Sentences We Love

[mogui]

A child enjoyed having a bedtime story every night, but his mother insisted it be something educational. Finally, when the mother brought the History of Australia to the bedside, the child complained, "What did you bring that book that I don't like to be read to out of on down under up for?"

How many prepositions can you chain at the end of a sentence?

Then there is the story about Winston Churchill:

Supposedly an editor had clumsily rearranged one of Churchill’s sentences to avoid ending it in a preposition, and the Prime Minister, very proud of his style, scribbled this note in reply: “This is the sort of English up with which I will not put.”

[mogui]

Sometimes, as an expat in China, I am asked to teach English. I like to use humor. Some of the lines from vaudeville elucidate culture:

George: Gracie, did you put the cat out?
Gracie: I didn't know he was on fire!

One: Who was that lady I saw you with last night?
Two: That was no lady! That was my wife!
One: But I thought your wife was a big tall girl!
Two: She was, but she has settled down a lot since we got married.

I'll let you be in my dream if I can be in yours.

-- Bob Dylan

[NatCh]

Originally Posted by kovidgoyal

Don't want to nitpick but hearing test and prove in the same sentence hurts. You can't prove anything by testing. As a matter of fact you can't prove anything, period. But especially not by testing. You can prove things within an axiom structure, but even there there are statements that are unprovable.

Hmm. It seems like you're trying to prove something there, but I can't quite put my finger on what ... nah, I must just be misunderstanding.

[kovidgoyal]

Indeed one of the few things you can prove is that you can't prove anything ;-)

[mogui]

Originally Posted by kovidgoyal

. . . Greek philosopher Epimenedes. He said,
"Epimenedes, the Cretan, says that all Cretans are liars. Does he tell tell the truth?"

This was problem was shown to hold for any axiom system (i.e. any system of knowledge) by Godel, in his famous Incompleteness Theorem. So no we cannot answer every question, even theoretically.

Given that as a starting point might humble us somewhat. It is one of the more important ideas of our modern era. Should we consider it unproven?

Actually, I find it quite relaxing

[alex_d]

oh, boy, not godel...

godel isn't wrong per se, but everyone's interpretation of his proof IS.

First of all, Godel's statement isn't "I am a liar." That's just a plain old self-contradictory statement.

Rather, a Godel statement is something like "A person who says only truths will never say this sentence." Will a person who says only truths say the aforementioned sentence? If the sentence is true, he might say it. But then the sentence becomes false. If the sentence is false, he won't say it. But then the sentence becomes true.

What happens in the end? Big surprise: in the end the guy doesn't say it. The sentence is true.

However, the truth teller wouldn't have told you that. The truth teller can't even tell you what's true about his own behavior. So much for his wisdom.


At least, that's everyone's interpretation: "There are things that are true about a logical system like math which the system itself can't prove." Ie, "you can't use math to know everything that's true about math." And then people go "whoa... Incredible!"

That interpretation is as wrong as it seems. It's just as wrong as is Zeno's paradox. It is based on the false presumption that infinities are impossible.

In fact, if you sit by the man and listen to every truth that has has to say, ad infinity, and note that the sentence "the truth-sayer will never say this sentence" is never uttered by him, it IS a proof that the sentence is true. The truth-teller does, in fact, prove it all on his own. And like a buddhist monk, he makes his point with silence.

Zeno of ancient Greece argued that motion is impossible because any movement would require passing through an infinity of distances. You can't move through an infinity of distances, so you can't move! Ooo! He even had a nice story to illustrate his point starring the legendary Achilles and a crappy old turtle that had a head-start. Every time Achilles would catch up to where the turtle was, the turtle would have already moved a little further. When Achilles reached that new point, the turtle would move yet another millimeter ahead. An infinity of catching up would be required. That story was passed around by sophisticated folk for about two thousand years seemingly proving that Achilles could never best the crappy old turtle.

Godel essentially argued that some mathematical statements will take an infinity of steps to prove. You can't have an infinity of steps, therefore some statements that are true about math can't be proved by math! Ooo!


The truth is that infinities are perfectly possible and valid. You can move through them, you can (theoretically) wait them. Thus Godel's theoreom must actually be "some things about every logical system can't be proved in a finite amount of time/steps. But, given infinite time, math will be able to prove everything that's true about it." This sounds much more reasonable and less mystical, doesn't it? And a lot less fun, eh?


In fact, I would argue that acknowledging that infinites are valid mathematical constructs, and that infinite proofs still count as proofs, gives many more "whoa" moments and moves mathematics ahead far more than the defeatist 20th century interpretation of Godel.

Ok, so... let's now please stop going around saying Zeno was right.

