More manuscript reading. Apparently, I missed out a section where I had contributed.

scientificamerican.com/article

Good article about two books I recently read. For anyone who spends a lot of time thinking about climate change, read these two books:

"The Uninhabitable Earth" by David Wallace-Wells and "Apocalypse Never" by Michael Shellenberger. These two books take diametrically opposite stances on climate change whie being very informative.

My stomach is still warm from all the tea that I had to consume. Thanks mathstodon.

Alright. Second attempt at being productive.

Go manuscript, go!

Two hours later, I find myself watching Rambo (2008) on a random telegram channel. Sigh.

Here is a small proof that the multiplicative group $$B^*$$ of a unital Banach algebra $$B$$ is open. For this, we need to show that every $$x\in B^*$$ has an open ball around $$x$$ WRT the norm. For this, observe that $$x + a$$ is invertible whenever $$||x^{-1} a || < 1$$.

That's because $x+ a = x(1+x^{-1}a)$ and the following is an inverse of this:$(1 - (x^{-1}a) + (x^{-1}a)^2... ) x^{-1} .$

It converges because of the norm condition.

This manuscript is about a very strange area of mathematics called Non-commutative differential equations (NCDE). They're differential equations for things that take values not in real or complex numbers, but rather over a non-commutative algebra.

These things are used to talk about symmetries of a whole family of functions, for example the (generalized) polylogarithm functions. In this sense, NCDEs can be a whole family of differential equations packed into a single equation.

For the next few hours, I am committing myself to reading a manuscript that I have been avoiding for a while.

I will be active on Mathstodon for this duration, as an experiment to see if it helps me become more productive.

Rational dodecahedron inscribed in unit sphere: cp4space.wordpress.com/2020/07

It's easy to inscribe a dodecahedron in the unit sphere: just use a regular one of the appropriate size. And it's not hard to construct a dodecahedron combinatorially equivalent to the regular dodecahedron but with integer coordinates: see johncarlosbaez.wordpress.com/2

Now Adam Goucher shows how to do both at once, in answer to an old MathOverflow question (mathoverflow.net/q/234212/440)

Sometimes I feel such strong anxiety regarding climate change! I don't even know what to do.

There's a change.org petition going on that wants to revoke Arnab Goswami's academic degrees. Please support this by uniting against this vile hateful man.

chng.it/GnhnJGb8

I wish they could do something like that in India. An after-riot party.

Fdroid is asking me to uninstall firefox klar because of a security vulnerability.

It is my debut into making music.

<< If you read math papers it pays to keep this in mind:

Most mathematicians are not writing for people. They're writing for God the Mathematician. And they're hoping God will give them a pat on the back and say "yes, that's exactly how I think about it". >>

--- John Baez