A study of some issues raised in a paper by Wood and Reynolds

Description

• cours magistral
• exposé

A study of some issues raised in a paper by Wood and Reynolds Frank Legge, Jan 11, 2007 (Peer-reviewed Letter) The title of the paper by Wood and Reynolds, dated December 14, 2006 was “The Scientific Method Applied to the Thermite Hypothesis”. I will not attempt to answer the paper line by line but will copy and address the most salient points. The copied paragraphs are indented. For clarity my responses to each are in bold.

• paper line by line
• radio control
• explosive rdx so a smaller amount
• many pieces
• towers
• columns
• steel
• amount
• evidence

Sujets

• Cours magistral
• Exposé
• Grimmer
• Johnson
• Department of Defence
• Advisory Committee
• New York City
• Évidence
• Control
• Explosive
• Towers

Informations

• Publié par: udwi
• Nombre de lectures: 23
• Langue: English

Extrait

Centre for Advanced Study
Newsletter no. 1 May 2002 10th year
The Myths about the
Constitution
It is a myth that Norwegian
democracy rests safely on the
Constitution from 1814. In reali-
ty the Constitution does not
protect central political rights
such as the freedom of associ-
ation, the freedom of assembly,
the freedom to demonstrate
and the right to strike.
"In practical political life Nor-
way protects human rights to a
far greater degree than follows
from the Constitution. Let’s
hope that things continue that
way," say the experts on the
Constitution, Eivind Smith and
Bjørn Erik Rasch.
Pages 4-5
The lions in front of the Storting are guarding Norwegian democracy and the proud Norwegian
Constitution – which looks more like a little pussycat
Mathematics is older than the Greeks
"Pythagoras and the Gre-
eks have been given
undeservedly much of the
credit for having invented
classical mathematics.
Many of their ideas can be
traced back to anonymous
Mesopotamian mathema- The Genius and
ticians," says Professor
Jöran Friberg (picture). the Grammar
The proof is to be found in
School Teachersuch places as on the
small tablets of clay in the The Norwegian mathematician Niels Henrik
Schøyen Collection. Abel (right) became world-famous in 1824.
Ludwig Sylow (left) is one among Norwegian
Pages 4-5 mathematicians who assumed the mantle after
Abel.
Pages 2-3

