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Suppose you are fighting exact copy of yourself in perfectly balanced arena. Replica is doing same moves as you do. How would you defeat it ?

edit1:
Committing suicide 100% defeat for you and clone.
Now how to reduce percentage?
e.g. Have gun that fires 50% of time (Schrödinger style radioactive source trigger ) or smoking cigarettes can cause cancer (twins predisposition)
edit2:
perfectly balanced arena means that offer no macroscopic advantage to participants
e.g. no terrain advantage (flat and mirrored),no random spikes on the wall, no random holes in ground

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    $\begingroup$ Do you have to defeat it, or just not be defeated? $\endgroup$ – Cort Ammon Dec 17 '15 at 23:29
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    $\begingroup$ Don't be alarmed, you're actually just standing in front of a mirror. $\endgroup$ – Samuel Dec 17 '15 at 23:53
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    $\begingroup$ Perhaps you are the replica, and just making the real you have to work harder to win the fight. Its worth noting that the existence of a cloning machine and a perfectly balanced arena suggests that there's more context here that could matter! $\endgroup$ – Cort Ammon Dec 18 '15 at 0:15
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    $\begingroup$ Is it perfectly mirroring your moves, or is it a fully functioning separate copy of yourself? If it is mirroring your moves exactly with no delay, then it would also be important to know: does "perfectly balanced arena" mean that the arena is perfectly symmetrical? $\endgroup$ – Darcinon Dec 18 '15 at 0:24
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    $\begingroup$ Curse you, water temple! $\endgroup$ – PipperChip Dec 18 '15 at 0:39

14 Answers 14

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You can't defeat an exact copy of yourself making the same moves you do. You can only fight your mirror to a draw. You certainly can't do it alone. You need to recruit a friend who can come into the arena so you can double down on your copy. Of course, your copy will probably bring in their own ally, in which case, you and your copy can just sit back and watch, and eventually you won't even remember what you were fighting about.

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    $\begingroup$ Quite right: In the question as written, both sides will do the exact same thing and be subject to the exact same external influences. Since you can't prevent your double from doing the same thing as you, the only way to introduce an imbalance between the two sides is to change the outside influences, either by bringing such an influence in or by moving outside of the arena. $\endgroup$ – user867 Dec 18 '15 at 3:37
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Okay, I'm going down the rabbit hole, wish me luck!

An exact copy of yourself is not actually a mirror match. It's actually a symmetry around a point. If you strike out with a sword in your right hand, you will see an oncoming swords coming at you on your left (their right).

Now clearly there's some third party pulling the strings here. Making clones of people, somehow setting up a perfectly symmetric battle where every strike is responded to with its mirror. It almost seems like Moriarty is up to his devilish schemes, trying to break my deductive reasoning skills

enter image description here

Let's examine our assets, shall we?

I have my clothes, my good looks, a full compliment of weapons including swords and guns intended to be used against my clone. I have my clone, if that is an asset.

I have an instinct for survival, so if the clone is anything like me, it has an instinct for survival too. It also would be deducing how to get out of this situation. We think alike, that, could be a valuable asset. But is it really a clone of me? Let's deduce. Key assets: two pairs of hands

Action: Ro Sham Bo. 10 games straight, a tie each time. The clone knows we have a perchance for throwing scissors statistically more often than we should, but has yet to adapt to rocks. 20 games. Now we both have moved to throwing mostly rocks. 30 games. We are indeed clones in every way shape and form.

I make the conscious decision to think not just in terms of the survival of this one body, but to think in terms of our shared survival. My clone naturally does the same. Now I have one fewer opponents, and one more ally.

Suppose you are fighting exact copy of yourself in perfectly balanced arena. Replica is doing same moves as you do. How would you defeat it ?

"It" is a potentially ambiguous antecedent. A lesser man might presume it has to mean defeating my replica, but one with my deductive capacities can easily see through this. At best, only one of us can defeat the other, and it matters not which one. Thus, clearly the antecedent of "it" is not my clone, but the "perfectly balanced arena."

