[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]
Assessing risk is something everyone must do every day. Yet few are very good at it, and there are significant consequences to the public’s collective inability to accurately assess risk.
As a first and very important example, most people presume, as an indisputable fact, that the past century has been the most violent in all history — two devastating world wars, the Holocaust, the Rawanda massacre, the September 11 attacks and more — and that
Continue reading Innumeracy and public risk
In two articles [BaiBor2011a; BaiBor2011b], two earlier blog posts [BlogA; BlogB] and a Conversation piece, we have examined the discovery and development of our modern system of decimal arithmetic with zero, which discovery we believe to be among the greatest of all historical mathematical achievements. It is certainly nontrivial, as evidenced by the fact that it escaped even Archimedes, that extraordinary genius of the ~300 BCE Greek culture who anticipated much of modern mathematics, including numerical analysis and calculus. And the impact of this ingenious discovery in our modern computer-oriented society cannot be overstated.
One key aspect of this history
Continue reading That mysterious but important number zero
[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]
From time to time, the scientific community is rocked with cases of scientific fraud. Needless to say, such incidents do not help instill confidence in the public mind that is already predisposed to be skeptical of inconvenient scientific findings, including biological evolution and global warming.
One notable case of fraud came to light in 2002, when Bell Labs researcher Hendrik Schon, once described as a “rising star” in the field of nanoelectronics, was accused of
Continue reading Mathematics and scientific fraud
[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]
Introduction
Many of us know that the sun is approximately 150 million km or 93 million miles away, a distance that is known as the “astronomical unit” (AU). Neptune, the most distant planet, is 30 AU from the sun, or some 44.8 billion km (27.9 billion mi). The Voyager 2 spacecraft, launched in 1977, reached Jupiter just two years later, but did not reach Neptune until 1989.
The nearest stars, Alpha Centauri A-B and Proxima
Continue reading How far away is everybody?
[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]
Introduction
During a lunch in the summer of 1950, physicists Enrico Fermi, Edward Teller and Herbert York were chatting about a recent New Yorker cartoon depicting aliens abducting trash cans in flying saucers. Suddenly, Fermi suddenly blurted out, “Where is everybody?”
Behind Fermi’s question was this line of reasoning: Since there are likely many other technological civilizations in the Milky Way galaxy, and since in a few tens of thousand of years at most they
Continue reading Where is everybody?
The Conversation, an online forum from the Australian academic research community and aimed at the interested public, has featured an essay written by the present bloggers. Entitled “Magic numbers: the beauty of decimal notation,” it is available here: Conversation article.
This piece briefly mentions the history of positional decimal arithmetic, from its original discovery by unknown Indian mathematicians approximately 2000 years ago, to its modern incarnation (at least in binary) in computers. The article then speculates how history may have changed if either arithmetic had been discovered earlier, or it had been communicated to Greek mathematicians such as Archimedes.
It
Continue reading Magic numbers
The “nature versus nurture” debate refers to discussions of the relative importance of a person’s innate qualities (“nature”) versus the importance of upbringing and experience (“nurture”). Such debates have been ongoing for centuries. Shakespeare even referred to such a debate in his play The Tempest (4:1). The phrase “nature versus nurture” in the current sense was first used by Francis Galton in the 19th century, in commentary on the work of Darwin, his cousin. Along this line, philosopher John Locke coined the term “tabula rasa” (“blank slate”) to refer to the “nurture” view that all or almost all human behavior
Continue reading Is math ability inborn or developed?
One of the most fascinating aspects of modern mathematics is the extent to which developments in “pure” mathematics are subsequently, and often quite unexpectedly, found to have direct relevance to the physical world. Albert Einstein asked, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” [Jammer1921, pg. 124].
One source that is often cited in this context is Eugene Wigner’s 1960 essay “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” [Wigner1960]. He cites numerous examples:
Newton’s laws and planetary motion. Wigner notes that Newton’s
Continue reading Is mathematics invented or discovered?
[Note: A condensed and revised version of this article was published here in The Conversation, an online forum of academic research headquartered in Melbourne, Australia.]
Introduction
Monumental inventions of history can be grouped into three categories: (a) those whose origin is well known and well appreciated; (b) those whose origin is completely lost to history; and (c) those who origin may be known, at least in general terms, but which are not very well appreciated in modern society. Among those in the first category are efficient steam engines (by James Watt in 1765), movable-type printing (by the Chinese inventor Bi
Continue reading What if base-10 arithmetic had been discovered earlier?
The Conversation is a recently established web journal dedicated to making academic and related policy issues accessible to an informed public. The editors write:
The Conversation is an independent source of information, analysis and commentary from the university and research sector – written by acknowledged experts and delivered directly to the public. As professional journalists, we aim to make this wealth of knowledge and expertise accessible to all.
So far this has been done in a most lively and stimulating fashion; it is garnering readers within and without the academy from across the world let us hope it can be
Continue reading Turning IBM’s Watson into a maths genius
|
|