The Tautology Club

THE RABBIT, THE FOX AND THE WOLF: A FABLE

One sunny day a rabbit came out of her hole in the ground to enjoy the weather. The day was so nice that the rabbit became careless, so a fox sneaked up to her and caught her. 

"I am going to eat you for lunch!", said the fox. 

"Wait!", replied the rabbit, "You should at least wait a few days." 

"Oh yeah? Why should I wait?" 

"Well, I am just finishing my Ph.D. thesis." 

"Hah, that's a stupid excuse. What is the title of your thesis anyway?" 

"I am writing my thesis on 'The Superiority of Rabbits over Foxes and Wolves.'" 

"Are you crazy? I should eat you right now! Everybody knows that a fox will always win over a rabbit." 

"Not really, not according to my reserch. If you like, you can come to my hole and read it for yourself. If you are not convinced, you can go ahead and have me for lunch." "You are really crazy!" But since the fox was curious and nothing to lose, it went with the rabbit into its hole. The fox never came back out. 

A few days later, the rabbit was again taking a break from writing and sure enough, a wolf came out of the bushes and was ready to eat her. 

"Wait!", yelled the rabbit,"you cannot eat me right now." 

"And why might that be, you fuzzy appetizer?" 

"I am almost finished writing my Ph.D. thesis on 'The Superiority of Rabbits over Foxes and Wolves." 

The wolf laughed so hard that it almost lost its hold on the rabbit. "Maybe I shouldn't eat you, you really are sick in the head, you might have something contagious," the wolf opined. 

"Come read for yourself, you can eat me after that if you disagree with my conclusions. " So the wolf went to the rabbit's hole and never came out. 

The rabbit finished her thesis and was out celebrating in the lettuce fields. Another rabbit came by and asked, "What's up? You seem to be very happy." 

"Yup, I just finished my dissertation. " 

"Congratulations! What is it about?" 

"It is titled 'The Superiority of Rabbits over Foxes and Wolves" 

"Are you sure? That doesn't sound right." 

"Oh yes, you should come over and read it for yourself." 

So they went together to the rabbit's hole. As they went in, the friend saw a typical graduate student abode, albeit a rather messy one after writing a thesis. The computer with the controversial dissertation was in one corner, on the right there was a pile of fox bones, on the left was a pile of wolf bones, and in the middle was a large, lip-licking lion. 

The moral of the story:

The title of your dissertation doesn't matter. All that matters is who your thesis advisor is.

Travelling Salesman Problem

Travelling Salesman Problem

Compiler Complaint

Compiler Complaint

You Know

The Lament of the Real Programmer :-Sir Roger Needham (Cambridge)

Oh once I could program, the best in the land
I wrote in raw hex with unwavering hand.
My mind's eye could follow all possible paths
But now I can't manage the new-fangled maths

I cut lots of code for unaudited cash
And nobody cared that I rarely did wash
But now I'm burned out and admit with a sigh
That the kids from the High School are better than I

I lasted a while as an old-fashioned hack
Because I could knock out a protocol stack
But the mathmos are here now - they've come pretty far
And there's nothing for me but to prop up the bar!.

A proof that the Halting Problem is undecidable By:- Geoffrey K. Pullum

No general procedure for bug checks succeeds.                                                          Now, I won’t just assert that, I’ll show where it leads: I will prove that although you might work till you drop, you cannot tell if computation will stop.

For imagine we have a procedure called P that for specified input permits you to see whether specified source code, with all of its faults, defines a routine that eventually halts.

You feed in your program, with suitable data, and P gets to work, and a little while later (in finite compute time) correctly infers whether infinite looping behavior occurs.

If there will be no looping, then P prints out ‘Good.’ That means work on this input will halt, as it should. But if it detects an unstoppable loop, then P reports ‘Bad!’ --- which means you’re in the soup.

Well, the truth is that P cannot possibly be, because if you wrote it and gave it to me, I could use it to set up a logical bind that would shatter your reason and scramble your mind.

Here’s the trick that I’ll use -- and it’s simple to do. I’ll define a procedure, which I will call Q, that will use P’s predictions of halting success to stir up a terrible logical mess.

For a specified program, say A, one supplies, the first step of this program called Q I devise is to find out from P what’s the right thing to say of the looping behavior of A run on A.

If P’s answer is ‘Bad!’, Q will suddenly stop. But otherwise, Q will go back to the top, and start off again, looping endlessly back, till the universe dies and turns frozen and black.

And this program called Q wouldn’t stay on the shelf; I would ask it to forecast its run on itself. When it reads its own source code, just what will it do? What’s the looping behavior of Q run on Q?

If P warns of infinite loops, Q will quit; yet P is supposed to speak truly of it! And if Q’s going to quit, then P should say ‘Good.’ Which makes Q start to loop! (P denied that it would.)

No matter how P might perform, Q will scoop it: Q uses P’s output to make P look stupid. Whatever P says, it cannot predict Q: P is right when it’s wrong, and is false when it’s true!

I’ve created a paradox, neat as can be --- and simply by using your putative P. When you posited P you stepped into a snare; Your assumption has led you right into my lair.

So where can this argument possibly go? I don’t have to tell you; I’m sure you must know. A reductio: There cannot possibly be a procedure that acts like the mythical P.

You can never find general mechanical means for predicting the acts of computing machines; it’s something that cannot be done. So we users must find our own bugs. Our computers are losers!