Personal Blogs

What surprises me is how little these words have changed in a thousand years, and also that if you speak them aloud, articulating all the letters, you get a kind of feel from how they might have sounded then.

forma and oðer have been replaced by first (which looks like a natural vowel and then consonant shift perhaps, I think the German is erste) and second, from Latin secundus.

I went to a fancy dress party in a costume made of porridge. I called it my Oat Couture.

These elegant birds (altho the one of the right looks a bit grouchy) are Cattle Egrets. These birds (like many others) have been steadily extending their territory northward. (I suppose similar things have happened in the southern hemiphere, although less perhaps, since land masses are more separated there.)

My brother Simon snapped these Cattle Egrets in Bedfordshire.

Cattle Egrets are often seen in wildlife documentaries, usually perched on the back of cattle. They pick out and eat ticks and other pests, and it's a form of symbiosis. But round here they don't seem to do this; probably because there are relatively fewer cattle, and more other food opportunities, as seen in the photo.

Ants you can trust to get your sums right for you.

While I was having my dinner this puzzle occurred to me.

Assume the quadrilateral is convex, and has no re-entrant corners of the sort shown in this example.

After a bit of sketching quadrilaterals and points, I saw what the really beautiful answer is. Scroll down to read more.

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Then I went off to do some research, and of course there is nothing new under the sun. Fagnano wrote about this question ca. 1750. But similar questions still arouse research interest. Suppose we had different ways of measuring distance? Or we weren't on a flat surface? Or what about 4 points in space? Or more than 4 points in the plane?

Watched a video about low-carb dieting. So inspirational. It just took my bread away.

A pun

Is fun.

Today I was reading a book about Christmas traditions (Vintage Christmas Traditions, by Linda Davis) and found this early appearance of Father Christmas or something like him. The earlest know record of the carol is from the 15c (see here) and seems to be from the Ritson manuscript, a 15c choirbook in the British Museum.

The version below comes from A garland of Christmas carols, ancient and modern. Including some never before given in any collection (J.C. Hotten, 1861) which I found on the Internet Archive.

I am not religious, but still fond of tradition, and religion-friendly, so I did (apprehensively) venture to the local church for a service of readings and music (congregation not allowed to sing; nor, I was amused to read, to hum).

The music was the organ and the choir, who are permitted to sing and hum too, I guess. Last year the church was packed; this year only 24 of us. Everything was very safety-first and well organised and I was glad I went. I didn't pray but I did think about the lives that have gone before, and about those that must once have sat in the same pew I occupied, on my own because of social distancing.

The local choir was going to perform Carmina Burana but they’ve decided to Carl it Orff.

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?

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