An Eternal Triangle

penrose triangle

Similarly, in a waking dream, the greater world is somehow represented in the mind. Part of the wonder here is the wonder of consciousness itself, which William James expressed so clearly when he asked, ‘How can the [world] I am in be simultaneously out there and, as it were, inside my head, my experience?’ Many people think there is still no good answer to this question that I know of — although I recently heard the mathematical physicist Roger Penrose identify a striking corollary of it. It is as if, he said, there are three distinct worlds, equally real, and yet each somehow encompassing the others. There is, first, the world of mathematics — unbounded and infinite, and something that Penrose, following Plato, believes really exists. Then, within the world of mathematics there is the relatively small set of equations that, Penrose says, can explain all of physical reality. And finally, within and made possible by that physical reality there is the world of conscious beings and what they can experience. And yet somehow these conscious beings (or at least the ones who are good enough mathematicians) are capable of comprehending the mathematical world. Each world is therefore somehow nested in turn within another in an eternal loop, like the triangle devised by Penrose that has been called ‘impossibility in its purest form.’

— Caspar Henderson, A New Map of Wonders, 2017

| Oddities

And That Meant Comfort

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Image: Flickr

At a 1994 conference on indoor air temperature standards, participant M.A. Humphreys considered the thermal environments of hobbits. If we wanted to prepare a hole for some visiting halflings, we could study the physics and physiology of their current living arrangements, hoping to find a scientifically optimal solution, but it might be wiser simply to give them the means to adjust the conditions themselves, according to their own changing preferences. In that case:

  1. We did not need to know anything at all about the thermal physiology of Hobbits, such as the diurnal cycle of their body-temperature, the metabolic heat production of their various activities, whether they could sweat or shiver or pant, or whether the Dubois relation between height, weight and skin surface-area held good for Hobbits;
  2. we did not need to know anything about the heat exchange between Hobbit-skin and the hole, such as the surface heat-transfer coefficients by convection or by radiation, the mean skin temperature and at what sites it is best measured, the thermal insulation of their colorful clothing-ensembles, or the vapour permeability of their clothing materials.

“It would be fascinating to know about these things, and thermal comfort researchers whose original education was, like mine, in the physical sciences would only with great difficulty be able to restrain their curiosity. Such knowledge would help to explain quantitatively the thermal balance of Hobbits, and would give us a theoretical explanation of their comfort conditions, and might be useful in identifying potentially dangerous environments, but it would not be needed to enable us to provide comfortable apartments for our Hobbits. This is not surprising if we recall that achieving thermal comfort pre-dates by thousands of years the development of the theory of heat exchange.”

(M.A. Humphreys, “Thermal Comfort Temperatures and the Habits of Hobbits,” in Standards for Thermal Comfort: Indoor Air Temperature Standards for the 21st Century, 1995, 3-13.)

| Literature · Science & Math

Black and White

abdurahmanovic puzzle

This puzzle, by F. Abdurahmanovic, won first prize in a 1959 Yugoslav tourney. It’s a helpmate — how can Black, moving first, cooperate with White to get himself checkmated in two moves?

Click for Answer
| Puzzles

Podcast Episode 272: The Cannibal Convict

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In 1822, Irish thief Alexander Pearce joined seven convicts fleeing a penal colony in western Tasmania. As they struggled eastward through some of the most inhospitable terrain on Earth, starvation pressed the party into a series of grim sacrifices. In this week’s episode of the Futility Closet podcast we’ll follow the prisoners on their nightmarish bid for freedom.

We’ll also unearth another giant and puzzle over an eagle’s itinerary.

See full show notes …

| Crime · History · Podcast

A Good Eye

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Image: Wikimedia Commons

Australian minister Robert Evans holds an unusual record: He’s discovered 42 supernovae by eye. Using a staggeringly retentive memory, he’s memorized the appearance of more than a thousand galaxies and can spot changes in them simply by looking at them through a telescope.

This preternatural ability has made him a sort of John Henry: He began hunting supernovae in 1955, and it was only in the 1990s that automated telescopes began to scan the sky with comparable quickness and accuracy. He kept up with them for a time, but they’ve now outpaced any single person.

“There’s something satisfying, I think, about the idea of light travelling for millions of years through space and just at the right moment as it reaches Earth someone looks at the right bit of sky and sees it,” he’s said. “It just seems right that an event of that magnitude should be witnessed.”

(Thanks, Jon.)

| Science & Math

Unusual Books

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Image: Flickr

Adam Thirlwell’s 2012 novel Kapow! and Mark Z. Danielewski’s 2000 House of Leaves (above) are typeset unconventionally, with some text appearing in separate blocks, aslant, and even upside down.

To create his 2010 book Tree of Codes, Jonathan Safran Foer took Bruno Schulz’s 1934 short story collection The Street of Crocodiles and physically cut out most of the words to produce a new story.

Marc Saporta’s 1962 novel Composition No. 1 consists of 150 unbound pages that can be read in any order.

Anne Carson’s 2010 Nox is an accordion-folded facsimile of a handmade book of memories of her brother, including old letters, family photos, and sketches.

Holes have been cut in several of the pages in B.S. Johnson’s 1964 novel Albert Angelo, allowing the reader to glimpse events further ahead in the story.

The plot of Serbian novelist Milorad Pavić’s 1988 Landscape Painted With Tea is constructed like a crossword puzzle, with chapters that can be read “across” or “down.” “The solution of the puzzle is supposed to lead to the solution of life.”

| Literature

Will I Am

In the year 1611, when the King James Version of the Bible was published, William Shakespeare was 46 and 47 years old. The 46th word from the start of the 46th Psalm is shake, and the 47th word from the end is spear. Also, the 14th word is will, and the 32nd word from the end is am, preceded by I. And 14 + 32 = 46.

Remarkably, these coincidences obtain also in Richard Taverner’s 1539 Bible, which uses a different wording.

(J. Karl Franson, “A Myth About the Bard,” Word Ways 27:3 [August 1994], 154.)

| Literature · Oddities

Truth in Advertising

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Image: Wikimedia Commons

This giant cask, in Rhineland-Palatinate, has a volume of about 1.7 million liters, making it the largest in the world, large enough in fact to house a wine bar with space for 430 guests. It was built in 1934 by Bad Dürkheim cooper Fritz Keller, who fashioned each stave from a 40-meter spruce tree.

Magnificently, it is called the Giant Cask (Riesenfass). It surpasses the Heidelberg Tun, which had held the record previously.

| Oddities

Code of Conduct

For his 1933 novel A Fugitive Crosses His Tracks, Dano-Norwegian author Aksel Sandemose devised the Law of Jante, a list of 10 rules that summarize common attitudes in Nordic countries:

  1. You’re not to think you are anything special.
  2. You’re not to think you are as good as we are.
  3. You’re not to think you are smarter than we are.
  4. You’re not to imagine yourself better than we are.
  5. You’re not to think you know more than we do.
  6. You’re not to think you are more important than we are.
  7. You’re not to think you are good at anything.
  8. You’re not to laugh at us.
  9. You’re not to think anyone cares about you.
  10. You’re not to think you can teach us anything.

Sandemose intended this as satire, but it’s entered colloquial speech (Janteloven) to describe a general disapproval of individualism and unseemly ambition in Denmark and Norway. An 11th rule, “the penal code of Jante,” says, “Perhaps you don’t think we know a few things about you?”

| Literature · Society