This blog contains ideas from the future.

My name is Marius Buliga, I am a mathematician. Here are:

- my github pages
- arXiv papers (some of the papers which are not on arXiv can be downloaded from my homepage)
- my youtube videos.

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**This is an open notebook****. It has multiple purposes: **

**as a work depository**

**as a tool for establishing collaborations on various projects****as a place where I can express my opinions.**

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* Contact:* firstname dot name at imar dot ro OR gmail dot com, for:

- sharing ideas
- career opportunities
- consulting or expertise requests
- new ventures.

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The name of the blog is composed by two parts: chora AND similarity. (“chora” is a word invented by Plato, it’s meaning comes from “place” or “space”. )

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**Interesting stuff: **

Vision and theater series:

- Vision theater part I, part II , part III, , part IV, part V, part VI, part VII, part VIII , part IX
- The cartesian disease part I, part II, part III

Other mathematical series:

- Curvdimension and curvature of a metric profile, part I, part II, part III,
- Gromov-Hausdorff distances and the Heisenberg group part 0, part I, part II, part III,
- Curvature and halfbrackets part I, part II, part III
- Noncommutative Baker-Campbell-Haussdorf formula part I , part II
- The origin of emergent algebras part I, part II, part III,
- Emergent algebras as combinatory logic part I, part II, part III, part IV,
- Ancient Turing machines (ancient CS) part I, part II, part III, part IV, part V,
- Digital materialization, Euclideon and fractal image compression part I, part II, part III,

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I had a totally uncompletable idea about neural computation several years ago. Taking smallish graphs (like “nerve of cover” pictures) with weights and assume they can light up in different ways to make “mental conception of a number”. Then match these up to known psychological results about how quantity is represented in the brain (for example order-of-magnitude is more biologically natural than +1 counting). I concluded it was simply a false start (from too many pop-science articles)……

Quantity is never well represented in the brain, 1, 2, 3, many. What I want to know is how space is represented in the brain. Maybe “represented” is not the right word. I believe that space, understood as a set, or a collection of labels (coordinates), things like this, is not the way brain works with it. Instead I hope to prove eventually (or to falsify the following) is that space is represented in the brain via the spatial programs, i.e. via what can the body in the brain do in a space. If we would talk about usual computation, I would say that brain uses the world as a tape and keeps some part of the program in the memory as a pattern. Now, this is OK from the moment when one finds a way to “compute with space” without referring nowhere to points, coordinates or passive things like this. Hence my insistence on “emergent algebras” and my recent turn to lambda calculus, because I wanted to understand the computation content of emergent algebras. Now I try to go back to the original point of interest.

I agree this is a better question.

In fact this must ultimately be why geometry could be in the 20th century applied fruitfully to arithmetic (number-theory) questions.