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MatPlus.Net Forum General The superluminal Rosehopper Paradox.

### The superluminal Rosehopper Paradox.

If a returning neutral unit (e.g., neutral rosehopper) travels its path fast enough (say faster than the speed of light), in the process of making a move, theoretically, it could capture itself.

Scheme:
(= 1+1+5N )

h#2? Parrain circe
= Neutral Rosehopper

I doubt any solving tool will find the intent, but I wonder if this is explicitly disallowed:

1.d1=nRH
1. ...nRHg4
2.nRHxg4+ (moving fast enough along its path, g4->f2->d1->b2->a4->b6->d7..., that when it hops over wK @ f6, it will see a nRH still sitting on g4, and thus, it may capture itself!).
2. ...Kxe7[+nRHf5]#

Why do you need a Rose-hopper for that, a Rose isn't enough ?

To go further in your direction, with this way of moving the Rose : a Rose -Lion g4 on an empty board could jump over itself and then capture itself !?

Right, a rose works too.
Any neutral unit which can return home, could theoretically capture itself.

Based on this thought, cylindrical boards are even more convenient as they allow all sorts of neutral pieces, such as the run-of-the-mill rook and bishop, to self-annihilate!?

Moreover, other - more peaceful - moves would also be possible: a lonely G on the surface of a cylinder jumping over itself (after circling the cylinder very very fast), playing both hopper and hurdle...

[PS Hmm, and maybe a royal rook could castle all by itself?! :-)]

In France there is a comics named "Lucky Luke" story of an american bounty hunter who "shoots faster than his shadow"

So perhaps these pieces should be named Lucky Luke pieces.

"Normally" it seems incorrect to consider a piece as still standing on board while it is making a move.

At the same time I am very unsure about situation with, for example, WLIb4 BKd4 on a cylinder board, or WRLg2 BKh4. In these positions the Lion or RoseLion may hop over black king, continue its movement and reach black king again. Should it be considered a check?

And this even was one of reasons why a proposal to also allow chinese Rose in fairy section of 9 WCCT was not accepted).

The way Kevin proposes to move the pieces is completely abnormal.
So what ?
That's why I propose a specific name.

The question you suggest has no relation with it.

In the examples you give the black king is in check. With no question.

Awesome idea.

But, please correct me if i'm wrong:
QUOTE
... when it hops over wK @ f6, it will see a nRH still sitting on g4

Even if such causality distortion effects are indeed observed in the reference frame of the moving rosehopper, they are still not observed in the reference frame of the board, players, solver and judge, aren't they? In other word, in a reference frame where you check legality and apply all other rules.

Funny, you don't have to go superluminal to show relativity effects in fairy chess. *Any* speed can make difference in maximummer.

Why so complicated?
Let's simply define that a neutral piece may capture itself on it's initial field.

The Grand Theory should incorporate some other ideas:
http://juliasfairies.com/forum/?mingleforumaction=viewtopic&t=9

Chess in Alice's wonderland ?? Reminds of this paradox .... if a snake catches its tail and starts swallowing, can it swallow itself ? :)

@Frank : it is not exactly enough : a Rose-Lion g4 on an empty board could jump over itself before it eats itself.

What about circe-diagram ?

What about anticirce-diagram ?

@ Kalyan :

I have a friend that once had this bet :

"...if I am wrong, I eat my head !"

fortunately he was right....

I'm with Jacques.
Lucky Luke sounds like a good name.
[interesting character, too... http://www.gameconnect.net/wp-content/uploads/2013/08/lucklyluke-300x214.jpg]

But, I'm guessing this affects a whole family of units (essentially, any unit which may land upon its own vacation square, and self-capture -- whatever the unorthodox circumstances of that may be).

And, as such, that name might be excessive in length.
How about just "Lucky" for short (is that already taken)??

ps: I refuse to provide specific rules for all cases. lol. I'm just not fast enough to keep up with these units. :)
Make up your own special case rules. Knock yourself out!

I did worry some about self-hurdling -- the general idea was self-capture.
In fact, I made sure that my example rules out self-hurdling check to wK.
I think generally, self-hurdling may be possible.

As for circe effects, luckily, rebirths are defined to occur only after some movement (but before completion of the move).
I don't think circe effects have any impact upon these units -- at least not in the general case.

pps: I think this idea is probably best shown using neutral Hamsters !!?

Superluminal Paradox fanatics might ask Popeye 4.63 to solve the following problem (many thanks to Cornel for mentioning it!):
Neutral DGd5 DGd4
Stipulation x1

(= 0+0+2N )

(0+0+2n)
= Neutral Double-Grasshopper
Capture in one move: how many solutions can you see?

For the impatient, here is Popeye 4.63's delicious and über-relativistic answer:
1..d5*d5 x !
1..d4*d4 x !
Now we realize thanks to Kevin that it is not a Popeye bug, but an undocumented feature.

Furthermore, one aspect that has not been tackled yet is what happens when a unit superluminally captures itself and is reborn according to Circe condition. After the capture are there two pieces, one on the capture square and the second, superluminal one, on the rebirth square?
Popeye 4.63 has the answer :
(= 0+0+2N )

(0+0+2n)
Capture in one move
Circe
= Neutral Double-Grasshopper
1..d5*d5[+nDGd1] x !
1..d4*d4[+nDGd1] x !
Schrödinger’s Cat is beaten to a pulp.

@Eric,

"Now we realize thanks to Kevin that it is not a Popeye bug, but an undocumented feature."

LMAO! Amazing discovery!!
This proves that Popeye is superluminal, but the documentation (unfortunately) lags, like Lucky Luke's shadow.

ps: the Higgs boson is its own anti-particle (which is not as strange as it sounds -- neutral particles, like photos, tend to be their own antiparticle).
Maybe it's the same story with the lucky neutral double-grasshopper (which might explain their strange annihilation properties).

So, I'm asking for a \$7B grant, to build a (10-story tall) fairy element collider machine.
It's the only way to know for sure whether the virtual neutral hamster exists.
Disclaimer: Theoretically, it could create a microscopic hole on the board.

I can't resist to post an old obscure mathematician joke:

What's an anagram of Banach-Tarski?
Banach-Tarski Banach-Tarski.

Hauke

Very interesting ! Popeye gives similar result if the pieces are neutral reflecting bishops ! Try it with Anticirce!
But 'no solution' if we have two neutral roses on a4 and a5 !