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April 30, 2007

Physicists Prefer Turkeys

Geneticists have their fruit flies, pharmacologists have their mice, physiologists have their primates, and psychologists have their pigeons; but physicists prefer turkeys. Benjamin Franklin performed some of the first experiments with electricity after retiring from his printing business in 1745. Indeed, Franklin was one of the founders of the scientific study of electricity. Of course, many scientists look for practical application of their work, and Franklin believed that electrocuted turkeys were much more tender than otherwise prepared birds. In the summer of 1749, Franklin hosted a barbecue in which an electrocuted turkey was roasted and served. The fire was lighted electrically, and Franklin had improvised an electrically actuated motor to rotate the turkey on a spit.

Franklin may have tempered his experiments with turkeys after 1750. On December 23, 1750, Franklin attempted to electrocute a turkey for his Christmas dinner. He used two large Leyden jars (a primitive air dielectric capacitor) which he described as having the capacity of forty typical jars. He took a shock through his arms that knocked him unconscious. When he came to his senses, he felt a "violent, quick shaking of my body, which gradually remitted." Franklin was numb for a while, and he was sore for a few days thereafter. Franklin communicated this accident to others who were experimenting with electricity to warn them of the dangers. He went on to conduct experiments that proved that electrical charge was conserved, and he invented the lightning rod after observing that sharp points more easily released and accepted charge. His experiments are summarized in his book, "Experiments and Observations on Electricity."

More than two hundred years later, in 1981, scientists at IBM's Thomas J. Watson Research Center used leftovers from a Thanksgiving turkey in their discovery of excimer laser surgery. Possessing one of the first ArF excimer lasers, they knew that high fluence pulses from the 193 nm laser light would cleanly cut plastic. They did some quick experiments on their fingernails, which patterned easily, but knowing the dangers of ultraviolet radiation on skin, they weren't willing to see what would happen on skin. One of them, Rangaswamy "Sri" Srinivasan, brought some leftover Thanksgiving turkey to the lab, and they observed very clean incisions of cartilage, much cleaner than incisions made with a 532 nm Q-switched, frequency-doubled, YAG laser. This led to a patent [3] and the subsequent development of laser refractive eye surgery.

1. December 23, 1750: Ben Franklin Attempts to Electrocute a Turkey, APS News vol. 15, no. 11 (December 2006).
2. James J. Wynne, "Ben Franklin Blazes Trail for IBM Inventors," APS News vol. 16, no. 3 (March 2007).
3. Samuel E. Blum, Rangaswamy Srinivasan, James J. Wynne, "Far Ultraviolet Surgical and Dental Procedures," US Patent No.4,784,135 (Nov 15, 1988).

April 27, 2007

Physics and Math Education - A Mixed Report Card

Engineers live by the motto, "If you can't measure it, you can't improve it." Data collection is an important part of our attempts to improve materials and systems. Since 1969, the National Assessment of Educational Progress (NAEP) has measured the performance of US students in reading, mathematics, science, writing, the arts, and other areas. NAEP reports are essentially the report cards for the nation as a whole. Unfortunately, the latest report card shows that we're failing mathematics [1]. According to the report on the latest (2005) assessment [2], only 23% of graduating high school students are considered to be proficient in mathematics, while 61% performed at a basic level. Not surprisingly, male students scored higher than female students on average in areas concerning spatial reasoning, something that has always been true.

Although there are several ways to address the problem of low math and science scores, Washington state has decided on a novel approach. It is considering eliminating those pesky math and science sections of its standardized test, the Washington Assessment of Student Learning (WASL), that so few students pass [3]. They would be replaced by tests administered right after students finish their courses in these subjects.

It's always surprised me that physics is not a required subject at the secondary school level. Most students have the option of not taking a physics course. A recent study by the American Institute of Physics shows that enrollment of high school students in physics is at an all time high. Physics Bachelor and Ph.D. degrees are being granted at higher rates. Presently, 30% of high school seniors have taken physics, and bachelor's degrees have increased 31% since 2000. Females now represent 47 percent of high school physics students. Although some of these students have taken conceptual, or non-computational, physics courses, they still have enough understanding of physics to make informed decisions as to where their tax dollars go.

1. Jeffrey Mervis, "U.S. Math Tests Don't Line Up," Science, vol. 315. no. 5818 (16 March 2007), p. 1485 (Subscription Required).
2. The Nation's Report Card: 12th-Grade Reading and Mathematics 2005
3. Linda Shaw, "Seattle Times: 10th-grade WASL may ditch math and science (March 26, 2007)
4. Turner Brinton, "High school physics enrollment hits record high." (American Institute of Physics, January 10, 2007)

April 26, 2007

Extrasolar Planets

The biggest idea in physics is this, that physical laws are the same everywhere in the universe. Until the time of Copernicus, most people believed that the heavens were composed of a different substance than earth - something crystalline and very perfect. Newton made a fundamental advance in science by proposing that the gravitational force acting between an apple and the earth was the same as that acting between the moon and earth. Conservation of angular momentum is a physical law, and when it's applied to stars it yields an interesting possibility. Stars form from the gravitational condensation of matter (mostly hydrogen) around a nucleus. Because of angular momentum conservation, any small spin in this condensing cloud produces a huge angular momentum that must be conserved as a star forms. This means that the stellar nucleus must spin at a faster and faster rate. With a statistical distribution of initial angular momentum, some cases will result in a nucleus spinning so fast that it becomes unstable, and it divides into parts. The result is often a binary star system in which angular momentum is conserved as the orbit of two stars around a common point.

Not all star systems are binary, so where does this excess angular momentum reside? Planets, which orbit at quite a distance from the central star, are a good sink for this excess angular momentum. When I studied astronomy in the 1960s, the common theory was that single stars should all have planets, but the first confirmed detection of an extrasolar planet did not occur until 1995. More than 200 extrasolar planets, or exoplanets, have been detected to date, and the detection rate is about twenty a year. These were first detected by the wobble in position of their central stars caused by their orbital motion. Now, advanced spectrometric techniques can measure the change in velocity of a star caused by the motion of its planets, and this is a more sensitive means of detection. Astronomers estimate that at least ten percent of single star systems have planets.

Most of these planets are more like Jupiter than the Earth. Jupiter is a "gas giant" that's more like a failed star than a planet. Astronomers would rather discover more interesting planets, planets like our own, or in Star Trek parlance, "Class M" planets. Astronomers from the European Southern Observatory (ESO) have done just that in their recent detection of a planet orbiting a star called Gliese 581 (Right Ascension 15h 19m 26s, Declination 07o 43' 20"). The discovery was made at the ESO 3.6-meter telescope in La Silla, Chile.

