Edit: Oh boy, wall of text crits for 10k.

His explanation was rather short and somewhat misleading. Maybe they thought a proper explanation would have been too dry or too lengthy to be of any interest for a sufficient number of their viewers.

tl:dr

If all rotor settings are indicated to be correct, a feedback loop within the circuit indicated a subset of correct connections on the plugboard, even if the initially assumed connection turned out to be wrong. It didn't show all connections, but enough to run it through a modified Enigma to determine if it's a false positive or in fact the correct setting. If it was correct, the rest could be done by hand.

----------------------- Long version -----------------------

Apologies in advance. We had to recreate parts of the Bombe as a simulation, but a) it's been a while and b) it was in German. I'll try to explain the concept behind it, hopefully without screwing it up entirely.

The combination of clear message and code snippet (2:25) is called a crib. This can be used to create a graph, wherein letters are the vertices and connections together with their numerical positions are the edges.

For example, at position 1, "A" corresponds to "W". So you'd create an edge between "A" and "W" and mark that edge as "1". At position 4, "B" corresponds to "T", so there's the edge marked as "4". All edges are bidirectional, the transformation at a specific position can go either way.

Once your graph is finished, you check for loops. These are essential. Without loops, you're boned. In this case, one loop can be found at positions 2,3,5 in form of "T->E->Q->T".

Here the Bombe comes into play. It uses scramblers, each combining all three rotors plus reflector of an enigma into one segment. This way, one Enigma setting is functionally equal to a single scrambler.

Now you can use those scramblers to create an electrical circuit that corresponds to your graph -- scrambler = edge. All scramblers are set to the same initial configuration. The first scramber remains at in the inital configuration, while the second and third get configurations in relation to their edge's numerical value. Configuration in this case means the value of their internal three rotors, so there are 26*26*26 possible settings within each scrambler.

It's basically a sequence of three encryptions.

Example: in our little TEQ triangle, the first scrambler (TE, 2) gets a random starting position. The second scrambler (QE, 5) gets turned three notches, the third scrambler (QT, 3) gets turned one notch. The initial configuration might be wrong, but only the relation between the scramblers matters. A wrong result simply tells you to turn all scramblers another notch, until you get it right.

You have a possibly correct setting when the output matches the input. Specifically, a voltage is applied to the wire of letter "T", leading into the first scrambler. And on a test register attached to the last scrambler, the wire of letter "T" should have a voltage on it as well. If the setting is incorrect, a different letter will light up. Similarly, all incorrect inputs for this particular setup will always light up a different letter at the the end, never the same (thanks to the reflector). If output equals input, you're golden. And if several loops are used, all with the same input/output letter, each of their outputs must equal the input.

To reduce the number of false positives, you need as many connected loops within the crib as possible.

So far, that's an Enigma without a plugboard. To account for that, they introduced feedback loops into the circuit. In our small scale case, the output of the third scrambler would be coupled back into the input of the first scrambler. The number of loops determines the number of possible outcomes with each specific setting. All of these are fed back into the first scrambler of each loop.

The plugboard, however, changed the input into the system of rotors. Instead of a "T" in our example, it might be a "Z", if those two letters were connected on the board.

A random hypothesis is made and fed into the machine. If the scramblers are set incorrectly, a different letter comes out at the end of each loop and is in return fed back into the first scramblers. Result: (almost) everything lights up. If you start with a good graph, everything will light up.

-----
A key element for this was the "diagonal board", which represented a) all possible connections on the plugboard and b) the bidirectional nature of those connections (AB = BA). Maybe it can be explained without pictures, but I sure as hell can't, so "a grid of all possible connections between scramblers and letters + forced reciprocity" will have to suffice.
-----

If, however, the setting was correct, a wrong hypothesis for the input connection merely meant that everything except the right connections was lit up.

Let's say the fix point of the loops in our graph is the letter "T". We assume that it's connected to the letter "Z" on the plugboard. A voltage is applied to "Z" on the test register, and thereby inserted into the circuit at the first scrambler. Loop #1 applies voltage to the letter "A" on the test register, #2 lights up "B", #3 lights up "F". These three outputs are now fed back into the first scrambler, so now the scrambler has voltage on ZABF, which in return lights up ZABF+GEK on the test register.
This goes on until everything except "U" is lit up on the test register. That means three things: a) the settings are correct, b) the hypothesis is wrong, c) "T" is connected to "U".

Reasons:
a) if the settings were incorrect, the entire register would be alive
b) if the hypothesis was correct, only the letter "Z" would be alive on the register
c) due to the feedback loop, the only way for the output to be "U" is if the input was also "U", and the reciprocity within the system makes it impossible for any other input to generate the output "U". Since "T" was the fix point for our loops, "T" is connected to "U".

