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.)

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