Mathematical growth
in Abel’s footsteps
Niels Henrik Abel was one of the greatest mathematical geniuses the world has ever
fostered, and this year’s 200th jubilee is being used to mark his achievement. It is not
quite so well known that along the path Abel left behind him there was flourishing
growth of considerable importance.
"You don’t have to open many textbooks in pletely but not managed to complete the writing. called Lie groups. They are to this day a cen-
advanced mathematics before you come Sylow worked a great deal on interpretati- tral object of mathematical research and a
across Axel Thue’s theorem, Sophus Lie’s ons and improvements of Abel’s works, and central aid in theoretical physics.
groups or Ludvig Sylow’s theories. As a nati- was concerned with elliptical functions and In the 1890s he was ill a great deal. The
on Norway was over-represented with out- theories of equations. But it was first and writer Bjørnstjerne Bjørnson took the initiati-
standing mathematicians at the end of the foremost a publication from 1872, with des- ve to have a professorship established for him
19th century," says Geir Ellingsrud, who is a criptions of the three Sylow theorems within in Oslo, and in 1898 Lie moved home. But he
professor of Mathematics at the University of group theory, which made him immortal. was at that time seriously ill with pernicious
Oslo and a member of this year’s research Sylow was never given an appointment at anaemia and he died in the early part of 1899.
group in mathematics at the CAS. the University of Kristiania, but remained a
"Also Thoralf Skolem, Viggo Brun, Ernst secondary school teacher at Fredrikshald Axel Thue
Selmer, Vilhelm Ljunggren and not least Sel- (Halden) for 40 years from 1858. He was (1863 – 1922)
berg made important contributions to the Gol- granted leave to undertake a study tour to Axel Thue wor-
den Age of number theory," says Ellingsrud. Paris and Berlin in 1861, to substitute for ked on number
Broch in the period 1862-1863, and to edit theory, logic,
A systematic development Abel’s works in co-operation with Sophus Lie geometry and
Professor Jens Erik Fenstad in the Depart- from 1873 to 1877. In 1894 he was made a mechanics. He is
ment of Mathematics at the University of doctor honoris causa of the University of most famous for
Oslo agrees that Norway has fostered unusu- Copenhagen, and in 1898 the Storting nomi- his works on
ally many outstanding mathematicians. "On nated him professor extraordinary with an arithmetical pro-
both sides of the year 1900 we had many mat- emolument of 3000 kroner per year instead of perties of alge-
hematicians who were right at the top of the his secondary school teacher’s pension. braic numbers,
international research league, but on the other and theorems of
hand we had no profession around them. The Marius the (un)solvability of Diophantine equations,
great change came after the Second World Sophus Lie i.e. equations where the solution is a whole
War, when a more systematic development (1842-1899) number. He is also famous for his pioneer
was started. Today we don’t perhaps have Sophus Lie deve- work on what he called "Zeichenreihen" or
many researchers in the forefront internatio- loped original "word problems".
nally, but what we have got is a broad profes- and innovative Thue was known to go his own ways, and
sion with points of impact in many areas of theories for he preferred developing his own ideas to
Norwegian society, says Professor Fenstad. transformations making a study of other people’s works. He
of geometrical became a teacher at the Institute of Technolo-
Peter Ludvig objects (lines, gy in Trondheim in 1894 and in 1903 he
Meidell spherical surfa- became Professor of Applied Mathematics in
Sylow (1832- ces etc) and for Oslo.
1918) the integration of Thue thoroughly reformed the lectures on
Ludvig Sylow ordinary and partial differential equations. He mechanics. It is said that he dictated his lectu-
qualified as a was appointed as an extraordinary professor res, stopped at the nearest comma immediate-
teacher of scien- at the University of Oslo in 1872, and in 1886 ly the time was up, and carried on from there
ce and mathema- he became a professor in Leipzig as the on the next occasion.
tics in 1856 and famous mathematician Felix Klein’s succes-
became a pupil sor. The point of departure for Lie’s works Thoralf Albert Skolem
of Ole Jacob was his own and Klein’s idea that geometry (1887 – 1963)
Broch, who star- and analysis ought to be built up around the Thoralf Skolem published as many as 177
ted him off on concept of group, as Galois had built up his papers in the course of his long career. The
Abel’s works. Sylow became extremely con- theory of algebraic equations. Lie made a stu- most important of his works were done within
cerned with an unfinished Abel manuscript on dy of differential equations from this point of logic and Diophantine equations.
the theory of equations, and he gradually docu- view and built up a general theory of "trans- Skolem obtained his doctoral degree in
mented that Abel had solved the problem com- formation groups" or what have since been 1926 for a work on integral solutions of cer-
2 Newsletter no. 1 May 2002 10th year

tain algebraic
equations and
inequalities. Then
he was a resear-
cher at the Chris-
tian Michelsen
Institute in Bergen
from 1930 to 1938,
after which he
became a professor
in Oslo. When he
reached the age of
retirement in 1957 he was for a couple of
years Visiting Professor at Notre Dame Uni-
versity in the United States.
His works in logic broke new ground (inter
alia the "Skolem-Löwenheim Theorem"), and
his results with respect to Diophantine equati-
ons and the "Skolem-Nöther Theorem" in
algebra are outstanding. His commitment to
his work led among other things to his being
commissioned to write about Diophantine
equations for the German Springer-Verlag’s
series Ergebnisse der Mathematik, and to-
gether with Viggo Brun he edited the second
impression of Eugen Netto’s Lehrbuch der
Kombinatorik.
Viggo Brun
(1885 – 1978)
Viggo Brun is best
known for his
work on prime
number theory, but
he also made a
great contribution
within continued
fractions, generali-
sations and combi-
natorics. Among
other things he developed a famous sieve met-
hod, which he later used to develop two
hypotheses in number theory that had previ-
ously been considered impossible to prove.
One of these hypotheses had been formulated
by Goldbach and stated that every even num- An outstanding number theorist
ber can be written as a sum of two odd prime
numbers. Atle Selberg (born 1917) is considered appointed a professor in 1951.
The sieve method has been taken further by to be one of the world’s most outstanding Selberg is also famous for his elementary
among others Gelfond in Moscow and Atle number theorists of all times. His most proof of the prime number theorem, with its
Selberg at Princeton and it has shown itself to famous work is his elaboration of what is generalisation to prime numbers in a random
be very effective. Brun was also interested in known as Selberg’s trace formula. Selberg’s arithmetical series. When Selberg’s collected
the history of mathematics, and in 1952 he doctorate from 1943 with amplifications on papers were published in 1989 and 1991, the
found the lost manuscript of Abel’s Paris dis- what is called the Riemann zeta function critics were in agreement that the author is a
sertation in a library in Florence. remained for at least 30 years as the most out- living classic who has exerted considerable in-
He was made a professor at the Norwegian standing work within its field. fluence on his subject