It’s finals week around here. Over the last two days I have graded just over a thousand calculus problems (many of them, let’s face it, not worked out properly). So let’s unwind with lighter fare tonight.

There are plenty of books and websites explaining the basics of scientific thinking. Riveting reading, certainly, but as a simple illustration of what’s involved I’ve always liked the following piece of dialogue. It comes from Agatha Christie’s novel Murder on the Links. This was the second Hercule Poirot novel (the first being The Mysterious Affair at Styles).

It will help to know that “Giraud” refers to a rival detective investigating the same crime as Poirot. That crime is the murder of a man named Renauld.

Poirot has just returned from a short trip during which he investigated some details relevant to the case. There have been some developments since he left, and his friend Hastings is keen to let him know about them. Poirot speaks first.

Mon cher ami, I have succeeded–but succeeded to a marvel!”

“Indeed? I’m delighted to hear it. Have you heard the latest here?”

“How would you that I should hear anything? There have been some developments, eh? The brave Giraud, he has made an arrest? Or even arrests perhaps? Ah, but I will make him look foolish, that one! But where are you taking me, my friend? Do we not go to the hotel? It is necessary that I attend to my mustaches–they are deplorably limp from the heat of traveling. Also, without doubt, there is dust on my coat. And my tie, that I must rearrange.”

I cut short his remonstrances.

“My dear Poirot–never mind all that. We must go to the villa at once. There has been another murder!

I have frequently been disappointed when fancying that I was giving news of importance to my friend. Either he has known it already or he has dismissed it as irrelevant to the main issue–and in the latter case events have usually proved him justified. But this time I could not complain of missing my effect. Never have I seen a man so flabbergasted. His jaw dropped. All the jauntiness went out of his bearing. He stared at me open-mouthed.

“What is that you say? Another murder? Ah, then I am all wrong. I have failed. Giraud may mock himself at me–he will have reason.”

“You did not expect it, then?”

“I? Not the least in the world. It demolishes my theory–it ruins everything–it–ah, no!” He stopped dead, thumping himself on the chest. “It is impossible. I cannot be wrong!” The facts, taken methodically and in their proper order, admit of only one explanation. I must be right! I am right!”

“But then–”

He interrupted me.

“Wait, my friend. I must be right, therefore this new murder is impossible unless–unless–oh, wait, I implore you. Say no word–”

He was silent for a moment or two, then, resuming his normal manner, he said in a quiet, assured voice.

“The victim is a man of middle age. His body was found in the locked shed near the scene of the crime and had been dead at least forty-eight hours. And it is most probable that he was stabbed in a similar manner to M. Renauld, though not necessarily in the back.”

It was my turn to gape–and gape I did. In all my knowledge of Poirot he had never done anything so amazing as this. And, almost inevitably, a doubt crossed my mind.

“Poirot,” I cried. “you’re pulling my leg. You’ve heard all about it already.”

He turned his earnest gaze upon me reproachfully.

“Would I do such a thing? I assure you that I have heard nothing whatsoever. Did you not observe the shock your news was to me?”

“But how on earth could you know all that?”

“I was right then? But I knew it. The little gray cells, my friend, the little gray cells! They told me. Thus, and in no other way, could there have been a second death.”