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IamMe
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« on: March 07, 2008, 03:50:39 PM » |
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There are five equally sized discs, two identical red discs and one each of blue, green and white. In how many ways can these discs be stacked if the two red discs must be together on the top or on the bottom? This was a rather poorly worded question that appeared on the Irish Maths Leaving Cert. a few years ago. It caused an argument (essentially between me and my maths teacher) in our class that reminded me very much of a philosophical debate we had here a while ago about Star Trek and identity and zombies (Callum will remember). The answer I got was: 2*2*3! My reasoning: 2 ways to arrange the two red discs * 2 for top and bottom * 3 factorial for the other 3 discs. However, he disagreed with the first two. The two discs were identical, he said, hence order did not matter. So the answer was 2*3! The argument was about identity: I argued that there are two ways to stack two objects, even if they happen to look the same. Similarly, I would say that with a Star Trek transporter, what you have is two separate individuals. Spock et al do not teleport, they are killed and a copy of them is created elsewhere. (If you are lost it is because I'm talking about an old thread that most people weren't involved in.) |
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\\\\"Anarchism is the ideal to which all societies should approximate\\\\" - Bertrand Russell
If you strike me down I shall become more dead than you can ever imagine.
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Maxmillian
Full Member
Karma: +6/-5
Posts: 125
Voluminious words don't make one perspicacious.
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« Reply #1 on: March 07, 2008, 07:52:39 PM » |
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Well, for a start, you're correct, obviously.
Secondly, I've always wondered about that Star Trek thing - didn't they realize they were walking to their deaths? It's not like it's all "oh, you'll be fine, a slight tingle is all, that's just the atomization. But you'll be fine, because there'll be a replica of you on the other end!"
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Callum
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« Reply #2 on: March 08, 2008, 01:35:33 AM » |
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There are five equally sized discs, two identical red discs and one each of blue, green and white. In how many ways can these discs be stacked if the two red discs must be together on the top or on the bottom? This was a rather poorly worded question that appeared on the Irish Maths Leaving Cert. a few years ago. It caused an argument (essentially between me and my maths teacher) in our class that reminded me very much of a philosophical debate we had here a while ago about Star Trek and identity and zombies (Callum will remember). The answer I got was: 2*2*3! My reasoning: 2 ways to arrange the two red discs * 2 for top and bottom * 3 factorial for the other 3 discs. However, he disagreed with the first two. The two discs were identical, he said, hence order did not matter. So the answer was 2*3! The argument was about identity: I argued that there are two ways to stack two objects, even if they happen to look the same. Similarly, I would say that with a Star Trek transporter, what you have is two separate individuals. Spock et al do not teleport, they are killed and a copy of them is created elsewhere. (If you are lost it is because I'm talking about an old thread that most people weren't involved in.) You were (of course?) correct. The disagreement comes from an equivocal use of 'identical' and I am suprised that a mathematician din't see it. The two red discs are not 'mathematically' identical. They are similar: they have identical properties IN MOST RESPECTS, but not all their properties are identical - notably their location in timespace. By contrast, the planet Hesperus is identical to the planet Phosphorus (and both are identical to Venus). One plus one is identical to two. Personal identity is another matter. Mathematically speaking the person who began writing this sentence is not the same as the person who typed this full stop -> . I am spatially displaced from that entity, the compostion of part of my blood is different, some skin cells have decayed and fallen off, etc. Identity-through-time is quite a challenge to define. Locke came up with psychological continuity. That seems to cover the Star Trek disjunction IF (BIG if) you can accept the break in spatial continuity..... I imagine our theist friends would be divided on that as the philosophical community. Max seems to be having it both ays by using 'replica'. |
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IamMe
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« Reply #3 on: March 08, 2008, 01:54:05 PM » |
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There are five equally sized discs, two identical red discs and one each of blue, green and white. In how many ways can these discs be stacked if the two red discs must be together on the top or on the bottom? This was a rather poorly worded question that appeared on the Irish Maths Leaving Cert. a few years ago. It caused an argument (essentially between me and my maths teacher) in our class that reminded me very much of a philosophical debate we had here a while ago about Star Trek and identity and zombies (Callum will remember). The answer I got was: 2*2*3! My reasoning: 2 ways to arrange the two red discs * 2 for top and bottom * 3 factorial for the other 3 discs. However, he disagreed with the first two. The two discs were identical, he said, hence order did not matter. So the answer was 2*3! The argument was about identity: I argued that there are two ways to stack two objects, even if they happen to look the same. Similarly, I would say that with a Star Trek transporter, what you have is two separate individuals. Spock et al do not teleport, they are killed and a copy of them is created elsewhere. (If you are lost it is because I'm talking about an old thread that most people weren't involved in.) You were (of course?) correct. The disagreement comes from an equivocal use of 'identical' and I am suprised that a mathematician din't see it. The two red discs are not 'mathematically' identical. They are similar: they have identical properties IN MOST RESPECTS, but not all their properties are identical - notably their location in timespace. By contrast, the planet Hesperus is identical to the planet Phosphorus (and both are identical to Venus). One plus one is identical to two. Personal identity is another matter. Mathematically speaking the person who began writing this sentence is not the same as the person who typed this full stop -> . I am spatially displaced from that entity, the compostion of part of my blood is different, some skin cells have decayed and fallen off, etc. Identity-through-time is quite a challenge to define. Locke came up with psychological continuity. That seems to cover the Star Trek disjunction IF (BIG if) you can accept the break in spatial continuity..... I imagine our theist friends would be divided on that as the philosophical community. Max seems to be having it both ays by using 'replica'. Yeah, but that is where we differed last time (I think). Why would there be psychological continuity? I mean, obviously we could postulate it as part of the apparatus and leave it at that, but if we say it works by copying each and every quark and lepton exactly to the new location (i.e. assembling so they are the same) does one consciousness not end and another begin? |
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\\\\"Anarchism is the ideal to which all societies should approximate\\\\" - Bertrand Russell
If you strike me down I shall become more dead than you can ever imagine.
