Currently browsing the Math Category

Brain Reorganizes As It Learns Math

Brain reorganizes to make room for math

It takes years for children to master the ins and outs of arithmetic. New research indicates that this learning process triggers a large-scale reorganization of brain processes involved in understanding written symbols for various quantities.

The findings support the idea that humans’ ability to match specific quantities with number symbols, a skill required for doing arithmetic, builds on a brain system that is used for estimating approximate quantities. That brain system is seen in many nonhuman animals.

When performing operations with Arabic numerals, young adults, but not school-age children, show pronounced activity in a piece of brain tissue called the left superior temporal gyrus, says Daniel Ansari of the University of Western Ontario in London, Canada. Earlier studies have linked this region to the ability to associate speech sounds with written letters, and musical sounds with written notes. The left superior temporal gyrus is located near the brain’s midpoint, not far from areas linked to speech production and understanding.

In contrast, children solving a numerical task display heightened activity in a frontal-brain area that, in adults, primarily serves other functions.

Related: Brain DevelopmentThe Brain Hides Information From Us To Prevent MistakesHow The Brain Rewires Itselfposts about brain research

Engineers and Scientists in Congress

I started maintaining a list of Congressmen with PhDs and graduate degrees in science, engineering and math awhile back.

Please comment with any additions that you know of.

The following were re-elected:
Vernon Ehlers, Michigan, physics PhD; Rush Holt, New Jersey, physics PhD; John Olver, Massachusetts, chemistry PhD; Brian Baird, Washington, psychology PhD; Bill Foster, Illinois, physics PhD.

Other scientists, engineers and mathematicians that were reelected include: Ron Paul, Texas, biology BS, MD; Jerry McNerney, California, mathematics PhD; Dan Lipinski, Illinois, mechanical engineering BS, engineering-economic systems MS; Todd Akin, Mississippi, management engineering BS;Cliff Stearns, Florida, electrical engineering BS; Louise Slaughter, New York, microbiology BS; Joe Barton, Texas, industrial engineering BS, Pete Stark, California, engineering BS, Mike Honda, California.

Lost: Nancy Boyda, Kansas (BS chemistry).

Newly elected: Bill Cassidy, Louisiana (BS Biochemistry, MD); Pete Olson, Texas (BA computer science); Kurt Schrader, Oregon (Doctor of Veterinary Medicine); Martin Heinrich, New Mexico (BS engineering), Gregg Harper, Mississippi (BS chemistry), Joseph Cao, Mississippi (BA physics); Brett Guthrie, Virginia (BS mathematical economics); Erik Paulsen, Minnesota, mathematics BA; Parker Griffith, Alabama (BS chemistry, MD); Cynthia Lummis, Wyoming (BS animal science and biology).

Before you leap to the conclusion that scientists are taking over Congress, remember 2 things: 1) I have probably been missing plenty that were in congress already and 2) this is still a total of less than 10% with even a BS in science, math or engineering. I attempted to determine the status of all those newly elected this year.

Please comment, if you know of others in Congress with science and engineering backgrounds. If we get this list to be relative close to accurate then we can start tracking the total representation in congress and see if it is increasing, decreasing or randomly fluctuating over time.

Related: Scientists and Engineers in CongressChina’s Technology Savvy LeadershipScience and Engineering in PoliticsThe A to Z Guide to Political Interference in Science

Compounding is the Most Powerful Force in the Universe

A talking head with some valuable info. I remember my father (a statistics professor) getting me to understand this as a small child (about 6 years old). The concept of growth and mathematical compounding is an important idea to understand as you think and learn about the world. It also is helpful so you understand that statistics don’t lie but ignorant people can draw false conclusions from limited data.

It is unclear if Einstein really said this but he is often quoted as saying “compounding is the most powerful force in the universe.” Whether he did or not, understanding this simple concept is a critical component of numeracy (literacy with numbers). Also quoted at times as: “Compound interest is the eighth wonder of the world.” My guess is that people just find the concept of compounding amazing and then attribute quotes about it to Einstein.

