Astle's stream

On Nature of Computing

The nature of mathematics is a well explored and talked about question (1) while being a profoundly deep one. On the pathway to answer it, we have created entire sub-branches of fields and areas of study.

As intriguing and fascinating as this question is, I find myself leaning in towards a particular sub-branch, which is the pragmatic realization of mathematics in our physical world: computer science, and how this recent branch of mathematics might help us speculate an answer for the ancient question.

My approach in discussing this topic in the essay is to simply draw parallels to ideas I have encountered in two papers: On proof and progress in mathematics and TheAge of stochasticity. These papers are, coincidently, both written in the previous century (1994 and 1999 respectively), and it really shows the deep insights of the authors in predicting the nature of modern technology, through speaking about the nature of mathematics.

We shall start things off with the first paper, written by the fields medalist mathematician, William Thurston. In this non-technical paper, Thurston talks about his personal experience in learning, contributing and teaching mathematics. He expresses the the idea that the goal of mathematical proofs, and the very reason people study them, is to understand them. The communication of mathematical ideas must be focused upon, where although obscure formulae and derivations are important, the transfer of ideas is more crucial still. Thurston's point that the reason we humans do not want the answers and proofs to certain questions, but want to understand them, is universal, and brings us to my first parallel: programming as a means of communicating ideas.

Now anyone who knows programming would find the above statement confusing, and some might even claim it to be completely false, since, the very act of programming involves communicating with a computer, with almost always no other human in-between. This is true, but not just for computer science, but for any field out there. The literal act of studying a particular subject is different then what W. Thurston is talking about: the purpose is to explore the very nature of mathematics/computers, and collaborative research is the only way to move forward. We need to communicate ideas to other people in order to build something new and expand the very boundaries of a field. Programming as a medium of communication with fellow developers is an idea seldom talked about explicitly, but is very well known by experienced programmers implicitly. Collective effort has given us the gift of modern mathematics and modern computer science .

The second paper is a rather interesting one. D. Mumford talks about the underlying thought process of mathematics and challenges the assumptions and the way we have approached them for the past two millennia. Logic and formalism have dominated not only mathematics, but also our own thought processes, and was viewed as a dominant approach to accurately approximate and model the reality around us. Rigour being ingrained in how we approach mathematics can be traced back to Euclid's postulates, and building up from there, to eventual reconsiderations and reformations. However, logic and mathematics still seemed to be intertwined until the end of the previous century, when alternative ideas and ways of thinking won over the mathematical community, including people like our author, D. Mumford.

So what is the alternative ? The above excerpt might be a bit misleading, and make it seem that the alternative idea is some poorly explored, extremely niche topic. On the contrary, it is a well known and one of the most prominent fields of study today: Probability and Statistics. More precisely, it's the probabilistic view of our mathematical structures and models that out-performed classical methods in practical use cases and applications that led us to finally challenge the dogma that logical reasoning, with precise formulae and riguor would help us model reality better, when it was a probabilistic view of the world that succeeded. While the evidence can be found in the triumph of probability and statistics in almost every field, we shall explore narrow our focus on one particular field: computer science.

The computational model, famously proposed first by Alan Turing, and which came to be known as a Turing Machine, initially relies heavily on logic. Even the real-life implementation of actual computers chips relies solely on what we call logic gates. These formal models of computing, paired with the real-life implications of systems build upon them point to a clear winner, logic: formal, precise and deterministic.

A more probabilistic model of computing is recent, and quite heavily researched today: Quantum Computing. The point of speculation, that Quantum Computers can better simulate real life particle interactions then classical computers, due to the fundamental reality of our world being quantum is a good indicator of a very basic fact about the nature of mathematics, one emphasized by Mumford in the above paper: to better model reality, a probabilistic view of the world is a necessity (2)

The above papers, in their exploration of the very nature and purpose of mathematics, helped us shed some light on the nature and purpose of computing. Computing or programming as a medium of communication and it's underlying nature being probabilistic are two schools of thought that emerged since the dawn of computers, benefiting from the two millennia of mathematical research in a few decades, and quickly dominated the research and corporate communities.

