Washington's Birthday Eve

George Washington was a gentleman,
A soldier and a scholar;
He crossed the Delaware with a boat,
The Potomac, with a dollar.
The British faced him full of joy,
And departed full of sorrow;
George Washington was a gentleman.
His birthday is tomorrow.

When approached by fellow patriots,
And asked for his opinion,
He spoke in accents clear and bold,
And, probably, Virginian.
His winter home at Valley Froge
Was underheated, rather.
He possessed a sturdy Roman nose,
And became his country's father.

His army was a hungry horde,
Ill-armed, worse-clad Colonials;
He was our leading President,
And discouraged ceremonials.
His portrait on our postage stamps,
It does him less than justice;
He was much respected by his wife,
The former Mrs. Custis.

He routed George's scarlet coats;
(Though oft by Congress hindered)
When they fortified the leeward side,
He slashed them from the windward.
He built and launched our Ship of State,
He brought it safe to harbor;
He wore no beard upon his chin,
Thanks to his faithful barber.

George Washington was a gentleman,
His birthday is tomorrow.
He filled his country's friends with joy,
His country's foes, with sorrow.
And so my dears, his grateful land
In robes of glory clad him.
George Washington was a gentleman.
I'm glad his parents had him.

Ogden Nash

Judge Judy and the two parasites

Here's who you support with your taxes
The Judge was correct in ordering this tape be sent to Congress. Multiply these two parasitic morons by many millions and you get the picture.

Archie Bunker called it

• It's just hit me !!
  
  
• My dog sleeps about 20 hours a day.
  
  
• He has his food prepared for him. He can eat whenever he wants, 24/7/365.
  
  
• His meals are provided at no cost to him.
  
  
• He visits the Dr. once a year for his checkup, and again during the year if any medical needs arise.
  
  
• For this he pays nothing, and nothing is required of him.
  
  
• He lives in a nice neighborhood in a house that is much larger than he needs, but he is not required to do any upkeep.
  
  
• If he makes a mess, someone else cleans it up.
  
  
• He has his choice of luxurious places to sleep.
  
  
• He receives these accommodations absolutely free.
  
  
• He is living like a King, and has absolutely no expenses whatsoever.
  
  
• All of his costs are picked up by others who go out and earn a living every day.
  

I was just thinking about all this, and suddenly it hit me like a brick in the head.......

My dog is a Democrat!

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.