Hot and Cold

The vortex tube is a bit of a magic trick: When a stream of compressed gas is injected into the chamber, it accelerates to a high rate of rotation and moves toward the nozzle on the right. Because of the nozzle’s shape, though, only the quickly rotating outer shell of this gas can escape; the rest moves back through the center of the vortex and escapes through the opening on the left.

The result, perplexingly, is that even though the tube has no moving parts, it emits hot air (up to 200°C) on the right and cold air (down to -50° C) on the left.

Could this principle be used to air-condition a home or vehicle? “That’s what everyone thinks when they first hear about it,” engineer Leslie Inglis told Popular Science in 1976. “I always tell them that they wouldn’t buy a toaster for the kitchen if they had to buy the generator to produce the electricity. You’ve got to think of this as a compressed-air appliance.”

Podcast Episode 169: John Harrison and the Problem of Longitude

john harrison

Ships need a reliable way to know their exact location at sea — and for centuries, the lack of a dependable method caused shipwrecks and economic havoc for every seafaring nation. In this week’s episode of the Futility Closet podcast we’ll meet John Harrison, the self-taught English clockmaker who dedicated his life to crafting a reliable solution to this crucial problem.

We’ll also admire a dentist and puzzle over a magic bus stop.


Working in an Antarctic tent in 1908, Douglas Mawson found himself persistently interrupted by Edgeworth David.

In 1905, Sir Gilbert Parker claimed to have seen the astral body of Sir Crane Rasch in the House of Commons.

Sources for our feature on John Harrison:

Dava Sobel and William H. Andrews, The Illustrated Longitude, 1995.

William J.H. Andrewes, ed., The Quest for Longitude, 1996.

Katy Barrett, “‘Explaining’ Themselves: The Barrington Papers, the Board of Longitude, and the Fate of John Harrison,” Notes and Records of the Royal Society of London 65:2 (June 20, 2011), 145-162.

William E. Carter and Merri S. Carter, “The Age of Sail: A Time When the Fortunes of Nations and Lives of Seamen Literally Turned With the Winds Their Ships Encountered at Sea,” Journal of Navigation 63:4 (October 2010), 717-731.

J.A. Bennett, “Science Lost and Longitude Found: The Tercentenary of John Harrison,” Journal for the History of Astronomy 24:4 (1993), 281-287.

Arnold Wolfendale, “Shipwrecks, Clocks and Westminster Abbey: The Story of John Harrison,” Historian 97 (Spring 2008), 14-17.

William E. Carter and Merri Sue Carter, “The British Longitude Act Reconsidered,” American Scientist 100:2 (March/April 2012), 102-105.

Robin W. Spencer, “Open Innovation in the Eighteenth Century: The Longitude Problem,” Research Technology Management 55:4 (July/August 2012), 39-43.

“Longitude Found: John Harrison,” Royal Museums Greenwich (accessed Aug. 27, 2017).

“John Harrison,” American Society of Mechanical Engineers (accessed Aug. 27, 2017).

J.C. Taylor and A.W. Wolfendale, “John Harrison: Clockmaker and Copley Medalist,” Notes and Records, Royal Society Journal of the History of Science, Jan. 22, 2007.

An Act for the Encouragement of John Harrison, to Publish and Make Known His Invention of a Machine or Watch, for the Discovery of the Longitude at Sea, 1763.

John Harrison, An Account of the Proceedings, in Order to the Discovery of the Longitude, 1763.

John Harrison, A Narrative of the Proceedings Relative to the Discovery of the Longitude at Sea, 1765.

Nevil Maskelyne, An Account of the Going of Mr. John Harrison’s Watch, at the Royal Observatory, 1767.

John Harrison, Remarks on a Pamphlet Lately Published by the Rev. Mr. Maskelyne, 1767.

An Act for Granting to His Majesty a Certain Sum of Money Out of the Sinking Fund, 1773.

John Harrison, A Description Concerning Such Mechanism as Will Afford a Nice, or True Mensuration of Time, 1775.

Steve Connor, “John Harrison’s ‘Longitude’ Clock Sets New Record — 300 Years On,” Independent, April 18, 2015.

