Seated in a chair, raise your right foot from the ground and start moving it in a clockwise circle. While continuing to move your right foot, extend your right for finger and draw a figure 6 in the air. What happens? 

See here for a YouTube video about this surprising effect.

It appears on lots of web sites, often under the title 'How smart is your right foot?' but I hadn't come across it before.

I’ve just bought 12 baby polyanthus plants via Amazon. When they flower they will be an assortment of 6 colours and I’m assuming there will be 2 plants of each colour. But at the moment they all look pretty much the same.

I’m planning to give 4 plants to a friend. Given we will be picking the 4 at random…

What is the probability that my friend will receive 4 plants all different colours?

What colour leaves you in the dark? Light blew.

New TV series about falconry. Britain’s got talons.

"By their very nature bureaucracies have no conscience, no memory, and no mind."

I've been trying to remember this quote. I found it striking when first told it but I'd partly forgotten it so it's taken a while to track down. It’s by the American anthropologist Edward T. Hall, although I still can’t find where he wrote or said it

I read today in the New Scientist about “Miracle Berries”, seen below. Eat one and for twenty minutes or so sour things will taste sweet. Isn’t that remarkable?

A link to the NS article is below, and there is also information on Wikipedia.

Naturally I want to grow some and the seeds are on their way.

https://images.newscientist.com/wp-content/uploads/2022/08/30202824/SEI_120900398.jpg?width=800

The origin is Old Norse hus-thing, “house meeting”, and referred to an assembly of the people in the household of a noble man or woman. Over time its meaning has come to mean a platform for politicians to make speeches from.

The thing element just meant assembly and survives today in the name of the Icelandic supreme parliament, the Alþingi.

Old English also had folk-moot, “folk meeting”. Here moot is the same as in the phrase “a moot point” = a point to be discussed and also found in moot hall. Folkmoot survives but mainly in historical contexts.

A few days ago I wrote about an elegant proof that a regular dodecahedrons has 4 diagonals that all intersect at a point other than the centre of the polygon, see https://learn1.open.ac.uk/mod/oublog/viewpost.php?post=248909

Since then I have found a paper by Poonen and Rubenstein ^[1] in which they completely solve the problem of concurrent diagonals in regular polygons. They prove several interesting facts, including:

If the number of sides is odd there can never be 3 concurrent diagonals.

The smallest number of sides that allow 3 diagonals to meet at a point other than the centre is eight, for diagonals twelve sides are needed, and for 5 concurrent diagonals eighteen sides.

To get more than 5 diagonals meeting at a point other than the centre we need to go to thirty sides. The regular triacontagon has sets of 6 and 7 concurrent diagonals.

And then suprisingly it stops. No regular polygon, however many sides it has, can have eight or more diagonals intersecting at a point other than the centre.

[1] https://mathproblems123.files.wordpress.com/2011/03/ngon.pdf

Looks like all the graphics have disappeared.

I got this message in my Celestial Mailbox