Comments on the book "William Henry Harrison" by Gail Collins
This is a well written book that is interesting for the American History it describes from the very late 18th century to 1841, which was when William Henry Harrison died. The author, Gail Collins, provides vivid descriptions of people and events of those times in the Ohio and Indiana territories, which involve Native American, or Indian, people and tribes with their tragic, but provocative histories.
Gail Collins' histories of the Whig and Democratic parties and the evolving American politics, very modern or contemporary in some ways, are also very informative.
Sunday, January 29, 2012
Thursday, January 26, 2012
Experimental Blog #99
Quotations from "Newton's Gift" - How Sir Isaac Newton Unlocked the System of the World by David Berlinski
The copyright year of this book is 2000.
"{Newton's} definitions have now spread and enlarged themselves so that they cover and explain virtually every aspect of material behavior that is larger than the atom and smaller than the universe."
"The law of gravitation constitutes the frame of the universe because its sphere of application is every material object, whether large or small, here or there, to the uttermost ends of the cosmos."
"We are acquainted with gravity through its effects; we understand gravity by means of its mathematical form. Beyond this, we understand nothing."
"Newtonian mechanics is now complete. Almost all problems that can be posed within the structures that it provides have been solved. It is only turbulence that remains a significant and baffling question."
"There have been in the tide of time four absolutely fundamental physical theories: Newtonian mechanics, of course, Clerk Maxwell's theory of electromagnetism, Einstein's theory of relativity, and quantum mechanics."
"The attempt to explain the biological world in terms of the laws of physics has not been a notable success."
"There is much in nature that cannot be explained in terms of purely mechanical forces - electricity and magnetism, to take one example, the behavior of light, to take another."
"Within the Newtonian universe, the laws governing the behavior of particles in motion hold dominion over the past, the present, and the future."
"Newton's discovery that very significant aspects of the physical world behave in ways that would appear to have nothing to do with the exercise of any will is, when properly understood, deeply disconcerting...."
The copyright year of this book is 2000.
"{Newton's} definitions have now spread and enlarged themselves so that they cover and explain virtually every aspect of material behavior that is larger than the atom and smaller than the universe."
"The law of gravitation constitutes the frame of the universe because its sphere of application is every material object, whether large or small, here or there, to the uttermost ends of the cosmos."
"We are acquainted with gravity through its effects; we understand gravity by means of its mathematical form. Beyond this, we understand nothing."
"Newtonian mechanics is now complete. Almost all problems that can be posed within the structures that it provides have been solved. It is only turbulence that remains a significant and baffling question."
"There have been in the tide of time four absolutely fundamental physical theories: Newtonian mechanics, of course, Clerk Maxwell's theory of electromagnetism, Einstein's theory of relativity, and quantum mechanics."
"The attempt to explain the biological world in terms of the laws of physics has not been a notable success."
"There is much in nature that cannot be explained in terms of purely mechanical forces - electricity and magnetism, to take one example, the behavior of light, to take another."
"Within the Newtonian universe, the laws governing the behavior of particles in motion hold dominion over the past, the present, and the future."
"Newton's discovery that very significant aspects of the physical world behave in ways that would appear to have nothing to do with the exercise of any will is, when properly understood, deeply disconcerting...."
Sunday, January 22, 2012
Experimental Blog #98
Summary of "The Great Equations - Breakthroughs in Science from Pythagoras to Heisenberg" by Robert P. Crease
The "great equations" in this book refer to 10 single or groups of several equations in the history of mathematics.
The first equation is the well known Pythagorean Theorem from around the 6th century BCE, but it apparently had been known for over 1000 years in Babylonia, and it was also apparently independently known in ancient India and ancient China. There are over 500 proofs for this theorem.
The second and third equations were formulated by Isaac Newton. They are: Newton's Second Law of Motion, that is, motive force equals mass times acceleration, and Newton's Law of Universal Gravitation. The work of several other people of Newton's time contributed to one or both of these equations.
The fourth equation was derived by Leonhard Euler in the 1740s, and it has been called the "Gold Standard for Mathematical Beauty". It involves rational numbers, irrational constants, and an imaginary number in an almost "mystical" relationship.
The fifth equation is the Second Law of Thermodynamics; that is, entropy, or disorder, is "forever" increasing in the universe. Robert Crease lists 12 contributors from the 19th century who contributed to this most simple equation.
Number 6 are the equations of James Clerk Maxwell that describe the relationships between electricity and magnetism. These equations were reformulated into a more understandable form by Oliver Heaviside in 1884.