Gliese 581 is a relatively close star, just 20.5 light years away, in the constellation Libra. This planet was detected by the spectrometric technique of measuring the velocity change of the parent star caused by the planet's orbital motion. This planet, named Gliese 581 c, is about five times the mass of the Earth, and its surface gravity is estimated to be a little more than twice that of Earth. The "c" designation marks this planet as the third discovered planet in the Gliese 581 system. Two other planets, about eight and fifteen Earth masses, were discovered in 2005. If it has a composition similar to the Earth, Gliese 581 c would be about 50% larger in diameter. Gliese 581 c is very close to its star (6.7 million miles), but the star is a red dwarf, which is one third the mass of the sun and cooler. The average temperature of Gliese 581 c is estimated to be between 0 and 40 oC, so liquid water can exist. Gliese 581 c orbits its sun once every thirteen days.

How does a star get a name like Gliese 581? Gliese 581 is listed in a 1969 catalog of stars created by astronomer Wilhelm Gliese, who complied this catalog of all stars within about eighty light years of Earth. Gliese 581 is the 581th entry in this catalog. Of course, the question always arises as to whether an Earth-like planet supports life, possibly intelligent life. Since Gliese 581 is so very close to earth (at least on a cosmic distance scale), the region of this star has been scanned for radio signals by the SETI Institute twice before the discovery of this planet. If they found anything, we would have heard about it.

1. Astronomers Find First Earth-like Planet in Habitable Zone (ESO Press Release (25 April 2007).
2. Preprint of S. Udry et al., "The HARPS search for southern extra-solar planets : XI. An habitable super-Earth (5 M-Earth) in a 3-planet system", submitted as a Letter to the Editor of Astronomy and Astrophysics.
3. Katharine Sanderson, "The most Earth-like planet yet," Nature Online (25 April 2007).
4. Hazel Muir, "'Goldilocks' planet may be just right for life," New Scientist Online (25 April 2007).
5. For several years in the 1970s I was a member of the Astronomical Society of the Pacific.

April 25, 2007

Einstein's Assistant

Today (Wednesday, April 25, 2007) is Administrative Professionals' Day, a day when we honor the person in our department who does all the things we never want to do. This day was known as Secretary's Day, and the tradition began in 1952 with a proclamation by U.S. Secretary of Commerce Charles Sawyer.

If anyone was in need of assistance, it was Albert Einstein, who was known for wearing a different color sock on each foot, when he wore any socks at all [1]. It is apparent that Einstein's mind was focused fully on his work, and he didn't have time for correspondence or paying bills. Fortunately, from 1928 until his death in 1955, he was cared for by his assistant, Helen Dukas.

Helen Dukas (1896 - 1982), was originally a kindergarten teacher, but then worked as a secretary in a Berlin publishing house. Her mother was from the same town as Elsa Einstein, Albert Einstein's second wife, and with this personal connection Dukas was considered for the position as Einstein's secretary and was hired in 1928. Elsa died in 1936, and Helen took over the additional tasks of housekeeper at the Einstein residence at 112 Mercer St, Princeton, New Jersey. Helen Dukas became a naturalized American citizen on the same day as Albert Einstein and his stepdaughter Margot, October 1, 1940. Dukas never married.

When Einstein died in 1955, his Will specified that Dukas, along with Otto Nathan, a German-American economist, would hold rights to his entire literary corpus. Dukas had organized Einstein's papers over the years, so she was an excellent choice for preserving this heritage. Dukas and Harvard Professor Gerald Holton compiled The Collected Papers of Albert Einstein. The original documents were subsequently placed in an archive at the Hebrew University of Jerusalem.

Dukas co-authored a biography of Albert Einstein, "Einstein - Creator and Rebel," with Banesh Hoffmann, one of Einstein's scientific collaborators. She maintained residence in Einstein's Mercer Street house until her death on February 10, 1982.

I present one of my favorite Einstein anecdotes [1].

One day during his tenure as a professor, Albert Einstein was visited by a student. "The questions on this year's exam are the same as last year's!" the young man exclaimed. "Yes," Einstein answered, "But this year, all the answers are different."

1. Einstein Anecdotes.
2. Short life history: Helen Dukas
3. Eulogy for Helen Dukas, Einstein's secretary, delivered by Abraham Pais 1982.

April 24, 2007

Harder than Diamond

Diamond is renown for its hardness. There is a calculation that another material, beta-carbon nitride (β-C3N4) may be harder, but it has not been synthesized. Cubic boron nitride (β-BN) is nearly as hard as diamond, and it is used also as an industrial abrasive. Synthesis of β-BN requires a pressure of about eighteen GPa and very high temperatures (1730-3230oC). All these materials have short covalent bonds, which are particularly incompressible, and these seem to be the key to their hardness. A group at UCLA lead by Sarah Tolbert has used this principle to discover a material which may be as hard as diamond. That material is rhenium diboride (ReB2) [1-3]. Rhenium diboride has been known for many years, but mechanical measurements were never done. The important feature of this material is that it is synthesized under ambient pressures.

Tolbert and her group of six other scientists at UCLA prepared specimens of ReB2 by arc melting to produce ingots a few centimeters in size. They did microindentation hardness tests on them to reveal an average hardness of 48 GPa (diamond has a hardness of more than 140 GPa, and β-BN has a hardness of about 50 GPa) [4]. Although this measurement would indicate that ReB2 is not as hard as diamond, perfectly crystalline ReB2 may be. Tolbert found that some of her specimens would scratch diamond. Since ReB2 has the hexagonal crystal structure, it may have a higher hardness along some crystallographic directions, although a material just below the hardness of diamond (e.g., β-BN) will still scratch diamond.

X-ray diffraction analysis of pressurized specimens gave a bulk modulus of 360 GPa for ReB2, close to that of diamond (443 GPa). Although not as hard as diamond, osmium has the highest reported bulk modulus (462 GPa) [5]. Osmium is not as hard, however, because metallic bonds as more flexible than covalent bonds. One advantage that ReB2 will have over diamond, aside from the easier synthesis, is the fact that diamond cutting of iron alloys creates iron carbide, which dulls the cutting edge.

