For my December 2016 diary, go here.

Diary — January 2017

John Baez

January 1, 2017

Chmutov octic

You can get some very fancy surfaces using just polynomial equations. Here Abdelaziz Nait Merzouk drew one using polynomials of degree 8. That's why it's called an octic.

Why is it called the Chmutov octic? Well, that's because it was constructed by V. S. Chmutov as part of an effort to build surfaces with lots of ordinary double points, meaning points that look the place where the tips of two cones meet. This one has 144 ordinary double points!

That's not the best you can do: the octic with the highest known number of ordinary double points is the Endrass octic, shown here:

The Endrass octic has 168 ordinary double points. Nobody knows if that's the best possible.

The Chmutov octic is just one of a series of surfaces invented by Chmutov. There's a Chmutov quadratic, a Chmutov cubic, a Chmutov quartic, a Chmutov quintic, a Chmutov sextic, a Chmutov septic, a Chmutov octic, a Chmutov nonic, a Chmutov decic, a Chmutov hendecic, a Chmutov duodecic, a Chmutov triskaidecic, a Chmutov tetrakaidecic, a Chmutov pendecic, a Chmutov hexadecic, a Chmutov heptadecic, a Chmutov octadecic, a Chmutov enneadecic, a Chmutov icosic, and so on. In fact you can see a quick animated gif of all of these — from the quadratic to the icosic — here:

Again, it was made by Abdelaziz Nait Merzouk. You'll notice that most of the Chmutov surfaces of even degree look a lot like the octic here, while those of odd degree extend out to infinity.

Chmutov made these surfaces to get a lower bound on how many ordinary double points we could cram into a surface of a given degree. In most cases other people have beaten him by now. But still, these surfaces are cute! They're defined using some polynomials invented by the Russian mathematician Chebyshev — also known as Chebychev, Chebysheff, Chebychov, Chebyshov, Tchebychev, Tchebycheff, Tschebyschev, Tschebyschef, or Tschebyscheff. Apparently he suffered from a rare psychological disorder that made him forget how to spell his name — so each time he wrote another paper, he signed it a different way!

Happy New Year! (You may not have heard, but this year April Fool's Day has been scheduled on January 1st instead of April 1st.)

This may be my last Visual Insight post for a while — I'm getting burnt out on these, and I have a lot of projects on my plate: my work with Metron:

the Azimuth Backup Project: three papers to finish, and five grad students to manage. Like last quarter I'm teaching two courses and also my seminar on network theory; this heavier work load will let me take the spring as a non-teaching quarter, but right now it's making me a bit frenetic. It will pay off in having more time to write during the spring, and also, I hope, visit Hong Kong!

January 11, 2017

A 'luminous red nova' is something brighter than a nova but less bright than a supernova, which can happen when two stars merge. An example is shown above.

In this new paper, astronomers predict a new luminous red nova will occur sometime between September 2021 and September 2022, which could become the brightest object in the night sky here on Earth:

The stars in KIC 9832227 have been orbiting each other faster and faster over the last three years, and they seem to be surrounded by a shared envelope of gas. If they indeed merge, this will be the first such event predicted ahead of time.

As Greg Egan noted:

Given that nobody knows exactly when this will happen, the main thing that determines how many people are likely to be able to see it is the declination, 46° N. So anyone in the northern hemisphere will have a good chance... while for someone like me, at 31° S, the odds aren't great: it will never rise higher than 13° above the northern horizon, for me.

Right ascension is the celestial equivalent of longitude, but without knowing the season in advance (and the error bars on the current prediction are much too large for that) we can't tell if the sun will be too close to the object, drowning it in daylight to the naked eye.

If that happens, I guess the only comfort is that there are still sure to be telescopes able to make observations, maybe including both Hubble and James Webb.

For my February 2017 diary, go here.

© 2017 John Baez