“The patient's skull was struck by a baseball bat. He has a perfectly legitimate reason for subarachnoid hemorrhage. He already had a CT [computed tomogram] of the head showing the bleed in good detail. Why another?” I remonstrated with Watson, the neurosurgeon.

“But you don't know that there is no intracranial aneurysm. You can't rule that out. He needs a CT angiogram of the brain immediately,” protested Watson.

Hit by a hard object (cause) and blood in brain (effect) is deductive reasoning at its simplest. But Watson was correct: I could not rule out cerebral artery aneurysm without a CT angiogram. I could not, for that matter, rule out bleeding brain metastases from lung cancer. Perhaps the patient needed a CT of the chest, I suggested facetiously.

The diagnostic permutations in medicine are innumerable, and what prevents doctors from descending into parody is the application of conditional probability: Bayes' theorem. Without clinical context we stare into the abyss.

The likelihood that someone with cerebral aneurysm hit by a bat develops subarachnoid hemorrhage (near certainty) is not the same as the likelihood that someone who develops subarachnoid hemorrhage after high impact trauma has an aneurysm, hitherto undisclosed …