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Captain's Conundrum


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19 replies to this topic

#1 mmiguel

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Posted 21 September 2012 - 05:52 AM

A captain hires a crew for his ship, "The Flying Scotsman" and sets out to sail for a voyage to last many years across the seven seas.
As the years pass, The Flying Scotsman succumbs to wear and tear:
In the Atlantic ocean, the ship's mast is blown away by a storm, and it is replaced in the Caribbean.
In the Pacific ocean, the ship runs aground and the hull is severely damaged. Fortunately, they are able to hire natives to aid in the repairs.
...etc

After 8 long years, the captain looks at his beloved "Scotsman", and thinks fondly of how it has served him, he has a realization: over the course of this grand adventure, every piece of The Flying Scotsman has been replaced due to wear and tear.

The captain begins to feel uncomfortable.... if I'm standing on different wood.... aren't I standing on a different ship?

Question:
Is it the same ship?
Spoiler for If so

Spoiler for If not


The captain fainted from philosophical exhaustion.

Edited by mmiguel, 21 September 2012 - 05:54 AM.

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#2 Yoruichi-san

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Posted 21 September 2012 - 07:24 AM

Can two objects ever truly be the same?



Pauli would say so ;P.
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#3 mmiguel

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Posted 21 September 2012 - 07:26 AM

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Pauli would say so ;P.


If they are completely the same, how are we even able to recognize them as being 2 objects instead of 1?
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#4 Yoruichi-san

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Posted 21 September 2012 - 08:50 AM

If they are completely the same, how are we even able to recognize them as being 2 objects instead of 1?


http://en.wikipedia....usion_principle

In layman's terms, like two equally attractive women, they try to avoid each other ;P.

Edited by Yoruichi-san, 21 September 2012 - 08:51 AM.

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#5 mmiguel

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Posted 21 September 2012 - 08:56 AM

http://en.wikipedia....usion_principle

In layman's terms, like two equally attractive women, they try to avoid each other ;P.


I knew what you were talking about.
From the article, it is easy to see how two fermions might be different -> they must have different quantum state according to exclusion principle.
So.... they aren't the same... and no two fermions can ever truly be the same - proof thanks to Wolfgang P.

I would have had to work a little harder if you tried bosons.

Edited by mmiguel, 21 September 2012 - 08:57 AM.

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#6 Yoruichi-san

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Posted 21 September 2012 - 09:53 AM

I chose fermions exactly because the exclusion principle gives a logical conclusion to the argument :P.

They are the same in all ways except that they do not occupy the same quantum state. And they cannot occupy the same quantum state exactly because they are identical in every other way.

So if you say that they must occupy the same quantum state to be identical, you are admitting identical bosons that occupy the same quantum state are the same, since the principle defines everything else as the same. That is the answer ;).

Edited by Yoruichi-san, 21 September 2012 - 10:02 AM.

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#7 mmiguel

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Posted 21 September 2012 - 10:25 AM

I chose fermions exactly because the exclusion principle gives a logical conclusion to the argument :P.

They are the same in all ways except that they do not occupy the same quantum state. And they cannot occupy the same quantum state exactly because they are identical in every other way.

So if you say that they must occupy the same quantum state to be identical, you are admitting identical bosons that occupy the same quantum state are the same, since the principle defines everything else as the same. That is the answer ;).


They do need to occupy the same quantum state to be identical. This does not mean that bosons are identical.
True sameness means that every characteristic is the same, quantum state is but one characteristic.
There are characteristics that differ between two bosons that make them two bosons and not one boson.

A photon leaving my computer screen has at least one characteristic that differs from a photon leaving your computer screen.
Those are two bosons that are different.

Wikipedia may say that there are no differences:
http://en.wikipedia....tical_particles

but what they are really saying, (implicitly, and perhaps without realizing it), is that none of characteristics that they care about are different. They are not actually implying that no characteristics are different.
This implicit catch is behind every thought of sameness that anyone ever thinks.

A neat thing to notice, is that this requires a specification of what characteristics are important enough to consider, and what to ignore.
Importance itself, requires a subjective perspective.

Hence
Sameness doesn't exist, in the truest sense (in the objective reality, outside of our subjective noggins).