1. Hsiu-Ying Chung, Michelle B. Weinberger, Jonathan B. Levine, Abby Kavner, Jenn-Ming Yang, Sarah H. Tolbert, and Richard B. Kaner, "Synthesis of Ultra-Incompressible Superhard Rhenium Diboride at Ambient Pressure," Science, vol. 316. no. 5823 (20 April 2007), pp. 436-439.
2. Katharine Sanderson, "Scratching diamond just got easier: Ultra-hard material made in the lab without high pressures" (Nature Online, 19 April 2007).
3. Mason Inman, "Super-tough material mimics metal and crystal" (New Scientist Online, 19 April 2007).
4. Florent Occelli, Paul Loubeyre and René LeToullec, "Properties of diamond under hydrostatic pressures up to 140 GPa," Nature Materials vol. 2 (2003), pp. 151-154
5. Hyunchae Cynn, John E. Klepeis, Choong-Shik Yoo, and David A. Young, "Osmium has the Lowest Experimentally Determined Compressibility," Phys. Rev. Lett. vol. 88, issue 13 (14 March 2002), pp. 135701 ff. Summary article here.
6. Tolbert Group at UCLA.

April 23, 2007

F. Albert Cotton

Nearly every chemist from my generation onwards has learned inorganic chemistry from one particular textbook; namely, "Advanced Inorganic Chemistry" by Cotton and Wilkinson [1]. I'm not a chemist, but my wife is, and she purchased the second edition of this book in 1969 when she was an undergraduate student. All chemists refer to this book, which is now in its sixth edition and has sold a half million copies, by the names of its authors, calling it "Cotton and Wilkinson." It is nearly encyclopedic in breadth, and before the internet I would refer to my wife's edition often for the basic chemical properties of materials. Cotton was sole author of another book, "Chemical Applications of Group Theory," which was known as "Cotton's book." Frank Albert Cotton (1930 - 2007), a prominent American chemist, died this year on February 20 at the age of 76 [2-4].

Frank Albert Cotton, known as "Al" to his friends and colleagues, was born in 1930 in Philadelphia. Originally not straying too far from home, he attended Drexel University; and then Temple University, from which he received his undergraduate degree in 1951. Cotten then left for Harvard, where he studied under Sir Geoffrey Wilkinson, who eventually won the 1973 Nobel Prize in Chemistry for his work on organo-metallic compounds. Not surprisingly, Cotton's 1955 Ph.D. thesis was on metallocenes. Cotton and Wilkinson's stays at Harvard were nearly concurrent. Wilkinson joined Harvard in 1951 and left for Imperial College of the University of London in 1955. It's likely that Cotton's thesis defense was hastened by Wilkinson's departure.

After Harvard, Cotton became a professor at MIT, and just six years later he became the youngest person (thirty-one) to have a full professorship at MIT. Cotton's work focused on a region of the Periodic Table that was usually ignored by chemists of his time - the transition metals. His first real fame came from his 1964 identification of a quadruple bond in the Re2Cl82- anion. Cotton was a proponent of the use of x-ray diffraction in the study of the structure of complex molecules. He and his colleagues elucidated the structure of about 2,500 small molecules. He originated the term hapticity (from the Greek ⌈απτειν, haptein, to grasp or touch) to describe transition metals complexes.

Cotton moved to Texas A&M University in 1972 as its Robert A. Welch Professor of Chemistry, and he stayed their until his death. Cotton was an author of more than 1600 scientific papers, and he supervised the training of 116 doctoral students (Cynics may insert a comment here about the effect of supply and demand on the salary of chemists). Among his many honors, he was a member of the US National Academy of Sciences and the American Philosophical Society. He was the recipient of the National Medal for Science, and the Priestley Medal, as well as twenty-nine honorary doctorates. He is known also for his stance in the Cold Fusion Wars. In 1994 he led a failed campaign to revoke the Distinguished Professor title of another Texas A&M professor, John Bockris, who conducted research on the generally discredited cold fusion process [5].

1. Cotton, F. A. and Wilkinson, G., Advanced Inorganic Chemistry, John Wiley and Sons: New York, 1988.ISBN 9780471199575
2. Tobin J. Marks, "Frank Albert Cotton (1930-2007)," Science vol. 316. no. 5822 (13 April 2007), p. 214.
3. Susan Morrissey, "Obituary: F. Albert Cotton," Chemical & Engineering News vol. 85 no. 9 (February 26, 2007), p. 11.
4. Professor F Albert Cotton (Telegraph (UK) March 3, 2007).
5. Steven Krivit, "Death of Cold Fusion Opponent Albert Cotton Under Investigation" (New Energy Times).

April 20, 2007

Nearly Magnetic Zinc

Zinc (Atomic Number 30) sits next to copper (29) in the first row of the transition metals in the period table, very close to the magnetic elements, iron (26), cobalt (27) and nickel (28). Zinc itself is non-magnetic, presumably because it has a closed shell of d-electrons. Crystal structure is an important factor in determining the magnetic character of a material, so things aren't that easy. If you alloy zinc (electronegativity, 1.65) with a more electropositive metal, such as yttrium (1.22), an electron acceptor, would you bleed enough electrons from the zinc atoms to give them a magnetic character? A team of physicists and chemists from the US Department of Energy Ames Research Laboratory at Iowa State University have done just this, by alloying zinc with iron and yttrium to form crystals that verge on ferromagnetism.

Paul Canfield, Sergey Bud'ko, and Shuang Jia prepared crystals of R1T2Zn20 (where R is a rare earth metal and T is a transition metal). They found that Y1Fe2Zn20 exhibits incipient ferromagnetic behavior, much like palladium. Palladium, especially Pd impurities in other metals, has been a favorite material for fundamental studies on magnetism. Interestingly, Y1Co2Zn20, an alloy modified by substituting cobalt for iron, is very much less magnetic, in line with our electron donor-acceptor theory. Substituting gadolinium, a ferromagnetic rare earth, to make Gd1Fe2Zn20, results in a ferromagnetic material, albeit with the low Curie temperature of 86K. Changing just one atom out of twenty-three has a large affect.

Commenting on this work, Canfield expressed an opinion of materials science that is true in my experience. "Experimentally, it's very important to have design, synthesis and characterization very tightly linked." [2]

1. S. Jia1, S. L. Bud'ko, G. D. Samolyuk & P. C. Canfield, "Nearly ferromagnetic Fermi-liquid behaviour in YFe2Zn20 and high-temperature ferromagnetism of GdFe2Zn20," Nature Physics Online (25 March 2007, doi:10.1038/nphys568).
2. Saren Johnston, "Ames Laboratory Scientists Rethink Zinc." (Ames Laboratory Press Release, April 9, 2007).

