The lawyers want to stop the execution, arguing that if something goes wrong, he might ....asphyxiate.
So what happens if it goes right?
Painless drift into sleep, followed by asphyxiation, probably. I'm sure you understand why some people think it's important to stop an execution if the method could leave the subject conscious while they die. I bet you even agree that would mean the execution went wrong.
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Really, all these methods have the same problem to solve: Ensure that the subject isn't conscious while dying.
Some methods attempt to solve the problem by ensuring instantaneous death. Mechanical separation of the head from the neck at high speed, for example. We're easily able to build machinery that completes the action far faster than the human brain can follow. So it seems like this would be a good one. But... nobody can agree on exactly when death occurs, and how instantaneous it really is. Does the brain continue to function for a moment or two after separation? Is that enough time for them to register that they're dying? Is that experience, or the fear of that experience enough to qualify the method as "cruel"?
So let's table mechanical separation at high speed, for now. That includes hanging, which is a primitive mechanism, relying on gravity and body weight to accomplish the snapping of the neck. That's not especially fast, and requires extra effort to get right. And even getting it right, there's the drop, and the question of brain function after separation.
Other methods attempt to solve the problem by rendering the subject unconscious before the dying process begins. The main issue here is that not everyone responds the same to anesthesia. Pre-made doses may fail to perform in some cases. Sometimes it's a series of chemicals. First the knock-out drug, then the poison. You have to make sure the knock-out drug worked. There's also cases where the subject has regained consciousness during the process.
So. If the requirement is an ironclad guarantee that the subject will not consciously experience their own dying, then no proposed method is fit for purpose.
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And that's another answer to Darat's question, "why not hanging?" Because it's a clumsy, primitive method of mechanical separation. It doesn't guarantee that the subject won't experience their dying moments.
If we really are committed to the idea that (a) the death penalty is necessary, and (b) mechanical separation of the head is the method will satisfy our main requirement to an acceptable degree of reliability...
... Then we wouldn't choose hanging. We'd choose something faster and with less room for error. A high-pressure-driven guillotine, probably.
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There's also sudden catastrophic damage to the brain. A bullet to the head, for example. But you'd want it to be a big bullet, to make sure it got enough of the brain to guarantee failure to experience death. Might as well go with a mechanical elephant's foot, at that point.
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There are other problems, too. These are gruesome acts. Is it humane to charge someone with carrying them out, or overseeing them? Do we want to make a welcome place in our society for the kind of person that enjoys doing such things?
Some large amounts of grue aside, rapid and catastrophic destruction of the body seems promising. An explosive collar around the neck, for example. But I'm pretty sure such dismemberment or destruction of the body is anathema to some religions. Apart from religion, if the subject has a horror of such things, is it unacceptably cruel to cause them to anticipate that?
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It's easy to say that people who have committed heinous crimes, without remorse or any care for humanity, do not deserve such humane considerations as a guaranteed "clean" death, or a death compatible with their religious beliefs. But once we concede that some people deserve death, but do not deserve additional torment or disrespect, we are burdened with creating a method of execution that meets that standard.
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One elephant I run into, whenever I enter this particular room, is a general refusal to accept a less-than-perfect solution. Even the best system will occasionally convict innocent people. It is my belief that if due process is followed, then it is not a miscarriage of justice to convict an innocent person. Or rather, it is not more of a miscarraige than not prosecuting the accused, for fear of getting it wrong.
So I think that less-than-perfect methods of execution should be on the table for consideration. If we're 99.9% certain that rapid separation of the head prevents death-experience, then we should do that. If chemical sleep unto death is shown to work reliably on 99.9% of subjects, then we should do that. The debate should be about how many nines we want, and how we're going to measure them, rather than a binary "guaranteed perfect or nothing" demand.
If you're going to demand guaranteed perfect or nothing, why even have prisons?