Equations number 7 and 8 are Albert Einstein's: the equation for "Special Relativity", which attempts to solve{apparently successfully} contradictions between the physics of Isaac Newton and the physics of James Clerk Maxwell, and is about the conversion of mass and energy; and the equation for "General Relativity", which describes the curvature of space and time by mass. Several other scientists had achieved some progress on the equation for "Special Relativity", and Einstein's famous equation is derived, in part, from the Pythagorean Theorem. The equation for "General Relativity" is based, in part, on non-Euclidian geometry.
Equation #9, derived in 1926, is called "{Erwin} Schrodinger's Equation" and it is the "basic equation of Quantum Theory." It appears to be a long and very difficult equation, and it attempts to achieve a "compromise" between the wave and particle theories in physics.
Number 10, derived in 1927, is the "{Werner} Heisenberg Uncertainty Principle". It appears to be a simple equation, but, similar to equation #9, it has had many "critics" or "inputters".
The "great equations" in this book refer to 10 single or groups of several equations in the history of mathematics.
The first equation is the well known Pythagorean Theorem from around the 6th century BCE, but it apparently had been known for over 1000 years in Babylonia, and it was also apparently independently known in ancient India and ancient China. There are over 500 proofs for this theorem.
The second and third equations were formulated by Isaac Newton. They are: Newton's Second Law of Motion, that is, motive force equals mass times acceleration, and Newton's Law of Universal Gravitation. The work of several other people of Newton's time contributed to one or both of these equations.
The fourth equation was derived by Leonhard Euler in the 1740s, and it has been called the "Gold Standard for Mathematical Beauty". It involves rational numbers, irrational constants, and an imaginary number in an almost "mystical" relationship.
The fifth equation is the Second Law of Thermodynamics; that is, entropy, or disorder, is "forever" increasing in the universe. Robert Crease lists 12 contributors from the 19th century who contributed to this most simple equation.
Number 6 are the equations of James Clerk Maxwell that describe the relationships between electricity and magnetism. These equations were reformulated into a more understandable form by Oliver Heaviside in 1884.
Equations number 7 and 8 are Albert Einstein's: the equation for "Special Relativity", which attempts to solve{apparently successfully} contradictions between the physics of Isaac Newton and the physics of James Clerk Maxwell, and is about the conversion of mass and energy; and the equation for "General Relativity", which describes the curvature of space and time by mass. Several other scientists had achieved some progress on the equation for "Special Relativity", and Einstein's famous equation is derived, in part, from the Pythagorean Theorem. The equation for "General Relativity" is based, in part, on non-Euclidian geometry.
Equation #9, derived in 1926, is called "{Erwin} Schrodinger's Equation" and it is the "basic equation of Quantum Theory." It appears to be a long and very difficult equation, and it attempts to achieve a "compromise" between the wave and particle theories in physics.
Number 10, derived in 1927, is the "{Werner} Heisenberg Uncertainty Principle". It appears to be a simple equation, but, similar to equation #9, it has had many "critics" or "inputters".
Wednesday, January 18, 2012
Experimental Blog #97
Comments on "Infinite Ascent" - A Short History of Mathematics by David Berlinski and "The Artist and the Mathematician" - The Story of Nicolas Bourbaki, the Genius Mathematician Who Never Lived by Amir D. Aczel
The author, David Berlinski, describes mathematics as "a discipline dominated by men who were often hysterical and almost always vain." However, high school and college mathematics classes probably almost always have a few girls and women who are among the top students, but the "original geniuses", both past and present, seem always to be "guys and more guys", but not very "normal"; and they seem to understand each other almost clairvoyantly.
Although it turns out that most of these "original geniuses" often do a very great amount of long trial and error computation to arrive at their final formulas and theorems; but numbers, figures, spaces, collections, and other abstract mathematical objects are probably their passion, or even their obsession.
Amir Aczel, the author of the second book, more or less begins with a discussion of Einstein's Relativity theories in physics, and cubism, and the modern art of Pablo Picasso and Georges Braque. The intellectual life of the 20th century was then violently interrupted by the Bolshevik revolution in Russia, Facism in Italy, and, most of all, by Nazism in Germany. After World War II came the Existentialist philosophers in France, but Amir Aczel says that Existentialism was replaced by the movement of "Structualism" developed by the French anthropologist Claude Levi-Strauss working with the "Nicolas Bourbaki" group of mostly French mathematicians.
This "Bourbaki" group was founded in the 1930s by Andre Weil, and Amir Aczel writes about 19 members of this group in all. He divides them into three "generations", plus one "in-between". He also describes in very great detail the life and work of Alexander Grothendieck, a temporary member of "Nicolas Bourbaki". Alexander Grothendieck is described as "the most visionary mathematician" of the 20th century.