April 19, 2007

Combined Heating and Power

The major byproduct of electrical generation is heat. This is true for coal, gas, and nuclear generation. Technologies such as hydroelectric and wind turbine do not produce significant heat. In the Northeast, where I live, residential heating (in my house, a natural gas-fired boiler) is required for a good part of the year. It's no wonder that there is much present interest in combined heating and power (CHP) systems. Fuel is used to produce your electrical power, the excess of which can be sold to the power grid, and the waste heat will heat your home. It's a definite win-win situation.

Combined heating and power systems can utilize about ninety percent of the energy value of a fuel, and they are becoming common in large facilities, such as universities and hospitals. Communities in countries such as Denmark and the Netherlands, where it is common to have a central heating source, are also implementing CHP. Smaller versions of CHP systems have been introduced into Japan, and they have now become available in the United States. Not surprisingly, a company in my chilly hometown of Utica, New York, is in the forefront of CHP marketing.

ECR International of Utica has formed a joint venture with Yankee Scientific, Medfield, Massachusetts. This venture, Climate Energy, also located in Medfield, hopes to sell a few hundred 1.2-kilowatt residential CHP systems this year. It presently has fielded twenty-five systems manufactured by Honda, which has an installed base of about 50, 000 units in Japan. A residential CHP system sells for a few thousand dollars more than a standard gas furnace. In colder states, the payback period for a CHP system can be as short as two years, and there would be a savings of about $500 yearly, thereafter. A German firm, SenerTec, sells a larger 5-kW system for apartment buildings. Germany has an environmental surcharge for using natural gas, but this is waived for CHP systems, and the excess electrical power can be sold to the German power grid at higher than wholesale price. Unfortunately, government support for CHP systems in the US has lagged behind that of other countries.

Although there are many technologies suitable for CHP [2], residential CHP systems are based typically on an internal combustion engine driving an electrical generator. This is a well-developed, robust technology, so most of the implementation is just engineering. Climate Energy's engine runs on natural gas, so it could be fitted into my home, as well as most homes in the US Northeast. Peter Banwell of the U.S. Environmental Protection Agency says that CHP is economical if a home furnace is active more than 4000 hours in a year. There are roughly thirty million homes in the US that are in that category. The only economic disincentive is that the units would not be used in the summer, when electrical rates are the highest.

1. Prachi Patel Predd, "A Power Plant for the Home" (IEEE Spectrum).
2. US EPA Catalogue of CHP Technologies.
3. U.S. Combined Heat and Power Association Web Site.

April 18, 2007

Every Number Has A Story

Number theory is the field of mathematics concerned with the properties of numbers, but most particularly, the integers. The integers consist of the positive natural numbers (1, 2, 3, etc.), zero, and the negative numbers (-1, -2, -3, etc.). The proof of Fermat's Last Theorem [1] is an example of a number theoretic problem, and it was the front-runner number theoretic problem until it was proven by Princeton University mathematicians Andrew Wiles and Richard Taylor in 1994. Proof of the Riemann zeta hypothesis, an hypothesis concerning the distribution of prime numbers among the positive integers, is probably the current front-runner, although every mathematician has his favorite.

Number theorists can think of an unique property for almost any number. Srinivasa Ramanujan (1887-1920) and Godfrey Harold Hardy (1877-1947), two famous number theorists, invented the "Taxicab Numbers." Hardy rode a taxicab to visit Ramanujan one day, and he noted that the taxi was numbered 1729. When he arrived, Hardy told Ramanujan about the number, and said it seemed to be a "rather a dull number." Ramanujan replied that it was actually a very interesting number, since it was the smallest number that could be written as the sum of two cubes in two different ways; that is, 1729 = 13 + 123 = 93 + 103. The number 1729 is now called the Hardy-Ramanujan Number, and numbers that can be expressed as sums of cubes in several ways are called the "Taxicab Numbers."

Erich Friedman, a professor in the Stetson University Mathematics and Computer Science Department has a web site, "What's Special About This Number?," devoted to the positive integers and why they are "special" to mathematicians. I gleaned these gems just from the first hundred numbers, but Friedman has many more.

• 2 is the only even prime.
• 4 is the smallest number of colors sufficient to color all planar maps.
• 6 is the smallest perfect number.[2]
• 8 is the largest cube in the Fibonacci sequence.[3]
• 9 is the maximum number of cubes that are needed to sum to any positive integer.
• 18 is the only number that is twice the sum of its digits.
• 19 is the maximum number of 4th powers needed to sum to any number.
• 24 is the largest number divisible by all numbers less than its square root.
• 25 is the smallest square that can be written as a sum of 2 squares.
• 26 is the only positive number to be directly between a square and a cube.
• 31 is a Mersenne prime.[4]
• 34 is the smallest number with the property that it and its neighbors have the same number of divisors.
• 37 is the maximum number of 5th powers needed to sum to any number.
• 40 is the only number whose letters are in alphabetical order.
• 42 is the 5th Catalan number.[5]
• 50 is the smallest number that can be written as the sum of of 2 squares in 2 ways.
• 72 is the maximum number of spheres that can touch another sphere in a lattice packing in 6 dimensions.
• 76 is an automorphic number.[6]
• 77 is the largest number that cannot be written as a sum of distinct numbers whose reciprocals sum to 1.
• 81 is the square of the sum of its digits.
• 88 is the only number known whose square has no isolated digits (7744).
• 94 is a Smith number.[7]
• 96 is the smallest number that can be written as the difference of 2 squares in 4 ways.
• 100 is the smallest square which is also the sum of 4 consecutive cubes.

1. "If an integer n is greater than 2, then an + bn = cn has no solutions in non-zero integers a, b, and c."
2. Perfect numbers are positive integers that have factors that sum to the integer (e.g., 28 = 1+2+4+7+14).
3. Fibonacci numbers are numbers formed as the sum of their two nearest predecessors (F(n) = F(n-1) + F(n-2)). The first two Fibonaci numbers (needed to start the sequence) are 1 and 1.
4. A Mersenne prime is a prime number of the form M(n) = 2n-1. For M(n) to be prime, n must be prime. The numbers 3, 7, 31, 127, 8191, 131071, and 524287 are the first few Mersenne primes. You can see how this sequence leads to large numbers rather quickly.
5. Catalan numbers ennumerate the different ways a polygon can be divided into triangles. The are best understood by viewing this web page
6. An n automorphic number is a number (a) such that na2 has its last digit, or digits, equal to k. For n = 1, the first few automorphic numbers are 1, 5, 6, 25, 76, 376, and 625.
7. A Smith number is a composite (that is, non-prime) number for which the sum of its digits is the same as the sum of the digits of its prime factors. For example, 94 is a Smith number since 9+4 = 13, and 2+(47) = 2+4+7 = 13.

