Online Cortex Thoughts on Science and Technology

Gasoline prices are skyrocketing.  In some parts of the country, the price of gasoline is expected to hit $4.oo a gallon.  Furthermore, while there is a correlation between oil and gas prices, there has been an alarming net increase of gas prices with respect to oil.  Here I show that 60 cents per gallon of today’s gasoline costs are unexplained by the oil prices.

The above graph is taken from OILNERGY and shows the oil and unleaded gasoline prices (among others) over the last year.  Clearly one can see by visual inspection that the two curves are correlated.  The point to notice however, is that there has been a growing gap between the two curves indicating that gasoline prices have been increasing with respect to the oil prices.  This is what those in the media are referring to when they say that the prices are no longer correlated.

I collected the following data from the U.S. Energy Information Administration’s This Week in Petroleum website and made some useful graphs.  First look at the Crude Oil WTI prices

The gasoline prices are clearly correlated, as one would expect

To compare the oil prices to the gas prices, I adjusted the oil prices by subtracting the mean oil price, rescaling the oil price so that it is on the same scale as the gas price, and added the mean gas price:

where represents the standard deviation (scale) of the oil prices and represents the standard deviation (scale) of the gas prices .

The figure above plots both the gas prices with the rescaled oil prices.  The result is that the gas prices follow the rescaled oil prices pretty well, which indicates that the price of gasoline is approximately linearly proportional to the price of oil. However, since April 2007, the gas prices have begun to deviate from this linear correlation by as much as 62 cents a gallon on May 14. Given that the price of a gallon of gas was $3.07 on that date, this is a 20% unexplained deviation.  This difference plot is shown below, where green indicates that gasoline is lower than average from the rescaled oil price, and red indicates that it is higher than average.

This deviation is of a magnitude unseen in the last two years.  A 20% deviation like this requires an explanation, and the nature of the deviation indicates that a new mechanism is at work.

Kevin Knuth
Albany NY

Posted under Energy, Uncategorized

I finally received my long-awaited copy of Maximum Lego NXT: Building Robots with Java Brains by Brian Bagnall.  I was pleased to see that in addition to the in-depth discussions regarding writing code for these robots in Java, that there were also some interesting projects.

My favorite was the Lego implementation of the Rocker-Bogie suspension, which was used in the Mars Sojourner rover, as well as Spirit and Opportunity.  Note that the figure above is a prototype of Sojourner, which exhibits the Rocker-Bogie suspension.  I am looking forward to building it and learning how it works.

You can buy the book at Amazon.com here…

Kevin Knuth
Albany NY

Posted under Exploration, Fun, Intelligent Systems, Lego, NXT, Physics, Research

Ornithologists Alexander Cortés-Diago and Luis Alfonso Ortega recently announced the discovery of a new hummingbird in the cloud forests in the Serrania del Pinche in south-west Colombia.  The bird was sighted three times during surveys of the region in 2005. 

Surveys in 2006 yielded photographs of the bird, which enabled scientists at the International Bird Conservation/Zoological Research Museum in Germany to identify the bird as a new species.

The hummingbird, which has been named the Gorgeted Puffleg Eriocnemis isabellae, is named for the iridescent throat patch (after gorget which was a crescent-shaped piece of ornamental armor worn around the neck) and the puffy feathers around its legs. 

Currently Serrania del Pinche, the habitat of the Gorgeted Puffleg, is unprotected and is being threatened by slash-and-burn agriculutre and growing coca fields. 

Kevin Knuth
Albany NY

Posted under Birds, Wildlife

While working with POV Ray, I stumbled on this great article from the American Mathematical Society’s Monthly Essays.  This article examines the Lorenz attractor and its periodic orbits.  It turns out that the periodic orbits form knots, but not just any knots.  They comprise only a very small subset of possible knots.

The article continues to examine modular flows on lattices, and the periodic orbits that result.  It turns out that the knots defined by these periodic orbits on the modular flow coincide with the Lorenz knots!

Kevin Knuth
Albany NY

Posted under Mathematics

This is a fun Lego creation of mine.  Basically it is a large 2D version of a Hoberman sphere.  Why did I not make a large Hoberman sphere?  First, the parts to make the circle cost almost $80 US.  Second, I have other more pressing projects I am working on.

So here is what I call the Blossoming Lotus.  It is about 4 feet in diameter when completely extended and is pretty impressive.  Its relatively easy to make.  My design consists of two interlocking pieces: a single-claw arm and a double-claw arm.  The parts needed to make the two arms are illustrated below.

To make the entire circle, one needs 20 copies of each arm.  The job then is to put them all together.  I will post detailed instructions on a website in the near future.  For now, here is a closeup of the circle when completed.

And of course, the project wouldn’t be complete without that animation above made with MLCAD, L3PAO, and POV Ray.  The animation was straightforward—once you get the geometry right (which is not straightforward).  I will post a lesson on the geometry and the animation of this creation in the future as well.  For now, enjoy.

Kevin Knuth
Albany NY

Posted under Fun, Lego