Similarly, if the initial hypothesis is correct, everything on the test register except "U" stays dead.

The diagonal board provides registers for every single letter and allows the user to pick one as a test register. During operation, all the other registers serve as visual representations of the deductions based on the initial hypothesis. So you actually get to see more than just the initial connection, all based on the same concept.

We have another "official" contestant, pumkinandstorm has stepped-up the odds with this simple framework for a spattering of tasty dishes!!




Chinese Pork Tenderloin

Ingredients
2 pork tenderloins (1 -1/2lb or 750g)

Marinade
2 tbsp light soy sauce
2 tbsp hoisin sauce
1 tbsp sherry
1 tbsp black bean sauce
1-1/2 tsp minced gingerroot
1-1/2 tsp packed brown sugar
1 clove garlic
1/2 tsp sesame oil
Pinch five-spice powder

Directions
1. Trim any fat from tenderloins. Place in shallow glass.
2. Marinade: Whisk together soy sauce, hoisin sauce, sherry, black bean sauce, gingerroot, sugar, garlic, sesame oil and five-spice powder.
3. Pour marinade over tenderloins, turning to coat. Cover and refrigerate for 24 - 48 hours, turning occasionally. Let stand for 30 minutes at room temperature before cooking.
4. Place tenderloins on rack in roasting pan, reserving marinade; Bake, basting generously four times in 375F oven for 30 to 35 minutes or until meat thermometer inserted at 20 - degree angle registers 160 F and meat still has hint of pink.
5. Remove to cutting board and tent with foil. Let stand for 10 minutes.
6. Using sharp knife, slice pork diagonally into thin slice

Challenge Accepted!

I am by no means a cutty stabby person, but after this I looked around a bit. This is basically kendo: ( http://www.youtube.com/watch?v=VMxlqayAwG8&feature=related ) and you are right, it doesn't look like this at all.
What these guys are doing is called kenjutsu ( http://www.youtube.com/watch?v=MIxt3Zd6K0k ) which seems to be a whole other thing (kinda like comparing judo to karate). When you check out more of that kenjutsu stuff it all of a sudden looks a lot more "realistic".

Also, I am pretty sure that standing with your guard completely down and just moving your shoulders is probably not a valid sword fighting technique, but maybe this guy is just so bad-ass he doesn't care.

The stances employed according to far more geeky interweb friends is something like "Tamiya-ryu" or "Jigen-ryu" (somewhere between the late 15th and 16th century) and it actually involves mostly diagonal/vertical slices to the torso to try and kill your opponent in one blow. The goal was pretty much always to hit the enemy's throat and failing that slice the opponent in an up to down diagonal motion while denying your opponent to do the same.

well look at their prop! THERES YER PROBLEM,, you got this wooshy sideways prop that only moves diagonal

My apologies for missing your point, I sometimes tend towards the contentious. I think we have been arguing diagonally; of course religion (and faith) are the result of human traits, as is everything about human society. What I argue is that the unpleasant traits you rightly observe in other social institutions and widespread beliefs find a special form of propagation and protection from scrutiny in the supernatural aspect provided only by religious/supernatural belief. I still believe society would be better without religion, just as it would be without conspiracy theorists (often religious as well), state religion, and more generally the lack of critical thought. The reason religion is a worthy target when trying to effect social reform/progress is that, as I argue above, it ossifies and protects the negative traits you speak of, elevating them out of the sphere of human scrutiny/criticism by means of the supernatural argument.

>> ^jonny:

