Closing in on the Goldbach conjecture

Every odd integer larger than 1 is the sum of at most 5 primes.

Greta Garbo's strange encounter

Ah, sweet trivia.

Singular indeed!

She had me going for a while.

A little historical aural fun

I am pretty much an inveterate reader of newspapers. Recently, I saw a small notice of what I consider a rather remarkable event. A researcher discovered and "decoded" a cache of old Edison wax cylinders which an Edison representative (Adelbert Wangerman) had recorded in Europe in 1889. The two voices that are of greatest interest are those of the "Iron Chancellor" (Otto von Bismarck) and Field Marshal Helmuth von Moltke. Moltke was 89 when he made his recording. Thus from a purist standpoint, his is the only recording of a voice from someone who was born in the 18th century!

You can read of this interesting tale and hear the rather scratchy Bismarck recording at http://www.thespec.com/feature/article/664757--listen-historic-recording-of-otto-von-bismarck. The Moltke recording, which to my ears is less scratchy, can be heard at http://www.nps.gov/edis/photosmultimedia/audio-wangemann-1889-1890-european-recordings.htm.

If so inclined, take a break and enjoy these remarkable historical finds.

(From Berkeley :>)

More interesting than 22/7

This post is based on this posting from Futility Closet.

You set up an infinite series

1*x + 1*(x^2) + 2*(x^3) + 3*(x^4) + 5*(x^5) + 8*(x^6) + 13*(x^7) + ...

Call that expression A. Multiply A by x to get A*x =

1*(x^2) + 1*(x^3) + 2*(x^4) + 3*(x^5) + 5*(x^6) + 8*(x^7) + 13*(x^8) + ...

Then subtract these two expressions by subtracting each term of the second expression from the term of the first expression with the same power of x -- the resulting expression

A - A*x = 1*x + 1*(x^3) + 1*(x^4) + 2*(x^5) + 3*(x^6) + 5*(x^7) + ...

which except for the first term is exactly A*(x^2)

In other words

A - A*x = x + A*(x^2)

If you solve this for A by bringing all terms involving A to one side and then factoring out A, you end up with

A = x / (1 - x - x^2)

By now you're wondering what is the point of all of this. Well if you go back to the original series

1*x + 1*(x^2) + 2*(x^3) + 3*(x^4) + 5*(x^5) + 8*(x^6) + 13*(x^7) + ...

and substitute .001 for x, the terms become

.001 + .000001 + .000000002 + .000000000003 + .000000000000005 + .000000000000000008 + .000000000000000000013 + ...

which equals

.001001002003005008013 ...

so the same should be true if you substitute .001 for x in

A = x / (1 - x - x^2)

and if you do you get the fraction

1000 / 998,999

The decimal equal to this fraction begins with all the Fibonacci numbers with 1, 2 or 3 digits. If you want a fraction that has all the Fibonacci numbers with 1, 2, 3, or 4 digits, then you substitute .0001 for x into A (instead of .001).

Joseph G. Rosenstein
Professor of Mathematics
Rutgers University

Sistine Chapel panorama

Incredible work.

Fun with graphing equations

Link to NPR article

Fracking explained

Churchill on Italian Cruise Lines

A friend reminded me of a comment made by Winston Churchill.


After his retirement he was cruising the Mediterranean on an Italian cruise liner and some Italian journalists asked why an ex British Prime Minister should choose an Italian ship.

“There are three things I like about being on an Italian cruise ship” - said Churchill.

“First their cuisine is unsurpassed. Second their service is superb. And then, in case of an emergency, there is none of this nonsense about women and children first."

Lost in Translation

Ted Koppel of ABC and Rick Kaplan, his executive producer, are laughing at a misunderstanding which has just occurred with a friendly Kremlin functionary. The official approached the Americans and wished them a Happy Christmas. With a straight face Kaplan, who is Jewish, replied, "To me you will have to say "Happy Hanukkah". "Why would I have to say 'Happy Honecker'? asked the official, puzzled. The Americans bust out laughing at the official's assumption the Kaplan is referring to Erich Honecker, who fled to Moscow after the fall of the Berlin Wall two years earlier.

The Last Day of the Soviet Union
Moscow December 25, 1991
pp25-26
Conor O'Clery
Public Affairs