He sipped his wine. Then, leaning back, he ran his eye thoughtfully round the dining car. There were thirteen people seated there and, as M. Bouc had said, of all classes and nationalities. He began to study them. (1.3.13)
Ever observant, even when he isn't on a case, Poirot is a student of human nature. This certainly helps him later when he decides to solve the Ratchett murder mystery.
"I know something of your methods. This is the ideal case for you. To look up the antecedents of all these people, to discover their <em>bona fides</em> ¬– all that takes time and endless inconvenience. But have I not heard you say often that to solve a case a man has only to lie back in his chair and think? Do that. Interview the passengers on the train, view the body, examine what clues there are and then – well, I have faith in you! I am assured that it is no idle boast of yours. Lie back and think – use (as I have heard you say so often) the little grey cells of the mind ¬– and you will <em>know!</em>" (1.5.141)
Poirot's reputation precedes him, and M. Bouc urges him to use his brainpower to crack the case.
"See you, my dear doctor, me, I am not one to rely upon the expert procedure. It is the psychology I seek, not the fingerprint or the cigarette ash. But in this case I would welcome a little scientific assistance. This compartment is full of clues, but can I be sure that those clues are really what they seem to be?" (1.7.112)
While Poirot relies mostly upon logic and psychology, we also see he is not opposed to bringing scientific methods into his investigation.
Poirot shook his head violently.
"That is just it – it is <em>im</em>possible – quite impossible – that an honourable, slightly stupid, upright Englishman should stab an enemy twelve times with a knife! Do you not feel, my friends, how impossible it is?"
"That is the psychology," said M. Bouc.
"And one must respect the psychology. This crime has a signature and it is certainly not the signature of Colonel Arbuthnot." (2.8.118-121)
Unlike police today, Poirot makes his assumptions based on psychology, rather than on physical evidence such as fingerprints and DNA.
"I look first at my witness, I sum up his or her character, and I frame my questions accordingly. Just a little minute ago I am asking questions of a gentleman who wants to tell me all his ideas on every subject. Well, him I keep strictly to the point. I want him to answer yes or no, this or that. And then you come. I see at once that you will be orderly and methodical. You will confine yourself to the matter in hand. Your answers will be brief and to the point. And because, Mademoiselle, human nature is perverse, I ask of you quite different questions. I ask what you <em>feel</em>, what you <em>thought. </em>It does not please you this method?" (2.11.32)
Poirot explains, in detail, the way in which he approaches his interviews with suspects in order to get to the bottom of things. Notice how his method is different for every suspect.
"Did I not tell you that I was, like you, a very puzzled man? But at least we can face our problem. We can arrange such facts as we have with order and method." (2.13.16)
Poirot is a big fan of order and precision – from his neat little mustache to the list of clues that he makes for his friends.
"What to my mind is so interesting in this case is that we have none of the facilities afforded to the police. We cannot investigate the bona fides of any of these people. We have to rely solely on deduction. That, to me, makes the matter very much more interesting. There is no routine work. It is a matter of the intellect." (2.13.33)
Because they are cut off from the outside world because of the snowdrift, Poirot relies strictly on his own mind to solve the crime.
"The whole thing is a fantasy," cried M. Bouc.
"Exactly. It is absurd – improbably – it cannot be. So I myself have said. And yet, my friend, there it is! One cannot escape from the facts.
"It is madness!"
"Is it not? It is so mad, my friend, that sometimes I am haunted by the sensation that really it must be very simple…" (2.13.58-61)
Poirot points us to Occam's Razor: in essence, that most complicated problems usually have one very simple solution.
On the paper was written:
<em>Things needing explanation.</em>
1. The handkerchief marked with the initial H. Whose is it? (3.2.1-2)
A list! Here we see Poirot's orderly methods at work.
"I see, nebulously as yet, a certain explanation that would cover the facts as we know them. It is a very curious explanation, and I cannot be sure as yet that it is the true one. To find out definitely, I shall have to make certain experiments." (3.3.21)
Poirot tests his hypothesis using a logical and scientific method.