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Old 9th April 2011, 01:13 AM   #1
andyandy
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Can Two Things be Identical?

Something i was thinking about today....

when we get to the subatomic level, does it make sense to talk about individual atoms as distinct (if they share the same basic properties that is)? And if it doesn't - ie they are all from a scientific perspective identical, then where does the individualism of an object come from?

If I produce an exact replica of (say) a gold ring - right down to the molecular level, is that scientifically speaking identical to the original? The only distinction in that case would be the time-line of the two objects - but if this information is not carried in the atoms themselves this would not be relevant - it would only be an external recorder like (say) me, knowing that one was a copy of the other that would be able to distinguish between them....

As a associated thought experiment - if a machine produced such an identical copy (but at the expense of destroying the original), would there be any inanimate object that you own that you wouldn't be prepared to drop down it? (The classic example is something of sentimental value like a wedding ring....)

Discuss
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Old 9th April 2011, 01:26 AM   #2
Aepervius
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They would be interchangeable and non distinguishable by nature but not "identical" per see.

Think about this way : instead of duplicating gold ring you duplicate a human atom by atom. At the end you have wo live breathing human. They would be interchangeable (you can both ask the same question on their memory and get the same answer or reaction to a situation presented identically). You won't be able to distinguish between them, immediately after the copy. But let them go on, and they will go differening ways.

So for innanimate object, I would not care and would let it copy ad infinitum. It does not matter after all as long as they are not non distinguishable. But they are not identical.
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Old 9th April 2011, 01:30 AM   #3
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There's an old idea that one particle is actually zipping back and forth through time in every moment possible, and every particle you see is merely a double of this particle.

Even in the sandwiches you eat!
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Old 9th April 2011, 01:39 AM   #4
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Originally Posted by Aepervius View Post
But let them go on, and they will go differening ways.
But would they? Or would they actually make exactly the same choices from the same stimuli and therefore do exactly the same thing?

(of course, the fact that both of them were around would alter things - they couldn't occupy the same space, and one doing an action might prevent the second from also doing it....)

So, if the original was destroyed, would the clone behave any differently to how the original would have behaved in the future? I think we'd have to say that it wouldn't...

(this is straying dangerously close to a religion and philosophy free will debate already )
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Old 9th April 2011, 06:11 AM   #5
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Originally Posted by Halfcentaur View Post
There's an old idea that one particle is actually zipping back and forth through time in every moment possible, and every particle you see is merely a double of this particle.

Even in the sandwiches you eat!
Ah, my single-quark hypothesis.
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Old 9th April 2011, 12:21 PM   #6
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Originally Posted by quarky View Post
Ah, my single-quark hypothesis.
At least it was new to me when I stumbled on it, in the hideous confines of my imagination.
I still suspect that it is the right direction for our thoughts on the matter.
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Old 9th April 2011, 12:38 PM   #7
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I think what you're asking is largely a philosophical rather than a scientific question.

As far as science goes, we say that certain particles are "identical" if they share all the same properties. Two electrons are not going to exhibit different behavior under the same conditions (aside from the inherent randomness that exists in physics, that is). That does not mean they're one and the same thing. There is also an issue of distinguishability. If two electrons start in states A and B, and end in states C and D, and we could (in principle, if not in practice) have tracked their trajectories, then it's meaningful to say that the same electron that was in A is now in C, for instance. If there was no way to track their trajectories, and it's impossible in principle to know which electron is the one now in state C, then it's meaningless to say that a particular one of them is now in C. (That it is meaningless is confirmed by the applicability of Fermi-Dirac statistics to ensembles of electrons at low temperatures.)

If you want to throw some philosophy into this, I would say that the electrons can be given an identity by where they were at some time---this electron was once in state A, so we identify it as the electron once in state A. If an altercation happens so it's no longer clear whether it's "this" electron or some other electron in a new state C, then the electron has lost its identity.

Now, as far as the identity of composite objects go, I'd suggest looking up the Ship of Theseus. Ultimately I'm most comfortable with the idea that the identity of these composite objects is socially constructed, so whether the ship (and thus your gold ring) is "the same" or not is a matter of what you or your culture decide about the object's identity.
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Old 9th April 2011, 01:41 PM   #8
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Originally Posted by andyandy View Post
Something i was thinking about today....

when we get to the subatomic level, does it make sense to talk about individual atoms as distinct (if they share the same basic properties that is)? And if it doesn't - ie they are all from a scientific perspective identical, then where does the individualism of an object come from?

