writings on math, logic, philosophy and art


What’s the deal with Godel’s Second Incompleteness Theorem

I never understood what’s the deal with for Godel’s Second Incompleteness theorem in logic.

The consistency of a theory cannot be proved within the theory itself.

Duh! Did anyone thought that it could?

Federated networks

If done right, a federated network like Mastodon would be much more reliable and cheap to run than a centralized one: when the scale is big, the network has to be federated under the hood anyways (i.e. you have to have several caches in different locations, several database nodes that copy data from one to the other, several moderation teams etc.) and so the network that is federated by design has many advantages over the one that pretends to be centralized.

Maths and daily life

We don’t use maths in our daily life because other people have solved all hard problems for us and the solutions are encoded on the tools that we use, however not knowing math means that you will be forever a consumer, bound to use those existing tools and solutions.

Disclaimer: my definition of mathematics is much broader than the usual ones

Lambda the ultimate

Say what you want about functional programming being just one way to look at things, good only for specific problems etc, but for me looking at code written by a someone who doesn’t know lambda calculus is like looking at a blind person who is trying to find their way around the city - they might reach their destination eventually, but they would still be blind.

1 + 1 and programming paradigms

You can understand a log about different programming paradigms from the way in which they implement 1 + 1:

  • In imperative languages, such as C, it is just 1 + 1 - arithmetics is build in.
  • In object-oriented languages like Smalltalk and Ruby, it is 1.+(1) - plus is a method of the object 1.
  • In functional languages, like Haskell, it is actually +(1, 1) - plus is an inflix operator, which is actually a function. In Lisp you just cannot write (+ 1 1) directly.

Hard things in CS

Finally got the final list of the three hard things in computer science:

  1. Naming artifacts
  2. Concurrent
  3. Off by one errors. data processing

Conway’s game of life and the halting problem

Conway’s Game of Life” is the perfect setup for understanding the Halting Problem:

Given a pattern and a seed, producing an non-terminating sequence and the question, “Is this pattern a part of the sequence?” you cannot always answer that question.

If the answer is “No” you have to check the whole sequence and you cannot do that because it’s endless

If the answer is “Yes”, you can easily check it just as you can easily diagnose some issues with your code, but you cannot be sure it works.

Good theories

Whenever I think about good physical theories, I immediately think of Boltzmann’s statistical mechanics, not because he basically discovered the science of atoms and molecules, but simply because every time I see an ice cube in a glass, I see the particles, the Brownian motion, the way the heat and coldness dissolve etc.

And category theory is similar - it may not be a tool that I use to solve some important problems, that were otherwise unsolvable, but it is a tool that broadens my perception of the world, which is much more important and fruitful.

The dual to Occam’s razor

The principle dual to Occam’s razor is often under-looked:

  • Occam’s razor (or Negative Occam’s razor, as I sometimes think about it): Entities must not be multiplied beyond necessity i.e. when forming a theory, postulate no more than it is needed to explain the phenomena.

  • Dual Occam’s razor (or Positive Occam’s razor): Entities must not be removed beyond necessity i.e. if something is indeed needed to better explain the phenomena, it must be postulated.

David Deutsch uses this to makes a very compelling argument in “The fabric of reality”, regarding the Many-worlds hypothesis of #quantumMechanics that goes roughly like this: “if the other universes don’t exist, then where does the computation of quantum computing algorithms, such as Shor’s alghorithm, takes place?”

Short history of modern philosophy:

The biggest discovery of 19-th century philosophy was due to Kant, who discovered that you can have a framework that is entirely consistent with Plato, Aristotel, Leibniz et al, and at the same time consistent with empiric data, and with itself, provided that you accept that this framework is kinda subjective.

The biggest discovery of the 20-th century, due to Baudrillard, Barthes, et al (pardon my lack of French philosophy background), and at the same time by Wittgenstein, McLuhan and probably many other people, (actually, Hume was there all along) is that a framework that is subjective can actually be consistent with anything you want, as long as you don’t pose any specific criteria to what “subjective” is.

The biggest discovery of the 21-th century, is still due, I guess, but it would probably be some formalization of the idea of the subject, which would be a full circle towards the times before 19-th century.