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1: Is God is a mathematician ?

2: Another good example is our current leading theory (and implementation) of intelligence: large language models. These model's underlying assumption of the nature of intelligence is that it's probabilistic, and which has clearly outperformed any other method of achieving "Artificial Intelligence" upto this point.

Moments I felt the AI

Since 2020, there were only a few moments I was really fascinated by AI, and I thought about jotting them down here.

• When chatGPT (3.5) came out, I was intrigued by it (obviously), but more as a certain piece of software I needed to know the internals off, rather than it feeling like "AI". Nonetheless, it kick started my mild obsession of going through books and courses to understand the how.

• While travelling in a train, my friend mentioned the newly released GPT-4V, with vision capabilities. He then went on to click a picture of the floor and ask gpt-4 to describe it. That moment was a fuel for me to continue learning about these models (though I didn't really aim to be a model trainer or anything as such: just pure curiosity).

• YouTube was my go-to entertainment site, and here I came upon Gothamchess' AlphaZero vs Stockfish analysis. The match was thrilling (credits to Gothamchess' extremely entertaining commentary) and really excited me about the paradigm of Reinforcement learning, even though both RL and AlphaZero where old at that point (came out in 2017). Before that, I had bought a book on the chess engine, but it failed to awestruck me the way Levy did (the book heavily focuses on chess, rather than AI).

• I had been well into the lore of deep learning, LLMs and the AI paradigm, whence I came upon a blog which explores the entirety of llm training process, from the ground up. Now this blog does it simply through tracking the process of a new player in the AI league: DeepSeek. Simply reading this blog, and reading about the (then) 16 papers released by DeepSeek, I was hooked. It wasn't just transformers, it was distributed training, creative data preprocessing and many other things (as evident by their recent opensource week tweets) that set them apart, not to mention everything is open source. Probably my favourite blog on LLMs till date.

Types of codebases/software

In my little time of learning and loving programming, I have come about to view it as a tool. There are people who love and cherish their tool, there are those who simply use them to get work done, there those that want to master the tool, automate the tool's job, etc, etc.. This tool has given rise to enormous amounts of economic value, entertainment and livelihoods. This tool has led us to built projects, from big ones to small, from simple to complex. Here, I am writing about certain types of projects one might encounter on Github. Of course not every project will fit into these categories that I present, but I implicitly tend to categorise projects I encounter into some category, hence I might as well write about them here.

Small scale business applications, most programmers when starting on their journey to become an SWE would start here. These often serve a simple and small business need, and include a simple CRUD app with a db (all the various stacks). Note that it is not the stack, but the scale that determines that these projects are albeit easy to get into, and serve a real life need. Could be your To-Do lists or smaller scale e-commerce sites.

Small libraries, not a lot of programmers would venture out to build libraries, but still a lot actually do. These libraries generally serve a single purpose and do it well. They are generally written by some person(s) who came across a unique problem, and being the great programmer that they are, implement a solution and gift it to the world. Some good examples are MiniSearch, an in-memory text search library in Javascript, or HNSW in Go, which implements the HNSW vector index in Golang. Small, elegant yet powerful.

Large scale applications, one normally gets here by simply scaling up the above mentioned business applications, and eventually run into unique and hard problems. These problems are worked on and solved by some of the best programmers in the world, and often have a user base in the millions. Usual examples (at least the ones which are open-source), are Telegram, Tiaga and one of my favourite, Tldraw. (Is Tldraw a legit business application ? Don't know, but love the repository).

Large/Complex libraries, probably contains some of the best (if not THE best) code written by us. Larger libraries and business applications differ in their goal and how they plan on achieving it: one is profit oriented, while the other is more or less scientific. I am not sure if this distinction holds in some examples I am about to give, but nonetheless, these massive libraries are all open sourced, and hence provide for some excellent codebases to read through. Some favourites: Postgres, Linux, Torchlib, Glasgow Haskell Compiler, LLVM, React, Numpy, FFmpeg, SQLite, V8 and finally GCC.

Why more examples of larger libraries ? Because they more or less drive the software world ahead and have stood the test of time, with relentless innovations and selfless contributions from the open source community.