April 17, 2007

Chilling Out and Chilling In

The ratio of area to volume of a sphere goes as the inverse of the radius, so smaller droplets of liquid will have a much greater opportunity to lose heat by radiation and conduction and will cool at an equilibrium rate. Eli Sutter and Peter Sutter, two scientists at the Center for Functional Nanomaterials at Brookhaven National Laboratory, used this idea to good advantage in studies of the crystallization of zeptoliter (10-21 liter) quantities of molten droplets of a Au72Ge28 alloy [1]. This alloy has a melting point of about 350oC.

Crystallization in larger masses of molten metal typically begins at an impurity. Once crystallization has started, the crystallization front propagates very rapidly, too fast to be studied. Very pure substances will supercool, and then quickly freeze far from an equilibrium point, so the crystallization behavior is not the same as at the melting point. Conventional theory says that a random volume inside the molten liquid solidifies, initiating crystallization.

Sutter and Sutter used extremely small pipettes to produce nano-sized molten droplets of this low melting point alloy in a transmission electron microscope. They were able to image the droplets with nearly atomic scale resolution. What they found was astounding. As the droplets were cooled to just above the melting point, they developed facets on the surface, and these facets would continually form and decay. This liquid state could be maintained for hours, but when the temperature was brought below the melting point, the facets froze to form the resultant solid crystal. The Brookhaven researchers reason that the outside of the droplets was showing the first signs of solidification, and the crystallization front proceeded from the outside-in, rather than the inside-out for larger liquid masses.

1. Peter W. Sutter & Eli A. Sutter, "Dispensing and surface-induced crystallization of zeptolitre liquid metal-alloy drops," Nature Materials (online, 15 April 2007), doi:10.1038/nmat1894.
2. Researchers use smallest pipette to reveal freezing 'dance' of nanoscale drops (Brookhaven Press Release).

April 16, 2007

Symmetry Breaking

Last weekend, my wife and I attended the wedding reception of a young man from our neighborhood and his bride. We sat at a table of ten with four other couples from the neighborhood. As we sat there, I was reminded of this example of symmetry breaking. Consider a dinner table in which the napkins, water glasses, or other articles, are placed equidistant between the guest dinner plates. Do you take the item at your left, or at your right? You don't know. Then, one guest takes his napkin, and everyone else knows which napkin to take. Symmetry breaking is a process in which a small fluctuation acting on a system decides the final state of the system. Often, this fluctuation is invisible to an observer, or it's just noise in the system, so this symmetry breaking seems to be a mysterious process. If a guest at another table was observing this particular table to see which napkin to take, but looked away while the process happened, he would see everyone with a napkin in his/her lap, and he would still have no idea which of his napkins to take. Symmetry breaking is a principal method of pattern formation. It takes an indeterminate system and transforms it into a patterned state.

If we have a bead with a hole in it threaded onto a hoop and rotate the hoop slowly around a diameter, the bead will stay at first at the bottom of the hoop, but at a certain point it will drop to the other side. Continuing rotation, the bead will slide back to the other side, et cetera. If we attach the diameter to a motor, such as a stirrer commonly found in our laboratories, and ramp up the speed, we will eventually reach a speed at which the bead remains on one side only. The bead motion is initially symmetric with respect to the hoop diameter, but the symmetry is broken after a critical angular velocity is reached, and the bead ends up in one of two stable states [1]. Column buclking is another example of symmetry breaking in mechanics. As an example of this phenomenon, consider a flexible ruler [2]. If you hold the ruler at its ends and push inwards, the stress within the ruler is distributed uniformly, and it maintains its straight edge. As you push harder, the ruler bends one way, or the other. There was an initial slight buckling, and because of the geometry of the process, this aids further buckling, so the process is catastrophic. This buckling is an example of spontaneous symmetry breaking - the planar symmetry of the ruler has been broken.

Leonhard Euler, the Swiss mathematician and physicist, published an equation for the critical force for buckling instability in 1774, as follows:

Fcr = E I π2 / L2

in which E is the Young's modulus of the material, L is the length of the column, and I is the area moment of inertia of the cross section of the beam. This equation was proved by experiments on slender columns by A. Considère in 1889 [3]. It is interesting to see that it's the material elasticity, and not its compressive strength, that determines the critical load.

1. Spontaneous Symmetry Breaking (Wikipedia).
2. Theoretical Physics: On Spontaneous Symmetry Breaking (science Week).
3. A. Considère, "Resistance des pieces comprimes," Congr. Int. Proc. Constr. (Paris, 1891).
4. James B. Calvert, "Buckling"
5. Governing Equation for Elastic Buckling.

April 13, 2007

Kurt Vonnegut

Kurt Vonnegut, a preeminent American novelist, died Wednesday (4/11/07) at age 84. Vonnegut is often described as a writer of science fiction, but his novels were read by a wider audience since their scientific content was present only as a vehicle for his unique perspective on modern life. That's not to say that his scientific speculations weren't entertaining. In a previous post, I mentioned Ice-Nine, the miraculous phase of water in his novel, Cat's Cradle, that's a solid below 45.8 degrees Celsius. It has the unfortunate property that it crystallizes all the world's water on contact and ends all life on earth. Vonnegut, who worked for a short time in the public relations department at General Electric, said he got the idea for Ice-Nine from Irving Langmuir, the 1932 Nobel Laureate in Chemistry, who had worked at GE also. Vonnegut discovered a story about how Langmuir had pitched his version of an Ice-Nine story to H. G. Wells when Wells had visited GE. Langmuir hoped that Wells would write a story about it, but Wells didn't. Vonnegut considered the Ice-Nine idea to be free for him to use after both Langmuir and Wells had died.

