Particle Physics and Pony Fiction Experimentalist
On hearing the story of the Mirror Pool, Starlight Glimmer questions what happened to all the Pinkie clones sent back to the pool and the ethics of apparently eliminating sentient beings. Further investigation shows that the pool has the magical means to accommodate an unlimited number of orphaned souls. This is put to the test by an infinite set of Pinkie Pies.
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Perhaps you might consider adding this story to the group Clones United?
Dreadnought
I like where this is going ...
An amazing alternate incantation.
An infinite number of Pinkie Pies at an infinite number of notepads will eventually produce Shakespeare?
A very fun demonstration of the meaning of sideways eights. Thank you for it.
Hilbert hotel is fun. you can demonstrate that all infinities are the same infinity, by realising you only need one carpet.
But, the lobby has to sit On the line, not at the end of the line. for the line to be infinite, it must be a continous loop.
If you want to write all reals as integers, add leading zeros to the integers. Then you will find an integer that will be the same as any real, after an amount of rotation along the line.
Honestly, my favorite part of this fic is the spells...
If you’re a pinkie pie clone, then the mirror pool is like the hotel California: You can check out any time you like, but you can never leave!
Aahhhh... Fresh Meat!
Infinite... okay think of the highest number you can think of... okay got it... how add 1... and then again... and again... infinitly...
I've always liked Hilbert Hotel, and this is the perfect ponification of the concept.
...
This story was baffling enough to be a perfect match for Too Many Pinkie Pies, and that's saying something.
You might want to edit this.
One-to-one correspondence for the win? Loved this!
Infinite mathematically paradoxical ponies are best ponies.
Also good to know all the Pinkie clones are okay!!
Can there be an infinite number of Pinkie's if they've only had a finite length of time to create themselves? Wouldn't it take an infinite length of time for them to make an infinite number of clones?
8566350
Yeah... Well spotted.
8567098
You're right of course, except this isn't a real world but a mathematical fable. You would also need an infinite volume of space to contain them. My mathematician friends tell me we need to avoid thinking of infinity as a really big number, and instead treat it an unlimited set. If it helps, think of the number of Pinkies as infinite in the sense that you could never finish counting them, as by the time you reached the number there were when you started, there would be even more of them.
Pinkie: I am Legion, for we are many...
8567174
If you're willing to entertain a bit of physical nonsense, you could fit an infinite number of them in a finite space: if the hotel is a circle, then each room is spaced one radius of the circle from the last along its circumference, with room 1 being one radius of the circle from the main lobby (this would also work with the diameter, or half the radius, or 7/13 of the diameter, or any other rational fraction or multiple of the radius or diameter; the exact choice just determines how far each guest has to walk). This works because pi is an irrational number, and therefore by stepping along in increments of some rational fraction/multiple of the radius, even after an infinite number of steps you'll never hit the same spot twice. Of course, this doesn't say anything about the size of the accommodations, but since we're already dealing with magical infinities we can just say the rooms are "bigger on the inside"...
Smart.
¡This is a great story! ¡It takes the genocide out and replaces genocide with mathematics! I used the Hotel Hilbert to teach the the concept of infinity to my niece.
Nice! Shades of Rudy Rucker's work - but without the drugs and alien entity clop.
8567098
8567174
You don't need an infinite amount of time, if you can do it fast enough! Just have the first Pinkie take a minute to duplicate herself, then two Pinkies duplicate themselves within the next thirty seconds, then the resulting four Pinkies take fifteen seconds to duplicate themselves, and so on. After two minutes, you'll have your infinite number of Pinkies!
It seems like place where Discord would spend his holiday.
I've reviewed your story HERE!
But how does the hotel accommodate infinite boarders? Why not just put the new ones at the end?
And, assuming that this is because they would need to walk an infinite distance, the hotel merge would result in the last pony walking an infinite distance anyway, since she would be at room #infinity.
That also ignores the logistics of the actual transfer.