Through the Lens of Now: How Presentism Shapes Language Models

This meme is a good reminisce of the concept of historical myopia/Presentism, where we humans have a skewed/biased view towards our current times. Once being reminded of this, it also becomes clear that our exploration of technology is also largely based on how we view the said technology, and how we draw analogies to our surroundings/nature.

I am sure there maybe many more examples, especially after the age of computers, but here I would like to trace out our latest innovation: large language models. Since this seems to be our latest belief, we can even see how each time we climb a level of abstraction to borrow ideas from. (We went from taking inspiration about how the brain functions, anatomically, to taking inspiration to how it thinks).

Initially the research seemed to be more "computational", in the sense that we had to move away from how our brain functions to take into account statistics and data science to dish out what empirically worked: model training at scale. An analogy here is we are simulating millions of years of human brain evolution, by training a massive model on most of today's human knowledge (called the Internet). The next paradigm, which is recent (post 2021), also called Supervised Fine-tuning, is about further training the model to behave in ways expected by users/consumers. The analogy is easy: after birth, we are trained till 18-21 years of age to behave, while societal and cultural values are indoctrinated in our young minds.

The analogies may seem a bit far-fetched, but once viewed this way, they do make sense (humans love analogies after all). The next paradigm is even more obviously drawing it's inspiration from how humans think: spend more compute power on harder problems, called Test-Time Scaling. It is as simple as that: keep the model "thinking" and "reasoning" so it can solve harder problems.

At this point, further research tries to draw on more inspiration to how humans think, perceive and reason. Another research tries to make the reasoning process implicit, similar to how humans sometimes perform well versed reasoning task without explicitly thinking about it, also called System 1 vs System 2 thinking.

These analogies help us see not only how our current technology closely resembles us in more and more abstract sense, but how we try to mimic our own thinking processes to nurture said technologies to their absolute potential.

Software Design

Throughout my experience of reading about software (yes, reading and not writing :) ), I have come about to really like and admire the design decisions that take place, that eventually get implemented and either make or break entire codebases, especially when writing libraries and/or complex tools. This aspect of writing software not only comes from someone with experience, but also from someone with a purpose, and hence a vision they want to accomplish: which is fairly uncommon nowadays due to the career-driven nature and popularity of software engineering jobs.

Such decision processes and "philosophies" are prevalent in almost every widely used software product out there. No piece of software, used by millions, is mediocre. This provides for an extremely interesting and valuable source of information in order to learn from such examples. I am personally fascinated to read about the thought processes and design decisions taken by the architects of large codebases and software products utilised by generations of developers.

One subtle aspect of trying to read through these essays/blogs/walkthroughs is, it is not important to understand the technicalities and the inner workings of such massive projects, even professionals would take years! The best lesson, at least for me, is to look at the what, why and how of a particular decision and understand how similar situations and problems can arrive when I myself venture out to writing designing a project. The architects (most of the times) explain how they came about a problem, why they implemented (or didn't) a particular feature and other semantic decisions, which provide for a rich source of context and rationale behind the system's design.

All that being said, I think personally I am too inexperienced in order to learn a substantial amount from some of the blogs I have read, but nonetheless, it is often exhilarating to find common design patterns in unexpected places. Apart from that, it is often inspiring to read about certain codebases which are decades old. Others ? They offer valuable and quite intriguing examples of how/what problems certain developers faced, and how they came about the solutions. There are many other examples that are good, but due to being highly technical and niche, aren't pragmatic for the average developer. I nonetheless read through these blogs to at least understand their problem solving approaches (though to actually solve problems of that calibre, one needs to be an expert in the field).

I believe the want of designing any software comes from having a deep passion and appreciation of code, both as a tool to solve real life problems and an art. I personally tend to be more on the artistic side, but lately, I am trying to design some real life problem solutions as well.

Reading Levels

Often as a reader, when being approached by a non-reader (however one might define a non-reader, or novice), I am forced to think about reading in levels, and give it a type of hierarchy. One expects a reader of a certain level to find it "easy" to read material on their own level and below, while "difficult" or "draining" to read above.

