Month: July 2018

The notebooks of Sir Isaac Newton, who was famously reported to have suffered a (scientifically) earth-shaking blow to the head from an apple, are being scanned and published online by the University of Cambridge.

Newton, a Biblical numerologist when he wasn’t developing calculus or building the first reflecting telescope, founded classical mechanics with Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which was first published in 1687. In the book that made his name, Newton set out his three laws of motion, and his theory of universal gravitation (prompted by pondering what force plummeted the fruit straight down onto his head, or so goes the apocryphal tale).

Newton studied and later held the Lucasian Chair of Mathematics at Cambridge, which was given numerous manuscripts of his in 1872 and has since bought more. The online publication has started with Newton’s mathematical works of the 1660s and more papers will become available over coming months.

A philosopher of science at Flinders University, George Couvalis, said that Newton’s gravitational experiments – which largely corrected ancient observations of gravity – were sparked by his interest in magic and magnetism. “The idea that things might naturally attract one another is an idea that he got from magical ideas. He adapted it across to mathematical theory because it was a mystical theory,” Dr Couvalis said

It was important to remember that scientists of Newton’s era did not have what we would consider a modern sceptical outlook and – with the exception of the “exceptional” Galileo Galilei – instead held a fusion of views that we would consider deeply irrational, Dr Couvalis said.

“It was certainly far more common in the 17th and 18th centuries for scientists to be interested in magical beliefs and alchemical beliefs and religious beliefs. Johannes Kepler, for example, had all kinds of strange views about the music of the spheres, Copernicus had strange views about the sacredness of the sun, and Newton famously had views about the mysterious numerical meanings of Biblical passages and about alchemical material,” Dr Couvalis said.

Scientists of the period saw their work touching on many illogical and occult fields of interest, including Robert Boyle, a founder of modern chemistry, who had “an interest in doing experimental research on magical mirrors, which to us would sound bizarre but at the time it was thought to be a possibility,” said Dr Couvalis, who added that Boyle pulled back from some experiments for religious reasons. “He thought it might get him in touch with demons.”

Demonology may have fallen out of favour amongst scientists, but “the view that we’re getting everything right would be a serious mistake,” Dr Couvalis said. “To some degree science is always in the sway of the time it’s in; this is now the standard view of philosophers and historians.”

“Newton’s mechanics is in certain respects pretty much right, but in other respects it was shown by Einstein and others to be wildly wrong. By about 1900 we had people saying to their graduate students ‘You should give up physics because it’s all been done,’ but Einstein managed to show that it was wildly wrong in certain respects,” Dr Couvalis said.

The ideal of the scientific method is never met, and our beliefs and discoveries will likely on day be seen as flawed but perhaps useful stepping stones in the continuum of science, Dr Couvalis said. “People make mistakes, people have a lot of trouble leaving assumptions behind, and our tests are never rigorous enough to be absolutely certain that we’re getting things right. Future experimental studies and the sheer empirical facts will show us to be wrong in many ways that we can’t anticipate.”

“We work with what we have because we just don’t know anything better at the moment. It might turn out that Einstein’s special and general theories of relativity are wrong in some deep-seated way. It might turn out that some of our theories of the universe are wrong. It’s starting to look in biology as if neo-Darwinism isn’t completely right, so where will that go – I don’t know. Research will determine the direction. That doesn’t mean that we’re going to go back to being creationists – that view has been thoroughly debunked. Imre Lakatos wrote in the 1970s there are no good scientific theories, there’s only the best rotten theory we have.”

For more such insights, log into our website https://international-maths-challenge.com

Credit of the article given to Matthew Thompson, The Conversation

Mirrors of a magical scientist: Andromeda photographed through a Newtonian telescope.

The notebooks of Sir Isaac Newton, who was famously reported to have suffered a (scientifically) earth-shaking blow to the head from an apple, are being scanned and published online by the University of Cambridge.

Newton, a Biblical numerologist when he wasn’t developing calculus or building the first reflecting telescope, founded classical mechanics with Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), which was first published in 1687. In the book that made his name, Newton set out his three laws of motion, and his theory of universal gravitation (prompted by pondering what force plummeted the fruit straight down onto his head, or so goes the apocryphal tale).

Newton studied and later held the Lucasian Chair of Mathematics at Cambridge, which was given numerous manuscripts of his in 1872 and has since bought more. The online publication has started with Newton’s mathematical works of the 1660s and more papers will become available over coming months.

Striking a light for science.