Nice straw men. I didn't write anything close to "without religion there can be no inspired art", nor have I ever heard or read anyone seriously suggest such a thing. Using that phrasing, my comment would be "without religion there can be no religiously inspired art," which should be self-evident.
And again you have assigned a position to me that does not follow from my comments. I am not apologizing for religion, nor do I think it doesn't deserve criticism and scrutiny. (On a side note, I think we may be using the word "religion" differently. I always make a distinction between faith (an individual belief) and religion (a collective belief). The distinction is analogous to the personal/public distinction in language.)
I haven't reduced religion to the sociocultural evils you mention. That is what you seem to have done, with only a dismissive acknowledgement of any good that may arise from it. I have repeatedly tried to show that religion is not the source of the evils you mention, but an expression of them. Even the teaching of nonsense and propagation of willful ignorance, which to me is one of the greatest sins, is hardly unique to religion or even inherent to it. Counterexamples - birthers and Taoism.
Again, let me point out that my comments arose from PostalBlowfish's comment that "there is nothing positive to be gained from religion that can't be realized without it," and his and your attempts to equate religion with certain fundamental human traits. This is really the basis of our disagreement - namely whether traits such tribalism and demagoguery are intrinsic to religion. To say that they are intrinsic implies that no religion can exist without those traits, and that is patently false. On the other hand, you don't need to look very hard to find those traits in just about any other social organization (politics, sports, business, etc.). This is what I keep trying to get across. None of the evils you attribute to religion are unique to it. Even if religion somehow magically disappeared tomorrow, all of those unpleasant traits would still be with humans. And this is the most important point I've been trying to make - don't let arguments over religion distract from the vastly more important task of helping humanity overcome these terrible tendencies inherent in all of us.
>> ^hpqp:
You say you are not separating the inherent evil of superstitious/religious beliefs from the the social evils it perpetuates, but then you go and skirt my whole argument, reducing the negative aspect of religion (which you seem to reduce to "organised religion", suggesting it is the institution and not the fundamental beliefs that are at to be discussed) to... the sociocultural evils (creationism, pedophilia, etc.). My point remains made and unchallenged.
As for the whole "without religion there can be no inspired art", that is a myth organised religion (especially the RCC) likes to keep alive, and is doing a good job apparently. Great art celebrates nature, humankind, humankind's stories and mythos, illustrates its fears and desires, etc etc, all of which will go on after the belief in invisible sky-daddies dies away. Because the Church had money and power, they could buy the talent, that's all. I am sure some religious artists were inspired by their devotion, just like others are by drug trips, sex, fears, and of course by psychological disorders. That does not render religious belief a positive in society that needs to be preserved.
Like I've said elsewhere, it's good to want to reduce the symptoms, but futile if we do not also attack the disease behind them. So yes, there is a great need to argue against religion, which is what allows the sociocultural symptoms you mention to exist.

He's using Cantor's diagonal argument, but not explaining it very well. Read the article (because I won't be able to explain it any better). The set of all integers is countably infinite, and the set of all real numbers is uncountably infinite (has a larger cardinality larger than the natural numbers).

And then she ends up diagonal parking in a space 2 regular sized cars probably could have fit.

Comment hidden because you are ignoring dag. (show it anyway)

What about Knockturn Alley? "Nocturnally"? Rowling puts a hell of a lot of thought into all her madeup names. I hope she writes another book - she's a treasure.
>> ^dystopianfuturetoday:

Sadly, yes. >> ^Ryjkyj:
Did anyone else read the entire Harry Potter series before they realized that Diagon Alley was a pun?

Sadly, yes. >> ^Ryjkyj:

Did anyone else read the entire Harry Potter series before they realized that Diagon Alley was a pun?

In my expeience (which is quite extensive) weed effects about one out of every hundred people in a VERY negative way. People tend to forget or not know that it's a hallucinogen.

P.S.: Did anyone else read the entire Harry Potter series before they realized that Diagon Alley was a pun?

Tags for this video have been changed from 'electricity, shock, 9 volt, shock, women, jacket, attack' to 'electricity, shock, 9 volt, shock, women, no contact, jacket, attack, diagonal view' - edited by kronosposeidon

I had a printer for my TRS-80 that used small ball-point pens. It had 4 pens, black, red, green and blue and could draw some pretty cool shit.

Edit: After doing some searching I found it. It was a called CGP-115 Printer, though technically it's a plotter. It could print graphics like this Lego printer by doing lines, but when printing text it would actually write the letter by moving the pen. It could draw perfect circles and diagonal lines. You can see some of the stuff it could draw in this picture of it.

Well, that was the original challenge.

Hell, i wasn't aware it was POSSIBLE to run out of decimal places that i could go to. I thought EVENTUALLY i'd get there. Perhaps the sun would have burned out and life on earth lost/moved on by then, and possibly the numbers would get beyond the range of human comprehension, and the scope of "accuracy" would be something i could only argue with god himself, but ...?

I mean, my main aim was to say you could do root 2 using a calculator without having a root button. If you take what i did, feed it into a pc and loop it you'd end up with pretty much a calculator for getting the square root of 2, even if it kept going for a squillion years.

As for proving the exact square root of 2 exists, to be fair, i've not been taught any maths beyond a-level yet. This is all just me working stuff out. It doesn't make sense to me that i could ever run out of decimal places and thus be proved wrong that my method would eventually provide the answer. But there are many things that can only be explained mathematically, so perhaps that is the case afterall.

Edit:
Apparently (and then of course) the square root of 2 is exactly the length of the diagonal of a square with side length 1. How can such a thing not have an exact length?

Hmm. This dude can park his car in a "garage" with 1 inch clearance on either side of the vehicle, yet every day I see people who park diagonally across 2 spaces in perpendicular parking, directly on top of the line in angle parking, or 3-4 feet from the curb in parallel parking.

/sigh

That dire wolf totally provoked an AoO when it moved out of the diagonally adjacent space. And that's Fireball not Flaming Sphere, omg noobs.

I am focusing on the important part of the video.