It is tough to give such a ranking to various types of material, but easier to put forth an opinion on the same (and fun). One obvious thing to exclude is material meant for kids: I am only considering adults here. (As mentioned above, this ranking is entirely based on my opinion)

Coming up with titles for said ranking is tough (very subjective), nonetheless I shall give levels of reading material as:

Self-help

I didn't dwell on this level much, but I did start by reading some famous ones like Think and grow rich, Rich Dad Poor Dad, The man who sold his ferrari. Books meant more for the general audience and, of course, self-help. A person who claims to be a reader but has only read up-to this level should stop doing so.

Commercial

This level is mostly about novels and magazines, so more focused on entertainment. There are certain sub-levels, but overall this material here has easier language and provides the reader motivation to read further, hence is easier to get through as well. Some novels are mainstream (Harry Potter, A song of ice and fire, 1984) and easy, while others are harder to get through (Lord of the Rings, Sherlock Holmes and even Pride and Predujice. These aren't harder per say, but have an older language, same as any works of Shakespeare). Overall to be at this level is to be a consistent reader, and being passionate about reading novels. (Also I think I should mention the Discworld series here as well, just for the sake of it)

Introductions

Here we leave the realm of fiction and enter reality. Books here are generally considered for obtaining useful and often interesting information on various topics/concepts/fields . Books that I have read on this level are Guns, Germs and Steel, Sapiens, Poor Economics, Freakonomics, Deep Work and many more. These seem like a good introduction to a certain field when read for the first time, while being easy to read as well, though one has to be determined enough to get through it all.

Specializations

As the name suggests already, here we have entered the realm of academics. Most frequently read by graduate (pre/post) students and above, material here is generally not touched by the normal populace. Though a majority of students do read such material, it is only when one does it consistently and with enough passion that they can be considered a reader at this level. Ounce a person reaches here, they would hardly ever go back to the ones above. (Even if they do, it'll not be below the Introductory ones). Being a reader at this level is not about reading books/papers in a field as an assignment or in order to gain a degree, but reading them just for the sake of obtaining that knowledge.

Expert

One would usually find authors here, people who research and write often. They are either novelists, researchers or in some cases just passionate readers/writers. Years need to be spend in the level above in order to get to this level of reading. By this time one has read so much, one feels compelled to pour out all the words out into the world. (Not all authors are extremely into reading of course, but I think every "expert" level reader would eventually want to pen down their thoughts). I would love to be at this level someday.

This list is not meant to be accurate or rigorous, but somehow roughly maps my own reading levels through the years. I have put a list of everything I have read here, if anyone is interested.

The Computational Complexity Paradigm of Machine Learning

The bitter truth is by now well known amongst all those who wish to consume the knowledge behind anything Artificial Intelligence/Deep Learning. The lesson was simple: no matter how we structure our algorithms to mimic human capacity, it will always be outperformed by simple scaled architectures with massive amounts of data and parameters.

This lesson is quite reminiscent of the computational paradigm that Stephen Wolfram claimed to have started back in the 1980s, wherein the traditional mathematical thinking was left behind for the sake of exploration of a new way of thinking: from simplicity to complexity, through the power of computation. This would seem quite familiar to a form of Chaos theory, wherein simple initial conditions give rise to complex phenomena.

It was only then that I realised that the scaling law is but another beautiful aspect of computational paradigm, where in simple architectures (say embeddings + transformers) give rise to quite complex phenomena (whatever LLMs are capable of), and thus modern deep learning is a wonderful example for what we can elongate and call computational ML, or computational NLP.

This plays in tandem of the new era of computation that we can explore, where we need not abandon the older mathematical style of thinking, but rather complement it with the compute power it needs in order to show us rather astonishing breakthroughs. Simple linear algebra coupled with optimization algorithms turned out to mimic language quite well, and even learned to perform human-like reasoning. Such breakthroughs urge us to turn our attention to this new computational style of thinking, and explore further.

(In quite a fascinating way, mechanistic interpretability maybe one of this "holes" that Wolfram talks about, where the complex system that is the LLMs may not be computationally irreducible, but can indeed be reduced to it's simpler forms. This could ultimately not be true as well, and we may hit the truth that LLMs maybe computationally irreducible, but current research has been promising).

Finding useful connections from Wolfram's work into this field of ML was quite interesting, and indeed made sense. The mathematical foundations which were all discovered independent of the computational way of thinking turned out to pave the way to really great results when paired with computation and the complexity it brings with it. This also makes me wonder what would Ruliology + ML would look like, wherein we find simple "models" (not to be confused with ML models) which can lead to complex systems down the line (induction heads?).

While we explore more of this computational landscape, various new interesting modes would show up, and I would be just as excited to read (and hopefully contribute) to such paradigms.

Doctrines don't scale

The reason we have intra-species conflict is because doctrines do not scale effectively

Each individual person has, as is common knowledge, a mental model of the world. This mental model, as is given, is flawed. It's almost certain that any one person cannot truly grasp the reasons behind the what, why, and how of our world. These differences in flawed mental models are what primarily cause conflicts, and have been the primary reason since the dawn of Homo sapiens.

One could see this and come to a conclusion: since these mental models lose their malleability as we grow older, it'd be in vain to do anything about changing them, and thus more effort must be put into conflict resolution and cooperation.

Here we come upon another realization (at least I did) that we have been doing conflict resolution and cooperation on an unprecedented scale since the start of the agricultural revolution, in the form of cities, kingdoms, empires, and nations. It was finally religion that eventually captured the most number of people, and today is the main driver behind cooperation across thousands of kilometers.

But for human conflict to be truly gone, we need one single belief, shared by the entire human species. As of this moment, I cannot think of one. (There are people who do not even believe in the Earth being round, so...) Even the most widespread doctrines cannot capture the entirety of the human population, not to mention effectively capture their minds (how many Christians are actually devoted?)

This means that as of now, our primary tool of communication, language (and humans), has yet to come up with a doctrine that can scale to nearly eight billion minds. We do not yet have one nation, one religion, nor one language.

I think the reason is the difference in evolution of the hardware (the anatomy of our body/brain) and the software (our mental models). Our minds developed complicated theories much faster than our primate brains could evolve, hence we still live like the forager bands roaming in the savannah: just that our bands have gotten bigger and intermingled.

In the future, I am optimistic that at least one such belief would spread, leading to a true unification (one could argue that the fear of nuclear weapons is one such thing, but you never know) of the human species.

Unfeeling emotions

One of the things that I've heard most in my life is my lack of emotions, or rather my lack of empathy.

This results in most people viewing me as your average "logical", "rational" or "critical" minded person, wherein every conversation or debate seems like a formal proceeding in a court of law: no emotions, just facts.

Though in fact I had an almost opposite view of of my own self, shocking as that may seem. Overly emotional and unable to control them, going from short-bursts of anger to being over affectionate (puppies ofc) and sometimes, or I would say most of the times, overwhelming people around me.

This may seem contradicting, and any mention of this by me would lead people to think that either of those views of my self is wrong. (Either people are, or I am), and I would disagree

Both of those views are correct. While my internal self and external self may seem conflicting, I would actually put it under the umbrella of having intense emotions and living at the opposite ends of the spectrum, going from seeming overly emotional to seeming completely emotionless.

Is this an advantage ? The obvious answer is that it's impossible to decide which personality traits are advantageous in our modern society, as that would require us to define what having an advantage even looks like, but if it's genuine happiness, I guess I have it :)

Alternatives To Religious doctrine: why to live

• Homo Mathematicus. Going personal with this one, but it could truly be the "language of the gods" or the code that underlies mother nature. From higher dimensional spaces that we reside in, to quantum consciousness explaining our deepest mysteries, we revel in the idea of formalism and creative thinking. The glory of studying math being only bestowed upon the chosen few, we must spend a lifetime trying to find the answers to the mystery of the universe.

• Homo Economicus. The economic rational mind, always logical, always critical. Here we discuss the impact of marxism, socialism and Capitalism. The becoming of a society, the formation of culture. Thinkers and rationalists of this genre have put forth theories that continue to influence the thinking of large fraction of our populace. From financial institutions to the wealth of nations, this doctrine is as fascinating as it is vast.

