"They gave him an intelligence test. The first question on the math part had to do with boats on a river: Port Smith is 100 miles upstream of Port Jones. The river flows at 5 miles per hour. The boat goes through water at 10 miles per hour. How long does it take to go from Port Smith to Port Jones? How long to come back?
Lawrence immediately saw that it was a trick question. You would have to be some kind of idiot to make the facile assumption that the current would add or subtract 5 miles per hour to or from the speed of the boat. Clearly, 5 miles per hour was nothing more than the average speed. The current would be faster in the middle of the river and slower at the banks. More complicated variations could be expected at bends in the river. Basically it was a question of hydrodynamics, which could be tackled using certain well-known systems of differential equations. Lawrence dove into the problem, rapidly (or so he thought) covering both sides of ten sheets of paper with calculations. Along the way, he realized that one of his assumptions, in combination with the simplified Navier-Stokes equations, had led him into an exploration of a particularly interesting family of partial differential equations. Before he knew it, he had proved a new theorem. If that didn't prove his intelligence, what would?
Then the time bell rang and the papers were collected. Lawrence managed to hang onto his scratch paper. He took it back to his dorm, typed it up, and mailed it to one of the more approachable math professors at Princeton, who promptly arranged for it to be published in a Parisian mathematics journal.
Lawrence received two free, freshly printed copies of the journal a few months later, in San Diego, California, during mail call on board a large ship called the U.S.S. Nevada. The ship had a band, and the Navy had given Lawrence the job of playing the glockenspiel in it, because their testing procedures had proven that he was not intelligent enough to do anything else."
'Then there is the famous fly puzzle. Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels. Question: what total distance did the fly cover ? The slow way to find the answer is to calculate what distance the fly covers on the first, northbound, leg of the trip, then on the second, southbound, leg, then on the third, etc., etc., and, finally, to sum the infinite series so obtained. The quick way is to observe that the bicycles meet exactly one hour after their start, so that the fly had just an hour for his travels; the answer must therefore be 15 miles. When the question was put to von Neumann, he solved it in an instant, and thereby disappointed the questioner: "Oh, you must have heard the trick before!" "What trick?" asked von Neumann; "all I did was sum the infinite series." '
This is meant to sound very difficult (and might be, if you majored in journalism), but summing infinite geometric series is easy enough to do in your head if you're facile with fractions: (first_term) / (1 - step_multiplier).
Observe that, of the combined velocity of the fly and the bike approaching him, the fly always makes up 60%. That makes math easier since it eliminates division and time from the problem entirely.
On the first trip, the fly travels 12 miles and the bike approaching him travels 8 miles. There are now 4 (20 - 2 * 8) miles between the bikes.
On the second trip, the fly travels .6 * 4 = 2.4 miles and the bike approaching him travels 1.4 * 4 = 1.6 miles. There are now 0.8 miles between the bikes.
The part where people who are really good with math distinguish themselves from people who are not is realizing quickly that the problem they are looking at, with flies and bikes, quickly decomposes into "sum the series that starts 12, 2.4, etc".
12 / (1 - 0.2) = 12 * 5 / 4 = 15 miles total fly travel.
You can do it a little more formally if you want to verify the intuition that each step takes 1/5th the time (covers 1/5th the distance) of the previous step. (My intuition says "In the time that it takes the fly to go 5 units, the two bikes will chew up 4 units of that distance, so he is only left with 1 unit to travel the next time.")
Where intuition really comes in is finding the right hill to climb - http://en.wikipedia.org/wiki/Hill_climbing
I disagree. Feynman was famous for speaking his mind regardless of the context (Bohr insisted on Feynman's presence at critical points during the Manhattan project for exactly this reason, in fact -- everybody else was too inhibited around Bohr to speak up).
Feynman might have kicked himself afterwards, but wanting a job wouldn't have prevented him from pointing out an interviewer's errors.
PS: And yes, he would eventually walk around the office / data centers without footwear.
I agree. And I'm sure Feynman would have agreed... until he got excited about something, at which point he would have completely forgotten.
Or something linked from there.