Kurt Vonnegut was born on November 11, 1922, to German-American parents in Indianapolis, Indiana. His early interest in science is well documented by his academic career. He majored in biochemistry at Cornell University in the early 1940s. He transferred to the Carnegie Institute of Technology (presently, Carnegie Mellon University) in 1943, but shortly thereafter he joined the US Army to fight in World War II. He was held briefly as a prisoner of war, where he witnessed the firestorm that destroyed Dresden in February, 1945. Although Vonnegut has written that "The firebombing of Dresden explains absolutely nothing about why I write what I write and am what I am," [1] I believe that his Dresden experience was responsible for the overarching anti-technology, nearly Luddite, aspect of all his novels. His first novel, Player Piano (1952), is about a near-future (perhaps present-day) dystopia in which humans have been made obsolete, replaced by automation and machines. In The Sirens of Titan (1959), all human history was manipulated for the sole purpose of delivering a small piece of metal to a robot explorer (a machine) who crash-landed on Titan, the largest moon of Saturn.

There are several things I like about Kurt Vonnegut's writing. Unlike many present day authors who are too mindful that they are paid by the word, Vonnegut gets to the point quickly with less literary allusion. As a result, his books are short and can been read in a single sitting of a few hours. Most of all, his books are humorous. The following is a list of Kurt Vonnegut's major works.

Player Piano, 1951
The Sirens of Titan, 1959
Canary in a Cat House, 1961
Mother Night, 1961
Cat's Cradle, 1963
God Bless You, Mr. Rosewater, 1965
Welcome to the Monkey House, 1968
Slaughterhouse-Five, 1969
Breakfast of Champions, 1973
Wampeters, Foma & Granfalloons, 1974
Slapstick, 1976
Jailbird, 1979
Christmas Story, 1980
Palm Sunday, 1981
Deadeye Dick, 1982
Galapagos, 1985
Bluebeard, 1987
Hocus Pocus, 1990
Timequake, 1997
Fates Worse Than Death, 1991 (Nonfiction)
Happy Birthday, Wanda June, 1971 (Play)
Between Time and Timbuktu, or Prometheus-5, 1972 (TV script)
A Man Without a Country, 2005 (Nonfiction)

1. Kurt Vonnegut, "Fates Worse than Death, An Autobiographical Collage (ISBN 978-0-42-513406-1), 1990.
2. Christian Salazar, "Novelist Kurt Vonnegut Dies at Age 84" (Associated Press).
3. 'Cat's Cradle' novelist Kurt Vonnegut dies at 84 (Associated Press).

April 12, 2007

Data, Data, Everywhere

How much digital data is stored worldwide? The hard disk in a typical desktop personal computer has a storage capacity of about 50 gigabytes. That's 5 x 1010 bytes. How much data is stored in personal computers worldwide? For that calculation we need the number of personal computers worldwide. Aneki.com, a web site of data compiled from various sources, such as the United Nations and the US Central Intelligence Agency, lists the number of personal computers in the ten countries with the most computers.

• 1 United States 164,100,000
• 2 Japan 49,900,000
• 3 Germany 30,600,000
• 4 United Kingdom 26,000,000
• 5 France 21,800,000
• 6 Italy 17,500,000
• 7 Canada 16,000,000
• 8 China 15,900,000
• 9 Australia 10,600,000
• 10 South Korea 10,600,000

That's 363 million computers, but lower ranked countries must contribute substantially to the total number. My inspection of these data show that they closely follow an exponential distribution, so I modeled the distribution and extrapolated (Admit it, we all extrapolate in the privacy of our own offices). I found that there are fifty countries with at least a thousand computers, and my estimate of the number of computers in the world is 800 million. It's likely that most of these computers have fewer that 50 gigabytes of storage, so for argument's sake, let's estimate the average storage at a mere 10-12 gigabytes. With these estimates, the hard disk storage capacity of all the world's personal computers is 1 x 1019 bytes. The metric prefix for 1018 is "exa," so this is 10 exabytes of data. Of course, we've ignored other types of data storage, such as CDs (0.7 gigabytes each), and DVDs (4.7 gigabytes, typical), so the actual data archive per computer might be several times our 10 exabyte estimate.

Not all our data is stored. Most of it is transient data, such as viewing a video on our PC. IDC, a market intelligence firm, has recently estimated data production in the year 2006 as 161 exabytes [1]. This is quite a jump from a University of California, Berkeley, 2003 estimate of 5 exabytes. Of course, YouTube, and photo sharing web sites like Flickr didn't figure into the 2003 numbers, and the Berkeley estimate included only original data, not the multiple copies of items that are now common. Still, if the IDC estimate excluded all the cloned bytes, there would still be 40 exabytes of digital production.

What's the physical equivalent of 161 exabytes? According to IDC, this is twelve stacks of books piled from here to the sun, or three million times the information contained in all the books ever written. But watch out for 2010, when a zettabyte (1021 bytes) is expected to be produced!

1. Brian Bergstein, "Time to learn exabytes and zettabytes: Tech researchers calculate wide world of data." (Associated Press, no longer available online.)

April 11, 2007

Von Klitzing Constant

We're accustomed to the many constants littering our scientific landscape. There are such fundamental constants as the speed of light and Planck's constant; constants that relate to thermodynamic ensembles, such as the gas constant and the Boltzmann constant; and then there are important constants that are combinations of other constants. One such constant is the von Klitzing constant, which has the value 25812.807449 ohms. It is the inverse of one quantum of electrical conductance. Klaus von Klitzing, winner of the 1985 Nobel Prize in Physics, will present the first of the 2007 Honeywell Nobel Initiative Lectures at the Georgia Institute of Technology, April 12-13.

Klaus von Klitzing, a German physicist, was born in 1943 in Sroda Wielkopolska. He earned his Diploma in Physics in 1969 from the Technical University at Braunschweig, where his diploma thesis involved the carrier lifetime in indium antimonide (InSb). He received his Ph.D. from the University of Würzburg for work on the "Galvanomagnetic Properties of Tellurium in Strong Magnetic Fields," which is the same type of research as for his Nobel Prize discovery. Von Klitzing continued such studies at Clarendon Laboratory, Oxford, and at Grenoble. From 1980-1984 he was a professor at the Technical University, München, and since 1985 he is Director at the Max-Planck-Institut für Festkörperforschung (Max Planck Institute for Solid State Studies) at Stuttgart. It was at Grenoble in the High Field Magnet Laboratory (Hochfelt-Magnet-Labor) that his Nobel Prize experiment was performed. It relied on some extremely pure silicon crystals with high electron mobility prepared by G. Dorda and M. Pepper, and they were co-authors on his important paper [1].

So, what was this important work? The short abstract of this paper tells the whole story.