I strongly encourage you to watch at least the first 2 segments (a total of 15 minutes). And then take some time and think. Take some time to think about compounding in ways to help you internalize the concepts. You can also read his book: The Essential Exponential For the Future of Our Planet by Albert Bartlett.

Related: Playing Dice and Children’s NumeracySaving for Retirement (compound interest)Bigger Impact: 15 to 18 mpg or 50 to 100 mpg?Sexy MathThe Economic Benefits of Math

National Girls Collaborative Project for STEM

The National Girls Collaborative Project for science, technology, engineering, and mathematics (STEM) collaborates with those seeking to increase the participation of girls in STEM feeder activities. The goal is to encourage girls to pursue careers in science, technology, engineering, and math.

Collaboration as a Means to Building Capacity: Results and Future Directions of the National Girls Collaborative Project:

The purpose of the NGCP is to extend the capacity, impact, and sustainability of
existing and evolving girl-serving STEM projects and programs. The NGCP is structured to bring organizations together to compare needs and resources, to share information, and to plan strategically to expand STEM–related opportunities for girls.

Although we are still refining it, the NGCP collaborative model has shown its effectiveness through increased collaboration and minigrant projects with sustained results. As we have described, the success to date of the NGCP in developing collaborations has been demonstrated via data from the collaboration rubric, mini-grant reports, and metrics that show how collaborative activities have increased over the duration of the NGCP projects. As NGCP expands over the next few years to provide regional collaboratives across the entire United States and Puerto Rico, we will continue our assessment of its impact and hope to be able to report its influence on building capacity to attract and retain girls in STEM.

I support programs encouraging STEM activities for girls – and boys. NSF data shows for 2005 shows women outnumbered men in undergraduate degree in science and engineering. For post-graduate degrees men still outnumbering women but that gap has been reducing and seems like it will continue to. And the representations in the workplace seem poised to continue to show a reducing number of men and increasing number of women. Engineering is an example of an area with far more men than women graduating – the imbalance is equivalent to the imbalance the other way for psychology.

Related: Girls Sweep Top Honors at Siemens Competition in Math, Science and TechnologyFIRST Robotics in MinnesotaKids in the Lab: Getting High-Schoolers Hooked on Science

Problems Programming Math

Arithmetic Is Hard – To Get Right by Mark Sofroniou

I’ve been working on arithmetic in Mathematica for more than 12 years. You might think that’s silly; after all, how hard can arithmetic be?

The standard “schoolbook” algorithms are pretty easy. But they’re inefficient and often unnecessarily inaccurate. So people like me have done a huge amount of work to find algorithms that are more efficient and accurate. And the problem is that these algorithms are inevitably more complicated, and one has to be very careful to avoid insidious bugs.

Take multiplying integers, for example. The standard “schoolbook” long-multiplication algorithm uses n^2 multiplications to multiply two n-digit numbers. But many of these multiplications are actually redundant, and we now know clever algorithms that take n^1.58, n log n, or even fewer multiplications for large n. So this means that if one wants to do a million-digit multiplication, Mathematica can do it in a fraction of a second using these algorithms–while it would take at least a few minutes using standard long multiplication.

It’s not easy to get reliable numerical computation, and it’s not something one can “bolt on” after the fact. It’s something one has to build in from the beginning, as we’ve done in Mathematica for nearly 20 years.

Related: Who Killed the Software Engineer?Sexy MathFreeware Math Programs1=2: A ProofThings You Need to be a Computer Game Programmer

The Rush to Save Timbuktu’s Crumbling Manuscripts

The Rush to Save Timbuktu’s Crumbling Manuscripts

Fabled Timbuktu, once the site of the world’s southernmost Islamic university, harbors thousands upon thousands of long-forgotten manuscripts. A dozen academic instutions from around the world are now working frantically to save and evaluate the crumbling documents.