PS: "Tuva or Bust"
Edit: Sorry, I am having trouble finding it. There are several interviews that video is based on but they don't show the whole video.
From the BBC Horizon program in 1981.
Is there another word already in existence, that describes what I wanted to say? "A ficitonal interloculor to whom one attributes one's own's arguments in order to make them sound more profound."
(I just read Graham Farmelo's bio of Dirac, and I highly recommend it for those who are fascinated by genius physicists like I am)
Dirac is a legend there not only does he have a library named after him there, the National High Magnetic Field Laboratory at FSU is on Paul Dirac drive ;p
Fortunately, all's well that ends well. An old headhunter I'd used in the past tossed my info along (for FREE!) to my current boss. After talking to me on the phone, he gave me the old "We don't have a position open, but I'll call you if something opens up" line. I wrote it off, but he worked to get a position opened up for me and I'm genuinely doing what I love to do for a living these days. It involves Information Security, physical security/surveillance and general-purpose IT work (Sysadmin, programming and networking). I'm basically in geek heaven. It's also 6 miles from home, giving me the perfect excuse to ride my bike to work every day, rain or shine.
Coming from an AI background, I coded up an algorithm for state-space search.
They were expecting me to approach it as a person would, reasoning about how you rule out certain numbers (the constraint propagation), which is a second-order consideration for a game the size of sudoku.
I felt pretty smug when Peter Norvig shortly thereafter put up a blog post that essentially mirrored my solution.
If a square has only one possible value, eliminate it from the square's peers.
If a unit has only one possible place for a value, then put the value there.
For 16x16, it is more of a toss-up if one should use more advanced propagation. The solve-times are still so low though, that it doesn't really matter (tens of milliseconds). For 25x25 it starts to get interesting. In my experience, full propagation on lines, rows, and regions is needed, but more than that slows it down. Without a good heuristic (some learning process, prefferably coupled with randomized restarts), the solve-time easily goes up into hours. Wih a good heuristic, minutes seems to be a reasonable time-span to hope for.
In fact, if you ask people not from a CS background to explain the steps they would take to solve a puzzle, they probably wouldn't be able to think of a DFS, but they would state that they should rule out from each cell the numbers already present in its respective column, line and block. And for a Sudoku solver I don't think you really need more constraint propagation than that.
Anyway, I think you approached the problem the right away, I just think that you were so close to succeed in that test and it wasn't something that difficult to add to your solution.
EDIT: wrote the above before your edit. It's still appropriate though.
They were confused when I took a more disciplined approach and provided a solution that is robust to simple CP methods.
mhartl has already posted this excellent video: http://www.youtube.com/watch?v=wMFPe-DwULM, where he explains what the word "why" means in scientific inquiry. When we answer a "why" question, we don't really explain a concept in its entirety. At best, we're able to remove a layer of skin off the onion, but no one has ever really reached the center. I suppose science at it's heart is really just the elucidation of intermediate cause and effect scenarios.
For the question "why did the ball fall?", "Jimmy dropped it" is a perfectly valid answer. So is "Jimmy's motor neurons passed an action potential threshold, causing the muscles in his wrist to contract". So is "the ball moved along the curvature of space caused by the earth".
How far do we go?
I remember a conversation we had a year or so before his death, walking in the hills above Pasadena. We were exploring an unfamiliar trail and Richard, recovering from a major operation for the cancer, was walking more slowly than usual. He was telling a long and funny story about how he had been reading up on his disease and surprising his doctors by predicting their diagnosis and his chances of survival. I was hearing for the first time how far his cancer had progressed, so the jokes did not seem so funny. He must have noticed my mood, because he suddenly stopped the story and asked, "Hey, what's the matter?"
I hesitated. "I'm sad because you're going to die."
"Yeah," he sighed, "that bugs me sometimes too. But not so much as you think." And after a few more steps, "When you get as old as I am, you start to realize that you've told most of the good stuff you know to other people anyway."
We walked along in silence for a few minutes. Then we came to a place where another trail crossed and Richard stopped to look around at the surroundings. Suddenly a grin lit up his face. "Hey," he said, all trace of sadness forgotten, "I bet I can show you a better way home."
And so he did.