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Patton
Global Moderator
Hero Member
Karma: +105/-139
Posts: 1,807
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« Reply #4 on: March 08, 2008, 03:09:21 PM » |
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It would be like waving a magnet over a hard drive.
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Battle is the most magnificent competition in which a human being can indulge. It brings out all that is best; it removes all that is base. All men are afraid in battle. The coward is the one who lets his fear overcome his sense of duty. Duty is the essence of manhood
-George S. Patton
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Maxmillian
Full Member
Karma: +6/-5
Posts: 125
Voluminious words don't make one perspicacious.
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« Reply #5 on: March 08, 2008, 10:49:31 PM » |
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There are five equally sized discs, two identical red discs and one each of blue, green and white. In how many ways can these discs be stacked if the two red discs must be together on the top or on the bottom? This was a rather poorly worded question that appeared on the Irish Maths Leaving Cert. a few years ago. It caused an argument (essentially between me and my maths teacher) in our class that reminded me very much of a philosophical debate we had here a while ago about Star Trek and identity and zombies (Callum will remember). The answer I got was: 2*2*3! My reasoning: 2 ways to arrange the two red discs * 2 for top and bottom * 3 factorial for the other 3 discs. However, he disagreed with the first two. The two discs were identical, he said, hence order did not matter. So the answer was 2*3! The argument was about identity: I argued that there are two ways to stack two objects, even if they happen to look the same. Similarly, I would say that with a Star Trek transporter, what you have is two separate individuals. Spock et al do not teleport, they are killed and a copy of them is created elsewhere. (If you are lost it is because I'm talking about an old thread that most people weren't involved in.) You were (of course?) correct. The disagreement comes from an equivocal use of 'identical' and I am suprised that a mathematician din't see it. The two red discs are not 'mathematically' identical. They are similar: they have identical properties IN MOST RESPECTS, but not all their properties are identical - notably their location in timespace. By contrast, the planet Hesperus is identical to the planet Phosphorus (and both are identical to Venus). One plus one is identical to two. Personal identity is another matter. Mathematically speaking the person who began writing this sentence is not the same as the person who typed this full stop -> . I am spatially displaced from that entity, the compostion of part of my blood is different, some skin cells have decayed and fallen off, etc. Identity-through-time is quite a challenge to define. Locke came up with psychological continuity. That seems to cover the Star Trek disjunction IF (BIG if) you can accept the break in spatial continuity..... I imagine our theist friends would be divided on that as the philosophical community. Max seems to be having it both ays by using 'replica'. I'm simply remarking upon the absurdity of the whole Star Trek teleport thing - you don't actually teleport, you die, game over, insert coin. It's a completely different being that walks out the other end, albeit one with all your memories and genes and cool blue shirt. |
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Callum
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« Reply #6 on: March 08, 2008, 11:54:46 PM » |
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I'm simply remarking upon the absurdity of the whole Star Trek teleport thing - you don't actually teleport, you die, game over, insert coin. It's a completely different being that walks out the other end, albeit one with all your memories and genes and cool blue shirt.
Why would there be psychological continuity? I mean, obviously we could postulate it as part of the apparatus and leave it at that, but if we say it works by copying each and every quark and lepton exactly to the new location (i.e. assembling so they are the same) does one consciousness not end and another begin? The problem sems to me that our intuitions tell us that the new Kirk is 'the same' as the old. And I guess this is because we SEE a continuity not just of form but of mind. The process may have been relocated, but it is still the process..... Of course Max is right 'mathematically': new Kirk ¬= old Kirk. He is a replica. But is he the same or a different person? (And then we get variations on the thought experiment - to new Kirks for one old, Kirk instantiated in a bottle of ketchup, etc. But the first of these is easier to accept than the second, I guess....) Anyhow, as I said, defining identity over time is not easy! |
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IamMe
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« Reply #7 on: March 10, 2008, 01:52:05 PM » |
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I'm simply remarking upon the absurdity of the whole Star Trek teleport thing - you don't actually teleport, you die, game over, insert coin. It's a completely different being that walks out the other end, albeit one with all your memories and genes and cool blue shirt.
Why would there be psychological continuity? I mean, obviously we could postulate it as part of the apparatus and leave it at that, but if we say it works by copying each and every quark and lepton exactly to the new location (i.e. assembling so they are the same) does one consciousness not end and another begin? The problem sems to me that our intuitions tell us that the new Kirk is 'the same' as the old. And I guess this is because we SEE a continuity not just of form but of mind. The process may have been relocated, but it is still the process..... Of course Max is right 'mathematically': new Kirk ¬= old Kirk. He is a replica. But is he the same or a different person? (And then we get variations on the thought experiment - to new Kirks for one old, Kirk instantiated in a bottle of ketchup, etc. But the first of these is easier to accept than the second, I guess....) Anyhow, as I said, defining identity over time is not easy! My intuition doesn't tell me this, it tells me the opposite. |
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\\\\"Anarchism is the ideal to which all societies should approximate\\\\" - Bertrand Russell
If you strike me down I shall become more dead than you can ever imagine.
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Callum
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« Reply #8 on: March 11, 2008, 01:20:29 AM » |
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My intuition doesn't tell me this, it tells me the opposite.
Which is rather a good example then of how unreliable it is to build arguments on intuitions! Either of us/any of us. |
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