Ciro Santilli @cirosantilli 35

A Cartesian product that carries over some extra structure of the input groups.

E.g. the direct product of groups carries over group structure on both sides.

Two ways to see it:

It is just mind blowing that Christians, Muslims and Jews can have so many conflicts considering that their religions are basically the same. Uncanny valley comes to mind. See also remarks at: cirosantilli.com/china-dictatorship/zhong-gong

The transfiguration of Jesus is a notable example where Jesus/the Church tries to divert older religions into him. And then Muhammad does the same during isra and Mi'raj, and meets up with Jesus, John the Baptist and Abraham. The Kaaba was also clearly an earlier place of worship of local religions before Muhammad. But of course, Abraham was one of the builders of the Kaaba, so all good.

For some reason, Ciro Santilli is mildly obsessed with understanding and visualizing the real projective plane.

To see why this is called a plane, move he center of the sphere to $z=1$, and project each line passing on the center of the sphere on the x-y plane. This works for all points of the sphere, except those at the equator $z=1$. Those are the points at infinity. Note that there is one such point at infinity for each direction in the x-y plane.

${\mathbb{R}}^n$ with extra structure added to make it into a metric space.

The Royal Society's Nobel Prize.

royalsociety.org/grants-schemes-awards/awards/copley-medal/ says it is now open to international citizens, but having a quick look at the 2010 awards still suggests that it is very British centric, or at least anglophone centric, much like the society fellowship itself. That's likely the reason why the Nobel prize won, being much more international from the start.

Good background: www.theguardian.com/science/the-h-word/2016/oct/07/prize-science-medal-history-nobel

The Nobel Prize of computer software or hardware!

More like a "lifetime achievement" though, rather than the Nobel Prize, which tends to be for more specific achievements.

It is such a huge shame that you have to understand Portuguese to appreciate those songs... this is yet another great evil outcome of having more than one natural language is bad for the world.

The good songs stopped before of just after Ciro Santilli was born, they were originally heard by his parent's generation. Those young new kids are boring.

The place to start is definitely the Holy Trinity of popular Brazilian music:

Non trinity songs and artists: