Reputation
929
Top tag
Next privilege 1,000 Rep.
Create new tags
Badges
1 6 24
Newest
 Yearling
Impact
~26k people reached

Jun
22
awarded  Yearling
Jun
15
awarded  Announcer
May
8
suggested rejected edit on does this have a meaning?
Mar
28
accepted How does the Enigma machine ensure that no letter is substituted for itself?
Mar
28
comment How does the Enigma machine ensure that no letter is substituted for itself?
What I was missing in thinking about this was the simple fact that (regardless of the details of rotor wiring or position, as long as every letter is connected) there is a unique path that connects to a given letter at the begging/end, so that if, as is the case, the reflector switches between these paths, the letter at the begging and end must be different.
Mar
27
comment How does the Enigma machine ensure that no letter is substituted for itself?
Good point. But the key thing is: it's that feature of the reflector that drives the whole thing (assuming nothing special about the wiring of the rotors, etc.).
Mar
27
comment How does the Enigma machine ensure that no letter is substituted for itself?
So (1) unique path (through rotors and plugboard, in each direction) combined (critically) with the fact that (2) the reflector must perform complete swapping of all letters ensures that the machine as a whole does so. Correct?
Mar
27
comment How does the Enigma machine ensure that no letter is substituted for itself?
@ThomasAndrews: The question is, in part, in fact whether such knowledge is required to explain why there are no fixed points. If it is, saying so would be the start of an answer.
Mar
27
comment How does the Enigma machine ensure that no letter is substituted for itself?
@ThomasAndrews: That may indeed be part of the answer: it is a property of the specific wiring arrangements of the rotors that ensures that in all combinations and positions there are no fixed points. Is that the case?
Mar
27
comment How does the Enigma machine ensure that no letter is substituted for itself?
@Meelo: Correct, and, I think that highlights the question then: what properties of the Enigma (e.g. physical constraints or deliberate design) ensure that no letter is substituted for itself (i.e. that there are no fixed points).
Mar
27
comment How does the Enigma machine ensure that no letter is substituted for itself?
@whacka: "This" refers to property that whatever substitutions were performed would be swapping, but not (as written) that all letters are swapped. "Associated" is a bit less direct, but suggests that the fact that " no letter could ever be enciphered into itself" is a consequence of "this".
Mar
27
asked How does the Enigma machine ensure that no letter is substituted for itself?
Dec
17
comment How many ways can seven people sit around a circular table?
@OllieFord: I usually blame that sort of thing on posting from my phone.
Dec
17
comment How many ways can seven people sit around a circular table?
@OllieFord: $7 - 1 = 6$.
Dec
16
answered How many ways can seven people sit around a circular table?
Dec
8
awarded  Caucus
Nov
28
revised What is the correct term (and symbolic representation) for specific “un-modded” values?
Repair title.
Nov
28
comment What is the correct term (and symbolic representation) for specific “un-modded” values?
Come to think of it, what is the property $x \equiv x+k\cdot(b_u-b_l),\,\forall k\in\mathbb{Z}$ even called? It's not quite mod, is it?
Nov
26
asked What is the correct term (and symbolic representation) for specific “un-modded” values?
Nov
16
accepted Incomplete statement of commutativity of summation in Concrete Mathematics?