If I produce an exact replica of (say) a gold ring - right down to the molecular level, is that scientifically speaking identical to the original? The only distinction in that case would be the time-line of the two objects - but if this information is not carried in the atoms themselves this would not be relevant - it would only be an external recorder like (say) me, knowing that one was a copy of the other that would be able to distinguish between them....

As a associated thought experiment - if a machine produced such an identical copy (but at the expense of destroying the original), would there be any inanimate object that you own that you wouldn't be prepared to drop down it? (The classic example is something of sentimental value like a wedding ring....)

Discuss
If you're asking whether a thing can occupy two locations simultaneously then my answer is no.
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Old 9th April 2011, 01:58 PM   #9
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Originally Posted by Halfcentaur View Post
There's an old idea that one particle is actually zipping back and forth through time in every moment possible, and every particle you see is merely a double of this particle.

Even in the sandwiches you eat!
I like it

------------

Maybe I'm thinking about the OP in an overly simplistic manner, but suppose I have a vector based image file I want to print over and over again. The file will always contain the same information in it. In fact, the information therein is based on equations, not pixels.

So my data files is always the same. Always.

Yet, when I go to print this file out, the printout is different every single time. The differences might be minute, but they are there. Even on the same machine.

The reason for the differences (even though the end result is always the product of the same exact file origin) ultimately will boil down to: interaction with everything else, and the time it takes to do so. Yes?
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Old 9th April 2011, 08:10 PM   #10
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yes
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Old 10th April 2011, 12:39 AM   #11
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No but it does depend very much on how you define identical. Generally though no, even atoms of the same type will have differences between them. Different atoms will have different energy levels overall, electrons will have differing spins etc.
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Old 10th April 2011, 01:13 AM   #12
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There's functional identity, as in "this atom does all the same stuff as that one" and then there is historical identity, "this atom is the same one I had last night."

Historicity is a property that adds a storyline. Now, what I find interesting is whether or not you could transfer this property, historicity, between things that are also functionally identical. There's a granularity problem at some level that makes me think of Heisenburg and his question about whose beer is it really?
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Old 10th April 2011, 03:19 AM   #13
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Originally Posted by andyandy View Post
But would they? Or would they actually make exactly the same choices from the same stimuli and therefore do exactly the same thing?

(of course, the fact that both of them were around would alter things - they couldn't occupy the same space, and one doing an action might prevent the second from also doing it....)

So, if the original was destroyed, would the clone behave any differently to how the original would have behaved in the future? I think we'd have to say that it wouldn't...

(this is straying dangerously close to a religion and philosophy free will debate already )


They cannot be at EXACTLY the same place seeing the same things eating the same stuff, potentially not the same illness , not breaking bone the same way, not taking a bullet the same way, not having the same conversation,or having sexs with the same woman at the same moment (at least not from , ahem, the same orifice).

So very quickly they would diverge. Only by destroying the clone you would ensure that both would have the same potential life afterward, because you REMOVE the possibility of them diverging.

Heck : the isotopes in their body would not decay at the same time/place, the cell would not die at the same time, which cell divide, which cell get which protein/glucose , or even the cosmic ray ionising /x ray some part of the cell get ionised etc...

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Old 10th April 2011, 10:04 AM   #14
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Originally Posted by Aepervius View Post
They cannot be at EXACTLY the same place seeing the same things eating the same stuff, potentially not the same illness , not breaking bone the same way, not taking a bullet the same way, not having the same conversation,or having sexs with the same woman at the same moment (at least not from , ahem, the same orifice).
But as a thought experiment you can imagine controls for this -- even if it's a prison room with limited input. The question is then whether random effects would still lead to divergence because of the nature of quantum uncertainty. And then, you'd like to know how fast that happens and how to measure it.
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Old 10th April 2011, 02:40 PM   #15
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Originally Posted by marplots View Post
But as a thought experiment you can imagine controls for this -- even if it's a prison room with limited input.
But it's actually two prison rooms, though. We know immediately that they're not identical, because they're occupying two very distinct positions in spacetime.

