Wednesday 26 February 2020

The case of the mathematically challenged professor.

Sherlock Holmes was reading The Times whilst I, his companion Dr Watson, was reading The Telegraph. 

Breakfast had been over for approximately an hour and Mrs Hudson had long ago cleared away the table, leaving us with our coffees.  At some point we intended to exchange newspapers.

We were two gentleman at leisure, enjoying the fact they both had nothing, in particular, to do.

That was until our landlady, Mrs Hudson, knocked on the door, opened it, stepping into the room. 

“Excuse me Mr Holmes, but there is a gentleman who wishes to see you, if, as he said, ‘you could spare him a moment of your time’?”

Holmes quickly folded his paper up and thrust it down the side of his chair. “Is he an interesting looking gentleman, Mrs Husdon?”

She nodded, a slight smile on her face. “Oh, yes, Sir. He is that! He gave me his calling card.”

Holmes accepted the proffered card and said: “Good Lord, Watson! We are being visited by no other luminary than Isambard Kingdom Brunel, the famed railway and civil engineer! Mrs Hudson, please ask our esteemed visitor to join us and offer him whatever refreshments he may wish to partake of!”

When our visitor was shown into the room, we greeted him, warmly. When he took off his top hat we were surprised by the extraordinary height of it, we quickly realised this was to provide the trompe l'oeil effect of making the owner of the hat appear taller than he was. His height, we adjudged, to be just a shade over 5 feet.

Both of us being urbane gentlemen of the modern era, the height of Victorian sensibilities, we dealt with his extraordinary shortness by the simple expediency of ignoring it.

“Mr Brunel, it’s a great honour to welcome such an illustrious engineer to my home. What service might we be able to render to you?”

“Mr Holmes, on behalf of the Great Western Railway I am constructing the Box Tunnel which will pass through Box Hill on the Great Western Main Line between Bath and Chippenham.

“The railway tunnel will be 1.83 miles long. It will be of straight construction and descends on a 1 in 100 gradient from its eastern end.

“The problem I face is Professor Dionysius Lardner. He is approaching the Parliamentary Hearings and he proposes to criticise my design for the tunnel. He will claim that, according to his calculations, should the brakes of a train fail in the tunnel, it would eventually accelerate to a speed in excess of 120 mph and cause the train to fly into pieces killing train crew and passengers.”

Holmes looked thoughtful. “I presume this is untrue, Mr Brunel?”

“As far as I am aware it is certainly untrue. However, Professor Lardner has created something of a reputation for himself as an expert on railway matters. I am wondering why he is making this claim?”

Holmes was thinking. “Is it possible a rival has employed Professor Lardner to attempt to disrupt your railway project?”

“That’s possible,” said Brunel. “But I can’t think of anyone who would do such a thing.”

“Do you have his mathematical workings, Mr Brunel?”

“Yes, Mr Holmes. I have a copy here for you.” He took some papers out of a leather bag of the type common to Victorian Doctors.

The papers were covered in mathematical calculations. “Can you understand these calculations, Mr Homes?” asked Brunel.

“I cannot, I am afraid. However, I do know a fellow who can understand them. I promise that I will quickly get to the bottom of this matter for you. How may I get in contact with you, Mr Brunel?”

“Whilst in London I stay at the Diogenes Club. Do you know it?”

Holmes smiled “Yes, indeed I do. It was co-founded by my brother Mycroft, so I am fully away of that club and I know where it is.”

After discussing terms of payment (which they swiftly agreed on) Brunel left, heading back to the club.

“Watson, what do you know of Professor Dionysius Lardner?”

“Let us look in our file of press cuttings and information files.”

I was swiftly able to locate the information that we required.

“Professor Dionysius Lardner FRS FRSE is an Irish born scientific writer who is something of a polymath genius, he popularises scientific matters for the general public and is the editor of the 133-volume Cabinet Cyclopædia.

“He has also published books on steam railways with James Renwick. The Steam Engine Explained and Illustrated: With an Account of Its Invention and Progressive Improvement, and Its Application to Navigation and Railways; Including Also a Memoir of Watt. Also, Popular Lectures on the Steam Engine, in which Its Construction and Operation are Familiarly Explained: With an Historical Sketch of Its Inventions and Progressive Improvement, with James Renwick.”