Loophole unlocked.

Smile at myself. Now to defeat this arena's perfection. We need to know where it is. Grab an iron sword and a hammer. Point the sword in a direction, lay it in the ground, and tap it repeatedly with the hammer. Hypothesis: if this is the North-South direction, the sword will magnetize from the taps of the hammer. 10 minutes, no luck. Try 90 degrees from that orientation, no luck. Perhaps sword is not made of iron at all... or....

We're at the magnetic north pole. Of course Moriarty would have to put us at an exotic locale such as that to ensure the direction of earth's magnetic field didn't disrupt the perfection of his trap. His mistake though, for he forgot to think through one final detail.

The north pole is where Santa comes from. Certainly we can devise a way to flag Santa down as he passes for assistance.

So all I have to do is be a good boy... pair of good boys... for 7 days, 3 hours, 27 minutes and 30 seconds. Then Santa will come and bring me the present I always wanted: a 2 year old child a Costco sized container of pixie sticks.

No perfectly organized trap can survive the destructive potential of a 2 year old child, especially when hopped up on sugar. That perfect arena will lose its perfection, and be defeated!

Your move, Moriarty! Next time try to spring your trap when I have less Christmas spirit to use!

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    $\begingroup$ +1 for "Team up with your duplicate because why wouldn't you" and "break the symmetry of the arena." I can't imagine a better answer to this question. $\endgroup$ – user867 Dec 18 '15 at 4:40
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    $\begingroup$ I clicked "join this community" just so I could +1 for flagging Santa. $\endgroup$ – Dave Liu Jan 31 '16 at 22:37
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Surrender

Instead of actually injuring yourself, just say I surrender. Your clone will do the same. You have defeated your clone at the exact same time it defeated you, and in a way that involves the least harm (namely none).

Now that you are done fighting, proceed to start stabbing the arena until you break out, find something asymmetrical outside the arena, use it to break the perfect symmetry with your clone (think to yourself "the copy on the this side of this thing will gather food, and the other will start a fire." Symmetry will break down rather quickly after that) and go beat up whoever put you in that arena.

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Personally, I would refuse to fight myself; instead, I would choose to team up to defeat whoever put me in this insane scenario. However, maybe the scenario really does compel me to fight for some reason.

In either case, getting our paths to diverge is the first objective.

If we plan to cooperate, we can't do this effectively while we are both saying and doing the same things simultaneously.

Even if we plan to fight, we both agree to cooperate on this first. If we don't, then we will be stuck fighting to a draw until we both pass out or die, which is rather pointless. We would rather each have a 50/50 shot at winning the battle.

So, how can we get our paths to diverge?

The premise of this question is that my behavior is deterministic: as long as I have the same input, I will respond in the same way. Because both of us experience the same input in the symmetrical arena, we will both say and do the same things simultaneously forever.

How can we escape this pattern? By introducing a little randomness.

The first thing we try is that each of us will flip a coin. If one of my coins comes up heads, that me has to sit down (or do any trivial action). Once one of us has done something different, our thoughts and actions will be different from that point onward. We will be able to have a conversation, cooperate, or fight, depending on our choice.

Of course, each of us throws the coin exactly the same way. But how perfect is the symmetry in the arena? Are even the air molecules around us bouncing around in exactly symmetrical ways? This seems doubtful. Hopefully there are subtle differences in the environment that will eventually lead to one of our coins coming up differently.

Note: if we didn't have a coin we could easily do this with some other object, such as tossing a shoe and agreeing that it landing in a certain way has meaning.

After 1000 coin flips all coming up the same, we will try the next tactic: try to break stuff.

We are exact copies, but is everything we have an exact copy, even down to the molecule? We can each try to tear off a piece of our shirt, and whoever tears off the biggest piece has to do run a lap around the room (or whatever). Besides hopefully introducing something non-deterministic, it also gives us a nice "Captain Kirk fighting" look.