One of them had to travel just a little farther down the hallway to their room than their clone did. Or they turned right when the other turned left. Or they were escorted by a different orderly. Or they waited longer in the birthing room for the same orderly to come back for them after escorting the first one. Etc.

The controls you imagine are physically impossible.
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Old 10th April 2011, 02:44 PM   #16
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Didn't Star Trek already answer this with transporters?
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Old 10th April 2011, 03:44 PM   #17
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Originally Posted by marplots View Post
But as a thought experiment you can imagine controls for this -- even if it's a prison room with limited input. The question is then whether random effects would still lead to divergence because of the nature of quantum uncertainty. And then, you'd like to know how fast that happens and how to measure it.
I still think it's somewhat irrelevant ... in order to be absolutely identical, two separate things have to occupy the same space simultaneously (which would no longer produce two distinguishable things, rather you would have only one thing you could distinguish between). Otherwise ... even if they are identical in every way, they are still two separate things because they are each in their own unique place in space-time.

Maybe the question should be: can two identical things converge to the same point in spacetime ... and then cancel each other out/form one thing/etc ..... but still be capable of having the two distinctly identical things emerge post convergence. If that makes sense.
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Old 10th April 2011, 04:35 PM   #18
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Originally Posted by Trent Wray View Post
I still think it's somewhat irrelevant ... in order to be absolutely identical, two separate things have to occupy the same space simultaneously (which would no longer produce two distinguishable things, rather you would have only one thing you could distinguish between). Otherwise ... even if they are identical in every way, they are still two separate things because they are each in their own unique place in space-time.
I disagree with this argument. You can have two particles in a state such that they're measured to be in different positions (and even different distributions of positions, over repeat experiments), but it still makes no sense to ask which particle at what place (or has which distribution of positions).

In QM, take two elementary particles of the same type and put them in a state of the form ψ(x1)φ(x2)±ψ(x2)φ(x1). Then information about which particle in which state (ψ or φ) simply does not exist. Thus, they're still not distinguishable even in principle.

Originally Posted by Trent Wray View Post
Maybe the question should be: can two identical things converge to the same point in spacetime ... and then cancel each other out/form one thing/etc ..... but still be capable of having the two distinctly identical things emerge post convergence. If that makes sense.
If they're bosons, one can take ψ = φ, so that they'll have identical distributions of positions as well.
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Old 10th April 2011, 05:06 PM   #19
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The op reminds me of an old anecdote, logger is holding up his axe proudly, saying, "Been using this here axe for 30 years! Replaced the head three times, and handle ten, but it just keeps on going..."

Dealing with identity is a tough call, as the concept itself will vary from person to person. Dropping a wedding ring into the theoretical device is a good example I think. While technically it would be the exact same object, we as humans also assign a sentimental value to such objects based on what experiences that particular clump of atoms has been through, despite the fact that the time and experience could in no way make a difference between the original object and it's replacement. While completely irrelevant to whether or not the clone is the same as the original, we humans will still say to ourselves, "these atoms weren't there when I got married."
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Old 10th April 2011, 07:43 PM   #20
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Originally Posted by Vorpal View Post
I disagree with this argument. You can have two particles in a state such that they're measured to be in different positions (and even different distributions of positions, over repeat experiments), but it still makes no sense to ask which particle at what place (or has which distribution of positions).

In QM, take two elementary particles of the same type and put them in a state of the form ψ(x1)φ(x2)±ψ(x2)φ(x1). Then information about which particle in which state (ψ or φ) simply does not exist. Thus, they're still not distinguishable even in principle.
Hmm .... well if they are indistinguishable even in principle, then how do you know there are two of them and not fifteen of them, for example? What distinguishes one from the other? In other words .... when does the ability to claim "this is not that" become irrelevant ?