A philosopher of science at Flinders University, George Couvalis, said that Newton’s gravitational experiments – which largely corrected ancient observations of gravity – were sparked by his interest in magic and magnetism. “The idea that things might naturally attract one another is an idea that he got from magical ideas. He adapted it across to mathematical theory because it was a mystical theory,” Dr Couvalis said.

It was important to remember that scientists of Newton’s era did not have what we would consider a modern sceptical outlook and – with the exception of the “exceptional” Galileo Galilei – instead held a fusion of views that we would consider deeply irrational, Dr Couvalis said.

“It was certainly far more common in the 17th and 18th centuries for scientists to be interested in magical beliefs and alchemical beliefs and religious beliefs. Johannes Kepler, for example, had all kinds of strange views about the music of the spheres, Copernicus had strange views about the sacredness of the sun, and Newton famously had views about the mysterious numerical meanings of Biblical passages and about alchemical material, ” Dr Couvalis said.

Scientists of the period saw their work touching on many illogical and occult fields of interest, including Robert Boyle, a founder of modern chemistry, who had “an interest in doing experimental research on magical mirrors, which to us would sound bizarre but at the time it was thought to be a possibility,” said Dr Couvalis, who added that Boyle pulled back from some experiments for religious reasons. “He thought it might get him in touch with demons.”

Demonology may have fallen out of favour amongst scientists, but “the view that we’re getting everything right would be a serious mistake,” Dr Couvalis said. “To some degree science is always in the sway of the time it’s in; this is now the standard view of philosophers and historians.”

“Newton’s mechanics is in certain respects pretty much right, but in other respects it was shown by Einstein and others to be wildly wrong. By about 1900 we had people saying to their graduate students ‘You should give up physics because it’s all been done,’ but Einstein managed to show that it was wildly wrong in certain respects,” Dr Couvalis said.

The ideal of the scientific method is never met, and our beliefs and discoveries will likely on day be seen as flawed but perhaps useful stepping stones in the continuum of science, Dr Couvalis said. “People make mistakes, people have a lot of trouble leaving assumptions behind, and our tests are never rigorous enough to be absolutely certain that we’re getting things right. Future experimental studies and the sheer empirical facts will show us to be wrong in many ways that we can’t anticipate.”

“We work with what we have because we just don’t know anything better at the moment. It might turn out that Einstein’s special and general theories of relativity are wrong in some deep-seated way. It might turn out that some of our theories of the universe are wrong. It’s starting to look in biology as if neo-Darwinism isn’t completely right, so where will that go – I don’t know. Research will determine the direction. That doesn’t mean that we’re going to go back to being creationists – that view has been thoroughly debunked. Imre Lakatos wrote in the 1970s there are no good scientific theories, there’s only the best rotten theory we have.”

For more such insights, log into www.international-maths-challenge.com.

*Credit For article given to Matthew Thompson*

In a project that has long been overdue, Cambridge University, thanks to a hefty gift from the Polonsky Foundation (supporter of education and arts) and a grant from Britain’s Joint Information Services Committee (JISC), has put some of Isaac Newton’s original papers online for any and all to see. Of particular interest to most will be Newton’s own annotated copy of Philosophiae Naturalis Principia Mathematica, considered by many to be one of the greatest published works by any scientist ever. For those looking for a little behind the scenes work, the University has also published Newton’s so-called “Waste Book,” a diary of sorts that Newton inherited from his step-father which he took along with him and used for jotting notes about such things as his ideas on calculus while away from school due to the Great Plague in 1665.

In viewing the material, which can be paged through in a PDF type format, by clicking arrows, it’s easy to see that the digitization of Newton’s papers have come none too soon, as many of the pages are tattered, smeared and even burned-looking in some places. Thus, not only has putting the papers online made them accessible to anyone with a computer and an Internet connection, it has also caused them to be saved for posterity in an electronic form that will ensure they will be accessible to all those who may wish to view them in the future as well.

It was in Principia Mathematica that Newton laid out his theories on the laws of motion and universal gravitation which some suggest laid the groundwork for Einstein’s theories on relativity. And if that weren’t enough, Newton is also widely credited with “inventing” calculus, a mathematical science without which the modern world would simply not exist.

In all there are more than 4,000 pages of Newton’s work displayed on the site, which took a team of photo copyists the better part of this past summer to capture, though it’s obvious in looking at the results that there were many slow-downs as pages had to have some restorative efforts made in order to present them. Those working on the project are to be commended as the results show great care and dedication to a single purpose; namely showcasing one of history’s brightest minds.