Beyond our personal possessions, we can also try breaking parts of the arena. Hopefully the perfect symmetry only applies to its finished form. Once we break a wall, different parts of it might break in different ways, etc.

The next option is to try to break out of the arena into the normal, non-symmetrical world. This might be really hard or even impossible, but trying to defeat each other with perfectly symmetrical blows is definitely impossible (and cooperating without escaping would be kind of pointless anyway), so this is still the worth it even if there is little chance of success.


Edit: After trying to break out for a long time with no success, we may try yet another option: fake unconsciousness to get our captor into the arena. We either start fighting and pretend to knock each other out, or act like we are working ourselves to exhaustion until we pass out. Then we wait, hoping that our tormentor (who is surely watching this sick scenario) will come into the arena. If they do enter the arena, they will probably not being able to avoid doing something asymmetrical. However, this is a bit of a long-shot, as they are probably aware of the consequences of breaking symmetry and will want to avoid messing things up.

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    $\begingroup$ You both go on consciousness. Your captor comes in to check on you and plot twist there are two mirror image captors. $\endgroup$ – PyRulez Dec 19 '15 at 15:41
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I agree with @Jim2B, for the most part. If "Replica is doing same moves as you do" means that the replica is simply mirroring you in everything, (i.e. if you take a step forward, he takes on backward) this is extremely simple. You move over to the wall, slightly off kilter, so that you are facing the wall at, say, a 45 degree angle, and move your body in a way that doesn't injure you, but would him. For instance, kick hard with your shin sweeping to the left so that your foot missed it, but because it mirrors you, its shin will be shattered on the wall...and so on. Once it has a broken shin, it cannot mirror you effectively, however you can still do something like sweep your head downward and to the side to make it smote its ruin upon the mountainside ( oops, I mean smash its temple upon the wall)... But I digress.

However, if its not a mirror, and simply a duplicate, then it still is easier than one might think. I, in any given moment, will not simply do the same move every time without variation...I am a human being after all. I have an element of randomness imbued within my soul. therefore, I simply would not necessarily think the exact thoughts, at the exact time as my dupe. I would, therefore, attempt to utilize this element of randomness in my favor, before my copy does likewise.

This would probably mean I would attempt to distract my counterpart, just long enough to bring in the element of doubt, then I would swiftly and mercilessly overpower it before it could recover. This is possible because, knowing myself, if the other had done that, my initial reaction would be to trust it, for I would think that my own person would want to reconcile before attacking. in that split second of confusion, it could overpower me as well, for no one can react as quickly and intentionally as one can pro-act.

However, if I be in a different mood, I would probably be immediately suspicious, and would not trust my dupe, and therefore I would not feel that my dupe would trust me in such a scenario. In that case, I would probably turn around and sit down, and assume my dupe would do the same, and simply wait for the instigator to arrive. Change the status quo. This puts the ball in the dupe's court, so to speak, and almost certainly that would mean I would do the same as the original, for I again would trust myself to have good will and no deception.

All this is reminding me of the Prestige too much; you should watch that film and see if that changes your perspective.

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  • $\begingroup$ There was a part in the original Tomb Raider where you had to defeat your exact duplicate, and just firing at it led to your death. You ended up having to use the technique you describe here to kill her. $\endgroup$ – IchabodE Jan 29 '16 at 23:55
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Commit suicide.

This would, of course, defeat you as well, which might not be an acceptable outcome. This would not work if the replica had its own autonomy.

Alternatively, stop fighting. Unless your replica's defeat is mandatory for some reason.

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  • $\begingroup$ I was so tempted to answer this way. Glad you beat me to it! $\endgroup$ – Cort Ammon Dec 17 '15 at 23:30
  • $\begingroup$ @CortAmmon: I saw your comment right before I submitted & knew you were thinking the same thing. ;) $\endgroup$ – Wingman4l7 Dec 17 '15 at 23:31
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To beat yourself you must deceive yourself.