But wait.....
Explain why the concept is so prevalent then

Edited by mmiguel, 21 September 2012 - 10:34 AM.

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#8 Yoruichi-san

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Posted 21 September 2012 - 11:25 AM

I don't think there is an official, definitive, universal definition of "sameness". Some would define it as congruency, others indistinguishability, etc. By logical and scientific standards, my above assertions should hold. Bosons aren't like billard balls, it's not like one will have a unseeable to the eye dent in it or tiny hole in the center or something. They are fundamentally physically identical, the only difference is that they have a different history, i.e. they've been at different places at different times.

So it seems to me you're defining "sameness" in such a way that by definition no two things can be "the same", as they'd basically have to occupy the exact same space at the exact same times, thus making it actually one object. I guess if you subscribe to the branching universes theory then this might be interesting, but otherwise I don't see the utility of this definition and I don't agree with it. *shrugs*
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 3 is finally here!

When life hands me lemons, I make invisible ink.


#9 mmiguel

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Posted 21 September 2012 - 11:48 AM

I don't think there is an official, definitive, universal definition of "sameness". Some would define it as congruency, others indistinguishability, etc. By logical and scientific standards, my above assertions should hold. Bosons aren't like billard balls, it's not like one will have a unseeable to the eye dent in it or tiny hole in the center or something. They are fundamentally physically identical, the only difference is that they have a different history, i.e. they've been at different places at different times.

So it seems to me you're defining "sameness" in such a way that by definition no two things can be "the same", as they'd basically have to occupy the exact same space at the exact same times, thus making it actually one object. I guess if you subscribe to the branching universes theory then this might be interesting, but otherwise I don't see the utility of this definition and I don't agree with it. *shrugs*


Agree that this definition makes sameness pretty much useless, but sameness is an idealization.
There are many useful concepts that are useless in the ideal case.
When you stop caring about characteristics, and ignoring them, that is when sameness becomes a useful concept.

This process, the removal of characteristics, we can recognize as abstraction, or in another word, generalization.
Pick a word out of the dictionary - horse for example.
What does the definition say?
Any definition is essentially a list of characteristics.
No definition lists every characteristic of any real object, since we wouldn't be able to process that much information.

In order to get a more manageable amount of information, we selectively discard information in the form of unimportant characteristics.
Almost always, the first thing to go is spatio-temporal position.
I don't care where the horse is, and it doesn't matter where it is, I only care that it "is an odd-toed ungulatemammal belonging to the taxonomic family Equidae." (wiki was good enough for me: http://en.wikipedia.org/wiki/Horse).
Likewise, I don't care what color it is. I don't care how tall it is, I don't care how heavy it is, etc.

Why am I talking about this ---- because I feel that it provides insight into how we process information.
We are allowed to use "sameness" by willingly playing ignorant and removing information from what we observe.
This is also what allows us to group things together e.g. we can say two horses instead of one fundamentally unique entity and another "dissimilar" fundamentally unique entity.
Without this, numbers would not make sense (if we treated everything uniquely, how could we ever count higher than one? - numbers only make sense when applied to things considered the same)
It allows us to identify the ship from the OP as the same ship regardless of what it's made of (if we happened to remove such characteristics from our definition of the ship), but it doesn't contradict saying it's a different ship either.

With all this great stuff that generalization/abstraction does for us, it still seems like removing information is a form of lying to ourselves though, doesn't it? As if all of the concepts and definitions we have constructed to give meaning to our world are illusions, that we artificially make due to some evolutionary programming --- recognize a predator as an object, run away and hide, recognize food, eat it...

But this ignorance (removal of information -unimportant characteristics) also serves great uses, as I mentioned above.
Generally it feels like a bad thing to be ignorant, and even worse to want to be ignorant. This paradoxical idea is what has me so interested.

I was hoping someone else might come to a similar conclusion from my OP, but maybe not.....

oh well

Edited by mmiguel, 21 September 2012 - 11:51 AM.

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#10 CaptainEd

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Posted 21 September 2012 - 05:56 PM

A more compact form of this issue appeared in an ancient Moon Mullins cartoon, someone asks Lord Plushbottom how he keeps his bowler hat looking so beautiful year in, year out. He said, "I polish it daily, I take great care not to get it dirty, and I exchange it frequently at restaurants."
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