“So he is, or likes to appear to be seen as something of an expert on steam railways. If that is the case, why is he not working with Brunel? I shall have to raise this point with Mr Brunel this afternoon.”

“Holmes, how will you validate the mathematical calculations of Professor Lardner?”

“I shall approach the best mathematical mind of our generation. Another professor, Professor James Moriarty.”

“Moriarty?” I gasped. “Please be careful, Holmes!”

“Oh, you have no need to worry. As you will recall Moriarty is now safely ensconced at Her Majesty’s Pleasure, having been placed there by our good friend Lestrade.  I have nothing to fear from Moriarty.”

“Do you think he will help you, Holmes?”

“Oh, I am quite certain that he will. This will appeal to his vanity and also because I fully intend to sweeten the cake by offering to speak up for him at his sentencing. If he is willing to help me, that is.”

“What can I do, Holmes?” I asked.

“Watson, you can be of invaluable assistance by visiting the British Library for me today and undertaking some detailed research on Professor Lardner. I intend to speak with Brunel at his club to see what else I can glean from him on the gentleman in question.”

Certain aspects of the following are recreated from my conversations with Holmes.

Later that afternoon Holmes was enjoying a drink with Brunel at The Diogenes Club. “Please explain to me, Mr Brunel, why it is that Professor Lardner has no involvement with the Great Western Railway? After all, he has published several books on steam power, locomotives and railways and has accrued to himself a certain reputation for expertise in the field?”

Brunel shook his head. “But is it a deserved reputation, Mr Holmes? It is the opinion of many, and I find myself increasingly in that body of men, that the real work on those books was that of James Renwick, and that Professor Lardner merely added the icing to the cake, to coin a phrase, by adding his name to it and writing some non-technical passages in the book.”

“So you believe that his expertise is more apparent than genuine?”

Brunel nodded.

This gave Holmes food for thought.

That evening after our meal, we talked about our findings.

“So Professor Lardner is perhaps not as much of an expert as one might presume?” I enquired.

Holmes nodded. He said: “What did you learn for me at the British Library?”

“Holmes, in my research in the British Library I was able to confirm that Professor Dionysius Lardner is an Irish born scientific writer who is, as we established this morning, something of a polymath genius. Or he likes to portray himself as such, in any case.

“He writes on many different scientific and mechanical subjects and he popularises scientific matters for the general populace whilst also acting as editor for the Cabinet Cyclopædia.

“Professor Lardner is, or so it seems, always ready with a wide range of opinions on many scientific subjects and also some non-scientific subjects, too.”

“Thank you, Watson. Your research will, I feel certain, help us to establish exactly what game is afoot, at least concerning Professor Lardner.”

The next morning, with the assistance of a note written by his brother Mycroft, Holmes was granted an audience with Professor (or rather ex Professor) Moriarty.

“My dear Holmes” said Moriarty in an unctuous manner. “What brings me the dubious pleasure of your company?”

“The opportunity to offer assistance in a matter of the construction of a major railway project and the opportunity to have a letter to your sentencing judge pointing out how valuable your assistance was to this case.”

“Are you here to see Moriarty the Napoleon of crime? Or in another capacity?”

“I am here to see Professor James Moriarty one of, if not the, leading mathematical minds of our generation.”

“Then I shall accept your kind offer. In what way can I help you?”

Holmes swiftly outlined the problem and that Professor Lardner was going to present his findings to the Commission. He passed the papers to Moriarty.

Moriarty studied the calculations of Professor Lardner. He made clucking noises and shook his head. 

“Good Lord. So this is the work of the self-styled genius, the great Professor Dionysius Lardner?”

“You know of him?” asked Holmes.

“Yes, I do. In my line of work it pays to know a great deal about a large number of people. My informants have lead me to believe that Professor Dionysius Lardner, whilst not exactly a mountebank, is certainly not the genius that he likes to portray himself as.”

“Interesting” said Holmes. “How would you describe him?”

“Based on my informants I’d say that he is, to borrow a recently minted phrase from our American cousins, a bloviating braggart, a hack writer of articles of dubious value and of doubtful veracity.”

Holmes interrupted him. “Thank you for that potted biography of the man.  Have you had a chance to study his mathematical calculations, Professor Moriarty?”

