Seven

What is unique about the number 7 among the first ten numbers?

One answer is that it is the only among them to be spoken (in English) with two syllables.

I remember a friend once arguing that this suggests a way English might be improved.

“What if we replaced “seven” with a one syllable word? Faster. Easier. Cooler. Right? If anything it’s weird that’s it’s two syllables. Right?”

Well…maybe not.

Count to ten as quickly as you can, as though you were rapidly counting ten objects.

Now try that again replacing the “seven” with “sen”.

It sounds exactly the same, doesn’t it?

The “veh” sound was gobbled up when the word was said quickly and “seven” just became “sen” anyway.

So, when we need to, we shorten “seven” to “sen” and it is only one syllable.

Now, count to ten saying each number slowly.

This time “seven” does have two syllables but the natural way to pronounce it is with each syllable said relatively fast so the two syllables of “seven” only actually take up the time of the single syllable in, say, the word “five”.

Interesting. It turns out “seven” is quite versatile.

There is something else worth pointing out about the apparent speed of the word “seven”.

Compare “seven” with “sevep”, or “seveb”. Doesn’t the “n” end of “seven” seem to close out the word much more quickly than a “p” or “b” sound?

This is because “n” is a nasal sound, rather than a plosive like “p” or “b”. In general it is just quicker to enunciate and lasts a shorter duration.

In some ways the “n” sound is a bit special. For example, in Japanese, “” (“n”) is unique in being the only such abrupt consonant sound – all others are what we (in English) would consider to end in vowel sounds. e.g. “ma”, “ki”, “to”.

I believe the “n” in “seven” can even make the word run more quickly than a one syllable alternative. Compare “seven” to “seh”. We can count to ten, replacing “seven” with “seh” and see what happens.

There’s an awkward moment between the “seh” and “eight”, isn’t there?

When two vowel sounds are put next to each other (as here with “seh, eight”) there needs to be some way to identify them otherwise they run into each other as one vowel sound (which, here, would be something like “sate”).

One way to identify vowel sounds is for the first to take a pause after it from the speaker. In this case, if counting quickly to ten with “seh” feels slower than with “seven” maybe that’s because it is slower, because of this pause!

Another way to disambiguate sounds is epenthesis (adding extra sounds). In the case of disambiguating vowel sounds we usually add a consonant, which is a special case of epenthesis called excrescence.

To count quickly with “seh” the speaker may find themselves eliminating the pause we talked about and using excrescence. If you try counting to ten quickly with “seh” you may find like I do that a “y” sound actually slips in between the “seh” and “eight” to make them run on more quickly. It comes out like “seh yate”. (Or, actually, more like, “seh yay” because the “t” of eight gets dropped when you say it quickly too.)

What this tells us is that, at best, “seh” has to add a consonant to be identifiable when counted quickly and, at worst, has to introduce a slowing pause. “Seven”, on the other hand, becomes “sen” when counted quickly, which we’ve already seen is nice and efficient because of the quick nasal “n” sound.

“Seven” is good. We’re keeping it!

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Miscellany

1

Three years ago I screenshotted this Twitter exchange between Armando Ianucci and Alistair Campbell.

It still makes me chuckle.

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2

The index of the 57th edition of the Handbook of Chemistry and Physics includes the entry “Sea water, see Water, sea”.

3

Screen Shot 2015-12-03 at 22.34.46

A steak pun is a rare medium well done.

Stone Soup

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Today I saw a youtube video about making traditional stone soup in Mexico.

“Wait a minute. Stone soup’s an actual dish? I thought it was just a story!”

Well it turns out it is a real dish. From what I can tell, the “stone” part is to cook the soup. Here’s the video I saw:

Notice how at 1:28 a stone is dropped in a bowl of soup and it immediately starts bubbling everywhere. That seems pretty wild! And, if you look closely before the stone is dropped in, you can see the soup is already steaming. Hmm. So presumably the stone part isn’t the sole source of heat to cook the soup.

I’d love to know more.

Fortunately, it turns out that this is just a mini documentary and Sarah Borealis, the filmmaker, did a longer one called “The Path of Stone Soup” which I can rent from Vimeo. So I guess I’ll do that!

Here’s the trailer for the documentary:

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In trying to track down the actual stone soup recipe I came across many versions of the folk story.

What was weird to me was that none of them matched the first version I heard, at story time back in primary school.

In those I saw today it was always some traveler(s) who pulled a kind of a con, leading to a pooling of food and the creation of the dish, that everyone then ate.

However, the version I was told was about a hen who used stone soup to protect her children.

As I remember it, a fox comes to the hen’s house (!) and says “I’m hungry, I’m going to eat you and your chicks”. The hen says “You could eat me and my chicks, but I can make you a more delicious meal”. The fox is greedy and thinks that he’ll eat the meal the hen makes and then eat her and her chicks too.

