After summer is gone ...

It should be summer in the UK. Some days it feels as if it is; some days it doesn't. Autumn and winter are always certainties; they come every year without fail. One autumn I found this in the garden. Fascinated by the delicate skeleton within the leaf, I kept it.

More Dice

I can't remember found I came by these dice. (They may possibly have come from Christmas crackers.) Inside each of them is a heavy ball which helps them come to rest. As you can see from the die on the right, it is not entirely clear which of two numbers are uppermost. So if they were used competitively, no doubt there would be no end of argument between the players.

More subtly, the dots are not painted on in a consistent way. I just checked and found that if the 1, 2, 5 and 6 of both dice are lined up, the 3 and 4 are in reversed positions by comparison.

In fact there are 30 different ways in which the dots can be arranged on each die. The following (from Mathematische Basteleien) shows all 30:

(click)

The red die (number 3, in the diagram above) is the one used as standard. The person who painted the dots on the die on the right (top picture) has been clumsy and produced a number 9 instead of a number 3.

In addition to there being 30 different ways in which the dots can be arranged on each die, as Mathematische Basteleien goes on to point out, each set of dots can be can be arranged in four ways (since each face can be rotated four quarter turns). Because of rotational symmetry, this doesn't affect the appearance of the 1, 4 and 5 - they look the same at each turn. However, for 2, 3 and 6 there will be two different appearances (since the 2 and 3 are on a diagonal and the dots of the 6 are arranged 2x3). That, by my reckoning, would make a total of 240 different dice, if the orientation of the dots was also taken into consideration.

Barcode - 12

I've not posted a barcode for a few months, so here is another bit of absolute trivia: a Grid Matrix barcode (saying 'Marginalia55' as always).

Not the prettiest of barcodes. After looking at several barcodes, one gets to note something functional about them - the way the dots are set out etc. - and something aesthetic too.

I was about to write 'whatever way you look at this barcode, there is nothing aesthetically pleasing about it' but realised that I hadn't looked at it in any the other three (orthogonal) ways of looking at it. So, here they are (a quarter turn at a time):

  

(The) Multiverse(s)

This slightly flippant thought must have passed through (one or other of) the minds (see link) of those considering the notion of the multiverse and the many-worlds interpretation of quantum mechanics in particular. It is this, if the universe splits each time a decision is made - for example, each time a coin is tossed it splits into one for heads and one for tails - why then do I keep ending up in this one?

Worse than eating horsemeat

It seems that the British horsemeat scandal has largely blown over. Things could have been worse though. Look at the homecooked food this pub is offering!