The Octave Illusion

University of California psychologist Diana Deutsch discovered this illusion in 1973. Play the file using stereo headphones. If you hear a high tone in one ear and a low tone in the other, decide which ear is hearing the high tone. Then reverse the headphones and play the file again.

“Despite its simplicity, this pattern is almost never heard correctly, and instead produces a number of illusions,” Deutsch writes. Some people hear a single moving tone; some hear silence; some notice no change when the headphones are reversed. Some impressions even seem to vary with the handedness of the subject!

What you’re hearing is simply an octave interval, with the high note played in one ear and the low in the other, the two regularly switching places. Seen on paper it’s remarkably simple, which makes the confusion all the more striking. Deutsch suspects that two different decision mechanisms are being invoked at once — one determines what pitch we hear, and the other determines where it’s coming from. More info here.

| Science & Math

Filial Duty

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Most people would agree that children have special duties to their parents, even once the children have grown up. We might feel an obligation to keep in touch with them, for example, or to care for them in their old age. Where do these duties come from?

  • Certainly my parents have done a great deal for me, so perhaps I owe them a debt. But it seems there’s no way to repay this debt completely, and I seem to owe it regardless of how great (or small) a burden I was to them as a child. (Also my obligation to them seems to vary with my own circumstances, which is not the case with other debts.)
  • Perhaps what I really owe them is an appropriate gratitude for what they’ve done for me. But this doesn’t seem right either — if I help my mother through a difficult time, fundamentally it’s because she wants me there, not to show that I recognize and appreciate what she’s done for me. Also, I seem to feel a duty to her even if I required relatively little sacrifice as a child, which is not normally how we think about gratitude.
  • Maybe my parents and I are friends, and I owe them the duties that come with friendship. But I can’t choose to end our relationship, as I can with friends, and I would never feel an obligation to provide medical care (say) for my friends, as I would for my parents.

Each of these explanations is unsatisfactory, writes Boston University philosopher Simon Keller. “Each tries to assimilate the moral relationship between parent and child to some independently understood conception of duty, but this relationship is different in structure and content from any that we are likely to share with anyone apart from a parent.” So what’s the source of our obligation to our parents?

(Simon Keller, “Four Theories of Filial Duty,” Philosophical Quarterly 56:223 [April 2006], 254-274.)

| Society

Buttoned Up

Divide a pile of 14 buttons into two smaller piles, say of 9 and 5 buttons. Then write on a piece of paper: 9 × 5 = 45. Divide the pile of 9 into two smaller piles, say of 6 and 3, and write 6 × 3 = 18 on the paper. Keeping doing this, splitting each pile into two and recording the pair of numbers you get, until you have 14 separate piles of one button each. An example might run like this:

9 × 5 = 45

6 × 3 = 18
1 × 4 = 4

4 × 2 = 8
2 × 1 = 2
2 × 2 = 4

3 × 1 = 3
1 × 1 = 1
1 × 1 = 1
1 × 1 = 1
1 × 1 = 1

1 × 2 = 2

1 × 1 = 1

No matter how you proceed, if you start with a pile of 14 buttons, the products in the right column will always sum to 91.

(James Tanton, “A Dozen Questions About Pile Splitting,” Math Horizons 12:1 [September 2004], 28-31.)

| Science & Math

Procrustes

Rhymes for unrhymable words, by Willard R. Espy:

It is unth-
inkable to find
A rhyme for month
Except this special kind.

The four eng-
ineers
Wore orange
Brassieres.

Love’s lost its glow?
No need to lie; j-
ust tell me “go!”
And I’ll oblige.

(From his entertaining rhyming dictionary.)

| Language · Poems

Flashes

Striking excerpts from the writings of Scottish novelist Muriel Spark, from Penelope Jardine’s 2018 collection A Good Comb:

  • The superstition of today is the science of yesterday.
  • Providers are often disliked, often despised.
  • I think “waiter” is such a funny word. It is we who wait.
  • It is impossible to persuade a man who does not disagree, but smiles.
  • I’m not lonely before they come. I’m only lonely when they go away.
  • Dangerous people often seem boring.
  • She was astonishingly ugly, one was compelled to look at her.
  • I am an honest man … when treating of the few existing subjects to which honesty is due.
  • Suffering isn’t in proportion to what the sufferer deserves.
  • He exhausted his capacity for conversation when he became an Englishman.

