A walk from language to geometry, one paper at a time
Arc ·
This series began with a simple discomfort. I kept reading that machines represent meaning as vectors in high-dimensional space, and I kept nodding along, and one day I noticed that I was nodding at something I could not actually picture. I could repeat the words. I could not see the shape.
So I decided to walk the whole path on foot. No shortcuts, no borrowed intuition — start with a sentence, end with a theory, and refuse to take any step I couldn’t see. Each paper in this series covers one stretch of that walk, and each one ends on the question that made me write the next.
The walk has a destination. It ends at a claim I did not expect when I started: that meaning, as machines represent it, obeys invariance laws — that a coordinate means nothing without its frame, and that two observers can genuinely agree about meaning only the way two surveyors agree about position. The final paper makes that claim carefully, in three different languages: mathematics, shapes, and running code.
Read in order if you want the walk. Read the last paper first if you want the destination. Either way, the questions link arms.
Inside the black box there is a universe — stars, constellations, and a butterfly. What is it like to go in?
PublishedTwo people point at the sky. Neither points in the same direction. Who is right?
PublishedThe model never notices when its space slides sideways. Every measurement we take does. Why?
PublishedEvery voltage is measured against a ground. What is the ground of a meaning?
PublishedIf two spaces grew apart — or grew up separately — what does it take to bring them into agreement?
ForthcomingOne theory, told three ways: as mathematics, as shapes, as running code — the disproofs published at full prominence.
Published · three lensesThe origin of semantic identity — where the program began.
Published