The Banach-Tarski Theorem describes how to split a sphere and re-arrange the pieces to make two spheres of volume equal to the original sphere.
Turns out it works on dragons, too.
(Cover taken from http://mlp.wikia.com/wiki/File:Spike_ID_S3E05.png and slightly modified)
For other stories of similarly duplicated characters, take a look at Second Sun by Carabas and Amphelion by Monokeras.
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Great little story. Everything went better than could be expected, as scary as the spell's mechanism sounds. Cut into pieces? Ow.
Short, but to the point. Nice job.
Maths! Yay! Though I'm relatively certain that it doesn't cut the volume up, just the surface. So if you flay Spike, you can make two dolls of him, but you can't make two Spikes.
Oh, and just saying, the theorem doesn't apply to Spike, since he's a torus, not a sphere. Digestive tract and all that.
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That's why it's (probably) lethal to ponies. But dragons are remarkably hard to kill, fortunately for Spike...
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No, I'm pretty sure it's the volume. Though I admit I have only the vaguest understanding of Banach-Tarski (and most of that comes from a perusal of the Wikipedia page on the subject) - but the Wikipedia page does specify that certain points within the sphere (including the central point) are included.
Ah, now that's a much more valid objection. To which I can only respond that the sphere that was duplicated included Spike and his checklist and the quill he was holding and the contents of his digestive tract and quite a lot of air. So while Spike is topologically a torus, he can still be encased within a sphere and then that sphere can be duplicated.
(I'm not sure if Banach-Tarski works on toruses or not. The Wikipedia article claims it works on "all 'reasonable' solid objects", but then gives two examples that are isomorphic to a sphere, so I don't know if 'reasonable' is intended to include toruses (torii? toruseseseseses...es?) or not)
4679218 Topology isn't my strong suit. I'll trust Wikipedia here and be like, "K brah, totes does the volume".
Ooh, I misunderstood the way it worked. That's totally cool then. And I'm a derp.
So if the resulting dragons are the same size as the original, does this mean that the duplicated Spikes have half his original density? Thus they're half-dragon, half-air?
Speaking of the personality split, were those qualities chosen along a right-brain, left-brain (emotional, logical) separation?
watched
You don't have to break the flow of the story to footnote this. It works just fine immediately after the sentence that references it.
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It's worth bearing in mind that a dragon's body is capable of producing mass from nowhere. When Spike experiences a greed-growth burst, he ends up not merely bigger, but heavier. It seems reasonable to consider that Spike's body can use a similar mechanism to recover lost mass in a case like that.
No, but that would have been a good idea. The original prompt was based on an episode of Star Trek, where Captain Kirk was split into two Kirks by a transporter accident (one good and one evil).
Spike's personality split here was along the lines of one Spike having a lot of motivation and no restraint - so that he does and says all those little things that one thinks of but doesn't actually do - and one Spike with a lot of restraint and no motivation, so that he has trouble doing anything at all and is nearly incapable of putting his wants before anyone else's.
Whoops, fixed.
I almost left that line out entirely... hmmm. I'll think about it.
Best "transporter accident" pony story I've ever read.
What? Spike was separated into sets of zero-dimensional points, then reassembled. Leptons are indivisible point particles. The analogy is sound.
Also, looking at the Wikipedia article, I'm a bit disappointed you didn't do anything with the "chop up a pea and reassemble it into the Sun" explanation. I'm sure Celestia would be less than thrilled with that one.
In any case, thank you for a delightful pony-flavored exploration of exotic topology.
I'm beginning to suspect this second Spike should have a big moustache.
Cute little story, if shorter than expected. I think this does the show thing where they take an idea big enough to hang a great deal of content off of, and use that to explore a single facet of it.
I'm vaguely disappointed that in the epilogue Twilight doesn't clone herself, but that might have been more silly than you were going for. Anyway, nice job.
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The original prompt was actually based on an episode of Star Trek, where a transporter accident led to Kirk being split into good and evil halves...
So, well spotted.
Well, that would just lead to a pea the size of the Sun...
Unless it's Discord doing the chopping-up, of course, in which case anything goes.
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Personally, I think that this trope is a better fit... but if the second Spike really needs a moustache, I'm sure Twilight can provide one.
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Hmmmm. That... wouldn't be out-of-place in a sequel, perhaps. The Banach-Tarski Princess... aaargh. I have too many stories to write.
Interesting!
So, that's how it happens! I wonder what the distraction wanted? I guess I'll find out in the next chapter!
And so Twilight had to Pinkie-proof her chimney
Wow... um... I was not expecting the feels.
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You can never fully Pinkie-proof your house. NEVER!!!
Delightful title, and a nice feelsy little story to go with it.
I reviewed this story as part of Read It Later Reviews #89!
My review can be found here.
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A very fair and straightforward review. Thank you for it.
I have no idea what my previous comment meant about a Distraction wanting something...
But now on more fine re-read of my re-read... I wonder what happened last week...
Found this through a search that went badly. Forgot I ever read it, so I'm reading it again! ... *read* ...
----
Typos:
Confrontation
:
one of the instincts
Is he still feeling a bit fuzzy? Otherwise:
Epilogue
:
How come Rarity turned up at Sugarcube Corner just then?
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Fixed, thanks.
...I'm pretty sure that both formulations of this sentence are grammatically correct.
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I've never heard of "How come did" until, but if you're sure...
You can has review!