“I have Holmes. And I have to say that, under some utterly unique circumstances his calculations would be valid. However, due to the fact that he omitted some crucial components in his mathematics, his calculations are utterly worthless.”   

“I had hoped that might be the case, my dear fellow. But mathematics is a foreign language to me, I am afraid. It is as if I can pick up the odd word or phrase here and there, but that’s really all. What did he omit?”

Professor Moriarty nodded. “He omitted two key components from his calculations. He failed to take into account the effect of the air in the tunnel causing wind resistance and he also failed to take into consideration the resistance of the metal train wheels on the metal railway lines.

“His calculations would only be valid if the train was travelling in a perfect vacuum and was travelling upon a surface that had zero resistance. Those are the two unique circumstances that I alluded to.

“Even with all our scientific advances, Holmes, we have yet to be able to achieve such wonders as those. One day, perhaps we might. But not at all in the immediate future.”

After chatting for a few more minutes, the two old adversaries parted, if not as friends, certainly with a deeper understanding one of the other.

Later that afternoon Homes rapidly write a letter to the sentencing judge as he had promised Moriarty he would. A member of the Baker Street Irregulars posted it in the post box in Baker Street.

I was absolutely astonished by what Holmes told me. “But that’s disgraceful, Holmes! Utterly indefensible that Lardner could risk damaging the work of Mr Brunel by using dubious and erroneous mathematical calculations,” I said, aghast.

“Oh, I agree,” said Homes.

I spoke thoughtfully to Holmes: “Do we have any ideas as to who might have employed Professor Lardner, Holmes?”   

Holmes poured us both a glass of single malt Scotch (a gift from a grateful client who was a Scots Laird) and splashed some water in the glasses before he spoke.

“I have concluded that Professor Lardner is not in the employment of anyone. I suspect that he was deeply unhappy about not obtaining a paid position as a consultant with the Great Western Railway and that he wished to try to damage the reputation of that company, but more so to sully the reputation of Brunel.”

I said, somewhat dubiously, “Do you think he deliberately omitted those parts of his calculations?”

“Having spoken further with Moriarty, I have concluded that he did not leave those components out of his calculations on purpose. In fact Moriarty was able to show to my satisfaction how and why Lardner made the mistakes that he made. His calculations were sloppy and, because they appeared to prove that Brunel was wrong, he failed to double check his arithmetic.

“There was no mysterious paymaster behind him, urging him to prove that Brunel was wrong. I think he was driven by hubris.”

“Ah,” I nodded in response. “In the context of over confident in one’s self, plus an excess of self-pride?”

“Precisely so,” beamed Holmes.

“That’s a singular difference between you and Lardner, Holmes,” I opined.

“Oh?” Holmes was clearly intrigued. “Please tell me what you have deduced, my old friend.”

“Holmes, you are an expert on a number of specific topics. You are conversant in the law, in botany, geology and the like, have a deep knowledge of Chemistry, know more than most medical students about anatomy and you have a passable knowledge of medical matters.

“But on subjects of which you know nothing, such as politics, literature and philosophy, you would readily and cheerily admit your lack of knowledge. I doubt that poor Lardner could do that. He would have to play the part of the expert, even if his knowledge of a particular subject was somewhat lacking, perhaps?”

Holmes raised a toast to me. “A capital statement on the good professor! And I am sad to say that you are almost certainly correct in your judgement of the man.

“I saw Brunel at his club this afternoon and I passed on the findings of Professor Moriarty. Tomorrow poor Professor Lardner will give his evidence to the Parliamentary hearings which are discussing the proposal of the Great Western Railway. And Brunel will refute them. I almost feel sorry for the fellow!”

Holmes lit his pipe and smoked contentedly.

The next day at the hearing Brunel took Professor Lardner to task, pointing out that his calculations, whilst superficially correct, were ultimately completely wrong because he had omitted to take into consideration the twin factors of air-resistance and friction.

This was, Brunel told the hearing, a basic error that completely negated Professor Lardner’s calculations.

Lardner should have been disgraced, but he took his humiliation in his stride.

This was not the last time that Lardner’s calculations proved fallible. Several years later he stated, with great certainty, that steamships would be unable to carry adequate coals to make a crossing from Britain to America, because, according to his calculations, this would be impossible.

