For my September 2017 diary, go here.

Diary — October 2017

John Baez

October 1, 2017

Mystery of the gray ribbons

Abdelaziz Nait Merzouk has done it yet again: he's created a mathematical work of art! This one is a traditional Islamic tiling pattern that flirts with the impossible... namely, 5-fold symmetry. See all the small green 5-pointed stars?

The most exciting feature is one you might not notice at first. It's the gray ribbons! Follow one with your eye and see where it goes. What does it do?

If you followed it forever, would it loop around back to where it started?

I don't know, so this makes a nice puzzle. Let's do it systematically.

In this picture you can see a lot of purple stars.

Puzzle 1. How many points does each purple star have?

Next to each purple star are a bunch of 5-pointed stars with light green points. I'll call these green stars.

There are also some more complicated things where two green stars overlap, sharing 2 points. I'll call these twin stars.

Puzzle 2. How many points of each purple star end in a green star?

Puzzle 3. How many points of each purple star end in a twin star?

If you look carefully, all the designs are formed by gray ribbons. And that's where things get really interesting. What happens to a gray ribbon as you follow it along? It's hard to say because the picture isn't big enough to see. But you can figure it out anyway.

When a gray ribbon goes through a green star an into a purple star, it turns either left or right and pops out.

Then the gray ribbon continues until it hits another purple star, and the story goes on. So we can keep track of its progress like this:


...unless it hits a twin star!

When hits a twin star, it makes a slight turn either left or right. In this case let's write a lower-case "l" or "r". It then quickly reaches a purple star. It goes in, and as usual it turns either left or right and pops out.

So, we get a sequence sort of like this:


I'm just making this one up, it probably ain't exactly right.

Puzzle 4. What's the pattern of this sequence?

I believe it's the same for every gray ribbon that hits a purple star. Some gray ribbons just go along straight lines, minding their own business. But let's ignore these.

Puzzle 5. If we follow a gray ribbon that hits a purple star for long enough, do we get back where we started? Is the answer the same for every gray ribbon?

For more of Abdelaziz Nait Merzouk's tiling patterns, go here.

The twin stars look like 'defects', but they're inevitable. Greg Egan and I explained the math here:

You can see answers to the puzzles in the comments on my G+ post. Xah Lee colored the ribbons in a way that shows the different kinds:

October 30, 2017

A visitor from outside the Solar System!

It came from the direction of the star Vega in the constellation Lyra. It shot toward us at 26 kilometers per second. That's much faster than the escape velocity of the Solar System. So it wasn't orbiting the Sun. It's an interloper from interstellar space! We've never seen such a thing in our Solar System before.

As it fell toward the Sun it picked up speed. It shot past the Sun at 88 kilometers per second. It took a sharp turn... and now it's leaving.

It soon received the name 1I/2017 U1. It was discovered on October 19th. Rob Weryk, a postdoc at the University of Hawaii Institute for Astronomy, was the lucky fellow. He spotted it using a telescope at the University of Hawaii. Every night this telescope helps NASA search for potentially dangerous near-Earth objects. This was his lucky night.

It came fairly close to Earth: 24 million kilometers, about 60 times the distance to the Moon. It was never a threat. It's an intriguing puzzle!

Weryk immediately realized this was an unusual object. "Its motion could not be explained using either a normal solar system asteroid or comet orbit," he said. Weryk contacted Institute for Astronomy graduate Marco Micheli, who had the same realization using his own follow-up images taken at the European Space Agency's telescope on Tenerife in the Canary Islands. But with the combined data, everything made sense. Said Weryk, "This object came from outside our solar system."

"This is the most extreme orbit I have ever seen," said Davide Farnocchia, a scientist at NASA's Center for Near-Earth Object Studies (CNEOS) at the agency's Jet Propulsion Laboratory in Pasadena, California. "It is going extremely fast and on such a trajectory that we can say with confidence that this object is on its way out of the solar system and not coming back."

What is it? At first people thought it was a comet and called it C/2017 U1. But on October 25, incredibly detailed photos taken at the Very Large Telescope in the deserts of Chile showed it had no tail. So, it's probably made of rock. It was renamed A/2017 U1, becoming the first comet to be reclassified as an asteroid. But it's not a normal asteroid, so it was later called I1/2017 U1.

If it's a rock that reflect 10% of the light that hits it, it would be roughly 160 meters in diameter.

On October 25th another telescope, the William Herschel Telescope, saw that it's red. This is a big clue, because objects way out in the Kuiper belt, beyond Pluto, tend to be red. That's because they're covered with tholins — a messy and mysterious mix of complex organic chemicals formed by billion-year-long exposure to radiation.

It's on its way out now, and astronomers are watching it carefully, desperately trying to squeeze a bit more information out of this encounter. How does a rock escape another solar system? How long has this object been shooting through the icy depths of interstellar space before it reached us? How many of these things are there?

"We have been waiting for this day for decades," said CNEOS Manager Paul Chodas. "It's long been theorized that such objects exist — asteroids or comets moving around between the stars and occasionally passing through our solar system — but this is the first such detection. So far, everything indicates this is likely an interstellar object, but more data would help to confirm it."

The quotes are from NASA's webpage:

and so is the animated gif. Later this object was named 'Oumuamua, a Hawaiian word that means 'scout' or 'messenger'. So, you can learn more here:

For more, see the comments on my G+ post.

For my November 2017 diary, go here.

© 2017 John Baez