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Richard Walker

*Do* Think of an Elephant

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Edited by Richard Walker, Saturday, 19 Dec 2020, 23:19

Here's something I wrote a few years back and had forgotten about. It's an experiment you can try anywhere, when you have a few spare moments.

Equipment

Your imagination.

A stopwatch (or phone app or you can just count seconds: one hundred, one hundred-and-one, one hundred-and-two, one hundred-and-three… or get someone else to do it for you).

Background

There is no background, you must imagine it.

Preparation

Have your stopwatch (or phone app, or mental counter or helper) handy to start and stop without needing to look at it (you’ll see why shortly). Then:

READ THE INSTRUCTIONS BELOW before starting the experiment.

Because for most of the time your eyes need to be closed tight shut.

I had to rehearse it myself. It’s not that hard but a dry run helps with starting and stopping the timer without breaking concentration.

Instructions

Shut your eyes and think of an elephant.

Your elephant is facing directly toward you. Picture its eyes, tusks, greyness, sturdy legs, big flapping ears.

Are you ready? Do you hold a solid four-ton elephant in your imagination?

Rehearsal

Now you must rotate your elephant.

Your mind alone must do the heavy lifting (or in this case heavy rotating). Think of yourself as using the power of thought to act on the imaginary elephant, which you have to heft round so it is now facing away from you, so you see its bum and tail.

1. Ready steady go! Mentally rotate elephant.

2. When elephant in correct orientation stop timer.

3. Open eyes and write down time.

Experiment

Now that you have conducted the rehearsal:

1. Repeat the same procedure, that is record how long you take to turn the elephant so it goes from facing you to facing away from you.

2. Do it again but with this variation: now you have to mentally rotate the elephant full circle so that at the end it looks toward you again, and note the time as before.

Results

If you are like me you find that rotating the imaginary elephant takes time! Something is happening inside your head that is like physically manipulating an object, even though there is no real object. And a full rotation of my elephant takes about – guess what – twice as long as a half-rotation. It varies but usually I take about 6 s for a half rotation, 12 for a whole turn.

Conclusion

This is not of course a rigorous scientific experiment. But it does suggest that when we move mental objects we base the imaginary movement on experience of shifting real things. There is a considerable body of research on this, involving much better experimental designs that leaves little room for doubt. Shepard and Metzler were the pioneers (scroll down to find their article).

And did you rotate your elephant to the left or right? I didn’t say which to do. Are you are left or right handed? I’d be interested if you could post a comment to tell me the two things, so we can see if there is a connection.

And does the size of an imaginary animal matter? What if you try to mentally rotate a blue whale, about 50 times bigger by weight than an elephant? Or a human, about 50 times smaller?

Permalink 1 comment (latest comment by Richard Walker, Saturday, 19 Dec 2020, 23:24)
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Richard Walker

The Perfectionist's Bar (set very high)

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Richard Walker

Tom Swifty

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Edited by Richard Walker, Friday, 18 Dec 2020, 21:29

"Quick, try to grab the toy bear's attention!", said Tom distractedly.

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Richard Walker

Ethical Film-Making

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I’ve just finished making a thriller about a symphony orchestra.There’s quite a few violent scenes, but we didn’t harmony musicians in the making of it.

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Richard Walker

Coincidentally speaking

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Edited by Richard Walker, Thursday, 17 Dec 2020, 00:07
Whenever someone says, "I don’t believe in coincidences", I say, "Oh my God, me neither!"
Alisdair  Beckett-King

Tonight I was doing a pub quiz with a friend. For obvious reasons we were not in a pub; or together; but online. The pub element was there to the extent we had a few drinks mind you.

So I had to nip to the loo, and while I was there I thought about isolation; and then about how much we need to talk to other people. And then I thought of Robinson Crusoe in the book and how terrible being marooned must be, even with a Man Friday to be a companion. A desert island is just that – deserted. Even with two people it's so lonely. And then I thought, "Who was the real-life inspiration for Robinsoe Crusoe?" and remembere it was Alexander Selkirk.

When I came back we started the next quiz, Classic Novels, and Oh My God, guess what? Question 13 was

"Which Scottish adventurer was the inspiration for the character of Robinson Crusoe?"

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Richard Walker

Haiku

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Inbox, "Apple turnover"
Thinking delicious dessert, but no
Just business news.

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Richard Walker

We'll go no more a roving

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So, we'll go no more a roving
   So late into the night,
Though the heart be still as loving,
   And the moon be still as bright.

For the sword outwears its sheath,
   And the soul wears out the breast,
And the heart must pause to breathe,
   And love itself have rest.

Though the night was made for loving,
   And the day returns too soon,
Yet we'll go no more a roving
   By the light of the moon.

This is by Lord Byron and very evocative. It may be his best-known poem today. Manfred and Don Juan made a huge stir 200 years ago. I've not read Manfred but I have read Don Juan, and probably will again. But it is not a moving poem; it is funny and racy and cleverly-versified; and the references were topical at the the time it was written. I like it, but I don't think it is very deep.

Lord Byron was an Hellenophile and famously went out to support the fight for Greek independence. He died at Missolonghi in 1824, during the military campaign, it seems of malaria, and becames a Greek national hero. When I first visited Greece in the 1970s, small bars and restaurants often had a picture of Lord Byron on the wall, 150 years after his death.





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Richard Walker

Jingle

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Clean your Spring with "Spring Clean™"
It only takes a sprinkle.
And then your Spring will glow and shine,
And coruscate, and twinkle.
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Richard Walker

Kitchen Table

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Richard Walker

20 Anglo-Saxon Tree Names

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You can probably recognise most of these!
Notice the two Christmassy ones come together.

ac
æpel
æsc
æspe
aler
bece
beorc
boxtreow
cirse
elm
eow
fyrh
hæsl
hagaþorn
holen
ifig
mapulder
peru
pintreow
sealh
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Richard Walker

Procrastination

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I'm determined to beat procrastination. Starting tomorrow.

