My crystal ball broke down so I took it back to the shop. They said they’d look into it.

If Musk got involved in a cover-up, would it be stretching things to call it Elongate?

We know that from a Sun-centred point of view the Earth goes around the Sun and the Moon round the Earth. If we could magically hover above the plane of the Sun-Earth-Moon system, remaining at rest relative to the Sun, what would the path of the Moon look like from that vantage point?

Intuitively I thought it would trace a loopy path, something like the dotted trajectory in my sketch below.

I was surprised to find out how wrong my intuition was. The actual path is like the one below, which was generated by an nice simulation from the University of Colorado ^[1].

This is not to scale of course, the diameter of the Earth is about 8,000 mi and the distance from the Earth to the Sun 93,000,000 mi so if the orbit were drawn to scale your screen would need to be (roughly) 40 m wide, or the Earth drawn so small it would be a speck.

[1] https://phet.colorado.edu/sims/html/gravity-and-orbits/latest/gravity-and-orbits_all.html

A friend said she thought I must have some phobia about tidiness (what, me?) so I wondered if there is a word for such a condition. There wasn't but there is now, because I invented it.

Eutaxiophobia

Etymology : from Ancient Greek eu- (εὖ) "good" + taxis (τάξις) "arrangement" + phobia (φόβος) "fear"

Then I validated my new word by asking DeepSeek what it meant. It told me that it was not a commonly recognised word but if it existed it would mean "a fear or aversion to orderliness or tidiness", which fits the bill perfectly.

It's possible I am not the only person with this particular phobia.

oscine : pertaining to songbirds

This word came into English from Modern Latin in the late 19th century. The ancient Latin word is oscen, whose elements according to Etymonline are ob- and canere "to sing". These in turn have Proto-Indo-European origins, epi-, which has a broad prepositional meaning of spatial nearness and kan-, "to sing".

Other words that seem to be from kan_ include accent, charm, descant, enchantment and Carmen, and many others.

Oscine is a rare word. I came across it in Times 2 Word watch column and I'd never seen it before. It only occurs on average 0.01 times per million words. So in this blog post it has come up with a frequency that would normally only appear once in every 200 million words. 

If you had to pick a size of spiritualist, what would you go for?

The Art of Uncertainty, by David Spiegelhalter, someone who I have long admired. I watched an Oxford Mathematics Public Lecture Chance, luck, and ignorance on YouTube and really liked the content and the way he presented it.

Early in the talk he quotes an Italian statistician de Finetti who famously declared "probability does not exist". Spiegelhalter goes on the say that after 50 years of mulling things over he has decided that Finetti was right! I don't think he is claiming that we can't attach numbers to whether we think some event will happen or not, only that probability (with the possible exception of subatomic particles) probability is not a property of the world but something humans have made up, a "personal expression of our uncertainty".

By this point he had won me over and I bought the book. The lecture, which I watched right through was fascinating. Towards the end he gave an arresting example using a pack of playing cards as a prop.

Randomly shuffle a pack of cards*. Now the order of cards has almost certainly never, ever happened before in the entire history of humankind. If every person ever born had lived to be 100 and shuffled a pack of cards every second of those 100 years the chance of any of them having generated the same order as the pack you hold in your hands is infinitesimally small. Here are the sums:

Estimated number human who have ever lived 120 billion

Seconds in 100 years about 3 billion

So all those people shuffling away could have produced only(!) 120,000,000,000 x 3,000,000,000

= 360,000,000,000,000,000,000 = 3.6 x 10²⁰ shuffles. Let's call it 4 x 10²⁰ to simplify the arithmetic coming in a moment.

But the total number of ways to order the pack is 52 x 51 x 50 x ... x 3 x 2 x 1 = 52 factorial, which my calculator says is about 8 x 10⁶⁷.

That means the chance that one of those people generated the same order as you is

4 x 10²⁰ ÷ 8 x 10⁶⁷ which is 1 in 4 with 47 zeros after it

It's theoretically possible but the chances it will are almost unimaginable small. 

* To do this properly you need to do at least 7 successive riffle shuffles or 1 minute of "smooshing", see the fascinating Numberphile video The Best (and Worst) Ways to Shuffle Cards. Anything less than this the pack is probably not truly randomised.

I came across this crossword clue

enclose : indeterminate number of clothes

Previously I posted a well known problem which asks: suppose we are on a circular boating lake when fog descends. We know the size and shape of the lake and can travel any distance and in any direction we please, but we don't know where we are on the lake, so we are rowing blind. What is the shortest distance we must be prepared to row to be sure of escaping from the pond. and what path should we follow?

The answer is that you should row in the straight line until you hit the bank and may have to travel a distance equal to the diameter of the pond, and this cannot be improved on. My proof is here. I actually found this for myself some years ago but it turned out to have already been published 40 year before. so I was late to the party.

A follow up question was: what if we are on a pond in the shape of an equilateral triangle? The diameter of an equilateral triangle is just the length of one of its sides and this is the least escape distance if you keep to a straight line. But rather surprisingly (well I think it is) a zig-zag escape path exists which is shorter, at about 0.98198 of the side length.

Here are two pictures of the path in different positions and you can probably see how it manages to always reach the perimeter of the triangle even though it is shorter than the diameter.