Quote:
If they're bosons, one can take ψ = φ, so that they'll have identical distributions of positions as well.
If I'm talking out of my league (and I might be), so be it. But I would ask the same question here I just asked above: is there a point where it's no longer possible to say "this is not that" when considering two particles ?
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Old 10th April 2011, 08:13 PM   #21
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Originally Posted by Trent Wray View Post
Hmm .... well if they are indistinguishable even in principle, then how do you know there are two of them and not fifteen of them, for example?
Because there's twice as much stuff there as one of them.
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Old 10th April 2011, 08:17 PM   #22
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Originally Posted by yy2bggggs View Post
Because there's twice as much stuff there as one of them.
So they are not identical ... since you can distinguish between one verses two verses fifteen ..... right? That was my point in asking . In my eyes, I'm just pointing out the obvious, but perhaps I'm missing something

----------

One of my favorite (family friendly) jokes:

Q: When ducks fly in that big "V" shaped overhead ..... you know why one line is always longer than the other? More ducks in that line.
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Old 10th April 2011, 08:19 PM   #23
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Originally Posted by theprestige View Post
But it's actually two prison rooms, though. We know immediately that they're not identical, because they're occupying two very distinct positions in spacetime.

One of them had to travel just a little farther down the hallway to their room than their clone did. Or they turned right when the other turned left. Or they were escorted by a different orderly. Or they waited longer in the birthing room for the same orderly to come back for them after escorting the first one. Etc.

The controls you imagine are physically impossible.
Well, you can still run the experiment if you know all the differences and account for them. Remove from your analysis all the causes and effects that mark the two as different and see if anything remains.

So, for instance, you might say, "Well, cellular degeneration is more advanced in this clone because it is slightly older." But then see if the pathway is identical when you time shift. In other words, look only at those things which were identical (are there any?) and see if they diverge with no outside causation.

I'd point out that this is, in fact, how we do repeatable experiments. We do not demand strictly identical, but only identical to some degree and in some important ways. The assumption is that relevant differences have been accounted for.

This is my new thought experiment. Have at it.

Last edited by marplots; 10th April 2011 at 08:20 PM.
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Old 10th April 2011, 08:23 PM   #24
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Originally Posted by Trent Wray View Post
Hmm .... well if they are indistinguishable even in principle, then how do you know there are two of them and not fifteen of them, for example?
You measured how many and got two. Whether you did it by shining some light at the system and observing it to scatter at two places or measured in some other way is not particularly important.

Originally Posted by Trent Wray View Post
What distinguishes one from the other? In other words .... when does the ability to claim "this is not that" become irrelevant ?
Before you measured them, nothing distinguishes them whatsoever.

After you measured them, they'll be in a state that does tell them apart. But this is a different state, and you'll be still unable to say that "this electron" is the same as "that one" in the state it was before.

Originally Posted by Trent Wray View Post
But I would ask the same question here I just asked above: is there a point where it's no longer possible to say "this is not that" when considering two particles ?
Yes. The above is an example: the state describes all the physical information, and yet because it's symmetric under interchange of the two particles (or anti-symmetric, for -), it does not distinguish the particles in any way. While the particles are in that state, there is not "this" or "that" particle. There's just two particles.
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Old 10th April 2011, 08:31 PM   #25
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Originally Posted by Trent Wray View Post
So they are not identical ... since you can distinguish between one verses two verses fifteen ..... right? That was my point in asking . In my eyes, I'm just pointing out the obvious, but perhaps I'm missing something
As an imperfect analogy, imagine I have two cups, cup x and cup y. In cup x we'll put a cup of milk; we'll call that "Tom's milk". In cup y we'll add a cup of milk, and let's call that "Tina's milk".

Now we pour both cups into a pitcher together, then pour the milk from the pitcher into two new cups--cup m and n.

Whose milk is in cup m? Whose is in cup n?

Though there's two cups in the pitcher, the identity of the original cups of milk get lost in there.

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Old 10th April 2011, 08:36 PM   #26
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Originally Posted by Vorpal View Post
You measured how many and got two. Whether you did it by shining some light at the system and observing it to scatter at two places or measured in some other way is not particularly important.


Before you measured them, nothing distinguishes them whatsoever.

After you measured them, they'll be in a state that does tell them apart. But this is a different state, and you'll be still unable to say that "this electron" is the same as "that one" in the state it was before.


Yes. The above is an example: the state describes all the physical information, and yet because it's symmetric under interchange of the two particles (or anti-symmetric, for -), it does not distinguish the particles in any way. While the particles are in that state, there is not "this" or "that" particle. There's just two particles.
Okay so before observation/measurement, they are indistinguishable. Where they physically are is essentially irrelevant.