The author, David Berlinski, describes mathematics as "a discipline dominated by men who were often hysterical and almost always vain." However, high school and college mathematics classes probably almost always have a few girls and women who are among the top students, but the "original geniuses", both past and present, seem always to be "guys and more guys", but not very "normal"; and they seem to understand each other almost clairvoyantly.
Although it turns out that most of these "original geniuses" often do a very great amount of long trial and error computation to arrive at their final formulas and theorems; but numbers, figures, spaces, collections, and other abstract mathematical objects are probably their passion, or even their obsession.
Amir Aczel, the author of the second book, more or less begins with a discussion of Einstein's Relativity theories in physics, and cubism, and the modern art of Pablo Picasso and Georges Braque. The intellectual life of the 20th century was then violently interrupted by the Bolshevik revolution in Russia, Facism in Italy, and, most of all, by Nazism in Germany. After World War II came the Existentialist philosophers in France, but Amir Aczel says that Existentialism was replaced by the movement of "Structualism" developed by the French anthropologist Claude Levi-Strauss working with the "Nicolas Bourbaki" group of mostly French mathematicians.
This "Bourbaki" group was founded in the 1930s by Andre Weil, and Amir Aczel writes about 19 members of this group in all. He divides them into three "generations", plus one "in-between". He also describes in very great detail the life and work of Alexander Grothendieck, a temporary member of "Nicolas Bourbaki". Alexander Grothendieck is described as "the most visionary mathematician" of the 20th century.
Sunday, January 8, 2012
Experimental Blog #96
Comments on the books "Incompleteness" - The Proof and Paradox of Kurt Godel and "Betraying Spinoza" - The Renegade Jew Who Gave Us Modernity by Rebecca Goldstein
The first book, "Incompleteness", is about Kurt Godel, who was born into a Sudenten German family in Brno, Moravia, but he "considered himself always Austrian and an exile in Czechoslovakia". Perhaps the most stimulating part of this book is Rebecca Goldstein's vivid description of Vienna, especially its unsurpassed intellectual life and culture of the late 19th and early 20th centuries.
However, this is a book about mathematics, which Rebecca Goldstein seems to understand very well. For a "math challenged" reader to summarize the "Incompleteness Theorem" and say that Kurt Godel mathematically proved that, "There are some things that are true, but they can not be proven to be so," probably mostly reveals the reader's lack of ability to follow so much abstract and abstruse mathematical reasoning.
Rebecca Goldstein's second book, "Betraying Spinoza", also provides quite a lot of vivid history, especially Jewish history in Western Europe. The author's account of how the Inquisition was mostly directed at Jews is especially informative. Other accounts, by comparison, tend to minimize this interpretation. The resulting formation of the Jewish community of mostly former "Marranos" from the Iberian Peninsula in the Netherlands is described in great detail.
In this book of philosophy the philosophical works of Baruch, or Benedictus{which means blessed} Spinoza are quoted and enlarged upon many times. However, Rebecca Goldstein never very clearly explains just how or why she is "betraying" Spinoza. Besides that, when she defines and writes about the meaning of "modernity", Rebecca Goldstein gives the impression that "modernity" is not the "good thing" that most people probably assume that it is.
As for things that can not be proven or things that can not be rationally understood; is it or is it not true, that nobody really ever escapes from their fate or destiny? And that history always is confirmed, every day and in every human life, one day and one life at a time?
The first book, "Incompleteness", is about Kurt Godel, who was born into a Sudenten German family in Brno, Moravia, but he "considered himself always Austrian and an exile in Czechoslovakia". Perhaps the most stimulating part of this book is Rebecca Goldstein's vivid description of Vienna, especially its unsurpassed intellectual life and culture of the late 19th and early 20th centuries.
However, this is a book about mathematics, which Rebecca Goldstein seems to understand very well. For a "math challenged" reader to summarize the "Incompleteness Theorem" and say that Kurt Godel mathematically proved that, "There are some things that are true, but they can not be proven to be so," probably mostly reveals the reader's lack of ability to follow so much abstract and abstruse mathematical reasoning.
Rebecca Goldstein's second book, "Betraying Spinoza", also provides quite a lot of vivid history, especially Jewish history in Western Europe. The author's account of how the Inquisition was mostly directed at Jews is especially informative. Other accounts, by comparison, tend to minimize this interpretation. The resulting formation of the Jewish community of mostly former "Marranos" from the Iberian Peninsula in the Netherlands is described in great detail.