Three years after he made this Delphic prognostication, whilst on one of our rare visits to America, Holmes and I were amused to see that we were sharing the steamship with none other than Professor Lardner himself, who was making the apparently impossible journey.

Holmes and I joked about approaching Lardner and questioning him about this, another example of his errant calculations, but we decided to restrain ourselves and did not do so.

After all, we were both urbane gentlemen of the modern era, the height of Victorian sensibilities.

(Note: The story is based on factual events. Professor Dionysius Lardner FRS FRSE was a real character and did make the errors outlined in this story. And Brunel took him to task at the hearing.)

Father Brown and the commercial traveller

(The following story is written in homage to and celebration of the G. K. Chesterton Father Brown character. It is a new work of fiction)


The priest who arrived at the reception of the large, well-to-do hotel looked a very unlikely person to provoke a strong reaction, good or bad, in anyone. He had a round, unremarkable face, he was short, some would say stumpy, his black, priestly clothing was somewhat shapeless and his large umbrella had seen better days.

However, the shouts of genuine, heartfelt joy from a tall Irishman who had just entered the reception through an internal door, the small middle-aged priest provoked a strong reaction upon being recognised.

“Is that you, Father Brown?” his voice, more appropriate to a parade ground, boomed across the room.

Momentarily the shorter man looked bewildered as he tried to place the source of the voice. But then he responded: “Why bless me! It’s Clonmel, County Tipperary’s, favourite son, Detective Sergeant John O’Connor, of the Metropolitan Police Force! What brings you to this part of the Home Counties?”

The two men vigorously shook hands and in a quieter, more confidential tone of voice O’Connor said: “I’m here to help the local police force apprehend a ruthless, cold-blooded killer. The local force believes a young man, who was treated exceptionally badly by the victim, to be the killer.”

At this point, O’Connor tapped his nose with a finger before adding: “But my instinct and my policeman’s nose tells me he’s not the man we’re looking for. The man I fancy as the killer is, I believe, staying at this very hotel!”

“Goodness me,” said Father Brown.

O’Connor said “Please join me in the resident’s bar. It’s my treat. I’ll have a drop of Guinness and I believe your tipple is still a half pint of brown ale?”

“It certainly is,” Father Brown agreed, affably. He excused himself momentarily to give the porter a gratuity to take his bags to his bedroom.

“Now, why don’t you tell me all about it?” he said as they companionably walked through the door into the residents’ bar.

With their drinks delivered to their table, O’Connor began talking. “We received intelligence a local businessman had become involved with a gang of criminals. Unfortunately, he crossed them because they ordered a professional killer to come here to murder him and the informant was able to tell the police the killer was staying in this hotel.”

“The local police were involved and decided a small-time criminal by the name of Peter Finch was the killer.”

Father Brown took a reflective sip of his brown ale. “You disagree, John?”

“I do Father Brown, I do! I know Finch. Yes, he’s a bit of a crook but he’s no killer. But I have to convince the local police force of that.”

“Why are you involved?” asked Father Brown.

“It’s complicated. I was following Peter Finch as we suspect him of being a member of a gang of car thieves, involved with the murdered local businessman who owned a second-hand car showroom. But when I arrived in town my superiors decided to put me on secondment to the local police force to offer them my services.”

“And did they not like that? Asked Father Brown, perceptively.

“That they didn’t! They had their noses put out of joint! So they arrested young Finch and whilst he is languishing in a police cell the murderer is going to get away Scot free unless I can do something.

But I’m not quite sure what I can do. Oh, of course, I’ve sent a telegram to my boss at Scotland Yard and doubtless, he’ll be trying to pull some strings from his end, but at the moment it’s a bit of a waiting game, I’m sorry to say.”

Father Brown said: “And who is this man you suspect of being the hired killer?”

“He’s in the hotel under the name of Harold Pritchard and he claims to be a commercial traveller selling cheeses. He is booked to leave tomorrow, this evening will be his last night here. He’s out now, attending to business, or so he told everyone very loudly this morning.”

Father Brown sat, thinking, a slight smile playing on his lips. Eventually, he spoke. “I think I have the germ of an idea. Let’s go to see the hotel manager.”

In fictional detective stories, hotel managers either demand to see a search warrant or ask for bribes to allow the detectives to enter the room.