Robin McKie, “Clockmaker John Harrison Vindicated 250 Years After ‘Absurd’ Claims,” Guardian, April 18, 2015.

Listener mail:

Charlie Hintz, “DNA Ends 120 Year Mystery of H.H. Holmes’ Death,” Cult of Weird, Aug. 31, 2017.

“Descendant of H.H. Holmes Reveals What He Found at Serial Killer’s Gravesite in Delaware County,” NBC10, July 18, 2017.

Brian X. McCrone and George Spencer, “Was It Really ‘America’s First Serial Killer’ H.H. Holmes Buried in a Delaware County Grave?”, NBC10, Aug. 31, 2017.

Daniel Hahn, The Tower Menagerie, 2004.

James Owen, “Medieval Lion Skulls Reveal Secrets of Tower of London ‘Zoo,'” National Geographic News, Nov. 3, 2005.

Richard Davey, Tower of London, 1910.

Bill Bailey reads from the Indonesian-to-English phrasebook Practical Dialogues:

A few photos of Practical Dialogues.

This week’s lateral thinking puzzle was contributed by listener Oskar Sigvardsson, who sent these corroborating links (warning — these spoil the puzzle).

You can listen using the player above, download this episode directly, or subscribe on iTunes or Google Play Music or via the RSS feed at

Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at Thanks for listening!

The Trinity Hall Prime

On Thursday, Numberphile published this video, which features a startling wall hanging in the Senior Combination Room at Trinity Hall, Cambridge: Junior research fellow James McKee devised a 1350-digit prime number whose image forms a likeness of the college’s coat of arms. (The number of digits is significant, as it’s the year that Bishop William Bateman founded the college.)
Image: Math Stack Exchange

It turns out that finding such “prime” images is easier than one might think. In the video description, McKee explains: “Most of the digits of p were fixed so that: (i) the top two thirds made the desired pattern; (ii) the bottom third ensured that p-1 had a nice large (composite) factor F with the factorisation of F known. Numbers of this shape can easily be checked for primality. A small number of digits (you can see which!) were looped over until p was found that was prime.'”

Indeed, on the following day, Cambridge math student Jack Hodkinson published his own prime number, this one presenting an image of Corpus Christi College and including his initials and date of birth:

Hodkinson explains that he knew he wanted a 2688-digit prime, and the prime number theorem tells us that approximately one in every 6200 2688-digit numbers is prime. And he wasn’t considering even numbers, which reduces the search time by half: He expected to find a candidate in 100 minutes, and in fact found eight overnight.

(Thanks, Danesh.)


When blues singer Sally Osman filed for divorce from ventriloquist Herbert Dexter in 1934, she named his dummy, Charlie, as a co-respondent.

When she and Dexter had married two years earlier, she agreed that Dexter could take the puppet along on their honeymoon, as he had often complimented her through Charlie’s voice. But when they developed a new stage act, the dummy began to interrupt her songs with cruel ad libs and rob her of applause by making rude wisecracks. She asked Dexter to change the act so that she could sing without interruption, but he refused.

In I Can See Your Lips Moving, Valentine Vox writes, “She also accused the duo of physical cruelty, telling the court how she constantly received on-stage blows from the mechanical figure, which left her with severe bruises. One night in particular, Charlie had hit her so hard between the shoulder blades that he knocked the wind out of her.”

Osman further testified that Dexter would take the dummy everywhere they went and spent more time talking to it than to her. “I got to hate Charlie so deeply that homicidal thoughts began to haunt my mind,” she said. “Sometimes when I had Charlie alone and helpless, I fear that I would have thrown him out of the window, had I been able to unlock the coffin-like trunk in which he was kept.”

Dexter never contested the case, and Osman got her divorce. When the judge asked why she hadn’t requested alimony, she said, “I wouldn’t be able to collect it anyway; he spends all his money on Charlie.”

A Soaring Heart

From an advice column in Home Companion, March 4, 1899:

‘Sweet Briar’ (Swansea) writes in great trouble because her lover will persist in his intention to go up in a balloon. She urges him not to imperil his life in this foolhardy manner, but he only laughs at her fears.

