I just watched the same video and it was one of the most insightful things that I have seen recently. Feynman is simply acknowledging that there are a few things in physics which are very difficult reduce to layman concepts. The other bit, about "why questions", is also quite interesting. I have come to believe that a lot of questions which sound very interesting, like "why do I exist?", don't really have good answers, and probably will never have. e.g. if it did turn out that we are living in a matrix, the question will simply reduce to "why does the matrix exist?" and soon. Thats what Feynman is trying to point out that "Why something happens?" is not a complete question unless we agree to some understanding beforehand. Otherwise you just go deep into the rabbit hole.
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This is pretty hilarious from the amazon review quoted in the article:
But even with these problems, The Story About Ping has earned a place on my bookshelf, right between Stevens' Advanced Programming in the Unix Environment, and my dog-eared copy of Dante's seminal work on MS Windows, Inferno. Who can read that passage on the Windows API ("Obscure, profound it was, and nebulous, So that by fixing on its depths my sight -- Nothing whatever I discerned therein."), without shaking their head with deep understanding. But I digress.
The OP is correct. Cardinality in mathematics is the number of elements in a set[1]. What you are probably referring to is the concept of cardinal numbers[2]. I guess you can skip the smug tone.
We should be glad that open source (Linux/Ubuntu) works when it does. Its such a curious case that its expected of Linux to support all myriad kinds of hardware systems. Its the responsibility of the hardware vendor to provide the drivers, not the hackers who labor hard to reverse engineer the specs when the vendors even refuses to publish how the hardware works. Few vendors really care about Linux. On the other hand, Windows has it really easy. Before the release of a new version, vendors work their asses off with Microsoft to ensure that before the OS reaches market, their drivers are already up to date. Apple has to care about only one piece of hardware which is manufactured by them (leaving peripherals of course).
We should be just glad that it works when it does. Those who work to make it work, work hard.
Disclaimer: On my Lenovo laptop, today, every single device works now on Ubuntu 9.04 from the card reader to webcam. It didn't always.
"We should be glad that open source (Linux/Ubuntu) works when it does. Its such a curious case that its expected of Linux to support all myriad kinds of hardware systems."
It really is impressive that things work as well as they do, but OTOH, if Ubuntu is really going to be "desktop ready" then it has to support modern hardware.
I attempted an install of Ubuntu 9.10 on an HP box with a Dell LCD monitor and an nVidia graphics card, and though it started out OK, the screen eventually went black. Turns out there was no workable default video driver in place to allow even crude graphics. Even the text/low-res installation options failed.
I did finally get it running (assorted usage of virtual terminals and ftp'ing of driver), but hibernation and suspend still don't work. And gnome-terminal has acquired some bug where it never warns you if you're closing multiple tabs.
Maybe this is an apples-and-oranges deal, but when I read of new gee-whiz crap like twitter integration in the task bar, while core behavior such as hibernation is still a crapshoot, and key apps are buggy, it makes me wonder where the priorities are.
Perhaps I'm just bitter about KDE3 being dropped for the saccharine mess that is KDE4. :(
Bottom line seems to be that OSS developers, by and large, hate working on the mundane stuff, and much prefer to invent Really Cool Stuff, regardless of any real need for it.
Shouldn't bitch about stuff that's free, but I'd like to think the people calling the shots care if the end results are properly usable.
The Magic 8 ball is telling me "Xmonad looking REALLY good". :)
Lets just say that nobody reads popular science/physics books for "real" understanding. I always thought of them more as entertainers, giving a glimpse into the mysteries of modern physics, even if superficial or exaggerated, clearer than what probably the situation at the ground is. Not every one can spend enough time to go through the painstaking path of understanding physics up to the level of Quantum Mechanics or General Relativity. If I really wanted to understand what was happening, I would go pick up David Griffiths.
There is a certain subtlety to this problem which many people overlook. It is that whether the host <em>always</em> gives the option to switch. Only if the host always gives you the option to switch, there is a benefit in switching. If the host acts randomly(say deciding on a coin flip whether to give the option to switch), then the benefit of switching is nullified. Also, if the host is malicious (gives the option to switch only if you have the door with the prize), then of course switching decreases your chances of winning.
I believe that the reason several "PhDs" were confused over the answer has got to do with the fact that they might have assumed a host which acts randomly.
If the host gives you the option to switch based on a coin flip, that flip will be independent of the state of the game and just average the overall probabilities between a regular game and a switch-style game.
Now, allowing the host to act totally randomly will remove the advantage. In particular, the host needs to randomly choose which door to open from all three (including your own). If he finds the goat, you reset and play again perhaps, if he doesn't find the goat then you've got a 50/50 chance between the remaining doors. The probabilities are simple because each door was treated exchangeably and there could be no possible information flow that is mutual to, entangled with, the location of the goat.
As you said, "average the overall probabilities between a regular game and a switch-style game", which is 1/3 for a game with no-switching and 2/3 for a game with always-switching. Averaging gives you a probability of 1/2. So if you switch, you win 50 % of the time. But so do you if you do not switch. So there is no benefit in switching, which was basically my point.
EDIT: In both the versions of the game, I am assuming an omniscience host who always opens the door with a goat behind, if he does open a door at all.
You're absolutely right and my argument fails, but it doesn't invalidate the point I wanted to get at. In the long run, your coin flipping method does cause the game to behave as though there were only two doors, but in any given game you'll know whether or not the host is going to choose a door.
That means that, conditional on a good flip, you may still be able to act to your advantage since there's information transfer from the host to you.