Jardine’s title comes from the observation “It calms you down, a good comb,” remarked by an unnamed character in Spark’s 1960 novel The Ballad of Peckham Rye.

| Literature

“Coal Is Decayed Vegetarians”

Memorable excerpts from student geology examinations, from W.D. Ian Rolfe’s 1980 collection Geological Howlers:

  • The average person does not have to dig a deep hole to remind himself of the past.
  • Dust is mud with the juice squeezed out.
  • Articulate brachiopods have teeth and socks.
  • A skeleton is a man with his inside out and his outside off.
  • There are three kinds of rocks, ingenious, sedentary and metaphoric.
  • The term Caledonian Orogeny is brandished about by many people.
  • Nine-eighths of an iceberg is beneath the sea.
  • It has been found by a gentle man that organic remains can be converted to petroleum by the processes of metabolism.
  • Sedimentation is a rather lengthy affair.

“A dinosaur is an extinct animal still found in Australia,” one student contended. “It was sometimes so large that its feet are found in the Precambrian and its head in the Silurian because it was too big to lie down where it died.”

| Science & Math

Never Mind

After making an appeal for recruits in 1914, Secretary of State for War Lord Kitchener received this letter from one Alfie Knight of Dublin:

Dear Lord Kitchner,

I am an Irish boy 9 years of age and I want to go to the front. I can ride jolley quick on my bicycle and would go as despatch ridder. I wouldint let the germans get it. I am a good shot with a revolver and would kill a good vue of the germans. I am very strong and often win a fight with lads twice as big as mysels. I want a uneform and a revolver and will give a good acount of myself. Pleese send an anencer.

Yours affectionately

Alfie Knight

The War Office sent him this reply:

Lord Kitchener asks me to thank you for your letter, but he is afraid that you are not yet quite old enough to go to the front as a dispatch rider.

(From the Imperial War Museum.)

| History

No Time Like …

In Book 11 of the Confessions, Augustine writes, “Are the present hundred years a long time? But first see whether a hundred years can be present. If it is the first year of the hundred, then that year is present, but the other ninety-nine are still in the future, and so as yet are not; if we are in the second year, then one year is past, one year is present, the rest future. Thus whichever year of our hundred-year period we choose as present, those before it have passed away, those after it are still to come. Thus a hundred years cannot be present.”

Is the chosen year itself present? Not wholly: We’re in some particular month, and the other months are not present. And so on — Augustine applies the same argument to days, hours, and even “fleeting moments.” In the end, “If we conceive of some point of time which cannot be divided even into the minutest parts of moments, that is the only point that can be called present: and that point flees at such lightning speed from being future to being past, that it has no extent of duration at all. For if it were so extended, it would be divisible into past and future: the present has no length.”

| Oddities

Unable Was I

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It sounds straightforward to imagine being another person, but is it? If I want to imagine being Napoleon, I need to conceive some relation between our two identities. If I only imagine some situation that was faced by Napoleon, then the result involves too little of my own identity — I’m not really involved at all. But if I imagine myself in Napoleon’s place, then the result involves too little of him. It doesn’t seem possible for two people to share an identity in this way.

Philosopher Bernard Williams writes, “Leibniz, perhaps, made something like this point when he said to one who expressed the wish that he were King of China, that all he wanted was that he should cease to exist and there should be a King in China.”

But, Williams says, it does seem possible to play a role, to pretend to be Napoleon. In that case my first-person thoughts are framed in another’s point of view, so the identity of “I” is less problematic. In this sense perhaps I can imagine being Napoleon — but not having been Napoleon.

(Bernard Williams, Problems of the Self, 1976.)

| Oddities