"Measurements of the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field-effect transistor, show that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device. Preliminary data are reported." [1]

What was demonstrated was that in a Hall effect experiment, the electrical resistance is quantized in a precise quantity; namely, the von Klitzing constant. This quantized resistance RK is fundamental, and it can be expressed in terms of other fundamental constants

RK = h / e2

where h is Planck's constant, and e is the electrical charge. The significance of this discovery is evident by the short period that elapsed before the award of the Nobel Prize - only five years. The von Klitzing constant is important for metrology, since it can be used as a precise way to determine the fine structure constant α

α = e2 / 2εohc

Where e is the electrical charge, h is Planck's constant, c is the speed of light, and εo is the permittivity of free space.

1. K. v. Klitzing, G. Dorda, and M. Pepper, "New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance," Phys. Rev. Lett., vol. 45 (August, 1980), pp. 494-497.
2. Klaus von Klitzing on the Nobel Winners Web Site.
3. Klaus von Klitzing Curriculum Vitae on the Nobel Prize Web Site.
4. Nobel Prize Press Release
5. Quantum Hall Effect on Wikipedia

April 10, 2007

Greatest Material Events of All Time

What events are considered the most important in the history of materials science? What better group to ask than materials scientists themselves, and the results were presented at the February meeting of the Minerals, Metals & Materials Society (TMS) in Orlando, Florida. The Materials Society (TMS), as it's usually called, was celebrating its fiftieth year as a member society of the American Institute of Mining, Metallurgical and Petroleum Engineers (AIME). TMS publishes the Journal of Metals, and it has members in more than seventy countries. TMS polled these members, who are professionals in such diverse fields as mineral processing, primary metals production, and basic/applied research in materials, to produce a list of the Greatest Materials Moments in History. More than 900 of those surveyed responded, and the top fifty events were prsented. The top ten are as follow:

• 1 - 1864, Dmitri Mendeleev devises the Periodic Table of Elements.

• 2 - 3500 BC, Egyptians smelt iron for the first time.

• 3 - 1948, John Bardeen, Walter H. Brattain, and William Shockley invent the transistor.

• 4 - 2200 BC, The peoples of northwestern Iran invent glass.

• 5 - 1668, Anton van Leeuwenhoek develops optical microscopy.

• 6 - 1755, John Smeaton invents modern concrete.

• 7 - 300 BC, Metal workers in south India develop crucible steel making.

• 8 - 5000 BC, Liquid copper extracted from malachite and azurite in present-day Turkey.

• 9 - 1912, Max von Laue discovers x-rays diffraction by crystals.

• 10 - 1856, Henry Bessemer patents a bottom-blown acid process for melting low-carbon iron.

I present my favorites from the remaining forty.

• 16 - 1898, William Roberts-Austen develops the phase diagram for iron and carbon.

• 19 - 1450, Johannes Gutenberg devises a lead-tin-antimony alloy to cast his moveable type.

• 23 - 1934, Egon Orowan, Michael Polyani, and G.I. Taylor, in three independent papers, propose the theory of dislocations.

• 25, 1886, Charles Martin Hall and Paul Héroult independently discover the electrolytic reduction of alumina into aluminum.

• 27 - 1904, Leon Guillet develops the alloying compositions of the first stainless steels.

• 29 - 1500 BC, Metal workers in the Near East develop the art of lost-wax casting.

• 33 - 1709, Abraham Darby I discovers that coke can effectively replace charcoal in a blast furnace for iron smelting.

• 36, 1991, Sumio Iijima discovers nanotubes.

• 42, 1500 BC - Potters in China craft the first porcelain using kaolin.

• 43 - 1909, Leo Baekeland synthesizes the thermosetting hard plastic Bakelite.

• 44 - 1926, Paul Merica patents the addition of small amounts of aluminum to Ni-Cr alloy to create the first "superalloy."

• 46 - 1935, Wallace Carothers and colleagues patent nylon.

• 47 - 1805, Luigi Brugnatelli invents electroplating.

• 49 1890 - Adolf Martens correlates microstructure with the physical properties of materials.

• 50 - 1920, A. A. Griffith publishes "The Phenomenon of Rupture and Flow in Solids," and establishes the field of fracture mechanics.

1. Great Materials Moments, Science, vol. 315, no. 5819 (23 March 2007), p. 1643.
2. Full list on the TMS web site.

April 09, 2007

Alan MacDiarmid

I found myself in line recently at the Morristown Federal Credit Union with Ron Rohrbach, a Honeywell Fellow. Our conversation turned to Alan MacDiarmid who had died recently. Ron mentioned that MacDiarmid, a fixture in American polymer chemistry and a recipient (with Alan Heeger and Hideki Shirakawa) of the 2000 Nobel Prize in Chemistry, was born in New Zealand. I remembered that Ernest Rutherford, winner of the 1908 Nobel Prize in Chemistry and the "father" of nuclear physics, was also from New Zealand. I speculated that perhaps there was little else to do in New Zealand except science. In my experience, there's a positive correlation between good beer and good science. My favorite conference, the Annual Conference on Magnetism and Magnetic Materials, has a daily post-session Bierstube that encourages information exchange among participants. The New Zealand per capita beer consumption is 77.0 liters, just slightly behind that of the US (81.6 liters). We should expect great things from the Czech Republic (156.9 liters).

Alan Graham MacDiarmid (1927 - 2007) was born in Masterton, New Zealand, during the Great Depression. His father was an engineer, and Alan discovered his father's old textbooks at an early age and developed an interest in chemistry. He completed a master's degree in chemistry from Victoria University of Wellington, New Zealand, and came to the US in 1951 on a Fulbright Fellowship. The Fellowship enabled him to earn a Ph.D. at the University of Wisconsin-Madison, whereupon he received a scholarship which allowed him to complete a second Ph.D. at Cambridge University. An interesting stipulation of this scholarship was that he should remain single, but he married shortly after its fulfillment. He became a professor of chemistry at the University of Pennsylvania (Penn, not to be confused with Pennsylvania State University), and he remained there for 45 years.

Alan Heeger, a condensed matter physicist, was also at Penn. Heeger suggested a collaboration on the conductivity of (SN)x, a polymer of sulfur and nitrogen. MacDiarmid was initially disinterested, since he thought Heeger was talking about linear chains of tin, Snx. Their research took an unexpected turn in the mid 1970s with the discovery of the high conductivity of doped polyacetylene [1]. As most great scientific discoveries, the conductive polymers were discovered by accident. A student in Shirakawa's group misinterpreted Shirakawa's directions and made a conductive polyacetylene by using a thousand times the recommended quantity of a Ziegler-Natta catalyst for polymerization of acetylene. The experiment produced a conductive polyacetylene. MacDiarmid asked Shirakawa to join him for a year at Penn. They discovered that highly purified polyacetylene was less conductive, and purposely doped it with bromine, which greatly increased the conductivity. Eventually their doping with iodine raised the conductivity to 30 Siemens per centimeter. Subsequent research brought the conductivity to 105 S/cm, or nearly as conductive as copper.

