There is a proposition that Alperton to Mornington Crescent can be achieved in four moves. However proof has not been accepted for the existance of this number.
And so it begins...
Kilydd - I have attempted the first move as best I can so we can proceed swiftly to MC but all I have to show is
ton. The woory being that there may be an error which may lead to the unsuccessful method established be Sir Arthur Stanley-Smythe, his previous attempt in 1854 started at
Beckton and sadly ended in his public humiliation.
rab - Um, not much to go on, really. Any chance of being more specific?
Blob - I think Kilydd is correct in his estimation of
~tonness; it may help that looking at my Fronsky I perceive that the Central line must be avoided for at least the first two plays. I must say it was remarkably optimistic of Stanley-Smythe to even attempt initiation using the at-the-time super-foetal
Beckton - the DLR being in the mid C19 a concept "
beyond the imaginings of mere mortals" as Conan Doyle once referred to future line play.
By my calculations the only
TON stations (excluding ghosts) on the network are :
- ALPERTON
- BECKTON
- BRIXTON
- EASTACTON*
- EUSTON
- HIGHBURY & ISLINGTON
- HIGH STREET KENSINGTON
- KENNINGTON
- KENTON
- LEYTON*
- LOUGHTON*
- NORTH ACTON*
- PADDINGTON
- SOUTH KENSINGTON
- SOUTH KENTON
- WEST ACTON*
- WEST BROMPTON
- WEST KENSINGTON
Then of course there is MORNINGTON CRESCENT itself - but that is hardly going to be the starting station.
Finally there are two stations on the North London Line namely
But it would be a strange ruleset indeed that allowed initiation from the N.L.L.
The stations marked * above are on the Central Line and are therefore excluded by my Fronsky calculations.
I hope this little exercise will be of help.
Blob - Oh, and considering that the (move=0) station is
Alperton then the (move=1) station is not likely to be a doubling move either. If Beckton has been ruled out by Stanley-Smythe as reported, then that only leaves eleven possible stations by my reckoning - and Euston would seem highly improbable too. What d'you reckon folks ?
Artaud - Presumably this assumes a theoretically stable level of play (LV and snoods stable, escalators and lifts dormant, etc.)?
Kilydd - Valid point Artaud, initial formulas have found that we do require non-zero LV for the (move=1) station, and we will somehow need to equate these cofactors into the Fronsky calculations already mentioned by Blob.
The analysis by Blob is showing that the next move in avoiding the Circle line has put a strong emphasis on
'allowance of linear movement' so I agree Euston is unwise. My own extrapolations suggest we should focus on either Leyton or Loughton thus avoiding divisibile cardinal notation.
rab - Let me power up my Sinclair ZX81...
Simons Mith - I've had a cursory look at this and have found one flawed real-world solution and one ideal-world solution that only works in complex MC phase space. The Real solution is Alperton->Acton Town->Aldgate East->Moorgate->Mornington Crescent. The Imaginary solution is Alperton->Aldgate->Moorgate->Mornington Cresent. Unfortunately this is an odd-even move movement mapping which it is trivial to prove is irreconcilable. So you can cross that solution of your list as well. But this is only a first-pass approximation. It may be possible to use a one-move Expansion on the Imaginary at thereby unite the two. The trick, of course, is to do this without forcing a Real/Complex bifurcation.
Simons Mith - OTOH, if you can acheive it /with/ an Re/Im bifurcation, then it's been proved that a true real-only analogue move to the bifurcated move does exist - if only it can be found. Which is the most tantalising thing about this puzzle. Theorists are almost certain it /can/ be solved rigorously, but no-one has ever been able to prove it.
Blob - Just a thought, but running with Kilydd's L~ton hypothesis and selecting Loughton over Leyton due to its greater magnetic selectivity quotient, how about
stringing and ghost/live bifurcation on (move=2), possibly involving a recent ghost like Aldwych, or maybe Epping. The live side of course would have to be very lively indeed - maybe Baker Street or Bank. The dead:live dichotomy would perhaps then allow a move to a vortex station such as Sloane Square (Dollis Hill being unusable for obvious reasons). This might then lead to (move=3) being a Magenta station, though not if Baker Street had been used in (m=1) of course, it being a Magenta itself. What d'you reckon ?