In this book of philosophy the philosophical works of Baruch, or Benedictus{which means blessed} Spinoza are quoted and enlarged upon many times. However, Rebecca Goldstein never very clearly explains just how or why she is "betraying" Spinoza. Besides that, when she defines and writes about the meaning of "modernity", Rebecca Goldstein gives the impression that "modernity" is not the "good thing" that most people probably assume that it is.
As for things that can not be proven or things that can not be rationally understood; is it or is it not true, that nobody really ever escapes from their fate or destiny? And that history always is confirmed, every day and in every human life, one day and one life at a time?
Wednesday, January 4, 2012
Experimental Blog #95
Comments on the books "A Strange Wilderness" - The Lives of the Great Mathematicians by Amir D. Aczel and "Is God a Mathematician?" by Mario Livio
This book begins over 2500 years ago in Ancient Greece and Alexandria describing the lives and works of Thales, Pythagoras, Archimedes, Euclid, and others, who were especially outstanding in geometry. The author, Amir Aczel, then provides some very interesting information on the mathematical accomplishments of India, Arabia, and Persia from around the 5th to the 12th centuries AD, who were very inventive, or original, in algebra and trigonometry. A few pages contain some information on the Chinese mathematical achievements from about the 3rd century BCE to the 15th century.
The author's attention then goes back to Italy and the rest of Europe beginning in the 12th century and culminating in the "great heresy" of Johannes Kepler, Galileo Galilei, and others of "heliocentrism".
Although the author describes many Italian, French, German, and other European mathematicians and their achievements, he seems to concentrate on Rene Descartes, Gottfreid Leibniz, Isaac Newton, Evariste Galois{who died at 20 years of age in a duel}, Georg Cantor{who died in a mental hospital, where he had often been a patient}, and Nicolas Bourbaki and his group who published papers and books even though Nicolas Bourbaki was a ficticious person who never lived.
The whole second book, "Is God a Mathematician", revolves around the never ending debate about whether mathematics is a science of "discovery" of the "absolute truth of the universe" that exists independently outside the human mind, which is often called the "Platonic" point of view; or whether mathematics is only an "invention", or creation, of human imagination, and would, and could not exist without the human brain.
Among much other information the author points out how virtually timeless mathematics seems to be; that is, it rarely really changes over time. For instance, Euclid's geometry is as true and useful today as it was 2300 years ago. Mario Livio also describes how so many things are not only explained, but have been, and can be predicted by mathematics to extraordinary degrees of accuracy.
By contrast, however, the science of biology is limited to our planet Earth, to an infinitesmal place in the universe with no known relationships to anywhere else. Mathematics seems to apply consistently and everywhere in space and time.
This book begins over 2500 years ago in Ancient Greece and Alexandria describing the lives and works of Thales, Pythagoras, Archimedes, Euclid, and others, who were especially outstanding in geometry. The author, Amir Aczel, then provides some very interesting information on the mathematical accomplishments of India, Arabia, and Persia from around the 5th to the 12th centuries AD, who were very inventive, or original, in algebra and trigonometry. A few pages contain some information on the Chinese mathematical achievements from about the 3rd century BCE to the 15th century.
The author's attention then goes back to Italy and the rest of Europe beginning in the 12th century and culminating in the "great heresy" of Johannes Kepler, Galileo Galilei, and others of "heliocentrism".
Although the author describes many Italian, French, German, and other European mathematicians and their achievements, he seems to concentrate on Rene Descartes, Gottfreid Leibniz, Isaac Newton, Evariste Galois{who died at 20 years of age in a duel}, Georg Cantor{who died in a mental hospital, where he had often been a patient}, and Nicolas Bourbaki and his group who published papers and books even though Nicolas Bourbaki was a ficticious person who never lived.
The whole second book, "Is God a Mathematician", revolves around the never ending debate about whether mathematics is a science of "discovery" of the "absolute truth of the universe" that exists independently outside the human mind, which is often called the "Platonic" point of view; or whether mathematics is only an "invention", or creation, of human imagination, and would, and could not exist without the human brain.
Among much other information the author points out how virtually timeless mathematics seems to be; that is, it rarely really changes over time. For instance, Euclid's geometry is as true and useful today as it was 2300 years ago. Mario Livio also describes how so many things are not only explained, but have been, and can be predicted by mathematics to extraordinary degrees of accuracy.
By contrast, however, the science of biology is limited to our planet Earth, to an infinitesmal place in the universe with no known relationships to anywhere else. Mathematics seems to apply consistently and everywhere in space and time.
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