https://www.scientificamerican.com/article/does-optimism-on-climate-change-make-you-pro-trump/

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.

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.

Rational dodecahedron inscribed in unit sphere: https://cp4space.wordpress.com/2020/07/25/rational-dodecahedron-inscribed-in-unit-sphere/

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 https://johncarlosbaez.wordpress.com/2011/09/12/fools-gold/

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

From:

https://en.wikipedia.org/wiki/Exodus_Collective

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

Nice math podcast.

@Breakfastisready Nice work!

<< 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

https://twitter.com/johncarlosbaez/status/1249055680033460225

This place isn't anything like twitter or facebook or instagram, its so much more fucking valuable than corporate, monetized social networks can ever possibly be.

I don't care if the fediverse disappears tomorrow, it already has done way more good in my life than a lifetime of corporate social networks could.

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I research mathematics.

I'm here to try and pursue an acceptable way to procrastinate away from mathematics.

Joined Aug 2018