• Homo Philosophicus. From the western influence to the eastern, this doctrine spans thousands of years and is the mother of all disciplines. A form of thinking itself, nihilism, absurdism, modernism and post modernism are a few areas were countless intellectuals have tried to find answers to the question that is the Human. Modernism and Post-modern would try to amalgamate with modern epistemology to make behavioural models, while other forms reject everything. This doctrine is a rabbit hole of paradoxes and logic, history and well ... philosophy.

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1. Is God is a mathematician

2. Economics Library

3. PostModernism/Rationality

The Spiritual Mutiny of Intellectual Subsistence

History has been the best story-teller, teacher and guide that humans have encountered. Recording the thoughts, laws and events of the past has been one of the best decisions humans have ever taken.

This leads us down an adventurous path, where we follow the Human across time, finding various reasons to live, while being burdened with knowledge and an excellent prefrontal cortex . We stumble upon mythologies, religions and belief systems spread across lands, the cause of miracles and wars, life and death.

These belief systems are drivers of the human will, an invisible hand forcing the human brain to act a certain way, while directing entire societies, regimes and cultures, and have been doing so since the dawn of time.

Philosophy would be an introduction to the study of belief systems. Though I personally have not delved deep, my personal belief systems have evolved throughout my childhood, and I am currently exploring the vast forest that we call the Internet. Deep within the net, we find some interesting thoughts, while other places, such as youtube, offer some different ones.

My intellectual journey will continue till I die, but I hope to enjoy exploring the depths of thought, language and reality as I go on. That will be by mutiny to the intellectual subsistence of the modern times.

Language Entropy

While on my daily crusade of reading research papers, I found myself being fond of a very particular feature that they have: more information in less amount of words. This made them information dense. I begin to wonder on the complexity of concepts, their measurement and precisely their measurement through the tool we call language. Formalism somehow seems to be tied to these, so let me define a few interesting words, before we continue.

I will discuss some key intuitions below, which come from various concepts spread across computer science and statistics, though the required knowledge is just surface level.

Abstractness: The measure of how far the definition of a word is from a tangible object.

Abstractness of a word can be thought of as the depth at which it appears in a Tree with ∞-children, where each node is a word, and the root nodes are all tangible, real and physical objects (articles, names and other words), and their children are other words derived from them, but with more abstraction. As we climb down the tree, the words grow more abstract, as they are in-turn dependant on less abstract words, all the way to the root, the tangible words. Hence the depth at which these words occur is the "Abstractness" of the word.

Entropy: The measure of randomness, uncertainty and disorder.

Entropy = 1/Abstractness. More abstract words have lesser entropy, which means a sentence with more abstractness contains a lot of information in less amounts of words, and hence are more efficient, a form of compression where the knowledge is not provided by the writer, but is assumed to be known by the reader. Hence sentences, paragraphs or any other piece of text has a total entropy which is the product of all the entropies of each individual words (the reason for a multiplicative model over an additive one is to wipe out the effect of the root words, which have entropy = abstractness = 1).

Understanding: The measure of how much of a new piece of information is known prior to the revelation.

Understanding of a concept, word or any information can be interpreted as the amount of times we have encountered it before. Every time we are exposed to the same piece of information, we understand it a little better (deliberate or non-deliberately), and hence our understanding increases. More abstraction means more levels to climb before we reach the root node (which we have a perfect understanding of since we can directly observe it), and hence more complex the piece of text.

Complexity of any written text is dependant on it's total abstraction or it's entropy. A sentence or paragraph with more root words than abstract ones has more entropy, and so the information is "spread out" among many simpler words. As we compress the words into more abstract ones, the entropy decreases, while the complexity increases. The increase in complexity can be attributed to the fact that we need to go higher up the tree to reach a root node, while the connections between each parent and child node must also be strengthened in order to develop a strong intuition of the piece of text.