Mr Jones, the manager of the Devonshire Arms hotel did neither. He was a no-nonsense man of the old school. As a child, he’d been raised to trust police officers and, for that matter, priests, so when a detective and a priest asked, very politely, to look round the room of another guest he immediately acquiesced to their request.

They found nothing in the room save for an empty suitcase and a modest chest of drawers containing the resident's clothing. On a shelf near the washbasin were a toothbrush and his shaving kit and a bottle of men’s scented water.

“Tell me, Mr Jones, does Mr Pritchard have anything else in storage within the hotel? Any other luggage? Does he have a car or a small van parked outside? Anything like that?”

“No Father, he doesn’t. Not a thing. This is all he has. He has no vehicle parked within our garage or our car park. ”

“Thank you,” said Father Brown. He turned to his friend and said: “I want you to sniff the air deeply. Tell me what you can smell.”

His companion obliged and said, puzzled, “All I can smell is a faint whiff of lavender polish and whatever scent Pritchard splashes on himself. What was I supposed to smell, Father Brown?”

Father Brown was looking thoughtful again, as his mind spun and whirred. “Under the circumstances as I am beginning to understand them, probably nothing, John.”

The detective made sure that they had disturbed nothing in the room and as the manager locked the door with his passkey Father Brown said: “Excuse me, but what time is dinner served this evening?”

“It’s served at 8 pm sharp. We used to have room service meals available but that was before the Great War when we had a full staff. Sadly things like that are lost into the past and I doubt we will ever see them again.”

Father Brown nodded, sadly. “Could you please arrange for Mr Pritchard to be placed on our table for dinner, presuming that he will be dining in this evening?”

“Oh, he will be dining in this evening. He specifically asked what was on the menu for his last meal here. It will be a matter of simplicity to arrange the seating arrangements as you desire them. The hotel is quite full and your room was the last one vacant, Father.”

Once back in his room, Detective Sergeant O’Connor began to puzzle as to why Father Brown  had told him told to sniff deeply in the room and what he would be able to ascertain from that.

Detective Sergeant O’Connor, and not for the first time since he had met Father Brown all those years ago when Father Brown was a relatively new priest and he had not long come out of being a probationary police constable, thought: “I’m thanking the good Lord above that you did not decide to live a life of crime, Father Brown! Because no policeman could ever have had your measure! You would have got away with everything that you put your mind to, every crooked plan and scheme and we would have been unable to stop you at all!”

That evening at 8 pm sharp everyone was seated in the hotel’s dining room. Its late Victorian splendour was clearly in the dim and distant past, but it was still obviously the dining room of the best hotel in the small Home Counties market town.

At the table was an unmarried middle-aged school teacher visiting her family who still lived in the town of her birth, but for a variety of reasons, she chose to stay at the hotel rather than imposing herself on her relatives.

After listening to what Sergeant O’Connor later described to Father Brown as her “whine list” they knew several things about Miss Carpenter. She was single, filled with her own self-importance and a dreadful bore. Or was that a dreadful boor? The difference was pretty much immaterial.

But Harold Pritchard! What a revelation that man was! He was thin to the point of looking somewhat cadaverous, almost as if an undertaker had taken a bet to starve himself to the point of becoming skeletal.

However, he had a perfectly normal appetite and ate heartily of the various courses of fine cuisine and excellent wines that the hotel’s chef and sommelier were able to offer.

Eventually, they talked about their jobs. They learned that Miss Carpenter was a teacher, they laughed when they said it was obvious that Father Brown was a priest and when Sergeant O’Connor revealed that although he was an Irishman through-and-through, he was not living in the Irish Free State, nor was he a member of the recently formed Garda Síochána, but rather the Metropolitan Police of London.

Father Brown watched Pritchard. To the casual observer, nothing had changed in the demeanour of the man. But Father Brown was not a casual observer. He was a keen student of human behaviour and was always willing to learn more and to discover more.

He had noticed that Pritchard’s pupil’s had suddenly dilated and that the carotid artery in his neck had pulsed, obvious signs of distress.

“And what is it that you, do, Mr Pritchard?”

Pritchard attempted to smile affably, though the effect was more alarming than reassuring, as it carried all the warmth of the kiss of the ice maiden’s dissolute older brother.

“I, Father Brown? I am a commercial traveller in cheese. I go up and down the entire island of Britain taking orders for cheese from department stores, large hotels, cheesemongers, large grocery stores and the like.”

