M's Gödel

Machine M thinks it's a real smarty pants that believes it will never print false statements and will eventually print all true statements. For the sake of argument, let's say it can print with at least the characters A-Z and *.

For example, M could print out ONE*PLUS*ONE*EQUALS*TWO, which could be a long-winded way of printing 1+1=2. Count that as a true statement.

ONE*PLUS*ONE*EQUALS*THREE ?
Count that as something M would never print if it's true to its belief that it will never print a false statement.

Now strings printed out by M of the following forms have particular meanings (M is "speaking" in the first person here):

P*x	"I will print x."
NP*x	"I will never print x."
PR*x	"I will print xx."
NPR*x	"I will never print xx."

For example, NPR*FOO means "I will never print FOOFOO." NP*FOOFOO means the same thing. If M ever did print both FOOFOO and NPR*FOO, then its belief in its truthfulness would be violated.

Now consider whether M would ever print

    NPR*NPR*      ("I will never print NPR*NPR*.")

If M does print NPR*NPR* at some point, it has printed a false statement.

But if M never prints NPR*NPR*, then NPR*NPR* is a true statement that M never prints.

So either M sometimes prints false statements, or there are true statements that M never prints!

Sorry, M. Not such a smarty pants after all.

*   *   *  

The above is derived from World's shortest explanation of Gödel's theorem, which relates all this to the limits of machines that produce only true statements in arithmetic.

High-speed sonnet

Let every boarding be a Hitchcock thrill,
a mystery express from east to west,
a silver bullet train that kills the still,
revive a broken, stagnant land distressed.

And high-speed lines, like healthy arteries,
send lifeblood to the countrysides and towns,
and trains of populated coaches be
America's corpuscles world-renowned.

Reactionaries want no part, it seems,
and therein lies bemusing irony:
When once rail moved a country and its dreams,
it now could be its high-tech destiny.

What fuels romance at every turn? The trains,
that also are the dreams of bright geek brains.




Commentary: Obama should set as his goal his legacy to include the USHSRS (United States High-Speed Rail System), in the way the Interstate Highway System is in the legacy of Eisenhower, the moon landing of Kennedy.

photo from US HIGH SPEED RAIL ASSOCIATION

placed in imaginary garden with real toads Open Link Monday and in dVerse Poets Pub OpenLinkNight

Gingrich's new site

I, of Newt, in tow of blog.



BTW: Happy Birthday, Emily Dickinson!

Feed of streams

From every stroke a feed of streams

that run throughout the sphere

of internetting clouds and teams

of current technogear.

They go by names—the streams, that is—

that brands their place to be

the kings of social network biz

that range from A to Z.

Of all the posts that do flow in

and sent electric'ly,

some subset only just begin

to wind way to me.

Then tap into that world, I say,

and send your bits of rhyme.

Who knows on whose crystal display

they'll spend a bit of time.

placed in the imaginary garden with real toads ~ Fireblossom Friday: Arrivals & Departures

Steven Wright, b. December 6, 1955

"Black holes are where God divided by zero."

"I bought some batteries, but they weren't included."

"I intend to live forever. So far, so good."

"I invented the cordless extension cord."

"I like to reminisce with people I don't know."

"I was at this restaurant. The sign said 'Breakfast Anytime'. So I ordered French Toast in the Renaissance."

"I'm writing a book. I've got the page numbers done."

"I'm writing an unauthorized autobiography."

"If you tell a joke in the forest, but nobody laughs, was it a joke?"

"Right now I'm having amnesia and deja vu at the same time."

"I'd kill for a Nobel Peace Prize."

"To steal ideas from one person is plagiarism; to steal from many is research."

"How do you tell when you're out of invisible ink?"

"I almost had a psychic girlfriend but she left me before we met."

"When I turned two I was really anxious, because I'd doubled my age in a year. I thought, if this keeps up, by the time I'm six I'll be ninety."

"A lot of people are afraid of heights. Not me, I'm afraid of widths."

"Do you think that when they asked George Washington for ID that he just whipped out a quarter?"

"Curiosity killed the cat, but for a while I was a suspect."

"I used to work in a fire hydrant factory. You couldn't park anywhere near the place."

"I think it's wrong that only one company makes the game Monopoly."

"Borrow money from a pessimist - they don't expect it back."

"Five out of four people have trouble with fractions."

"My theory of evolution is that Darwin was adopted."

"I mixed this glass of water myself. Two parts H, one part O. I don’t trust anybody!"

"There was a power outage at a department store yesterday. Twenty people were trapped on the escalators."

"When I was little, my grandfather used to make me stand in a closet for five minutes without moving. He said it was elevator practice."

"How young can you die of old age?"

"I busted a mirror and got seven years bad luck, but my lawyer thinks he can get me five."

"I had some eyeglasses. I was walking down the street when suddenly the prescription ran out."

"It doesn't matter what temperature the room is, it's always room temperature."

"You can't have everything. Where would you put it?"

"Cross country skiing is great if you live in a small country."

official site: gooddeedseats.com/steven-wright