Colony (biology) by Ciro Santilli 40 Updated 2025-07-16
It is hard to distinguish between colonies of unicellular organism and multicellular organism as there is a continuum between both depending on how well integrated they cells are.
From Wikipedia:
Multicellularity has evolved independently at least 25 times in eukaryotes
and:
Complex multicellular organisms evolved only in six eukaryotic groups: animals, symbiomycotan fungi, brown algae, red algae, green algae, and land plants.
Ciro Santilli's preferred visualization of the real projective plane is a small variant of the standard "lines through origin in ".
Take a open half sphere e.g. a sphere but only the points with .
Each point in the half sphere identifies a unique line through the origin.
Then, the only lines missing are the lines in the x-y plane itself.
For those sphere points in the circle on the x-y plane, you should think of them as magic poins that are identified with the corresponding antipodal point, also on the x-y, but on the other side of the origin. So basically you you can teleport from one of those to the other side, and you are still in the same point.
Ciro likes this model because then all the magic is confined just to the part of the model, and everything else looks exactly like the sphere.
It is useful to contrast this with the sphere itself. In the sphere, all points in the circle are the same point. But this is not the case for the projective plane. You cannot instantly go to any other point on the by just moving a little bit, you have to walk around that circle.
Figure 1.
Spherical cap model of the real projective plane
. On the x-y plane, you can magically travel immediately between antipodal points such as A/A', B/B' and C/C'. Or equivalently, those pairs are the same point. Every other point outside the x-y plane is just a regular point like a normal sphere.
The first proper galaxy near the Milky Way is the Andromeda Galaxy. Everything else in the middle is a satellite of either of of those.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
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    Video 3.
    Edit locally and publish demo
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