MacDiarmid was well liked by his colleagues, and he acted as a mentor to many younger scientists. He is named as an author on more than 600 published papers. Among his many honors, he was a member of the US National Academy of Sciences, and the Royal Society. He received the American Chemical Society Award in Materials Chemistry and the Rutherford Medal, which is New Zealand's highest award for science. Victoria University (Wellington) named the MacDiarmid Institute for Advanced Materials and Nanotechnology after him.

1. Chiang, C.K.; Druy, M.A.; Gau, S.C.; Heeger, A.J.; Louis, E.J.; MacDiarmid, A.G.; Park, Y.W.; Shirakawa, H., "Synthesis of Highly Conducting Films of Derivatives of Polyacetylene, (CH)x," J. Am. Chem. Soc., 100, 1013 (1978).
2. Andrew Holmes, "Obituary: Alan Graham MacDiarmid," Nature, vol. 446, no. 7134 (22 March 2007), p. 390
3. Ray H. Baughman, "Retrospective: Alan G. MacDiarmid (1927-2007)," Science, vol. 315. no. 5819 (23 March 2007), p. 1678.
4. Alan G. MacDiarmid Autobiography on the Nobel Prize Web Site.

April 03, 2007

Easter Holiday

I'll be away on an Easter holiday until Monday, April 9, 2007. While I'm away, check out the many faces of mu.

The Greek letter μ

μ, the SI prefix for micro

μ, the arithmetic mean of a statistical population

μ, the friction coefficient

μ, the magnetic permeability

Mu metal, an alloy of 75% nickel, 15% iron, with copper and molybdenum, having a very high magnetic permeability

μ, the Mu Meson (Muon)

μ Andromedae, a star in the constellation Andromeda (μ is a prefix for the 12th brightest star in any constellation)

Mu ring, the outermost ring of the planet Uranus

μ-law, an audio processing algorithm

Variable mu, a type of vacuum tube

μ-Calculus (mathematics)

μ-recursive function (mathematics)

μ-operator (mathematics)

Möbius μ function (mathematics)

μC++, a programming language

The lost continent of Mu

The MU puzzle (from the book, Gödel, Escher, Bach)

E-Mu electronic synthesizer

Mu wave, an 8-13 Hz brain wave

Mu Major, a jazz chord popularized by Steely Dan

Mu, a negative exclamation (No!) in Japanese and Korean

Long Mu, a Chinese woman deified as a goddess after raising five infant dragons

Cotton Pickin' Nano Crystals

Nucleation is an important part of crystal growth. In fact, the terms "nucleation" and "growth" are related to such an extent that Google gives more than a million hits in a search for the phrase "nucleation and growth." Epitaxy, in which a crystal layer is grown atop a wafer of the same lattice structure, becomes difficult if the strain between the layer and the substrate wafer exceeds a certain limiting percentage, since the layer will not nucleate. Heteroepitaxy, in which one crystal composition is grown on top of another, is generally possible only for certain lattice orientations of the substrate wafer that allow nucleation. Nucleation is easier for crystal cuts that have a multitude of lattice steps and terraces.

Yongsoon Shin and Gregory Exarhos of the Pacific Northwest National Laboratory have used selective nucleation as a method of producing uniform nanocrystals of gold, silver, palladium, platinum, and transition metals and metal oxide, quickly and of uniform size [1]. These crystals were grown on a template of acid-treated cotton fibers. Cotton was chosen since it is nearly pure cellulose, a natural polymer. The acid treatment produces hydroxyl radicals periodically spaced along the polymer chain. The treated fibers are then placed into a hydrothermal reactor in which metal salts are dissolved in solution and heated to temperatures up to 200 oC for several hours. Synthetic quartz crystals for frequency control applications are grown by this same technique [2]. The process produces nanocrystals at the hydroxyl sites. Monodisperse nanocrystals, such as those produced by Shin and Exarhos, could be useful for drug delivery and catalysis.

"Cotton picking" is a disparaging adjectival expression presumably related to people whose occupation is picking cotton. In the early to mid-twentieth century, the expressions, "bean-picker," or "pea picker" were sometimes used, disparaging migrant farm workers. Cotton pickin' has now become detached from its original meaning, much like "gee".

1. Bill Cannon, "A new form of metal crystals, brought to you by a cotton assembly line" (Pacific Northwest National Laboratory Press Release (March 26, 2007).
2. Robert A. Laudise, "Hydrothermal Synthesis of Crystals", Chemical and Engineering News, vol. 65, no. 39 (1987), p. 30 ff. Bob Laudise (1930 - 1998) was a member of the Mid-Atlantic Section of the American Association for Crystal Growth (AACG), for which I was treasurer from 1982-1983.

April 02, 2007

US Information Technology in Steep Decline

A recent report, Global Information Technology Report 2006-2007 [1], by the World Economic Forum ranks the US behind six other countries in Information and Communication Technology, as measured by its "Networked Readiness Index (NRI)." The NRI measures the extent that countries are able to employ Information and Communication Technology to enhance competitiveness. The World Economic Forum, operating since 1971 from Geneva, Switzerland, is a non-profit international organization that issues impartial assessments. It is considered to be a non-political, non-partisan organization independent of any country. The 2006 rank ordering of the top ten countries is as follows:

• Denmark
• Sweden
• Singapore
• Finland
• Switzerland
• Netherlands
• US
• Iceland
• UK
• Norway

The US fell from first to seventh place in the last year. The report states that this is a result of a "relative deterioration of the political and regulatory environment," but it gives the US high marks for its post high school educational system, government cooperation with industry, venture-capital, and the number of new business starts. What is interesting is the fact that a particular geographical region, the Scandinavian counties, the Nordic countries, and the Netherlands, captures six of the ten places. This may relate to the early adoption of Linux in these countries. India ranked 44 because of a weak infrastructure and lack of personal computers and internet connections in homes. China ranked 59.

1. US 'no longer technology king' (BBC News).
2. WEF Press Release.
3. Soumitra Dutta and Irene Mia, "Executive Summary: Global Information Technology Report 2006-2007".
4. Global Information Technology Report 2006-2007 Country Ranking List.