The Ahmed Baba Library alone contains more than 20,000 manuscripts, including works on herbal medicine and mathematics, yellowed volumes of poetry, music and Islamic law. Some are adorned with gilded letters, while others are written in the language of the Tuareg tribes. The contents remain a mystery.

Manuscript hunters are now scouring the environs of Timbuktu, descending into dark, clay basements and climbing up into attics. Twenty-four family-owned collections have already been discovered in the area. Most of the works stem from the late Middle Ages, when Timbuktu was an important crossroads for caravans.

Archaeologists have shown that an incredible system of underground canals up to 20,000 kilometers (12,422 miles) long once existed at Wadi al-Hayat in Libya. Thanks to such hydraulic marvels, the desert blossomed and crops sprouted in the fields of the Tuareg.

Related: digital library of scholarly resources from and about AfricaAfrican Union Science Meeting

Mathematicians Critique Journal Rankings

Mathematicians Critique Journal Rankings

Three international math groups joined forces to issue a report last week decrying the use of citation statistics to evaluate scientific journals, research institutions and individual scientists. These statistics, sometimes called “bibliometrics,” measure how frequently a given journal’s articles are cited by other journals.

Read the report on Citation Statistics. This concern is justified. I do have some interest in some of these (and related) statistics but one must always remember their limitations.

Related: Country H-index Rank for Science PublicationsRanking Universities WorldwideBest Research University Rankings (2007)Don’t Forget the Proxy Nature of Data

Shaw Laureates 2008

Image of the Shaw Prize Medal

The Shaw Prize awards $1 million in each of 3 areas: Astronomy; Life Science and Medicine; and Mathematical Sciences. The award was established in 2002 by Run Run Shaw who was born in China and made his money in the movie industry. The prize is administered in Hong Kong and awards those “who have achieved significant breakthrough in academic and scientific research or application and whose work has resulted in a positive and profound impact on mankind.” The 2008 Shaw Laureates have been selected.

Professor Reinhard Genzel, Managing Director of the Max Planck Institute for Extraterrestrial Physics, in recognition of his outstanding contribution in demonstrating that the Milky Way contains a supermassive black hole at its centre.

In 1969, Donald Lynden-Bell and Martin Rees suggested that the Milky Way might contain a supermassive black hole. But evidence for such an object was lacking at the time because the centre of the Milky Way is obscured by interstellar dust, and was detected only as a relatively faint radio source. Reinhard Genzel obtained compelling evidence for this conjecture by developing state-of-the-art astronomical instruments and carrying out a persistent programme of observing our Galactic Centre for many years, which ultimately led to the discovery of a black hole with a mass a few million times that of the Sun, in the centre of the Milky Way.

Supermassive black holes are now recognized to account for the luminous sources seen at the nuclei of galaxies and to play a fundamental role in the formation of galaxies.

Mathematical Sciences
Vladimir Arnold, together with Andrei Kolmogorov and Jurgen Moser, made fundamental contributions to the study of stability in dynamical systems, exemplified by the motion of the planets round the sun. This work laid the foundation for all subsequent developments right up to the present time.

Arnold also produced extremely fruitful ideas, relating classical mechanics to questions of topology. This includes the famous Arnold Conjecture which was only recently solved.

In classical hydrodynamics the basic equations of an ideal fluid were derived by Euler in 1757 and major steps towards understanding them were taken by Helmholtz in 1858, and Kelvin in 1869. The next significant breakthrough was made by Arnold a century later and this has provided the basis for more recent work.

Ludwig Faddeev has made many important contributions to quantum physics. Together with Boris Popov he showed the right way to quantize the famous non-Abelian theory which underlies all contemporary work on sub-atomic physics. This led in particular to the work of ”²t Hooft and Veltman which was recognized by the Nobel Prize for Physics of 1999.
Continue reading

Aztec Math

Aztec Math Decoded, Reveals Woes of Ancient Tax Time

By reading Aztec records from the city-state of Tepetlaoztoc, a pair of scientists recently figured out the complicated equations and fractions that officials once used to determine the size of land on which tributes were paid. Two ancient codices, written from A.D. 1540 to 1544, survive from Tepetlaoztoc. They record each household and its number of members, the amount of land owned, and soil types such as stony, sandy, or “yellow earth.”

