Music Space

We seem to think naturally of musical pitches as bearing spatial relations to each other, and of music reflecting movement within that space — we speak of notes neighboring one another, of being higher or lower than one another, of scales ascending or descending, and so on. Why is this? It’s true that “high” notes reflect higher frequencies, but people who don’t know this still tend to use these terms. Why don’t we call “high” notes “hot” or “deep”?

In summarizing several cross-cultural studies, Stephen Davis concluded that music’s being “heard in spatial terms would appear to be more or less universal.” The notes that Westerners call “high” some other cultures call small, weak, sharp, or white, while “low” notes are big, strong, flat, heavy, or black. But Davies finds these are all terms for spatial concepts and found no reversals of these “synaesthetic equations” (no cultures in which “high” notes are low, big, or heavy, for example).

Trinity University philosopher Andrew Kania writes, “[F]undamental though the phenomenon seems to be to our experience of music, it can be quite baffling to consider what we could be hearing moving in the music, and what space such movement could be located in.”

(Andrew Kania, Philosophy of Western Music: A Contemporary Introduction, 2020.)

The Peirce-Putnam Paradox

peirce-putnam paradox

Divide line interval AD at point P and separate the halves by a short distance.

What’s happened to point P? Did it become point B or C? It seems wrong to say that it’s neither of these, or that it’s only one of them.

But if the single point P has “become” the two points B and C, how can we say it was a dimensionless object?

(Hilary Putnam, “Peirce’s Continuum,” in Kenneth Laine Ketner, ed., Peirce and Contemporary Thought: Philosophical Inquiries, 1995, via Piotr Łukowski, Paradoxes, 2011.)


Allegedly this scheme was invented by a poet who wanted to write all night without interruption. He set up a row of candles and linked the base of each to the top of the next with a piece of twine. When the first candle burned down to the twine, “the latter naturally caught fire, and a tongue of flame would creep up to the adjoining candle, lighting it in the manner desired.”

“The scheme is a pretty example of the brilliancy of simplicity in idea, as compared with the complicated arrangements often devised to secure simple results.”

(James Scott, “Strange Devices,” Strand, August 1895, 184-189.)

A Remarkable Injury

This gruesome portrait illustrates an unconfirmed story: It’s said that in the 16th century a Hungarian nobleman named Gregor Baci survived for a year after being impaled through the head during a joust.

Did this really happen? We don’t know, but in 2010 surgeon Martin Missmann and his colleagues showed that it could have.

They had been presented with a craftsman whose head was transfixed by a metal bar that had fallen from a height of 14 meters. After two surgeries and a year of headaches and double vision, they said, the patient was symptom-free.

“This case shows that even severe penetrating traumas of the head and neck can be survived without sequelae of serious physiological dysfunction,” they wrote.

Brute Nature
Images: Wikimedia Commons

French painter Charles Le Brun (1619-1690) was a student of physiognomy, the notion that a person’s character or personality can be read in the face. In 1671 he presented a lecture to the Royal Academy of Painting and Sculpture in Paris in which he drew comparisons between the features of humans and animals. The lecture has been lost, but his sketches survive and are held at the Louvre. Here they are.


In an article on secret hiding places in the Strand, December 1894, James Scott describes an ingenious refuge in the space between two matched flights of stairs. The functional set of risers on top can be raised to reveal a false set below, and the fugitive can take his place in the space between the two. When the door is closed again, searchers see only an ordinary staircase, and if they examine the empty cupboard beneath they’ll see only the apparent undersides of the risers above, which match them in number and size. There’s no perspective from which they can view the purported single stair from both above and below, and thus no reason to imagine that it might be double.

“Tapping upon what they believed to be the underside of the proper stairs would produce a hollow sound; but as a similar response must be expected when legitimate stairs are tapped, that point would not be considered a valuable clue,” Scott writes. “The quarters would be truly uncomfortable, as the necessities of the position would demand that the prisoner should lie at full length in the cavity. Perhaps, however, some provision was made whereby slight relief was afforded.”


Reader Nick Hare just sent me this. The opening line of Oxford philosopher Derek Parfit’s 1984 book Reasons and Persons is “Like my cat, I often simply do what I want to do.” But in fact Parfit didn’t own a cat. David Edmonds describes the solution in his 2023 biography Parfit:

edmonds parfit quote

(Thanks, Nick.)

Cause and Effect

When we are praying about the result, say, of a battle or a medical consultation, the thought will often cross our minds that (if only we knew it) the event is already decided one way or the other. I believe this to be no good reason for ceasing our prayers. The event certainly has been decided — in a sense it was decided ‘before all worlds.’ But one of the things taken into account in deciding it, and therefore one of the things that really causes it to happen, may be this very prayer that we are now offering. Thus, shocking as it may sound, I conclude that we can at noon become part causes of an event occurring at ten a.m.

— C.S. Lewis, Miracles, 1947

Lewis adds, “Some scientists would find this easier than popular thought does.” In his 2016 book Time Machine Tales, physicist Paul J. Nahin writes, “It is a view that does find much support in the block universe interpretation of Minkowskian spacetime. Lewis never mentions the block concept by name, but it is clear that he believed in the idea of God being able to see all of reality at once.” See Asking Back.

In a Word
Image: Wikimedia Commons

adj. sharp, as a taste

n. a mistake, an error

mauvais quart d’heure
n. a short period of time which is embarrassing and unnerving

adj. worthy to be chosen

The label on Angostura bitters is larger than the bottle. When company founder Johann Siegert died, his sons planned to enter the tonic in a competition and divided the preparatory work between them. One oversaw the design of a new bottle, the other of a new label. They failed to coordinate the work, and by the time the mismatch was apparent they had no choice but to use the oversize labels. The oddity was so distinctive that it’s been retained as a branding measure.

(Thanks, Colin.)