Friday, December 31, 2010

One hundred years ago, in 1910...

Bertrand Russell and Alfred North Whitehead published the first volume of Principia Mathematica, (commonly abbreviated as PM) one of the most important works on the foundations of mathematics; the second and third volumes were published in 1912 and 1913. This monumental (both in size, scope and complexity) was attempt to derive all mathematical truths from a fixed set of rules and axioms in symbolic logic. Cited by The Modern Library as #23 of the hundred most important non-fiction works of the century, it's also referred to as 'the most important scientific or mathematical work, which no one has read." (Largely due to it's scope and the need to master a symbolic logic syntactical language invented by Russell and Whitehead.)
As an example, it takes until page 379 of volume I, for Prop. 54.43 to be proven. This is a proof that  -- given the limited number of axioms and relational rules posited in PM:
"1 + 1 = 2".
Here it is:



This proof is actually completed in the section on cardinal arithmetic in volume II page 86, accompanied by the comment, "The above proposition is occasionally useful."  :)

Sunday, December 26, 2010

IceCube: Badgers and Neutrinos at the South Pole

"Construction of the IceCube Neutrino Observatory was completed at the the South Pole in Antarctica on December 18, 2010 New Zealand time. This scientific milestone marks completion of the world's largest neutrino detector and a powerful tool for exploring the Universe" (from the link in the Title).
IceCube is the world's largest neutrino 'observatory' and is located at the Amundsen-Scott South Pole Station, at the earth's South Pole in Antarctica.
Badgers? The University of Wisconsin at Madison is the lead instituion of the project, which is funded by the National Science Foundation.
  The function of of IceCub is to detect and collect information on neutrinos (uncharged, extremely light particles created by the decay of radioactive materials, particles that lack an electric charge.) Trillions of neutrinos pass through each of our bodies every day, but there is little chance that even one of them would interact with an antom in our bodies in a lifetime.
  The IceCube devices located at the South Pole actually 'looks' North, using the entire Earth as a filter to block out surface radiation, etc.
  The telescope/detector consists of over 4000 Complex sensors, deployed on 'strings' like Christmas lights, at depths in the ice starting between 4750ft. and 8000 feet beneath the surface. (!). It turns our the one of the best materials to embed and enclose such sensors is pure ice, and the miles-thick Antactic ice bed is exactly such a material. The sensors on the strings lowered in holes drilled in the ice by hot-water drilling apparatus don't start until about a mile below the surface, to filter out excess particles coming from the surface.

  What is this all supposed to tells us: more information about the growth and death of stellar processes in the early universe, information about 'dark matter' and 'dark energy', the existense of WIMPS ('weakly interacting massive particles') and much more.

   The amazing part of the device/telescople is its size: more then one cubic kilometer.
Here are some illustrative diagrams:

(That's the Eiffel Tower on the right,
for size comparison)



Friday, December 17, 2010

Monday-Tuesday, Dec. 20-21: TOTAL LUNAR ECLIPSE IN ALL NORTH AMERICA

Well, it's been about three years since we in North America got to see a total lunar eclipse, but there will be one late Monday night-Tuesday morning:
 Earth's shadow will totally engulf the Moon from 2:41 to 3:53 a.m. Eastern Standard Time, or 11:41 p.m. to 12:53 a.m. Pacific Standard Time; the earlier parts of the eclipse start and end about an hour beforehand and afterward.
Alas, it looks like here in MN, it will be cloudy and not visible, but do check. The next total lunar eclipse visible in all North America will not happen until
April 14-15, 2014  :(

For more info, check: http://www.skyandtelescope.com/observing/home/111597159.html

Tuesday, December 14, 2010

"The Pale Blue Dot" - the greatest photograph ever taken

This is my nomination for the greatest photograph ever taken by mankind.
Taken by the spacecraft Voyager I in 1990,at a distance of 3,781,782,502 (almost 4 billion miles) from where it was launched. it shows our planet Earth -- "The Pale Blue Dot" as never seen before. The photo almost never happened -- it was not in NASA's approved activities, and it took a long series of ever-increasingly-public requests from the USA's most 'notable' writer on Astronomy -- Carl Sagan -- to finally convince NASA to try. NASA was worried that pointing Voyager I's narrow-field camera back toward the Earth (and the Sun) might damage it's sensors; but in the end, the photo was made.
Details:
The picture was taken using a narrow-angle camera at 32° above the ecliptic and it was created using blue, green, and violet filters. Narrow-angle cameras, as opposed to wide-angle cameras, are equipped to photograph specific details in an area of interest. The light band over Earth is an artifact of sunlight scattering in the camera's optics, resulting from the small angle between the Earth and the Sun. Earth takes up less than a single pixel—NASA says "only 0.12 pixel in size."
That's it -- that's us.
Voyager  I and its companion Voyager II continue on into interstellar space, and after 33 years, are still sending back data.
http://voyager.jpl.nasa.gov/

Here is a comment from Sagan's book "Pale Blue Dot", Random House, 1994.
https://planetary.org/bluedot_poster.html

From this distant vantage point, the Earth might not seem of particular interest. But for us, it's different. Look again at that dot. That's here, that's home, that's us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every "superstar," every "supreme leader," every saint and sinner in the history of our species lived there – on a mote of dust suspended in a sunbeam.


The Earth is a very small stage in a vast cosmic arena. Think of the rivers of blood spilled by all those generals and emperors so that, in glory and triumph, they could become the momentary masters of a fraction of a dot. Think of the endless cruelties visited by the inhabitants of one corner of this pixel on the scarcely distinguishable inhabitants of some other corner, how frequent their misunderstandings, how eager they are to kill one another, how fervent their hatreds.

Our posturings, our imagined self-importance, the delusion that we have some privileged position in the Universe, are challenged by this point of pale light. Our planet is a lonely speck in the great enveloping cosmic dark. In our obscurity, in all this vastness, there is no hint that help will come from elsewhere to save us from ourselves.

The Earth is the only world known so far to harbor life. There is nowhere else, at least in the near future, to which our species could migrate. Visit, yes. Settle, not yet. Like it or not, for the moment the Earth is where we make our stand.

It has been said that astronomy is a humbling and character-building experience. There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we've ever known."

Double click the image to enlarge, and see our entire planet , as the 'pale blue dot' in the upper band. The colored bands are artifacts of the multi-color-filtered imaging process.



A reproduction of this photo appears in NASA's public-viewing and movie gallery. The photo needs to be replaced several times a year, because it "wears out". So many people want to go up to it, and touch the "Pale Blue Dot" for themselves...

Wednesday, December 8, 2010

ALERT! The Geminid Meteor Shower

The largest and most impressive meteor shower -- called the 'Geminid' shower -- will occur this year on Dec. 13-14th. So bundle up if it's cold and go out and take a look.
Best viewing is after midnight until dawn on the Dec. 14th.
Of course, if in your area the night is cloudy, you're out of luck. :(
Otherwise, you can expect about 120 meteor streaks per hour, and possibly some large fireballs.
The other meteor showers during the year (like the Perseids) are believed to be caused by debris shed by comets during their orbits around our sun. The interesting part about the Geminid shower (named because it appears to be centered around the constellation Gemini) is that it's known to come from a particular weird object named 3200 Phaethon, which doesn't appear to shed nearly enough material to account for the year's largest meteor shower.

Information at: http://www.physorg.com/news/2010-12-geminid-meteor-shower-defies-explanation.html