“The ancient texts were extremely detailed and well organized, because landowners often had to pay tribute according to the value of their holdings,” said co-author Maria del Carmen Jorge y Jorge at the National Autonomous University in Mexico City, Mexico. The Aztecs recorded only the total area of each parcel and the length of the four sides of its perimeter, Jorge y Jorge explained. Officials calculated the size of each parcel using a series of five algorithms—including one also employed by the ancient Sumerians—she added.

Aztec math finally adds up

That meant that some of the unknown symbols had to represent fractions of a rod, she said. By trial and error, she decoded the system. A hand equaled 3/5 of a rod, an arrow was 1/2 , a heart was 2/5 , an arm was 1/3 , and a bone was 1/5 .

A set of at least five formulas emerged showing how the Aztec surveyors determined the areas of irregular shapes. In some cases, the Aztecs averaged opposite sides and then multiplied. In others, they bisected the fields into triangles.

Related: Sexy MathPixar Is Inventing New Math1=2: A Mistaken Proof

Thompson and Tits share 2008 Abel Prize (Math)

Thompson and Tits share the Abel Prize for 2008

John Griggs Thompson, Graduate Research Professor, University of Florida, and Jacques Tits, Professor Emeritus, Collège de France, have been awarded the 2008 Abel Prize “for their profound achievements in algebra and in particular for shaping modern group theory.” In the prize citation, the Abel Committee writes that “Thompson revolutionized the theory of finite groups by proving extraordinarily deep theorems that laid the foundation for the complete classification of finite simple groups, one of the greatest achievements of twentieth century mathematics.”

In 1963, Thompson and Walter Feit proved that all nonabelian finite simple groups were of even order, work for which they both won the Frank Nelson Cole Prize in Algebra from the AMS in 1965. Thompson also won a Fields Medal in 1970. In the Abel citation for Tits, the committee writes that “Tits created a new and highly influential vision of groups as geometric objects. He introduced what is now known as a Tits building, which encodes in geometric terms the algebraic structure of linear groups.” The committee noted the link between the two winners’ work: “Tits’s geometric approach was essential in the study and realization of the sporadic groups, including the Monster.” Tits received the Grand Prix of the French Academy of Sciences in 1976, and the Wolf Prize in Mathematics in 1993.

The Abel Prize is awarded by the Norwegian Academy of Science and Letters for outstanding scientific work in the field of mathematics. The prize amount is 6,000,000 Norwegian kroner (over US$1,000,000).

Related: Professor Marcus du Sautoy on Thompson and TitsMath’s Architect of Beauty2007 Nobel Prize in PhysicsPoincaré Conjecture

Offering Residency to Foreign Engineers and Scientists

Rep. Lofgren wants residency for foreign engineers

Foreign-born engineering, science, and math students in the United States should be automatically granted legal residency when they get a job in this country, said California Congresswoman Zoe Lofgren.

Lofgren, a Democrat, spoke to an audience Friday at the Joint Venture: Silicon Valley conference about threats to innovation in the area. She said that about 56 percent of the Ph.D. candidates at the finest schools in the United States are immigrants, and because of the government’s current immigration policy, many of those people leave the country.

I support such legislation. I also think it is only one, of many measure to take to encourage science and engineering excellence (which will in turn help the economy). I have no doubt that other countries are going to be successful establishing their own global centers of excellence and attract scientists and engineers from around the world: including from the USA. The Curious Cat Science and Engineering Blog now includes a tag cloud on the right side of our home page, tags for this post include: government and economy.

Related: Brain Drain Benefits to the USA Less Than They Could Beeconomic benefits of science and engineering excellenceUSA Losing Brain Drain Benefits