The new Macbook Wheel is really pushing the Human Computer Interface envelope.
UMBC alumnus Alark Joshi (PhD 2007) pointed out this great comic yesterday on Jorge Cham’s Phdcomics site. It shows one upside to the current financial crisis. Now that might sound self-serving, since I am part of the higher education industry that stands to profit. I think our society benefits as a whole if more people pursue an advanced degree, especially if the alternative is to become a yet another hedge fund manager.
Sometimes worse is not better, it’s just very bad. Here’s a good motivational poster for those of us who express ourselves in code or formal models.
According to Wikipedia, "On September 21, 1997, a divide by zero error in the USS Yorktown (CG-48) Remote Data Base Manager brought down all the machines on the network, causing the ship’s propulsion system to fail."
This post is scheduled to be released at an interesting moment in time: 08:08:08 on 08/08/08. The bad news is you’ve probably seen this sort of nonsense before — like eleven months ago. The good news is that we’ll only have to put up with it for another four years, after which we can take a break until early in the morning on January 1, 2101.
Numbers make the world go around. Here are ten digits that form the foundation for success. Mastering these can enrich not only your professional life, but your personal one as well. The path to successful integer management is not hard and you can start today. Many common mistakes can be avoided by mastering these ten digits. Once you have these down, you can put them together in various ways to improve your personal mathematics, unleash success, and accomplish your life goals. Remember: you are in control.
nine. Often confused for a six, nine is significant partly because it’s the largest single digit integer. Don’t listen to people who try to muddy he issue by talking about other bases — you are living in a base 10 world. Or should be. Nine is a perfect square, to boot. It’s a keeper.
eight. Crazy, some say, but as a child I developed a soft spot for this snowman of an integer. When I learned that it was two cubed, I knew it was special.
seven. Lucky seven. Seven-up. 7-11. Seventh son of a seventh son. Need we say more?
six. Wikipedia sums it up nicely: “6 (six) is the natural number following 5 and preceding 7.” It has found its niche and is a perfect fit.
five. Now five is definitely odd and considered untouchable, a combination that some find unique. You need five for a basketball team and, well, just look at one of your hands or feet.
four. Lots of things come in fours: bridge games; corners on a a square; Bob, Carol, Ted and Alice; and apocalyptic horsemen. Most vehicles have four wheels.
I just discovered (via del.icio.us/polular) an extraordinary proof of the halting problem by linguist Geoffrey Pullum, now at the University of Edinburgh. What’s unusual about it is that it’s written as a poem in the style of Dr. Seuss.
Geoffrey K. Pullum, Scooping the loop snooper: An elementary proof of the undecidability of the halting problem. Mathematics Magazine 73.4 (October 2000), 319-320.
It’s a marvelous proof, sure to liven up any undergraduate theory of computation class. But I noticed errors in the proof — not logical errors, but a transcriptional ones in the form of a mangled word, perhaps introduced by an OCR system. The third line of the fifth stanza reads “that would take and program and call P (of course!)” which has problems in syntax, semantics, rhythm and meter. I’d guess it should be “that would take any program and call P (of course!)”. Similarly, “the” in the third line in the third stanza should probably be “they”. Most of the online version I found had these errors, but I eventually found what I take to be a correct version on the QED blog. I’ve not been able to get to the original version in Mathematical Magazine to verify the corrected version which I include below.
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!