It’s intriguing to see the notes Newton himself made on the first edition of Principia Mathematica, in preparing for the second, and happily, the University has announced that they will be adding translations for all of the text and notes as early as next year.

The University has also announced plans to make the works of other famous scientists available as the future unfolds and hopefully will continue to add more of the Newton library too, as thus far only about 20% of their collection has been made available online.

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Credit of the article given to Bob Yirka , Phys.org

A major study of recent international data on school mathematics performance casts doubt on some common assumptions about gender and math achievement — in particular, the idea that girls and women have less ability due to a difference in biology.

“We tested some recently proposed hypotheses that try to explain a supposed gender gap in math performance and found the data did not support them,” says Janet Mertz, senior author of the study and a professor of oncology at the University of Wisconsin-Madison.

Instead, the Wisconsin researchers linked differences in math performance to social and cultural factors.

The new study, by Mertz and Jonathan Kane, a professor of mathematical and computer sciences at the University of Wisconsin-Whitewater, was published in Dec 2011 in Notices of the American Mathematical Society. The study looked at data from 86 countries, which the authors used to test the “greater male variability hypothesis” famously expounded in 2005 by Lawrence Summers, then president of Harvard, as the primary reason for the scarcity of outstanding women mathematicians.

That hypothesis holds that males diverge more from the mean at both ends of the spectrum and, hence, are more represented in the highest-performing sector. But, using the international data, the Wisconsin authors observed that greater male variation in math achievement is not present in some countries, and is mostly due to boys with low scores in some other countries, indicating that it relates much more to culture than to biology.

The new study relied on data from the 2007 Trends in International Mathematics and Science Study and the 2009 Programme in International Student Assessment.

“People have looked at international data sets for many years”, Mertz says. “What has changed is that many more non-Western countries are now participating in these studies, enabling much better cross-cultural analysis.”

The Wisconsin study also debunked the idea proposed by Steven Levitt of “Freakonomics” fame that gender inequity does not hamper girls’ math performance in Muslim countries, where most students attend single-sex schools. Levitt claimed to have disproved a prior conclusion of others that gender inequity limits girls’ mathematics performance. He suggested, instead, that Muslim culture or single-sex classrooms benefit girls’ ability to learn mathematics.

By examining the data in detail, the Wisconsin authors noted other factors at work. “The girls living in some Middle Eastern countries, such as Bahrain and Oman, had, in fact, not scored very well, but their boys had scored even worse, a result found to be unrelated to either Muslim culture or schooling in single-gender classrooms,” says Kane.

He suggests that Bahraini boys may have low average math scores because some attend religious schools whose curricula include little mathematics. Also, some low-performing girls drop out of school, making the tested sample of eighth graders unrepresentative of the whole population.

“For these reasons, we believe it is much more reasonable to attribute differences in math performance primarily to country-specific social factors,” Kane says.

To measure the status of females relative to males within each country, the authors relied on a gender-gap index, which compares the genders in terms of income, education, health and political participation. Relating these indices to math scores, they concluded that math achievement at the low, average and high end for both boys and girls tends to be higher in countries where gender equity is better. In addition, in wealthier countries, women’s participation and salary in the paid labor force was the main factor linked to higher math scores for both genders.

“We found that boys — as well as girls — tend to do better in math when raised in countries where females have better equality, and that’s new and important,” says Kane. “It makes sense that when women are well-educated and earn a good income, the math scores of their children of both genders benefit.”

Mertz adds, “Many folks believe gender equity is a win-lose zero-sum game: If females are given more, males end up with less. Our results indicate that, at least for math achievement, gender equity is a win-win situation.”

U.S. students ranked only 31st on the 2009 Programme in International Student Assessment, below most Western and East-Asian countries. One proposed solution, creating single-sex classrooms, is not supported by the data. Instead, Mertz and Kane recommend increasing the number of math-certified teachers in middle and high schools, decreasing the number of children living in poverty and ensuring gender equality.

“These changes would help give all children an optimal chance to succeed,” says Mertz. “This is not a matter of biology: None of our findings suggest that an innate biological difference between the sexes is the primary reason for a gender gap in math performance at any level. Rather, these major international studies strongly suggest that the math-gender gap, where it occurs, is due to sociocultural factors that differ among countries, and that these factors can be changed.”

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Credit of the article given to University of Wisconsin-Madison