Excellent!

This posting was so good, I had to copy it here.

Scooping the Loop Snooper

an elementary proof of the undecidability of the halting problem

Geoffrey K. Pullum, University of Edinburgh

No program can say what another will do.
Now, I won’t just assert that, I’ll prove it to you:
I will prove that although you might work til you drop,
you can’t predict whether a program will stop.

Imagine we have a procedure called P
that will snoop in the source code of programs to see
there aren’t infinite loops that go round and around;
and P prints the word “Fine!” if no looping is found.

You feed in your code, and the input it needs,
and then P takes them both and it studies and reads
and computes whether things will all end as they should
(as opposed to going loopy the way that they could).

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 I would use – and it’s simple to do.
I’d define a procedure – we’ll name the thing Q -
that would take any program and call P (of course!)
to tell if it looped, by reading the source;

And if so, Q would simply print “Loop!” and then stop;
but if no, Q would go right back to the top,
and start off again, looping endlessly back,
til the universe dies and is frozen and black.

And this program called Q wouldn’t stay on the shelf;
I would run it, and (fiendishly) feed it itself.
What behaviour results when I do this with Q?
When it reads its own source, just what will it do?

If P warns of loops, Q will print “Loop!” and quit;
yet P is supposed to speak truly of it.
So if Q’s going to quit, then P should say, “Fine!” -
which will make Q go back to its very first line!

No matter what P would have done, Q will scoop it:
Q uses P’s output to make P look stupid.
If P gets things right then it lies in its tooth;
and if it speaks falsely, it’s telling the truth!

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

So, how to escape from this logical mess?
I don’t have to tell you; I’m sure you can guess.
By reductio, there cannot possibly be
a procedure that acts like the mythical P.

You can never discover 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!

It's been...

... a wide spectrum of experiences. I didn't want to just say "fun" because it hasn't always been fun. But then again, it is work, so fun is an added bonus. The company I have been with for the last 8 years (plus a few more as a co-op student) is closing down. I've been trying to think of some words of wisdom, summaries, histories etc. but I don't think the time is right for that just yet. Instead, I found something in this article that nicely illustrated what I enjoyed about "the old days" at work.

The article is an ACM Queue interview with one of the original designers of the ARM chip, Steve Furber. During a description about why the original ARM chip was so small, power efficient and cheap, Mr. Furber commented that:

This is good management retrospective: by depriving us of resources of any sort, they forced us to make decisions in favor of simplicity. -- Steve Furber

There were many parallels to BBC Micro and my old company - both were small, had limited resources and was an outside player in a potentially large market. In those earlier days, trying to do the impossible seemed like the only way to survive, so we went for it. They were exciting times and it worked - for a while. The later down hill slide is where my old organization and BBC Micro differed. I believe the small size and lack of resources resulted in steps forward that could not be duplicated by the company we became.