Starting a thread on my process for creating a timeline visualizer. I am building this for visualizing and sharing my understanding of the history of Lambda Calculus.
Here’s some prior work I have done that gives an idea of what I am trying to achieve. It shows a subset of ideas, events, and collaborations among pioneers that influenced the course of logic. History is replete with such multi-actor conversations:
I am doing this to complement my Lambda Calculus project and the results of these explorations will be available here shortly: prabros.com/lambda-calculu…
I will eventually drive towards a visualization where ideas, events, and personalities are plotted together. But for the initial implementation, I am going to go for one where just the lifetimes are visualized as in this image I did for the history of functions:
During my search for inspirations one fine work of timeline visualization that I stumbled on is this visualization by polymath Joseph Priestly from 1765! en.wikipedia.org/wiki/A_Chart_o…
Trying something new with this thread. Going for a free form writing style with infocomic visualizations and see where it leads me. Here’s my views on narrating tangled networks of stories:
This is going to be a write up on how I see this timeline visualization process. It documents how a tangled network of ideas gets ordered into a somewhat linear space for narration.
This is how I conceptualize the braided space: A highly networked system of entities with various kinds of relationships between them. This could be anything from actors in an ecosystem to modules in a software system. It is an abstract representation of the configuration.
Entities in a space are connected together through links. A braided space can have a lot of circuitous paths between entities that cycle back in an (un)certain number of steps.
Here are some properties of the braided space: Entities can exist in isolation or can form multi/hyper graphs inside them. Such configurations have implications for the ways you choose to deal with such a system.
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Here’s a metathread that catalogues the topics I have been exploring for the past few years.
Volume 1:
1/ What is Life? 2/ Lambda Calculus 3/ Linguistics 4/ Computational Trinitarianism 5/ Chaos and Fractals 6/ Differentiable Computing 7/ Higher Dimensions
1/ What is Life?
Inspired by the dichotomy of “gear like” vs. “life like” in engineering proposed by Alan Kay, I started looking into biology to understand it deeply. In this thread I visualize “What is Life?” by Erwin Schrödinger as I read through it:
In my pursuit for developing a graphic design tool, I realized the need for a Turing complete set of primitives for building designs bottom up. This lead me to Lambda Calculus, a formal system to explore the Turing Universe:
A few weeks back, I stumbled on this memoir by Alfred Kempe on the theory of mathematical form published in 1886. Here’s a tweetstorm as I read the paper.
Alfred Kempe was the student of Arthur Cayley. In this philosophical work, he tries to unify geometrical form with logic. It would later influence Royce, Peirce, and a slew of mathematicians in their work on logic. It is available here: royalsocietypublishing.org/doi/10.1098/rs…
The scope of this memoir is to distinguish the necessary matter of exact thought from its accidental garbs. Kempe believes that algebraical, geometrical, logical, and other kinds of thinking share a unified connected form.
Seeing this tweet sparked a thought that iteration could be cast as a sort of dual of recursion. The idea in @CentrlPotential’s tweet is called factoring out the characteristic equation of a recurrence relation.
The characteristic equation extracted out can be used to arrive at Binet’s formula via Umbral Calculus. This formula is used to calculate the nth Fibonacci number.
Conversely, golden ratio is approximated through iteration of ratios of successive Fibonacci numbers.
Making this post, transported me 8 years back to 2012, when I posted this question on Quora: quora.com/Can-all-iterat…
Starting it off with Zā’irjahs: an Arab divination system popular in the medieval period. This is a good paper documenting them: alpha60.de/research/scram…
Zā’irjahs are said to influence the work of the medieval monk Llull in creating his Ars Magna which has the idea of truth tables implicit in their combinatorics. He also did some pioneering work in visualizing conceptual trees.
Visualized a timeline of some of the eminent mathematicians who contributed to the concept of function. Made this to know their face, their lifetime, and character of their work.
It’s a warm up work for an article I’m penning on the history of function on @patternatlas.
It is funny to see how this exploration of history of analysis I pursued because of its relevance to computation dovetailed with the history of logic that I was exploring parallely:
Just got to figure out that both Cantor and Boole were exploring ideas in analysis before making breakthroughs in logic.
Cantor worked on the trigonometric series before he published the paper on about 1-1 correspondence of algebraic and natural numbers: math.uwaterloo.ca/~snburris/htdo…