[HarryT]

Originally Posted by NatCh

Personally, I find that idea that the universe was designed requires a much smaller leap of faith than the idea that it all happened by accident.

But I'm willing to agree to disagree on the point, HarryT.

As to "why" the universe came into existance, I'm as happy to call that "God" as anything else. However...

There are some 300,000,000,000 stars in our galaxy, and at least 400,000,000,000 other galaxies out there. That means that the total number of stars in the universe is something like:

10,000,000,000,000,000,000,000

We know now that virtually all stars have planetary systems and that the Earth is just a very average planet around a very average star. It seems very likely that life is an equally typical phenomenon - just a set of chemical reactions, and that we are merely animals who happened, through a random chance, to evolve intelligence as a survival characteristic; something that's probably happened on countless billions or trillions of other planets.

Another thing to consider: the universe is approximately 13.7 billion years old. Modern humans have been around for no more than about 100,000 years. Was the universe just "hanging around" for 13.6999 billion years just waiting for us to show up?

We are just insignificant animals on an insignificant planet which orbits an insignificant star in an insignificant galaxy. To claim that the universe exists for our exclusive benefit seems to be a rather extreme case of self-aggrandization to me .

To get back at least vaguely on topic, have you ever read any of Richard Dawkins' books? "The Blind Watchmaker", "The God Delusion", etc? Great stuff - thoroughly recommended if you haven't. A man I have a great deal of respect for.

[mogui]

Originally Posted by Dr. Drib

Sentences we love
This might be an interesting thread to start, if there's enough interest.

Let me cast a vote for words we love as well.

Some years ago a fascinating and attractive lady of my acquaintance confessed to me that she suffered from "insecuriority".

[Steven Lyle Jordan]

Originally Posted by HarryT

To get back at least vaguely on topic, have you ever read any of Richard Dawkins' books? "The Blind Watchmaker", "The God Delusion", etc? Great stuff - thoroughly recommended if you haven't. A man I have a great deal of respect for.

Did that get us back on topic?

Actually, this entire off-topic discussion ended up providing us with some great sentences to love, didn't it?...

(When I say "Arthur" you say "C. Clarke!" "Arthur--" "C. Clarke! Go Thoughts!")

[HarryT]

Well - it got us back to talking about books, at least .

[NatCh]

Originally Posted by HarryT

...the universe is approximately 13.7 billion years old....

In the interest of not straying back off the topic, now that we've actually approached it again, I'll refrain from pointing out the difference between being a certain age, and appearing to be a certain age. Whoops, I guess I already did.

Originally Posted by HarryT

To get back at least vaguely on topic, have you ever read any of Richard Dawkins' books? "The Blind Watchmaker", "The God Delusion", etc? Great stuff - thoroughly recommended if you haven't. A man I have a great deal of respect for.

I can't say as I've ever heard of Richard Dawkins, though the titles do sound somewhat familiar ....

I'll have to hunt them up.



Here's another line, but it's more of a passage. Still, I find it very thought provoking:

Sometimes the things that may or may not be true are the things a man needs to believe in the most. That people are basically good; that honor, courage, and virtue mean everything; that power and money, money and power mean nothing; that good always triumphs over evil; and I want you to remember this, that love... true love never dies. You remember that, boy. You remember that. Doesn't matter if it's true or not. You see, a man should believe in those things, because those are the things worth believing in.

-- Uncle Hub (Robert Duvall), from the movie Secondhand Lions (an excellent flick)

[HarryT]

Dawkins is a fascinating chap. See:

http://en.wikipedia.org/wiki/Richard_Dawkins

As far as the age of the universe goes, you may know that I started life as an professional astronomer before figuring out that IT paid a lot better . One of the most interesting achievements of astronomy in the last 20 years or so is that there are a number of completely independent methods of measuring the age of the universe, and they all give the same answer - 13.7 billion years, give or take a few hundred million. That seems like a pretty definite number.

Doesn't answer the "last Tuesday-ists", of course, who claim that the universe was created last Tuesday, along with us with all our fake memories of the past implanted in our minds, galaxies receding from us to give the illusion of an ancient universe, etc etc, but there's just no answer to that .

[NatCh]

Well, see, that might just be evidence of how truly clever that God fellow really is.

Tell, ya what, ask me about it again in a few hundred years, I should have a definite answer by then.

[mogui]

We can't get wikipedia directly here in China but Answers gets us the info anyway!

If you have ever despaired at remembering what a second cousin twice removed might be, Dawkins has a simpler way. He expresses consanguinity with a number. "I'd like you to meet Doug. He is my 1/16th relative!"

[astra]

Originally Posted by mogui

We can't get wikipedia directly here in China

Do you mean the website is blocked to a whole country?