This can also be viewed as a simple function that maps a word to a scalar value.

f(word) -> R

R in this case can either be the abstractness or the entropy of that word. Which means the entropy of a sentence of a piece of text is:

Abstractness(Text) = Mult(Sum(f(words of Text))) Entropy = 1/Abstractness(Text)

Now with the advent of word embeddings, we can perform some more interesting operations. Let suppose a word is represented by an N-dimensional vector. Let the vector be called V. We can substitute the above given equation like so:

f(Rⁿ) -> R

Abstractness(M) = Mult(Sum(f(V)))

Entropy = 1/Abstractness(M)

Where M is a bunch of such word vectors put together, hence a matrix. The function simply maps the matrix to a scalar value (entropy or abstractness), which is an indicator of complexity. Here, we cannot ignore the fact that complexity itself is relative, and must factor it in as well. The complexity of a piece of text highly depends on the knowledge base of the person reading the text (A simple sentence in Chinese is extremely difficult for me to understand, as I would have to construct a new language-tree from the root up to even begin understanding it).

Let suppose the knowledge base of a person is represented by the amount of words he/she is familiar with, including the nodes, their children and the weightage assigned to their connection, and call it K. This knowledge base, being made up of nodes as well, has it's own entropy, Entropy(K). This should, logically, be subtracted from our initial overall complexity (the product of all entropies of a piece of text) to get to the final "Complexity" of a sentence.

C = Mult(Sum(f(words of Text))) - Entropy(K)

C = 1/Abstractness(M) - Entropy(K)

This is a mere play of words, a mixture of thoughts and the written expression of the same. Formalism to express realism has always fascinated me, and hence I write this small piece.

High(er) Dimensions

Dimensionality is an important concept in essentially every STEM field, and much more. The concept of dimensions and what they are, where they are useful and ultimately what they represent was multi-faceted and thus I was intrigued enough to write a note/essay or this particular topic.

What are dimensions? In a word: features. A dimension is just a feature or an attribute of another object, be it an inanimate object or a living organism. The dimensions we are most familiar with are the three dimensions of space: length, breadth and height. But wait....aren't there more ? Fourth could be time, and as far as theoretical physicists are concerned, there are a lot more. How can scientists even claim that there are more dimensions when it's impossible for us to even imagine a fourth one ? It's hidden in representations.

We represent our reality through numbers. They are a crude, but sometimes fairly accurate representations of our reality. Equations that scientists have created in a closed laboratory or a classroom have come to predict the movement of stars and other celestial bodies, so yeah, we trust our numbers to model the universe around us. Knowing this, we represent our dimension with a list of numbers, say [1, 2]. But we have three dimensions, so we put three numbers: [1, 2, 3]. These three numbers are fairly good representations of space in various mathematical equations. That is, a certain feature of space is being represented by a vector.

But what's stopping us from putting in more numbers in our vector like so : [1, 2, 3, 4, 5, ... ] ? An obvious answer would be reality itself. There's no point, no physical counterpart to a vector of more than 3 numbers in it (just like the word unicorn has no physical representation in our real world). This was true, until during the pursuit of solving various equations, physicists were forced to expand the dimensions in order to solve (or formulate) the equations. Our theories forced us to go beyond our own senses and come up with more and more "dimensions" or features that represent space itself. (Whether it is true or not is out of my ability to grasp)

The language that we speak was modelled to a great extent my large language models (LLMs) in recent times. Their response not only makes syntactic sense, but also semantic. This worked because we were able to model our language, using a crude approximation, or in other words: vectors. Each word has N dimensions, or in other words, N features which give the LLMs power to use the word in different construction settings, or in more human words: they understand what the word means!

Understanding being analogous to "being able to see multiple attributes of an object" was something I had never thought before. It's only when our mental models construct multi-dimensional vectors of certain concepts or words do we truly understand the said concept or word.

Finding analogies between mathematical concepts and real life is fun and in a way enlightening. Modelling our reality with such approximations means whenever we are right, we are gifted with the greatest reward: understanding ourselves.

Judicial and Political Correctness

In a recent discussion with a friend of mine, I found myself explaining my lack of opinions on political matters and the lack of interest in judicial ones as well. The former has been (and probably will be) criticised as ignorant behaviour and irresponsible . With the general populace yearning to discuss political matters, my disinterest stems from a number of reasons, which I shall mention here.