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Richard Walker

Cat jokes 🐈

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Edited by Richard Walker, Thursday, 10 Dec 2020, 10:22

I sent my daughter this

What do cats do when they change their genes?

Mew-tate!

Her friend saw my pun and raised me

You might think this is funny, but cat puns really freak meowt.


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Richard Walker

Dots and Lines

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Edited by Richard Walker, Monday, 7 Dec 2020, 22:11

I'm a big doodler. Last night I drew some dots in a rough octagon and started drawing lines joining pairs of dots.

Then I wondered how many lines I could draw before I formed a triangle. I don't mean a triangle formed by three lines (although that's an interesting question too), but one with dots at its three corners.

With any problem where you have a series it's always a good idea to look at the small cases. Sometimes it can be misleading though. Still I drew some little sketches

It's easy to be sure the count is right for n = 2, 3 and 4, but even by 5 it gets less obvious. Is there a general formula? I wondered if this was a novel puzzle (and hoped it was); sadly it turns out no, it was investigated by Mantel in 1907. There are various proofs of the result Mantel found, but they are more or less technical and not intuitive. So I wondered if I could present the basic idea of one proof in a more accessible way.

With 5 dots consider a pair x and y that are joined by a line. That leaves 3 others and if we think about any one of these, let's call it z, we see x and y cannot both be joined to z. Otherwise we would have a triangle! So the maximum of lines from either x and y to the other dots is 3. Finally focusing on the 3 other dots, the maxiumum number of lines possible amongst these is 2, otherwise we would have a triangle.

Adding this all up as shown the greatest possible number of lines is 1 + 3 + 2 = 6.

Let's see if we can generalise this idea. Suppose we have n dots and the maximum number of lines that can be drawn without forming a triangle is f(n).

Following the same argument as before, if we are to avoid a triangle, we can have one line joining x to y, a maximum of n - 2 lines joining either x or y to one of the remaining n - 2 dots, and f(n - 2) lines amongst tos n - 2 others. So

f(n) = 1 + n - 2 + f(n - 2) = n - 1 + f(n - 2)

So we can immediate calculate further values

f(6) = 6 - 1 + f(6 - 2) = 5 + f(4) = 5 + 4 = 9

f(7) = 7 - 1 + f(7 - 2) = 6 + f(5) = 6 + 6 = 12

f(8) = 8 - 1 + f(8 - 2) = 7 + f(6) =  7 + 9 = 16

So now we have (for completeness we include n = 1 with 0 lines)

0, 1, 2, 4, 6, 9, 12, 16

Can you spot a pattern?


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Richard Walker

Pixie Cups

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This other-wordly organism is a lichen, "Pixie Cups", photographed by my brother Simon at Sandy Lodge in Bedfordshire.


Thius seems to be related to the so-called "Reindeer moss", also a lichen of the genus Cladonia, which contains 276 species. Some are quite startling in appearance, see here.

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Richard Walker

New Job

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I’ve got a new job; vaccinating people. Can’t wait to get stuck in.


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Richard Walker

Haiku

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Edited by Richard Walker, Thursday, 3 Dec 2020, 03:22

Winter jasmine

Here already

What a short year

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Richard Walker

Tongue-Twister

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Edited by Richard Walker, Tuesday, 1 Dec 2020, 01:23

Repeat five times after me

"On an anonymous ominous omnibus."

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Richard Walker

Christmas Mondegreen

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Edited by Richard Walker, Tuesday, 1 Dec 2020, 00:57

I like this Mondegreen. Although it's entered into the folklore, and is found on numerous websites, it has the ring of a genuine Mondergreen; a bit like "Gladly, the cross-eyed bear".

"We three kings of porridge and tar."

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Richard Walker

One Liner

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I worked with a men’s neckwear company for many years. But it’s all over now, and we've severed our ties.

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Richard Walker

Listen up linguaphiles!

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I've just (10 mins ago) bought a marvellous book

THE LANGUAGE LOVER’S
PUZZLE BOOK Lexical Complexities and Cracking Conundrums from Across the Globe ALEX BELLOS

Bellos, Alex; Bellos, Alex. The Language Lover’s Puzzle Book: Lexical perplexities and cracking conundrums from across the globe.

It's only just been published but what sold it to me was Alex's talk from the Royal Institution

https://www.rigb.org/whats-on/events-2020/november/public-the-puzzle-of-language

It also made me subscribe to the Royal Institution. I remember the physical building from visits in my teenage years, where we sat in the same room where Michael Faraday lectured, and the lecturer stood behind the same laboratory bench. I've watched a few lectures on YouTube but I've probably missed some good ones, so now I'll get alerts.

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Richard Walker

One Liner

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The police caught me in their dragnet. First they threw an edible water plant over me. Then they shouted, “You’re under a cress!”

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Richard Walker

Electors

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Why are the other 25 Ectors being ignored? We demand the truth.

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Richard Walker

Electors

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Suppose inhabitants of Diss in Norfolk UK had been left without voting rights, as a result of some historical mix-up, and this anomaly was corrected. Then they’d be Diss-enfranchised. Hmm.


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Richard Walker

Response To W.H.Davies

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Edited by Richard Walker, Monday, 30 Nov 2020, 02:22

Davies

What is this life if, full of care,
We have no time to stand and stare?

Me

I often have the time to sit and muse,
Especially when I’ve had a lot of booze.

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Richard Walker

Epsom Downs

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There actually is a place called Epsom Downs. Think about it.

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