Doughnut Education

Pondering over the future, I told the kids the universal basic income and Doughnut Economics should be the next step. Simon game me an improvised lecture on doughnut topology. Well, what do you know? The very next day, Simon’s native city of Amsterdam announced it would be the first city in the world to embrace Kate Raworth’s doughnut model!

In the long run, this may even mean we’ll be able to return to our home in Amsterdam we left 4 yrs ago to be able to homeschool. Raworth’s model views the child as much more than simply future “workforce” and that could help personalise education and create legal bearing for Self-Directed Learning. Because let’s face it: Can Industrial-Age schooling really serve as a foundation for a new sustainable mindset?

Below are some impressions of Simon’s doughnut topology tutorial on April 7:

Doughnut is homeomorphic to a mug. ‘Homeomorphic’ is a fancy word for saying ‘topologically the same’.
How many cuts can you make in a hollow sphere to guarantee it isn’t broken into two parts? That maximum number is zero! In topology, we say “the sphere has genus zero”.
Are only shapes without a hole that way? No, this sheet of paper also has genus zero.
Only zero cuts can guarantee it’s not broken into two pieces.
No matter what cut I draw on this mug, it will stay in one piece. I need two cuts to break a mug or a doughnut into two pieces. On a regular doughnut, it corresponds to a ring on the inside and a ring on the outside. A doughnut and a mug both have genus one, one cut can still guarantee they stay in one piece.

Simon emphasised that this trick won’t work with a real doughnut, as Simon explains:

in topology, we’re talking about 2-dimensional manifolds (which means that they are hollow or that they’re just a flat surface). It doesn’t really make sense (not like it doesn’t make sense mathematically, but it just isn’t as interesting) to talk about 3-dimensional manifolds (filled 3D objects, not hollow) unless we’re doing it in 4-dimensional space. In other words, it doesn’t make sense to talk about 3-dimensional manifolds unless they’re embedded in 4-dimensional space.

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