Forgive me if this is way off .... but I'm picturing two photons in superposition before decoherence.
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Old 10th April 2011, 11:17 PM   #27
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If they are the same thing.
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Old 11th April 2011, 12:13 AM   #28
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Originally Posted by marplots View Post
Well, you can still run the experiment if you know all the differences and account for them. Remove from your analysis all the causes and effects that mark the two as different and see if anything remains.

So, for instance, you might say, "Well, cellular degeneration is more advanced in this clone because it is slightly older." But then see if the pathway is identical when you time shift. In other words, look only at those things which were identical (are there any?) and see if they diverge with no outside causation.

I'd point out that this is, in fact, how we do repeatable experiments. We do not demand strictly identical, but only identical to some degree and in some important ways. The assumption is that relevant differences have been accounted for.

This is my new thought experiment. Have at it.
But the point is whether the two person are *distinguishable* and *identical*. You cannot have every random event repeat itself with 100% perfection. It is enough that one spill a bit of sauce at one meal time and the other not, and poof you have a difference. It is enough that one develop appendicite, while the other not, because the infection did not go as far due to some random amount of leukocite being the right palce at the right moment.

The point is, because they are at different place and you CANNOT control every variable within their body or even outside, they *WILL* be diverging.

We do not have for most experiment too much difficulty for that, because the threshold for experiment is lower : it does not matter if the rest of the system diverge , if the stuff we are experimenting for is unaffected within a certain certitude factor. Heck, statistic even come in.

But in our experiment of copy above, diverge will be extremly rapid. After a few heart beat, all your hemathocyte and leukocyte will be at different place in both body. And with time it will increase. Cell which get repaired will not be at the same place, repaired in the same order. Connection in brain will not form the exact 100% same way. And then from here on the divergence will increase.

Why do you think twins are not identical ? Here you go.
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Old 11th April 2011, 12:18 AM   #29
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Originally Posted by marplots View Post
There's functional identity, as in "this atom does all the same stuff as that one" and then there is historical identity, "this atom is the same one I had last night."

Historicity is a property that adds a storyline. Now, what I find interesting is whether or not you could transfer this property, historicity, between things that are also functionally identical. There's a granularity problem at some level that makes me think of Heisenburg and his question about whose beer is it really?
Are you staring at my pint?
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Old 11th April 2011, 10:43 AM   #30
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Originally Posted by Aepervius View Post
But the point is whether the two person are *distinguishable* and *identical*. You cannot have every random event repeat itself with 100% perfection. It is enough that one spill a bit of sauce at one meal time and the other not, and poof you have a difference. It is enough that one develop appendicite, while the other not, because the infection did not go as far due to some random amount of leukocite being the right palce at the right moment.

The point is, because they are at different place and you CANNOT control every variable within their body or even outside, they *WILL* be diverging.

We do not have for most experiment too much difficulty for that, because the threshold for experiment is lower : it does not matter if the rest of the system diverge , if the stuff we are experimenting for is unaffected within a certain certitude factor. Heck, statistic even come in.

But in our experiment of copy above, diverge will be extremly rapid. After a few heart beat, all your hemathocyte and leukocyte will be at different place in both body. And with time it will increase. Cell which get repaired will not be at the same place, repaired in the same order. Connection in brain will not form the exact 100% same way. And then from here on the divergence will increase.

Why do you think twins are not identical ? Here you go.
Alright, that all sounds good. Except something has crept in that I'm wondering if you meant or didn't mean. Is identity strictly bound to some physical envelope or is it always connected to contextual background?

For instance, suppose we have two things that are, as far as we can tell, identical in composition. Let's take two very pure crystals of silicon. I'll suggest that some portion of those crystals matches up atom to atom (it doesn't have to be the whole crystal). Now, if one crystal is sitting here with me and another there with you, even if they are the same in the sense I outlined, are they still different because they are in different places?

