(Conjoined) Twinned Rainbows

The following is the next installment in a series of posts which began with the piece, Half Guilty.

Using computer simulations, a Google software engineer (Iman Sadeghi) and a professor of computer science at UCSD (Henrik Wann Jensen) have explained the rare phenomenon of twinned rainbows where the primary bow of a rainbow splits into two. The repercussions of their findings:

We ended up pushing the edge of rainbow science.

Via CNN.

Conjoined Twins as Legal Actors (III)

The following is the next installment in a series of posts which began with the piece, Half Guilty.

“Their brains are recording signals from the other twin’s visual field,” [Dr. Douglas Cochrane] cautiously concluded. “One might be seeing what the other one is seeing.”


A twin may be the instigator, but singling out one for punishment often doesn’t work. “When one gets in trouble and you try to discipline her, the other one kicks in and starts defending her sister,” says [their mother, Felicia] Simms. “I’ve just gotten to the point where if they don’t change their attitude when you talk to them the first time they both go into time out. How do you not?” she asks. “It’s just come down to?.?.?.?you can’t discipline one without disciplining the other. It’s just impossible.”

From Macleans.

Additional coverage at the NY Times.

Perceptual Delusional Bicephaly


Brad Pitt and Edward Norton, Fight Club

The following is the next installment in a series of posts which began with the piece, Half Guilty.

One afternoon in October 1980, a 39 year-old man entered the Royal Melbourne Hospital suffering from a self-inflicted gunshot wound to the head. Doctors were able to extract .22 caliber bullet fragments from the man’s left frontal lobe and evacuate a intracerebral blood cot, saving the man’s life. Over the next few days, the man’s condition improved and doctor’s were able to interview him. Doctor’s would later diagnose the man with schizophrenia. It was signficant that two years prior, the man’s wife died in a car accident in which he was the driver.

The man described having a second head on his shoulder that would antagonize him at night. He believed the head belonged to his wife’s gynecologist, who, he suspected, his wife was having an affair with prior to her death. He claimed the head belonging to the gynecologist was trying to take over his body by dominating his normal head. Additionally, he said that he could hear the voices of Jesus and Abraham conversing with each other. These voices were confirming that he did indeed have two heads, while the gynecologist’s head had been telling him that it was the “king pin” and that it was going to take his wife away from him.

After three weeks of nightly torment from his phantom head,  the man decided to do something about it. He first considered removing the second phantom head with an axe. But with the proximity of his own head to a swinging axe blade, he chose a different tact. The man fired six shots in total, the first at the phantom head. The man thought the first bullet nearly took the second head off, leaving it hanging by a thread. He fired the second bullet through the roof of his own mouth. He then fired four more shots, one of which appears to have gone through the roof of his mouth and three of which missed. He said that he felt good at that stage, and that he could not feel the other head any more. He then passed out.

During his interview with doctors the man explained his motivations for his unorthodox behavior:

“The other head kept trying to dominate my normal head, and I would not let it. It kept trying to say to me I would lose, and I said bull-shit. ‘I am the king pin here,’ it said and it kept going on like that for about three weeks and finally I got jack of it, and I decided to shoot my other head off.”

Years later, the man was admitted to the hospital again, suffering from seizures as a result of alcohol abuse. Doctors interviewed him about his previous psychological delusions:
Q. Could you see the other head?
A. Yes.
Q. You felt it, or you could see it?
A. I could see it.
Q. And the voices were coming from the other head?
A. From that head and my own head too.
Q. Whose voice was it?
A. It was the voice of my wife’s doctor.
Q. What was he saying to you?
A. He had an affair with my wife and he reckoned he was going to take her off me and all that kind of talk and I got antagonistic towards him and I decided to do something about it and I shot myself.
Q. Since that episode have you had anything like that?
A. Not really. I have not heard any voices for about two years, ever since I shot myself and I haven’t had any ideas that I have two heads again. When I shot myself it fixed it up.

Via David Ames, Self Shooting of a Phantom Head, British Journal of Psychiatry 145:193-194 (1984).

Mucking up Causation with Identical Twins

Orlando Nembhard was charged with the February 12th shooting death of Sir Xavier Brooks, 19, outside a Phoenix nightclub called Leonardo’s Da Vincci Code. There were eyewitnesses claiming to have seen Orlando pull the gun and they had a description of the shooter which matched Orlando. Then the prosecution’s case went to hell when it was revealed that Orlando Nembhard has an identical twin brother, Brandon Nembhard, who was also at the nightclub the night of the shooting. Now with conflicting stories and suspicious behavior from Brandon, prosecutors are questioning whether they’ve charged the right man.

Barbara Jones, the victim’s grandmother, recently said in an interview, “They need to put them in a room and let them battle it out,” calling to light a pariah in evidence law — probabilistic evidence. Courts have never been comfortable with using statistics to convict defendants, permitting its use only in some employment law cases and tort cases. But with the stakes so high in a criminal murder case, the burden of proof of “beyond a reasonable doubt” cannot be quantified.

When studying the law of torts, students learn the case of Summers v. Tice: two hunters simultaneously shoot and injure a third hunter, though only one bullet causes the man’s injury. Because the guns are identical it is impossible to tell which gun fired the  round. Common law holds that the hunters will be held jointly and severally liable, each of them responsible for the entire amount of the man’s injuries. The idea is that the burden shifts to the negligent parties to prove that they were not the cause of the injury. The problem with the application of this case is 1) this is tort law (civil, not criminal) and 2) there was only one shooter. In the case in Phoenix, only one of the brothers allegedly shot the victim.

Judge Richard Posner has long been a proponent of the use of statistics in legal fact finding. In Posner’s Economic Analysis of Law (2007) he writes:

In the typical civil trial, there is no basis for supposing that Type I errors (false positives, such as convicting an innocent person, or in the civil context, erroneously finding the defendant liable) on average impose higher costs than Type II errors (false negatives, such as an erroneous acquittal or the denial of a meritorious claim). So it is enough in the usual civil case to justify a verdict for the plaintiff that the probability that his claim is meritorious exceeds, however slightly, the probability that it is not.

Why should a tie go to the defendant rather than to the plaintiff? The principle of diminishing marginal utility of income implies that the loss to the deserving plaintiff who loses is probably slightly smaller on average than the loss to the deserving defendant who loses…. In addition an erroneous judgment for the plaintiff imposes a cost that is avoided when the error goes the other way – the cost of collecting the judgment….

Type I errors in criminal cases involve additional cost because the cost of imprisonment is high, that costs is of course avoided when a guilty person is acquitted, though such an acquittal will reduce deterrence by reducing the probability of punishment for the crime. But the asymmetric effect of the cost of imprisonment on convictions and acquittals means that it probably takes several erroneous acquittals to impose a social cost equal to that of an erroneous conviction. This is one economic rationale for requiring proof beyond a reasonable doubt in a criminal as distinct from a civil case and another is the inherent advantage that the prosecution enjoys in a criminal case, compared to a private civil plaintiff…. In an inquisitorial system, where the search is conducted by a presumably disinterested judge, the need for a heavier burden of proof in a criminal than in a civil system is attenuated.

But an economic approach to causation has never been popular as few juries can sit comfortably with the idea that they have knowingly convicted an innocent person for the sake of easing the burden of proof. Because statistical probabilities will inevitably scoop up innocent people, their use in the criminal context is utterly impermissible. Perhaps it’s Posner’s economic theory of law that have kept him off the Supreme Court (or maybe it was that article characterized as Posner’s argument for selling children; why not verify that claim yourself here).

Via the NY Times (thanks Matt!).