Introduction
Gravitational lensing revealing multiple copies of the same supernova
Sixty five years ago, in 1950, while having lunch with colleagues Edward Teller and Herbert York, who were chatting about a recent cartoon in the New Yorker depicting aliens abducting trash cans in flying saucers, Nobel physicist Enrico Fermi suddenly blurted out, “Where is everybody?” His question is now known as Fermi’s paradox.
Fermi’s line of reasoning was the following: (a) Most likely there are numerous (maybe millions) of other technological civilizations in the Milky Way galaxy alone; (b) if a society is less advanced than us
Continue reading Where is ET? Fermi’s paradox turns 65
“I Prefer Pi” is appropriate title for Pi Day (3/14, i.e., March 14), as it is one of the few palindromes involving Pi = 3.141592653589793… (a palindrome is a phrase that reads the same forwards or backwards).
Pi Day is particularly memorable this year, since only once a century can one celebrate this event in a year where the longer version 3/14/15 continues two more correct digits of Pi. The Museum of Mathematics in New York City, among others, is taking Pi Day 2015 one step further, by celebrating at 9:26am, i.e., 3/14/15/926, adding three more digits. See MoMath’s website
Continue reading I Prefer Pi: Background for Big Pi Day (3/14/15)
Prime numbers
In the field of mathematics, prime numbers are whole numbers that cannot be evenly divided by any integer other than itself and one. The first 12 prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37. Although the study of prime numbers is a very old field of mathematics, numerous intriguing questions remain. “Number theory,” as this field is known, is also increasingly indispensable in modern technology, as it underlies techniques for compressing and encrypting digital data.
One of the as-yet-unsolved questions in number theory is the twin prime conjecture, which asks if
Continue reading Is the nature of mathematical proof changing?
New Pew Research Center poll on scientists’ views versus public views
A new poll by the Pew Research Center has highlighted some stark differences between views of leading scientists, in particular members of the American Association for the Advancement of Science (AAAS), and those of the general U.S. public. The results are summarized in this NPR report, while the full results are available from the Pew website.
Here are some of the poll’s findings:
98% of AAAS scientists agree that humans have evolved over time, versus only 65% of the U.S. public. 88% of AAAS scientists agree that it is
Continue reading Does public opinion always agree with scientific fact?
The twin prime and prime gap conjectures
Paul Erdos, one of the 20th century’s most famed mathematicians (1913-1996) was well-known for offering prizes for the solution of various mathematical problems. Although most of these prizes were a token USD$25 or the like, he did offer a UDS$10,000 prize for the solution to a certain conjecture of his on prime gaps. Until very recently, it had not been solved.
The twin prime conjecture is that the gap between successive primes, namely gn = pn+1 – pn, is two for infinitely many n. This has not been proven, and is one of
Continue reading New results on the prime gap conjecture
Introduction
The world community is truly at a crossroads like never before faced in the history of our civilization. If we continue business-as-usual with the consumption of fossil fuels, then, according to the 2014 edition of the Intergovernmental Panel on Climate Change (IPCC)’s climate change report, grave consequences will almost surely ensue, including rising sea levels, extreme temperatures, flooding, drought, agricultural losses and, quite likely, violent conflicts among human societies. Delays may have already cost the world society USD$8 trillion.
Some who distrust the scientific consensus on climate change have taken heart at an apparent leveling off of world temperatures
Continue reading Low energy nuclear reactions: Papers and patents
June 23, 2014 was a very nice day for five mathematicians: Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Terence Tao and Richard Taylor. They were informed that they would be receiving the inaugural Breakthrough Prizes in Mathematics, each with a cash award of USD$3,000,000. They plan to share their good fortune.
The international, if still Euro-centric, nature of mathematics is obvious when we list where the five were born, educated and currently work:
Name Born Educated Current appointment(s) Donaldson Cambridge, UK Cambridge, UK; Oxford, UK Stony Brook, USA; Imperial College, UK Kontsevich Khimki, Russia Moscow State, Russia; Univ. Bonn, Germany IHES,
Continue reading Big Bucks for Big Breakthroughs: Prize recipients give three million dollar maths talks
When numbers of any sort are presented, whether in mathematics, science, business, government or finance, the default assumption is that the data presented are reasonably reliable to the last digit presented. Thus, if a light bulb is listed as using 3.14 watts, then its actual usage is presumably between 3.13 and 3.15 watts, and certainly not 2.8 or 4.2 watts. Or if the average interest rate paid on a set of securities is listed as 2.718 percent, then a reasonable reader presumes that the actual figure is between 2.717 and 2.719 percent.
The total number of significant digits can vary
Continue reading Dubious digits: Is this data really that accurate?
The IPCC report’s warning
The latest draft edition of the UN’s Intergovernmental Panel on Climate Change (IPCC) bluntly warns that business-as-usual increases in greenhouse gas emissions will cause “further warming and long-lasting changes” in the earth’s the climate system, with increasing likelihood of “severe, pervasive and irreversible impacts for people and ecosystems.” Specific dangers include rising sea levels, more frequent extreme temperatures, flooding, drought, harm to marine life and violent conflicts among human societies in the wake of agricultural changes. Delays may have already cost the world society US$8 trillion.
So what can be done? As we argued in a
Continue reading Fusion energy: Hope or hype?
Don Quixote
September 29, 2014 is the 467th birthday of Spanish author Miguel de Cervantes, whose immortal Don Quixote is widely regarded as one of the greatest works of literature in any language. In fact, in 2002 the Norwegian Book Club named Don Quixote as “best literary work ever written” in their listing of the world’s 100 greatest books.
Don Quixote describes the exploits the protagonist Alonso Quixano, a semi-retired Spanish gentleman who got so carried away with his readings of chivalry and knights-errant exploits that he adopted the name Don Quixote, donned some old armor, named a friend as
Continue reading Tilting at windmills
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