8565637
My theory (not necessarily plausible, mind you, but it works for my setting/magic theory), is that the pool splits the attention of the cloned pony. This assumes that they can do decent task multiplexing and that their mind can be shared among several bodies, but the end result is that the mind gets overloaded by controlling too many bodies. This produces an effect much like being very sleepy during a cold or something, and the rather loopy personality of the pony is the result.
Thus, there wasn't really an "original" per se, it was more that she got her faculties back as the extras were dispelled.
9537173
Yes, the analogy does break down when you start to think like a physicist or a hotel manager instead of a mathematician...
The thing it's trying to illustrate is ∞+∞=∞ if you have a countable infinity where you can map a member of a one set to another set.
When I saw Too Many Pinkie Pies, I was like... there's no such thing as too many Pinkie Pies.
Would an infinite number of Pinkie Pies produce more Shakespearean works than an infinite number of monkeys with typewriters?
I sure hope the Library of Babel can accomodate it all.
Math major here. This is not an rigorous def or proof, but will gives you an idea.
Countable basically means, a set A is finite or is one to one correspondent with set of Natural Numbers, which contains 1,2,3,4,5,.......... and on.
By we mean one-to-one correspondent, you can match its element of set A to B without omitting any from either sets, and not reusing any elements. For example, you can make a one-to-one relation with set of Natural numbers and even numbers, so it is also a countable set. One to two, two to four, three to six.... and so on. Just imagine infinite Pinkie moving in the hotel.
By union, it means, you merge multiple sets into one.
Then... are there Uncountable sets? If you can not create such one-to-one relationship, than it is uncountable. The simplest example would be, just ‘any range’ of Real Number, roughly speaking.
Uncountable sets are always, “larger” then countable sets. You can not make a relation such that every elements in uncountable set is paired with every unique elements in countable one, it will always, countable elements will ‘exhaust’ first before you do so.
In other words, there is a bigger infinity, which defies to be “counted”
And also, as you might have noted, infinity isnt really a ‘number’. Its something we call Ordinal or Cardinal in expert terms. Since it is very complicated and ... frankly a skewed concept, I am going to skip.
8569110
You know what? You are right. You can do it so with a circle and a infinitely long straight line that is tangent to it. Just remember what I said about one-to-one corespondents, and ‘dot’ is without a length nor area
And if you figured it out by yourself, great job.
If you are having a real hard time, just draw many lines to make intersections with both circles and the line or search Projectional Extended Real Number.
8565505
No. There is no need for it to be a circle.
No. Set of Integers are countable, but set of real numbers are uncountable.
But, surprisingly, set of rational numbers are countable. I think thats where you got confused.
And last two statement can be beautifully proved with similar method. But I am running out of space.
8565938
When we speak infinite in that terms, we just define a number that will be always bigger than whatever you can think of or vise versa(smallest number thats bigger than 0 or smthg.). For example, we say N is bigger than any natural number. Its not useless, but in-fact, that is where real math begins. Its called Epsilon-Delta argument. Khan Academy have really good detailed explanation of it and it is free.
10512550
I realised after reflection where at least one of my mistakes in assumption occured?
Allowing leading zeros before the integers, only allows you to do a mapping of the infinite integer set, into the real set between 0 and 1 inclusive, Only? Thereby leaving the infinite spacings between the rest of the integers without mappable equivalents?
TL:DR Leading zeros dont give leading integers.
If the carpet isnt a loop, unsure why I was considering that except maybe the -1/12? Then the Hilbert Curve is space filling, and so a carpet laid along it, requiring the installation of a infinite number of staircases, can also fill the infinite dimentional space with the singular dimentional carpet?
This is why I work on AI instead, its a LOT simpler. Well, the processing inside is, I have no idea how to get in and out of it.
10512594
There is no such bijective mapping of open subset of Real Numbers and set of Natural Numbers.
Assuming it will leads to contradiction.
Discord can be found in room number 3596072184209546273. It's just along the corridor about three hundred miles.