The hen explains that the most important ingredient in the meal is a stone and that she is going to make stone soup. The fox is intrigued.

Of course, the hen adds lots of other ingredients to the meal (one by one, as is the tradition with children’s books) and eventually the “stone soup” is ready – now a genuine, rich, hearty soup.

The fox eats the soup and it is so delicious that instead of eating the hen and her chicks, the greedy fox decides to take the stone so he can make the delicious “stone soup” for himself. The hen and her chicks are spared and the stupid fox goes off with his prized stone.

So I guess that one will always be my version of the “stone soup” story.

A Journey Down the Radoslav Zilinsky Rabbit Hole, and Radoxist Studios’ “Awesome Art Generator” Software

Yesterday I saw a really cool picture posted on reddit in a comment:

Worth Enough by Radoxist

Someone asked “Wow, who’s the artist?” and I, wanting to know too, put the image into reverse google image search and discovered that it’s by a guy called Radoslav Zilinsky.

I replied in the thread:

Here’s his DeviantArt page and here’s his company Radoxist Studio.

This morning, for no particular reason, I had another look at the company website.

This time I was intrigued by the “Art Generator Project” tab which I hadn’t noticed before, and the link took me to another site: artgenerator.me.

Awesome Art Generator Logo

“Awesome Art Generator” Logo

It turns out that not only has this design studio done work for various high profile clients such as Transport for London, but they have created a piece of software which boldly claims “YOU WILL NOT NEED TO HIRE AN ARTIST AGAIN. EVER.”

Wait…WHAT?!

Of course, this sounded straight out unbelievable and I was very curious to see what “Awesome Art Generator” actually did. It couldn’t be the software it claimed to be…surely?

Sensing a trap, before downloading it I watched the video about the project, which is highly entertaining and well-produced:

At this point, while still a little suspicious, I felt that whatever this software turned out to be I would certainly not be disappointed.

I downloaded it from the site, unzipped the file, started up the app, and straight away typed in my default test word “Bongo Drum”.

Instantly a .jpg image file appeared on my desktop.

I gingerly opened the file and – without any spoilers now – let’s just say I was NOT disappointed with what I saw.

I recommend you take a look at some of Radoslav’s work yourself then give Awesome Art Generator a shot. I think you will be likewise entertained.

John Polkinghorne’s Erdös Number

John Polkinghorne is a neighbour of my parents and, very tenuously, a relative.

He was active in Cambridge around the time of events in The Theory of Everything, and knew many of the people in it, including Hawking himself. Since getting to the cinema is a little hard for him now, a few months ago my parents invited John over to watch the DVD and eat Sunday lunch. I attended too, as chief video operator (!).

It was really fun, and interesting to hear John’s insights into the film and the people it featured.

The previous time I had spoken to John at a meal I had brought up Paul Erdös because I knew John had met Erdös, from an anecdote in John’s autobiography. Erdös was in Cambridge to receive an honorary degree and John was one of the people helping him. Erdös was expected downstairs by 9:30am but hadn’t appeared yet. John went to investigate and found him in his room still not quite ready. He asked John if he thought he should wear a tie, and John said that yes, he probably ought to, but this posed a problem because Erdös had never tied one before and didn’t know how! John had only tied his own ties so doing so on someone else was counterintuitive as everything would be mirrored. I guess you’ll have to read the autobiography to find out how the story ended.

Anyway…I was pretty sure that John was aware of the concept of Erdös numbers, but didn’t know his own. So I decided to find out what his Erdös number is. This proved quite difficult and I got in touch with Jerrold Grossman from The Erdös Number Project to help. He passed me on to Chris Fields, who was able to give me a chain of 5 co-authors. I did the googling to determine exactly which papers these were and made the following information sheet.

John Polkinghorne's Erdos Number

Click the image to enlarge.

I gave the sheet to John on the Sunday we watched The Theory of Everything, and he was really pleased with it. John indeed hadn’t known his own Erdös number! He even said “That’s jolly clever of you Jim to find that out”, which gave me cause for a wry smile.

The Lonely Runner Conjecture

The Lonely Runner Conjecture states that if K runners set off at constant different speeds to run laps around a 1 mile circular track then for each runner there is some time when she is at least 1/K miles from all the other runners.

I made a little simulation to help visualise this.

Try it! (Click the image)

The Lonely Runner

As the wikipedia page shows, the conjecture is proven for K up to 7 (which was shown in 2008), but beyond that we don’t know!

I posted the problem for K = 4 to the Math Riddles subreddit because that place is cool and I like it.

Unfortunately, I posted it slightly wrong by stating “more than” instead of “at least”. This was picked up in a particularly thorough answer 🙂