I am sorry, ‘Sweet Briar’, that your lover occasions you anxiety in this manner, and I can only hope that he will ultimately see the wisdom of yielding to your wishes. What a pity it is that we have not a law like that which exists in Vienna! There no married man is allowed to go up in a balloon without the formal consent of his wife and children.

One solution: Go up with him, and marry him there.

Straight Business

In 2014 I described the Peaucellier–Lipkin linkage, a mechanism that transforms a rotary motion into a perfect straight-line motion:
Image: Wikimedia Commons

That linkage was invented in 1864 by French army engineer Charles-Nicolas Peaucellier. A decade later, Harry Hart invented two more. “Hart’s inversor” is a six-bar linkage — links of the same color are the same length. The fixed point on the left is at the midpoint of the red link, and the “input” and “output” are at the midpoints of the two blue links:
Image: Wikimedia Commons

In “Hart’s A-frame,” the short links are half the length of the long ones, and the center link is a quarter of the way down the long links:
Image: Wikimedia Commons

Pleasingly, the motion perpendicularly bisects a fixed link across the bottom, which is the same length as the long links.

The Victim

It goes against masculine pride to have a wife helping support the household, and once a man’s pride is shattered, anything can happen to him. …

There was a couple I once knew in Chicago. At the time of their marriage the husband was earning $5,000 a year. Two years after marriage the wife went to work, and presently was making more than her husband. His home became a desolate place, for his wife’s job required her to travel to other cities. Driven to seek companionship to escape from the loneliness of home the man became addicted to drink. Today they are divorced. The woman is a notable business woman, and the man is a drunken drifter.

But, the women will comment, the husband drank. What of it? No husband drinks to excess unless there’s a reason for it. If the truth were known there are many men who began drinking because their wives took to work.

— William Johnston, These Women, 1925


In 2001, computer animator Wayne Lytle created “Pipe Dream,” a 3D music visualization in which falling balls trigger musical notes on vibraphones, tubular bells, bongos, and other instruments:

Entertainingly, in 2006 an email hoax claimed that the scene was not animated but real:

Amazingly, 97% of the machines components came from John Deere Industries and Irrigation Equipment of Bancroft Iowa, yes farm equipment!

It took the team a combined 13,029 hours of set-up, alignment, Calibration, and tuning before filming this video but as you can see it was WELL worth the effort.

The hoax was entertaining because it was preposterous — who could build such a thing in real life?

You can guess where this is going — in 2011 Intel created a real version in which 2300 paintballs trigger 120 unique notes on replicas of Lytle’s animated instruments:

That’s just 10 years after Lytle made the original animation.

(Thanks, Jacob.)


Excerpts from the notebooks of English belletrist Geoffrey Madan (1895-1947):

“Work shapes the mind; leisure colors it.” — Revd. James Dolbear (1861)

“In language, the ignorant have prescribed laws to the learned.” — Richard Duppa

“To speak highly of one with whom we are intimate is a form of egotism.” — Hazlitt

“Who loves, will not be adored.” — Revd. J.C. Lavater

“While philosophers were looking for a characteristic to distinguish man from other animals, inconsistency ought not to have been forgotten.” — Richard Duppe

“Never be afraid to think yourself fit for anything for which your friends think you fit.” — Dr. Johnson

“What passes in the world for enterprise is often only a want of moral principle.” — Hazlitt

“I see no reason to suppose that these machines will ever force themselves into general use.” — Duke of Wellington on Steam Locomotives, 1827

“The room smelt of not having been smoked in.” — R.A. Knox

“Never make a god of your religion.” — Sir Arthur Helps

Treachery is the very essence of snobbery.

Alive, in the sense that he can’t legally be buried.

To forget your own good sayings is the mark of intellectual aristocracy.

Conservative ideal of freedom and progress: everyone to have an unfettered opportunity of remaining exactly where they are.

“Perhaps the most lasting pleasure in life is the pleasure of not going to church.” — Dean Inge