Here’s some stuff I’ve been working on in AI.

# A Thousand Plateaus

A Thousand Plateaus by Gilles Deleuze & Felix Guattari
“The question is not: is it true? But: does it work? What new thoughts does it make possible to think? What new emotion does it make possible to feel? What new sensations and perceptions does it open in the body?” Brian Massumi, translator.
There is no way to “review” this book, any more than there is a way to review the experience of witnessing sunlight over the course of one’s life.

# Binet's Formula

This proof was shared with me by my friend Chuck Larrieu Casias, and I liked it so much I wanted to write it up here.
Suppose we have two similar rectangles, $A$ and $B$. Let $A$ have sides $a$ and $b$, and $B$ have corresponding sides $b$ and $a+b$.
Then $\frac{b}{a} = \frac{a+b}{b}$. Also, $\frac{b}{a} = \frac{a}{b} + 1$.
Call $\phi = \frac{b}{a}$. Then $\phi = \frac{1}{\phi} + 1$.
Multiply both sides by $\phi$ to get $\phi^2 = \phi + 1$.

# Data experience design

What signals should we attend to when studying a system? If we capture everything, how will we filter out the noise to listen to what matters? How do we know what matters? Does that change over time? How will we engage with what matters? Will it be on single metric? A two-dimensional chart? A 3D display? A 3D display that moves with color and sound adding further dimensional context?
These are the questions I think throughout my days with, until now, little context for exploring their histories and futures in the broader scope of analytics, interaction design, human computer interaction, and feminist computing.

# Godel, Escher, Bach

Oh my, this book is every bit as delightful as I had imagined it would be.
To be clear, I had slated this book as my “summer” read, imagining I would have stolen myself to an island somewhere to curl up alongside this book. But life found me in a data engineering fellowship in Palo Alto instead, drinking an endless stream of La Croix (La Croixes?) whilst building streaming pipelines and occassionaly drawing inspiration from the large bronze statue of Nikola Tesla that stood outside the office.

# Intersection of Convex Sets

Convex sets are interesting in the context of optimization, as they represent regions where we know we can find global minima. A convex region is a region where for every pair of points within the region, every point on the line that joins the points is also within the region.
Fun fact - the intersection of all convex sets containing a given subset A of Euclidean space, is called the convex hull of A, which is the smallest convex set containing A.

# Linear Algebra Basics

Useful terms and ideas diagonal matrix: Matrix with zero values except on the diagonal. change of basis matrix: Taking the product of this matrix provides a new basis, which is helpful to us if that basis transformation sets us up for an operation that requires the matrix to be in a particular form. For instance, a change of basis matrix could diagonalize the matrix, such as the choice of the orthogonal matrix as the change of basis matrix in PCA.

# Navier-Stokes Existence and Smoothness Problem

Let me say up front, I have not solved this problem, nor am I in the running. I came to math late in 2016 after a lifetime of music study, and while I am building a solid trellis upon which to grow my imagination, it will take me many years to capitalize on my potential. That being said, the Millenium Prizes are my one of my favorite sporting events, and the Navier-Stokes Existence and Smoothness Problem is my home team I’m rooting for to emerge next.

# Network Geometry

Network geometry is one of the topics that propelled me towards complexity research and machine learning. If we accept that interactions between agents in a networked system have themselves an impact on the dynamics of a system, it follows that we must investigate the emergence and charactertistics of these interactions. We start to wonder how we might reason about these system “overtones”.
I find Mulder & Bicaconi’s 2018 paper Network Geometry and Complexity to be a nice primer, so I’ll start there.

# Parrallelogram is convex

Let $S$ be the parallelogram consisting of all linear combinations of $t_{1}v_{1} + t_{2}v_{2}$ with $0 \leq t_{1} \leq $ and $0 \leq t_{2} \leq $, or equivlently $0 \leq t_{i} \leq $.
We remember that the line segment $PQ$ consists of all points $(1-t)P + tQ$ with $0\leq t \leq 1$, and that $PQ$ exists in vector space $S$ if all points $P, Q$ exist in $S$.
Proof. Let $P=t_{1}v_{1} + t_{2}v_{2}$ and $Q=t_{1}v_{1} + t_{2}v_{2}$ be points in $S$.

# Phenomenology of Perception

Phenomenology of Perception by Maurice Merleau-Ponty.
Originally printed in 1945 by Editions Gallimard, with English translation published in 1958 by Routledge & Kegan Paul. I am referencing the 2002 Routledge Classics edition.
Overview There are times in our lives when we notice the apparatus of our perception. Maybe we see a mirage emerge on the horizon, or grow determined to know why our ears are ringing. When we study such visual apparitions and sonic glitches, we align ourselves with generations of philosophers and cognitive scientists who have looked at perception’s outliers to help us understand what happens all along without our noticing.