TIL that light is an eigenvector of a Lorentz Transformation! I think this means that light plays the role of an invariant when you try to shift between two bases. For example: something like say truth value of an expression when you shift between two logical systems studying it. I am right now in the middle of researching something else and will have to return to this later, but this page has some real nice pedagogic material on Special Relativity: jila.colorado.edu/~ajsh/sr/sr.ht…

Can’t claim to have even remotely understood this article with the intended precision, but I just loved the exposition of ”Are deep networks just kernel machines?” here: m0nads.wordpress.com/2021/05/09/are… Stumbled on this discrete visualization of fundamental theorem of calculus by @PeterSaveliev and thought it was amazing!

There is more of such goodness in his lecture notes: dropbox.com/s/p8hxmgaygbb7…

A really cool visualization of Fermat’s Last Theorem by Andrew J. Hanson from 1990! (Part 1/2)

Source: legacy.cs.indiana.edu/~hansona/Ferma… This is the second part where Fermat surfaces are used to create a different visualization (Part 2/2).

Key takeaway: You can vary the geometric framework in which visualization is conducted to generate distinct forms for the curves.

Matrices can be visualized as functions! This enables us to see matrix multiplication as function composition. In this thread let us take a visual tour of these mathematical ideas. To get this thread as a PDF: patternatlas.com/v0/matrices-as… I stumbled on this idea as a part of my logical explorations. I saw how the matrix way of representing things has an intertwining between simultaneity and sequentiality which is awesome! Let us start uncovering the ideas here by representing matrices as pixel grids.

Catalog of Programming Languages for the Enthusiast: Starting a curation on some of the cool indie / lesser known programming language projects I have been stumbling on.

You can get the full listing here: patternatlas.com/v0/pl/ Starting off with Pikelet by @brendanzab. It is a continuous source of inspiration to see Brendan starting from game dev and getting into deep type theory stuff! Check out his language Pikelet: github.com/pikelet-lang/p… and his twitter stream for updates on his work.

Design ∩ Code Systems: Curating a thread on a topic I’m really interested in. Tools that blur the line between designing and engineering. Hope you find something inspiring here: patternatlas.com/v0/models-of-i…
@bahrami_ Nodebox (@nodebox) is a node based environment for generative data / interactive visualizations:

This people generator is an interesting application of it:

h/t to @tautau_co for reminding me. nodebox.net/node/
nodebox.net/gallery/2014/0…

Awesome ontology map of Mathematics by Daniel Tubbenhauer here: dtubbenhauer.com/Talk-Dublin-20…

After my explorations in the last few years, I arrived at an almost same global partitioning except that I had geometry and topology united and number theory featuring as a prominent circle. I found out previously that Category Theory derives from Kant’s work:

https://twitter.com/prathyvsh/status/1302515424240652288

but looks like Lawvere was attempting to formalize Hegel, who was inspired by Kant’s work!

Have a look at this nLab page to see how deep the rabbit hole runs: ncatlab.org/nlab/show/Scie…

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:

https://twitter.com/prathyvsh/status/1197525794245009408

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:

https://twitter.com/prathyvsh/status/1168695293166047233

@nathriche A very interesting post by @breandan that describes the various contexts in which graphs find application. Well worth a read! breandan.net/2020/06/30/gra… This is a laudable effort by @twarko in building a unifying ground for databases. It uses category theory to unify the different conceptual models of relational, key-value, graph, and other types of databases: mm-adt.org

This is one of the most important talks I have come across recently. It critiques the discrete alphabet oriented encoding which Longo locates as the LaPlacian computational paradigm for its determinism as being the reason behind many artificial bounds imposed on human inquiry.

https://twitter.com/patternatlas/status/1286555755978452992

Yet to arrive at a tractable way of expression for this in my programming work. But computation can be expressed as a traversal on a topological space. Here’s Longo’s paper that talks about topologies for computation: di.ens.fr/users/longo/fi…

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…

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.

https://twitter.com/CentrlPotential/status/1274169271631982597

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.

Catalogue of novel notation systems.
Repository: github.com/prathyvsh/nota… 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…

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:

https://twitter.com/prathyvsh/status/1188787773441888257

A subculture around “networked notebooks” like @RoamResearch / @nodebook_io is taking shape on Twitter. Me and @raghuveerdotnet are documenting them here: github.com/prathyvsh/netw…

Feel free to send a PR if you know more of these! Adding LambdaTank to this set. LambdaTank is an IDE+wiki platform that is built on top of LambdaTalk languages: lambdaway.free.fr/lambdaspeech/i…

Having a Turing Complete programming language as the base is a pretty intriguing way to create a networked notebook.

✨✍️ Component Designer Dev Diary 📔✨

I am starting a developer diary to document the making of an integrated web authoring tool for building websites instantly: prabros.com/towards-web-au… I am retroactively making my journal entries public as I needed time to evaluate my hypothesis. I wanted to work out the implications until a MV(aluable)P was created.

This happened towards April end. So now I’m happy to share my first entry from April 8: prabros.com/towards-web-au…

Found a neat (but incomplete) book called Category Theory Illustrated: boris-marinov.github.io/category-theor… Reading through this: boris-marinov.github.io/category-theor… I realized just that codomain obtained from a function application always has less or equal members to domain. That is, for any function application, the count of outputs is less than the count of inputs under a deterministic setting.

This is a problem I have been thinking about for a couple of years now. A good amount of time in programming is spent between trying to switch between various “modes of expressions“: data ⇄ code ⇄ graphics ⇄ data all of which are (homo/iso)morphisms among each other. Each mode of expression has a distinct value from a human viewpoint.

Data allows for operations on it using code. This produces distinct transformations (let’s call them representations) which can be serialized into a format which enables transferability.

Writing on Writing:

I reckon a lot of writing is coming up for me to communicate well about my endeavours. Here I catalog the good stuff that help me with my writing. First one is Bird by Bird by Anne Lamott. It’s a funny and truthful read on the challenges of writing. I did a review of it here: prabros.com/bird-by-bird-r…

Very intriguing article here: “The Structures of Computation and the Mathematical Structure of Nature“ by Michael S. Mahoney: rutherfordjournal.org/article030107.… Paradoxical constructs “application” and “abstraction” brought together leading the field forward.