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Welcome to The Tangent Space
The Tangent Space is a wiki & blog dedicated to sharing and collaborating on a selection of curious questions in math and computer science. The work here, so far, represents a collection of thoughts of a single mathematician, but this wiki can be edited by anyone (like wikipedia). The hope is that interested readers can become authors as well, and the content itself may converge to a more thorough treatment of the ideas and questions explored here.

16 articles so far :)
If you want to edit pages, read how to get an account.

  • Math Museum - speculative ideas towards a museum of math


Recent blog post

Introducing Context Spaces

Roman numerals are a terrible way to represent numbers relative to the base 10 arabic numerals we use every day. Have you ever wondered if there could be an even more efficient number system, one which makes current systems seem as shoddy as the old Roman system? Problems like this motivated me to think about a general framework within which to mathematically approach such general information representation questions.

This post is about looking for a universal model of communication - one that’s independent of sequential systems and probabilistic models. I emphasize this independence since a lot of excellent work has already been done on strings, languages (of strings), and information theory. But all of these corpora of known works, while very useful in many cases, do make assumptions about the way information is conveyed which excludes some interesting cases.

Examples of non-sequential data

You can use cell phone towers with triangulation to determine where you are on a map - first generation iPhones used this technique before they got GPS capabilities. We can think of the raw data of a triangulation as a set of 3 known coordinates (the cell towers) along with distances to each. If that data is accurate, there is a unique point on the planet determined by it. Yet there is nothing special about the order of the 3 cell tower positions. This is a data format which can be considered a set of unordered clues, which, taken together, uniquely determine a piece of information...

Read the full post    |   or the Context spaces wiki page.

Recent picture

plot(fft(eye(25)))

This is one way to visualize a single discrete Fourier transform (DFT) matrix.

This graphic was generated in matlab via the command plot(fft(eye(25))), which plots the columns of the DFT matrix of size 25x25. Each solid color line jumps 25 times around the center at regular intervals, representing the orbit of various roots of unity in the complex plane.

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