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There are many stories about twins being able to "feel" each other even when they are apart. Typically a twin would say that they felt that an accident or some other calamity happened to the other one even though they were in different cities etc. Has this been researched?

Vitaly Mijiritsky
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No, twins do not have any special magical powers, despite a number of studies investigating the claim.

A lightweight study was done in 1993 to examine if identical twins tended to have similarities in thinking, independent of any Extrasensory Perception (ESP).

The actual study that was performed is largely irrelevant here. What is interesting is the literature search in the Introduction:

Research on ESP in twins has been limited and sporadic.

It goes on to examine a fair number of studies that have been performed, and concludes:

Generally there seems to be little evidence of either a special ESP relationship between twins or a closer one between identical twins. Watson (1981) concludes that there is no evidence to support the idea of any parapsychological phenomena involved in the twin bond, and Palmer (1978), after reviewing the literature, concludes "There is no evidence that twins have any special aptitude for `telepathic' exchange

Oddthinking
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    Just to be clear what I have done here: There is no good evidence for twins having ESP. If they did, it would be a huge sensation, and have a huge impact of physics, neuroscience and psychology. However, it isn't sufficient on Skeptics.SE to simply assert that without references, so I have found someone who has done a proper literature search and cited them as saying there is no evidence to be found. – Oddthinking Oct 15 '12 at 09:59
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    but the ministry of suppression of magic among muggles may have magically influenced the results of that test! – Chad Oct 15 '12 at 16:24
  • Saying: "The research is limited and that limited research failed to demonstrate an effect", is different than saying "there's robust research showing that there no effect". In addition due to ethical issues most lap experiements are unlikely to put the participants in serious trouble like accidents. It therefore not clear that they would successfully detect an effect that only occurs when the twins are in trouble. – Christian Oct 15 '12 at 19:38
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    @Christian: (1) I included the "limited and sporadic" quote out of a sense of fairness, even though I didn't agree. The introduction did list many previous studies. – Oddthinking Oct 15 '12 at 23:01
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    (2) Yes, there is a general problem analogous to "the God of the gaps". As we eliminate possibilities, the conjectures get wilder to explain why the experiment didn't work. Even if we maimed and killed a large sample with no effect, that would still happen. "It doesn't work when disbelievers are watching." At some point, we have to say "When we have repeatedly tried to reproduce it in different ways, it has failed. Our current understanding of physics, genetics, anatomy, evolution and statistics preclude it. Let's go research malaria instead." – Oddthinking Oct 15 '12 at 23:03
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    Two words: Confirmation Bias. Case solved. :) – JasonR Oct 16 '12 at 15:33
  • @Oddthinking : (2) So you are saying that there no study that directly investigates whether the claim the question is about is true? If that's your position you should mention it in your answer. – Christian Oct 19 '12 at 11:14
  • @Oddthinking: (3) "At some point, we have to say "When we have repeatedly tried to reproduce it in different ways, it has failed. Our current understanding of physics, genetics, anatomy, evolution and statistics preclude it. Let's go research malaria instead." That bias is called motivated cognition. The fact that you aren't willing to expand resources to investigate a claim doesn't mean that you have conclusive evidence that the claim is wrong. Human are overconfident. They avoid saying "I don't know.". They always want to be able to say "Yes" or "No". – Christian Oct 19 '12 at 11:19
  • @Christian: (2) The question asks about the general case ("feeling each other"), then gives a typical, specific example ("accident or danger"). The answer addresses the general case. – Oddthinking Oct 19 '12 at 11:51
  • (3) We are getting into the philosophical nature of knowledge. Yes, I concede I should only say "There is absolutely no evidence of this, despite a number of studies", in the same way I should only say "The Sun will rise tomorrow, probably, but historical evidence is no certain proof that the inferences of our models of a physical laws will continue to be so successful tomorrow." At some point, enough evidence has been collected, and one's models have been sufficiently tested to provisionally accept something as true or false. I argue it is well past that time for this case. – Oddthinking Oct 19 '12 at 11:54
  • Also, I cannot see how the motivated cognition bias applies here; from what I have read it is inapplicable. I would love for telepathy to work. I would love to live during a period where physical laws were overturned (especially for the new products that would come from it!). Please explain further how it might apply here, and help me see past it. – Oddthinking Oct 19 '12 at 11:58
  • @Oddthinking: Whether or not it's effective to spend further resources on investigating psi pheomena should have zero effect on your P(psi pheomena exist). | " I would love to live during a period where physical laws were overturned (especially for the new products that would come from it!)." There's a blind spot. You don't consider the possibility that psi pheomena exist but are to loose to be practically useable. You think: Either "psi pheoma exist and then those guys should be able to do useful stuff" or "psi pheomena" don't exist. For a lot of modern physics that's also not true. – Christian Oct 19 '12 at 14:56
  • @Christian: Yes, P(psi exists) doesn't depend on future resources. Future resources ought to depend on P(psi exists). P(psi exists) depends on past experiments (see answer), and has already approached very close to zero - close enough to be very confident in saying it doesn't exist. If it existed, its ability to be harnessed would be important, but even its existence would be awesome. The Nobel Institute would need to triple production on prizes while the science books were being rewritten. – Oddthinking Oct 19 '12 at 23:02
  • @Oddthinking: I don't see how your personal P(Psi exists) should have a significant impact on the funding of experiments that investigate whether psi exists. Are you making an argument by authority? Important people which make funding decisions have a low P(psi exists) and therefore everyone should copy their P(psi exists)? I think that's begging the question. – Christian Oct 20 '12 at 13:08
  • @Christian: Of course, I never said that. If you don't want to draw a line under this conversation, time to take it to chat. – Oddthinking Oct 20 '12 at 22:39