To make it trickier, take a look at this equation: 3 + 5y = 33z. Is each of the 3's in that different or are they identical? Are the 3's on your screen the same as the 3's on mine? If they aren't, how is it that meaning is preserved? If they are, don't you owe me some 3's?
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Old 11th April 2011, 10:54 AM   #31
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Originally Posted by Aepervius View Post
But the point is whether the two person are *distinguishable* and *identical*. You cannot have every random event repeat itself with 100% perfection. It is enough that one spill a bit of sauce at one meal time and the other not, and poof you have a difference. It is enough that one develop appendicite, while the other not, because the infection did not go as far due to some random amount of leukocite being the right palce at the right moment.

The point is, because they are at different place and you CANNOT control every variable within their body or even outside, they *WILL* be diverging.

We do not have for most experiment too much difficulty for that, because the threshold for experiment is lower : it does not matter if the rest of the system diverge , if the stuff we are experimenting for is unaffected within a certain certitude factor. Heck, statistic even come in.

But in our experiment of copy above, diverge will be extremly rapid. After a few heart beat, all your hemathocyte and leukocyte will be at different place in both body. And with time it will increase. Cell which get repaired will not be at the same place, repaired in the same order. Connection in brain will not form the exact 100% same way. And then from here on the divergence will increase.

Why do you think twins are not identical ? Here you go.
Originally Posted by marplots View Post
Alright, that all sounds good. Except something has crept in that I'm wondering if you meant or didn't mean. Is identity strictly bound to some physical envelope or is it always connected to contextual background?

For instance, suppose we have two things that are, as far as we can tell, identical in composition. Let's take two very pure crystals of silicon. I'll suggest that some portion of those crystals matches up atom to atom (it doesn't have to be the whole crystal). Now, if one crystal is sitting here with me and another there with you, even if they are the same in the sense I outlined, are they still different because they are in different places?

To make it trickier, take a look at this equation: 3 + 5y = 33z. Is each of the 3's in that different or are they identical? Are the 3's on your screen the same as the 3's on mine? If they aren't, how is it that meaning is preserved? If they are, don't you owe me some 3's?
Here is what I'm summizing:

Two or more things can be identical, indistinguishable from each other ... as long as we don't examine them to see "where they are" and exactly what they are. And this takes into account a quantum state *crosses fingers*

And I think the math analogy falls flat because you have to ask "3 what".
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Old 11th April 2011, 11:11 AM   #32
marplots
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Originally Posted by Trent Wray View Post
Here is what I'm summizing:

Two or more things can be identical, indistinguishable from each other ... as long as we don't examine them to see "where they are" and exactly what they are. And this takes into account a quantum state *crosses fingers*

And I think the math analogy falls flat because you have to ask "3 what".
I like the math bit because it brings up concepts as identical rather than physical objects. That's an interesting can of worms there. To what degree is my mental concept of "2" the same or different.

But that aside, it seems that we are running into a kind of point of view thing. For instance, if you and I were to visit the Great Pyramid at Giza on subsequent days, the "identity" of the artifact would be different because our influences (gravity, breath and so on) were different. And the same could be said for a distant star viewed by two astronomers at the same time.

This is why I balk at "context matters" over inherent identity. The result is two different "things" that are the same thing. And it doesn't do any good to freeze the picture in some static way because our frames of reference could be different. In this extension, not only cannot two things (except maybe conceptual entities) be identical, but even the same thing cannot be identical with different observers. What a tasty bit of counter-intuitive maybe-nonsense that is!
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Old 11th April 2011, 08:15 PM   #33
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Can Two Things be Identical?

Probably but mostly, all so indicated God at prime level should be identical.
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Old 11th April 2011, 10:47 PM   #34
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Very interesting discussion...

If we say that things can only be identical if they occupy the same spatial coordinates....well OK - but if every sub atomic particle in my body has a non-zero probability of being somewhere else, then where exactly is my body?

Looking purely at the subatomic level, i guess this brings in interpretations of QM - what really exists? Is what "exists" the wavefunction? If that is true, then does anything really occupy a given set of co-ordinates?
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Old 11th April 2011, 11:53 PM   #35
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Originally Posted by andyandy View Post
Very interesting discussion...

If we say that things can only be identical if they occupy the same spatial coordinates....well OK - but if every sub atomic particle in my body has a non-zero probability of being somewhere else, then where exactly is my body?

