## Technical Column:  "Science for Everyone"

"Science for Everyone" was a technical column posted regularly on the VACETS forum. The author of the following articles is Dr. Vo Ta Duc. For more publications produced by other VACETS  members, please visit the VACETS Member Publications page or Technical Columns page.

Hot Water Freezes Faster Than Cold ???

If you live in the Midwest of the US or in Canada, on a freezing day in January, you put two pails of water outside. One has hot water (~95C) and one has cold water (~15C). Which one will freeze first? The answer is: if it is 18th century, the pail of hot water will probably freeze first; if it is Jan 1995 then the cold water probably will ...

Roots, Roots, and Roots!!!

... Twenty years ago, most junior-high students could calculate square roots without a calculator. Some high-school students today do not know how to divide two numbers without the little hand-held electronic thing. If this decay rate remains constant, twenty or fifty years from now, most people may not know how to multiply or divide...

Fermat 's Last Theorem (Part 1)

In the [SCIENCE FOR EVERYONE] column last week, I had three bonus problems posted and no one had solved any of them. All I heard was all kinds of discussion about the first bonus, the Fermat's last theorem. It asserts that "For any integer n greater than 2, the equation (a^n + b^n = c^n) has no solutions for which a, b, and c are integers greater than zero."...

Primes and FLT

... There are many kinds of prime numbers like Fermat numbers, Mersenne numbers, Lucas numbers, etc... Those primes can be very huge. But those methods do not calculate all the possible primes and each number calculated may have to be tested and the testing process may take hours of computer time. For the purpose of searching for a solution to the FLT (or set some lower limit), we may only need to find ALL the primes smaller than n, say like all primes less than 1 trillion ...

Who Is #1?

Today, there are many computer polls (New York Times, USA Today-CNN, ..., and individuals) that rank the teams based on many different mathematical formulas. The poll or rating that is used the most (?) is probably the Latest Line from Las-Vegas, Nevada. The ratings provide a numerical measure of a team's relative strength and have some value in predicting the outcome of future games. Each different ranking or rating method gives different results because each weighs important factors differently. So now the problem with computer polls is which model predicts best? There seems to be no easy answer for that just like the "which voters' poll is the best" problem...

Greenhouse Effect: Atmospheric Trends of Greenhouse Gases

It is now known that the presence of atmospheric greenhouse gases has a significant effect on climate. However, many questions about how the changing composition of the atmosphere will affect climate remain unanswered. Nonetheless, a number of researchers are attempting to determine what sorts of impacts on our environment may result from global warming. Computer models of the atmosphere and climate generally agree that an overall global warming will occur because of increasing concentrations of greenhouse gases, but they are much less certain in their representation of the spatial distribution of this warming...

Fermat's Last Theorem (Part 2)

Few days after the [SCIENCE FOR EVERYONE] FERMAT'S LAST THEOREM article was sent out last month, anh Phuong sent the news that the Fermat's last theorem problem was solved by Andrew Wiles and a colleague (I can not remember his name). What I heard at that time was that one of Wiles' colleague said that Wiles' new proof had no hole in it. I haven't heard any more news about that since. I'm wondering if Wiles' new proof has been published, or if the whole mathematical community has accepted the new proof, or if anyone has found new holes in Wiles' new proof. Do any of you hear any thing about that? ...

Greenhouse Effect: Carbon Removal and Recovery

Carbon dioxide (CO2) is estimated to contribute to about half the total global warming. Therefore, most of the attention on greenhouse gases has been concentrated on the analysis of technologies to reduce fossil-fuel CO2 emissions...

By Jove: Comet Crash Puzzles

It has been exactly half a year since the fragments of Comet Shoemaker-Levy 9 plowed into Jupiter. There is no better time to re-visit and re-live the excitement of the once-in-a-lifetime event. As of today, six months after the crash, scientists are still continuing their struggle to understand exactly what the impacts have revealed about the inside of the gaseous planet. But even if much of the Jovian interior remains a mystery, the collisions have shed some new insights about the giant planet's upper atmosphere...

Cosmology: A Journey Through Time

Cosmology, what is it? It is a study that deals with the origin, structure, and space-time relationships of the universe. Our understanding of the cosmos today is far different from that of our ancestors some thousands, hundreds, or even tens of years ago. And, perhaps, our perceptions and assumptions about our universe today may be dramatically changed and viewed as myths by our children. It is of interest to start the series by an article that brings us back to the distant past, to the ancient myths about the creation of the universe, and from there, we will gradually travel back to our present time, to a universe of unimaginable size that itself has no center at all...

The Big Bang

In the beginning... no, no, no! Before the beginning, there was no space and there was no time. There was nothing and there was God. And God said, "Let there be light". BANG!!! There was light! And there was the universe...

Dark Matter

For decades, astronomers have been increasingly puzzled by what might be called the "hidden mass" problem, according to which most of the matter comprising the Universe is apparently invisible. They discovered this problem while observing the rotation of spiral galaxies like our own. If the mass of a galaxy is concentrated where its light is, in the bright core, then just as the sun's gravity pulls distant planets around much more slowly than it pulls the inner planets, stars in the outer reaches of a galaxy should orbit much more slowly than stars in the center. But they don't. The conclusion is that there must be some form of matter surrounding the galaxy, in a spheroidal halo, that doesn't show up in telescopes. The problem is that we just don't know what form it takes...

Dark Matter (Part 2): WIMPs and other Exotic Particles.

In the last article, we learned that the known-to-exist objects such as collapsed stars, red dwarfs, massive compact halo objects (MACHOs), and neutrinos are not good dark matter candidates. Would that make the hypothetical weakly interacting massive particles (WIMPs) or some other hypothetical particles the winners by default? The word "hypothetical" means that these candidates exists on paper only and no one has ever seen or detected them. That is what keeps most of them in contention. Let's examine these hypothetical candidates to see if any one of them can be a real winner...

Spacetime-Travel and Relativity (Part 1)

... That "Calvin and Hobbes" comic strip was one of my favorites that I read many years ago. I think it is appropriate to start the spacetime-travel mini-series with a few lines from the comics with Calvin, a kid who has wild imaginations and often dreams of traveling to some unknown planets or going back in time...

Spacetime-Travel and Relativity (Part 2)

...The Schwarzschild black hole is the simplest form of black hole. It has one "event horizon" within it nothing, including light, can escape. This type of black hole, no spin and no charge, is not likely to exist. One particular property of this black hole is that it has a connection, called the Einstein-Rosen bridge or wormhole, connects this universe with another universe...

Lastest Known Prime Number Discovered

... About 2 years ago, Andrew Wiles, a researcher at Princeton, claims to have proved the Fermat's Last Theorem (FLT) and later a large gap was found in the proof. (The gap was filled later at the end of 1994.) At that time, we, the VACETSERS, had debated on proving the FLT using numerical methods (i.e., using computer to crank out the solutions to the famous theorem). One of the first steps in numerical method is to find the prime numbers, and from that, a "fastest prime number generator" war was waged among us the VACETSERS. The result of that "war" was that we were able to reduce the time from tens of seconds to find all the primes below 1 million to less than 1 second to find all the primes below 10 million. It was an improvement of more than 100. It was a fun war...

More to come ...

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