For instance planning to fake a punch, but unwillingly punching for real would probably deceive yourself as well as your copy - who would be sure that your punch was fake.

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    $\begingroup$ "planning to fake a punch, but unwillingly punching for real". How do you do this? Your answer would be strengthened by explaining this step-by-step. $\endgroup$ – user16107 Dec 18 '15 at 15:06
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    $\begingroup$ You don't. it must be an accident, or your copy would be acting the same way, since it thinks the same as you. $\endgroup$ – Necromaru Dec 18 '15 at 18:49
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Call upon the Hand of God. If my duplicate does so as well, there is no need to defeat him (a coaligned duplicate is an ally). If not, he loses (because he's an evil duplicate of me and the symmetry just broke in my favor).

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Since both copies are identical, both are you, and you will survive as long as one of them survives. There are 3 possible outcomes:

  1. One of them wins. Your existence continues.
  2. Both lose/die. Your existence ends.
  3. Both survive.

If you can make it work, go for option 3: team up and break the game, by escaping or exploiting a loophole in the rules. Otherwise agree to flip a coin and the loser offs himself. Whatever you do, don't mortally wound the other you while it kills you. Also: don't just kill yourself, because the copy will do the same.

If the copy isn't really you, then it isn't identical. In that case: find the difference, exploit the difference, win the game.

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This is a situation my cat has had to face in the past. I consider him something of an expert in the field. It always ends in a draw.

But what you can do is to claim the moral victory. When your opponent resigns it's because they know they can't win. When you resign it's because you know you've already won, or that you simply have nothing you need to prove.

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It Depends

If the copy is an unthinking automaton just mirroring your moves, then you could defeat it relatively trivially with a little thought.

The first thing that came to my mind was that certain portions of the skull are more vulnerable to impact than others. If you just start headbanging against a wall or other hard object in such a way that your skull impacts on one of the tougher portions and your copy's skull impacts on a vulnerable spot, then you could win easily.

I'm sure other variations of the theme could be even more successful with less pain for you.

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    $\begingroup$ I dunno, that solution sounds like I'd just be banging my head against a wall. $\endgroup$ – user867 Dec 18 '15 at 4:41
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As everyone else says, we need our paths to diverge.

This seems to be parity symmetry. (Let me know if i'm butchering particle physics.) All forces follow this symmetry, except the weak nuclear force. So our paths would slowly diverge if any radioactive decay occurred near me.

If the captor was smart enough to remove all radioactive particles, and there is no asymmetry in the arena, I would balance a stick (or myself if necessary) on its mirror image. If it was off by an atom, symmetry would be broken, and the sticks would fall. Even if they were symmetric, the Heisenberg uncertainty principle would quickly fix that.

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All outcomes will end in a draw. The mirror copies you exactly, if you punch a wall he punches a wall in the same way. This means you are injured at the same rate. No matter what happens you will eventually starve to death unless you are fed in which case you will die of old age.

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Stride up to them, directly and certainly, and wrap my arms around them in a hug.

A clone that knows me well enough to know how I fight knows me well enough to know I will claim any doubles, clones or doppelgangers as kin if they let me. Helpfully, I made this decision a long time ago (having read many storybooks) - so that any I encounter in the future will find the decision very certain and already made.

If they can't think and only just act in duplicate, as if a magical effect or illusion, they have mirrored me into nonviolence. If they are constrained in their choices (ie, can't not fight) they were never really a threat to me, since a being who is compelled or controlled, who has whole swathes of options blacked out and unavailable, is always less capable than a thinking and planning one... and I can hug them into submission while their brain recovers from being shorted out, caught between mirror-their-moves and cant-not-fight. And, in any other circumstance, they will call me kin back, and we'll work together, because if they wouldn't - they would not be my double.

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