Blob - Sorry, sorry, sorry - for
Epping in the above, read
Ongar obviously - the latter being a ghost, the former not.
CdM - This is probably a stupid question, but I am puzzled as to why this has not been solved by brute force and appropriate computing power. By analogy, think of how the four-color (or should that be for-colour?) map conjecture was eventually proved by reducing the problem to a finite (relatively small) number of maps and then checking them all. Here, at the level of actual moves, there is only a finite (and relatively small) number of four move combinations.
I'm aware, of course, that this is a simplification, because more than the pure moves come into play: there is a large (though still finite) set of possible initial placements on the board; token loadings can take on a large (though still finite) number of values; n-furcations are possible; and there are several continuous variables to worry about, such as LV and token weightings. Still, if this four-move combination is not a measure-zero possibility, one would expect that even a crude algorithm could easily limit the search space and pin down permissible ranges for LV and token weightings.
I must be missing something, but I'm not sure what.
Simons Mith - [CdM] Speaking only for myself; I'm too lazy to program it.
Anyway, did some more work on this today, and spotted an interesting complementary move to my Friday's suggestion.
Alperton->Kensal Green->St John's Wood->Mornington Cresent. This is just a straight horizontal. But curiously in the complex plane the sequence has five components
Simons Mith - .. not four, because it cuts the Metropolitan line between Finchley Road and Baker Street.
Anyway, I'm still looking, though.
Blob - [CdM] Well, I've got 347 stations in my database including N.L.L. and ghosts - and that doesn't yet have the old Met line stations to Brill - nor the Southend branch, nor some of the old District line stations.
Memo: Must update database ! : So say there are 380 stations all told - then as you say, as (M=0) = Alperton by definition, and (M=4) = M.Cresc, again by definition, then we only need to calculate M1,M2 and M3 i.e. 380 x 379 x 378, just 54,439,560 possible combinations. But of course that is without taking into account LV, token placings, Becks variance, Transient moduli etc. etc. It would be naïve in the extreme to think that the four-station solution would work under just any old set of initial conditions. So, let's hypothesise that about 0.1% of possible initial condition combinations will allow the required result then the figure of 54 million needs multiply be 1000 to 54 billion. This may take a bit of processing after all - as the initial conditions will have to be set up each time. I think we're back to skill, I'm afraid.
Kilydd - The more calculations are carried out I am sure it will end up staring us in the face. I have been struck by the elegant simpicity of a the General Theory of Relevance: where
e=mc2.(
e being Euston)
I disagree with this in one aspect and the is the appropriatness of the mc
2 given the Euston conflagration. The more sensible move and theory is e
2=mc, (
e being Euston Square) thus avoiding inverse coefficient of the magnetic modulus of previous BR station.
This brings me neatly to what may to some be a moment of
de jvu. I question at this stage about Alperton as a first move and propose the usage of
rabmc2
where
r=Ravenscourt Park: a=Alperton: b=Blackhorse Road : with the 2on the diagonal being Euston Square. Geometrically this three sided quadrilateral could work in parallell to a divergence of LV on the Jubilee Line.
Fat German - I proved all this ages ago with a Fronsky diagram drawn on a napkin. It was far too trivial for me to bother reproducing it here.
Graham III - Maybe I overlooked that napkin... I was wondering where I heard this could be done. I have a feeling
Bank maybe involved somewhere...
Dujon - Ahh! a most interesting
poserI suspect that Kilydd could be on the right track. The e=mc² seems to be the signal in this discussion. Change it to e=(mc)² and a whole new, previously unseen, network appears. Of course, the square root of (mc) is still unkown, the history of (mc) having been hidden in the depths of iniquity for time untold - plus - what "e" equates to is also a problem.