“What a fascinating job!” said Father Brown, being able to load his tone with just the correct amount of sincerity and interest.

Warming to his task Pritchard spoke of his life on the road as a commercial traveller in cheeses. The longer he went on, the more confident he became, managing to wrest wry grins and the odd chuckle from his captive audience of three souls with his stories.

Eventually, when he paused, the others at the table took up the conversation. Miss Carpenter expressed a dislike of all types of cheeses (which did not surprise the others, to be perfectly honest) and Detective Sergeant O’Connor opined that “you just can’t beat a nice chunk of Irish farmhouse cheese with some good freshly baked soda bread and some freshly churned farm butter!”

Everyone agreed, save for Miss Carpenter whose shudder indicated that her dislike of cheese was a deeply rooted matter.

Then Father Brown began to speak. “I agree with you, Sergeant. The many times that I have visited Ireland and enjoyed some good, farmhouse cheeses there, does tend to bear out what you say. However, I must admit that I like the French Roquefort cheese. It’s equal in taste to Stilton and it’s easy to see why the French describe it as the Queen of Cheeses. And the fact that the farmers of The Camargue exclusively make it with 100% goat’s milk is remarkable as it gives it that delicious tang.”

Pritchard agreed and said: “Ah, yes! The goat’s milk is the key to what makes that cheese so tasty, you are correct there, Father Brown! However, I tend to only deal with our own British cheeses, not any specialist continental types.”

After coffee, the diners took leave of each other and returned to their rooms. Except for Father Brown who went with Detective Sergeant O'Connor into his room.

“Why on earth were you going on about cheeses?” asked Sergeant O’Connor. “But I do know one thing, you will have had a damn good reason to talk to him about cheeses!”

“I did indeed,” said Father Brown. “When we went to his room, remind me, what was it we found?”
Sergeant O’Connor paused in thought for a few seconds. “Not much, now you come to mention it. His clothing, his toiletry items, shaving kit, not much else, really.”

“Exactly!” said Father Brown, emphatically. “If he really is a commercial traveller dealing in cheeses, where is his order book? Where are his samples of cheese? In the old days, commercial travellers who were attempting to sell cheeses to potential customers would have carried waxed samples of their various cheeses. And nowadays as we move on to a more technical and, or so we are told, brighter and better, more scientific future, there are even small vans with refrigerator units in them.

“And that’s another thing. If he is a commercial traveller in anything, where is his vehicle? I specifically asked the hotelier and he has no vehicle on the premises, not even an old Penny Farthing!

“So how does he take his cheese to his customers? Catch a train? Hop onto a bus?”

“But there’s something that just now has occurred to me,” said Detective Sergeant O’Connor. “When you asked me to sniff for something in the air of his room, I got the impression that you were asking me to sniff out something in particular. What was it?”

“Cheese! Just the smell of cheese! If he is a commercial traveller in cheese, why was there no smell of any types of cheeses? Oh, I know that kind of evidence such as it is would not stand up in court, far too insubstantial, a case depending on a smell, but very indicative, all the same.”

“And what of that conversation at dinner, just now? What did that tell us?”

“It confirmed what we already suspected, that Pritchard is no more a commercial traveller in cheeses than a swan could fly to the moon. That story I told him about Roquefort Cheese was a total canard, to borrow a French word.

 "Roquefort is not produced in The Camargue, it is produced in caves in Roquefort-sur-Soulzon, about 140 miles away. And although previously some farmers might have added a little goat’s milk or cow’s to the Roquefort cheese, it’s essentially 100% Ewe’s milk.

“And yet he made not the slightest effort to correct me or to ask me where I had received my information from.  Even if he didn’t sell French cheeses, he’d almost certainly be expected to know what the main cheese types in France are. And Roquefort is known as the King of Cheeses in France, not the Queen of Cheeses. And if I, an ordinary parish priest know that, a cheese salesman certainly would have been expected to know that. And a cheese salesman would be pleasingly plump, not as cadaverous as Mr Pritchard!”

“Thank you, Father Brown!  Now I’ll have to get the local police station to provide me with some armed officers and their senior detective to help put the cuffs on that murderer. And they’ll have to let Finch go. He’s an idiot, but he’s certainly no killer.”