, that is, since the time I was sixteen, I would have thought that was awesome. But I can tell I am getting old when I start thinking thoughts like, “That’s just too darn fast.”

Reading through the article I could only find two real reasons why this was considered a good idea. Unfortunately, both reasons are flawed:

1. “Carlos Lopez, director of traffic operations for the department, said a survey of both interstates found that 85 percent of motorists were driving up to 79 mph.”
   • I will definitely be passing that along to our resident statistician as a perfect example of an abuse of statistical data. This statistic really tells you nothing. It looks like an argument that a vast majority are already driving over the current speed limit of 70 so it makes sense to move the speed limit up. Unfortunately, this statistic doesn’t tell you how many people are breaking the current speed limit. Notice how the statistic includes all speeds from 0 up to 79 mph. What if we were to learn that 84.9% of all people were driving up to 70 mph? That is certainly possible under the provided statement. If nothing else, the statement needs to be clarified so as to indicate what percentage of drivers are breaking the current speed limit.
   • It also surprises me that 15% of drivers were found to be driving 80 or more. This brings up another good point: Are drivers “consistently” driving that fast or did the survey simply ask if a driver “ever” drove that fast? For example, we might conclude that those 85% of drivers set their cruise control on 79 everytime they hit the interstate, but just as likely, they may “occasionally” drive over the speed limit, and even less frequently, up to 79 mph. In the end, the argument that “Everybody’s doing it” is not only a bad argument but it is not supported by the information provided.
2. “It’s generally considered a safer condition when motorists are traveling at a uniform speed,” [Randall] Dillard said.
   • Let’s take that what he says is true. Is that independent of the speed at which we travel. For example, it seems that his argument makes perfect sense if the flow of traffic is 60mph and someone comes along and drives 20 mph. There is a lack of safety at that point. It’s simply the principle of relative motion, if two objects are moving in the same direction at different but constant velocities then the difference in their velocities represents their motion relative to each other. On the other hand consider the case where we might raise the speed limit to 150 mph. One car is traveling 150 mph and the other is 140 mph. That would be exactly the same relative velocity as if one were traveling 80 mph and the other 70 mph. And yet there is an obvious difference between the two scenarios. I think the second is much safer than the first simply due to the magnitude of the velocities and not their difference. Thus, Dillard’s idea must have some upper bound. That is, to a certain point it is safer when motorists are traveling at a uniform speed. So the question is whether 80mph is beyond that point. Again maybe I’m getting old, but it seems like it just may be.

The article makes a pretty good set of points in opposition to the proposal citing things like safety and gas mileage as clear drawbacks to the proposal. In fact, I was already planning on posting something with respect to this before I read the article.

I discovered this past week as I was commuting back and forth to Lubbock (a roughly 50 mile one way trip) that if I average 60 mph instead of my usually 73 mph that my gas mileage shot up from 29 mpg to 37.5 mpg. Wow, I say, Wow! 37.5 mpg is wonderful, especially if you consider that I will be making that trip 4 times a week. That is roughly 400 miles per week.

At 29 mpg that would run me about 13.8 gallons per week. At $2.749 a gallon, I’m paying $37.92 in gas a week.

At 37.5 mpg that would run me about 10.67 gallons per week, which comes to $29.32 in gas a week. I’m saving $8.60 a week for 12 weeks. A grand total of $103.20. Not bad. Now the final question is whether Lori thinks that the extra 18 minutes a day (or 14 hours and 24 minutes total for the summer) is worth $103.20.

written by SplineGuy