The referent "e" could be, as stated, a local station (or somewhere on the projected line) but it could also be the symbol for Euclid. This raises very deep and meaningful questions. Like other governmental organisations, the word "TIME" enters the equation - as indeed both Einstein and Euclid intended. Anyway, unlike rab with his Sinclair I am about to bring into the endeavour my whiz-bang VIC20 super computer; unlike rab's ancient device, this has at least twice the power... a bit like ticket inspectors really. Please check in occasionally as it should take no more than twenty years to bring this conundrum to its final conclusion.
Ibid - Now, come on, it's quite simple. The establishment where time is of the most importance, indeed the one where it is called out by name, is the licensed purveyors of intoxicating liquor. TIME, gentlemen, please. Therefore,
e is clearly
Elephant and Castle. From here, it's obvious. So I'll let you fill in the gaps. *looks shifty, legs it from scene*
Blob - Now then, according to CAMREC, who seem collectively to have taken a leaf (or several leaves) from the EEC when it comes to drafting their more recent legislation :
"A strile that is non-composite (other than demi-semi-striles set out for that purpose) may only be considered a strile in relation to stations which are neither perpendicular nor oblique. Furthermore, non-adjacent stations may be striled freely provided their quadrant ratios are zero, or +/- 1 ond. Semi-striles shall be considered impertinent in these circumstances and are only allowed when (a) all bridges have been lowered, (b) the token weighting at Hammersmith does not exceed the combined Becks-equivalent at Kew, (c) The DLR is not in spoon, or if in spoon has an obviated L.V. above 4.5, (d) There are no emus. All part-striles smaller than semi striles, and notwithstanding the demi-semi-strile alluded to parenthetically above, shall in non-polar conditions be wavered automatically, or alternatively put in vanche for three (or in exceptional circumstances, two) moves. However if any of the striles are semi-cubical, proto-parabolic or Gaussian then all transient vectors about the turning point must be considered neuter - or at best quasi-masculine. Trimming may occur in these circumstances. All the forgoing is reversed and/or transcended in the case of counter-striles which inherit their characteristic from the originating strile or part-strile. Unified Strile Theory suggests that a counter-ellipsoid-demistrile may in this instance be considered frank."
From this it is pretty clear that at least one of the stations
must be
Royal Oak, surely to goodness ?
rab - Well, since it's been six weeks in this position, I think we have to conclude it's just not possible to reach
Mornington Crescent from here.
Audience -
*shouts, screams, generally goes wild for rab* rab - [Audience] Shhh....
PaulWay - Actually, now that you've got me started from the previous game I think I can propose:
- 1. Hammersmith, with Zone 1-6 Travelcard.
- Then 2. Aldgate East, shuttling off the District and collecting a gold token for doing so.
- 3. Finsbury Park, using the Finsbury Option, which opens Euston via a reversed Easecliffe Denial (if you like, an Easecliffe Acceptance) for
- 4. Mornington Crescent, subtending the Northern at TOCR.
Watty -
*peers closely at this for some days* I have only one comment; it's just a passing comment, I don't think it affects anything, but perhaps our learned friend could clarify:
Playing a
Zone 1-6 Travelcard explicitly revokes everything northwest of Moor Park, which is fine, but I'm interested in the position of the Chesham spur at peak times. How does this affect the
freem around Aldgate East? Just asking.
Blob - [Watty,PW] Oh dear, Paul, I do believe Watty has spotted the flaw in your otherwise excellent and cunning plan. The freem count will be negative at Aldgate East as Watty surmises and so Finsbury Park will be in close jeopardy, and thus unplayable for three moves minimum. Darned close though.
Scuty - What is it about.
Blob - [Scuty] Is it not obvious ?
Darren - [Blob] I think Scuty was making a (correct) statement, rather than asking a question.
Chalky - ...and isn't it weird that it took around 20 months for poor Scuty to get a reply?
penelope - But it was a quality reply, Chalks ;o)
Darren - Not counting Scuty's name, that means we finally know that Blob thinks up his posts at a rate of one word every five months.
Blob - [Darren] I'll get back to you with a reply to that ... but it could take me a couple of years.
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This is the end of the line. There is no more.