Looking purely at the subatomic level, i guess this brings in interpretations of QM - what really exists? Is what "exists" the wavefunction? If that is true, then does anything really occupy a given set of co-ordinates?
That's more a problem with waves being distributed across space than things actually existing in two places at once. It exists but not in one place at once it is more diffuse than a point particle.
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Old 12th April 2011, 12:11 AM   #36
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Originally Posted by Calrid View Post
That's more a problem with waves being distributed across space than things actually existing in two places at once. It exists but not in one place at once it is more diffuse than a point particle.
I may be getting out of my depth here (but when's that ever stopped me before? ) but, isn't it possible for 2 particles to share the same wavefunction - and so wouldn't these 2 particles be identical from a positional perspective?
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Old 12th April 2011, 12:22 AM   #37
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Originally Posted by andyandy View Post
I may be getting out of my depth here (but when's that ever stopped me before? ) but, isn't it possible for 2 particles to share the same wavefunction - and so wouldn't these 2 particles be identical from a positional perspective?
Well since its impossible to measure the exact position of two particles then such an idea is moot anyway, all we can do is make a judgement about the probability of two particles being in the same place at once, but this is not a definitive statement of position. I believe though there are some pretty weird states of matter at approaching absolute zero where such a phenomena might happen, but it is still a hypothetical concern.
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Old 12th April 2011, 12:30 AM   #38
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Originally Posted by andyandy View Post
I may be getting out of my depth here (but when's that ever stopped me before? ) but, isn't it possible for 2 particles to share the same wavefunction - and so wouldn't these 2 particles be identical from a positional perspective?
If they're bosons, sure. One can even get the same kind of thing on a macroscopic scale with a Bose-Einstein condensateWP. For fermions, they can still have the same positional wavefunction, but the spins would have to be different, so they're very limited in that regard.
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Old 12th April 2011, 01:19 AM   #39
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Originally Posted by marplots View Post
Alright, that all sounds good. Except something has crept in that I'm wondering if you meant or didn't mean. Is identity strictly bound to some physical envelope or is it always connected to contextual background?

For instance, suppose we have two things that are, as far as we can tell, identical in composition. Let's take two very pure crystals of silicon. I'll suggest that some portion of those crystals matches up atom to atom (it doesn't have to be the whole crystal). Now, if one crystal is sitting here with me and another there with you, even if they are the same in the sense I outlined, are they still different because they are in different places?

To make it trickier, take a look at this equation: 3 + 5y = 33z. Is each of the 3's in that different or are they identical? Are the 3's on your screen the same as the 3's on mine? If they aren't, how is it that meaning is preserved? If they are, don't you owe me some 3's?
The point is to check whether two things are identical. They are not. The fact of the divergence make it clear that both artefact, or both cloned human are not identical. They are only interchangeable as long as no change occurs to them, but with human being that happens actually quite quickly.

I am not sure where you are going with your "3".
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Old 12th April 2011, 08:10 AM   #40
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Well, we seem to be here: Two things (humans) could, theoretically be created identical (I think we just took that as part of the givens). But soon/immediately, outside influences would cause them to diverge and they would no longer be identical. Makes sense on the face of it, but it bears some deeper thought.

For instance, I think we agree that not every single bit of a human would become "different" at the same time or rate. That means that you could find a portion that remained identical for some time. It makes identity something about where you draw your lines and makes identity a spectrum instead of a plain, lumpy, singular fact.

From there, you get all kinds of things going on. For instance, in two systems that are changing (demanded by the loss if "identical") you might suppose that at some point, purely by chance, they would again overlap (having, by chance, changed into the same thing).

I brought up non-humans and concepts to peek at other ways identity comes into play. I also think there may be forces at work that create stable equilibria so that even complex systems might be driven toward the same state.

The loss of identity (as in the QM mixed-states mentioned by others) is neat too and something we rely on in the macro world. For instance, when I deposit a $1000 (I wish) in the bank and then get $1000 back later, in-between the money has lost it's individuality and in some respects, I have the same money I had before. This is even more true with simple number symbols so that I depend on the "3" written here to be identical to the "3" you get on your screen.

Finally, how identical two things or situations are matters a great deal in the everyday world. It is essential when we want to predict the future knowing some similar example from the past, as in weather forecasting.

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