Any opinion, be it political, personal or moral, is believed to be the absolute truth by the individual. You have opinions because it is your belief that they reflect the objective reality around you. That is the sole reason you even have them: having a mental map (however approximate) helps us navigate through the world and "make sense" of it . But it's almost always the case that our opinions do not reflect the objective reality, in some cases, not at all. Our opinions are the amalgamation of our cultural thinking , personal opinions of people we grew up with and our own personality traits . None of these factors force our opinions to reflect the objective reality, hell, none of these factors even force us to rationally analysis the facts and come to a logical conclusion.

A personality trait of mine is I like objectivity (you could guess where I am going with this). Opinions on any matter aren't mostly objective at all, hence I find no meaning in having them. Whenever we believe in something with all of our heart (and rational brains), we should also have the courage to call them facts. If you are hesitant in calling a certain thing as a fact and more comfortable with the term "opinion", you know somewhere you aren't exactly right . The problem this creates, is that our opinions drive reality: in Judicial matters. Judicial laws are largely made on opinions of the time it was written in, which makes them highly susceptible to change and ridicule by future generations. I would refrain from talking further as this could spiral into a long essay.

Social responsibility isn't having political opinions. It's not that I don't care what's happening in the world by not bothering to read on it, it's that no matter how much I read, I'll never have a grasp on the actual objective reality of the situation and would thus always carry a bias with me. The bias would depend on where I grew up, who I talk to and what my own personality is. And as long as the reality is unknown to me, my opinion will always be wrong (that's a personal belief).

So what should we do ? Not learn anything of the outside world ? Live in our own little bubble ? I think we should acknowledge the facts, agree that no one individual can grasp the entire situation and take action towards betterment of everyone around us.

AI and God-Man

AGI = Artificial General Intelligence
ASI = Artificial Super Intelligence

Learning is the slope of gathering information in a way that can be utilised later (let's call it L). With that being said, the rate of rate of learning is an interesting concept: it's the second derivative of gathering information or how fast can we learn to learn new things (let's call it R). The distribution of L, or what my rate of learning things is, follows a left skewed distribution where our L peaks at childhood/adolescence and starts to deteriorate as we get older. What about R ? I think that's completely upto the individual's effort and willingness to exponentiate their ability to learn things, but most people do not bother to climb down the next derivative .

What if something else did ? What if we build a system that focuses on learning to learn better and faster ? It'll result in exponential growth of everything we know. Knowledge and by extension technology growing at an exponential rate is, in our current state, unfathomable. We'd be left in the dust, scrambling to look ahead while the vehicle zooms past us. That's AGI, on it's way to be ASI. It's not a what if anymore: we are trying to build one, and maybe are getting closer.

A controversial theory for consciousness was written by Julian Jaynes in his Origin of Consciousness, where he suggests that we evolved consciousness only 3000 years ago, which means our ancestors where pretty much unconscious before that time. That claim has deeper implications, and the one I'm focusing on here is: it suggests we humans have evolved our brains, without changing its biological anatomy and it resulted in progress on such a scale. Consciousness was a necessary step in evolution. And of course the most probing question is : can we do it again ? If yes what'll it even look like ?

My initial thoughts were ASI outcompeting and destroying us if we get there, but if ASI was to provide humans with adversities that we've never before seen (for at least 3000 years (?)), is another human evolution possible ? Mark Hamilton argues in his book that such an evolution will happen, and it'll be our last. We will evolve ounce more, to become what he calls a God-Man . This sounds exactly how it is: we become literal gods. I do not know if this theory is even legit, but if I had to guess, our next evolution could be the ability to drastically improve R and to keep doing it throughout our lives (something we expect ASI to do easily) . A human who can do that would be to us what we are to chimpanzees. This same analogy is used to compare an ASI and us. We are the chimpanzees.

So what'll happen ? ASI vs Humans ? That's doomsday for us. ASI vs God Man ? That depends on whether Julian Jaynes theory is even legit, and even if it is, will Mark Hamilton's claim of it happening again is legit and under what conditions.

This may sound very highly speculative and based on unproven theories, but that's the fun part of not knowing the future: trying to imagine it.