Log24

From the previous post, "The Large Language Model,"
a passage from Wikipedia —

"… sometimes large models undergo a 'discontinuous phase shift' 
where the model suddenly acquires substantial abilities not seen
in smaller models. These are known as 'emergent abilities,' and
have been the subject of substantial study." — Wikipedia

Compare and contrast 
this with the change undergone by a "small space model,"
that of the finite affine 4-space A  with 16 points (a Galois tesseract ), 
when it is augmented by an eight-point "octad." The 30 eight-point
hyperplanes of A  then have a natural extension within the new
24-point set to 759 eight-point octads, and the 322,560 affine
automorphisms of the space expand to the 244,823,040 Mathieu
automorphisms of the 759-octad set — a (5, 8, 24) Steiner system.

For a visual analogue of the enlarged 24-point space and some remarks
on analogy by Simone Weil's brother, a mathematician, see this journal
on September 8 and 9, 2022.