Meanwhile in the realm of science:

Newton discovers a scientific framework that is entirely consistent with Plato et al, if only you have the concept of an absolute space, but the concept of absolute space doesn’t agree with observation.

Einstein discovers a framework that that doesn’t include the concept of absolute time (which he doesn’t admit is Kantian).

Quantum mechanics discover that a framework that does not rely on the concept of absolute time is inherently subjective (depends on observer).

Early and late Wittgenstein

Hot philosophy take: The big difference between the early and late Wittgenstein is that the early Wittgenstein thought that a picture is supposed to have a single interpretation that can be communicated between interested parties, whereas the later Wittgenstein realized that this can never actually happen.

Intelligence and freedom of thought

Intelligence is just the practice of thinking freely about something, (without accepting any kind of external dogma as a-priori true.) Nobody can ever teach you to be intelligent.

99 percent of being intelligent is realizing that all those fucktards who give you advice like “Don’t marry” or “Go study this and that” are just fucktards who don’t have anything better to do and are using you as a means to raise their self esteem m by having people listening to them.

Most people recognize some of these people as fucktards, but few recognize and are able to break free from all of them.


You only truly understand the things that you yourself made up. And so if you think you truly understand something, either you are wrong or you made that thing up.

Science and philosophy

Science is just a special application of philosophy, in the same way in which the scientific method is an application to what philosophers call critical thinking:

Critical thinking is just asking yourself “what would be the consequence if a given thing that we accept as true is actually false”.

The scientific method is the practice of applying this question to empirical observations.

Not sure who needs to hear this, but Penrose’s theory and all other Godel-related strong AI refutations are stupid: “Human mind is different from a computer because humans are capable of detecting logically inconsistent theories and logical paradoxes and think outside the box in order to know that they are paradoxes.” Not true at all - our mind actually does nothing more than what a computer operating system would do if it sees a process that occupies a lot of memory and doesn’t produce a result - it would kill the process (or the thought that leads to paradox.) We aren’t able to escape an infinite cycle because we are more capable than computers - we are merely equipped with heuristics necessary to escape from a situation that does not benefit us in any way (sometimes).

Science is philosophy

Science is just a special application of philosophy, in the same way in which the scientific method is an application to what philosophers call critical thinking:

Critical thinking is just asking yourself “what would be the consequence if a given thing that we accept as true is actually false”.

The scientific method is the practice of applying this question to empirical observations.


This morning I woke up with the following question in mind: What are the characteristics of the mental process that strips life from it’s dreamlike properties and makes it dull and monotonous?

My theory is has to do with dishonesty.

Dishonesty are the processes in which we purposefully create an interpretation of the facts that we know is not the most truthful interpretation.

So by being dishonest, we have to maintain two separate interpretations - the true one (which would always exist), and the the one we want to believe and/or want others to believe.

the true interpretation is “alive” - it always updates, it always has something happening with it.

The false one, is less connected to reality, so it is static. Nothing happens in it, as we have to ignore the reality with which it is incompatible.

Principle of triviality

Marinov’s principle of triviality: any self-consistent set of laws believes etc. can be reduced, at least theoretically, to a (usually small) number of clear elementary postulates and what follows from them.

Any set for which it is not immediately clear what these postulates are, is not self-consistent.

Simply put: if you cannot explain the complete system using layman language and constructs there is probably inconsistency in it somewhere.

Example: most religious doctrines.

Roko’s basilisk

Roko’s basilisk is a super stupid thought experieriment but it has a solid point - you shouldn’t ever listen to people who clearly don’t know what they are talking about.

Here is a solution to Roko’s basilisk - even if there were 100% chance that Roko’s basilisk came to be I would neve cooperate with it, because I am not evil and I want to save my soul. Fuck you Roko’s Basilisk!

Meaning something

I think that the number one fallacy that is making people stupid is the idea that everything that happens, everything that we see has to mean something. It doesn’t, most of it is just noise. Remembering most of the things that happened and thinking about them is just useless, and leads only to confusion.

Science today

Reading books of philosophy of science from the (beginning of the) last century leaves you pretty disillusioned about the state of science today: seems that the efforts to unify different disciplines in order to answer the big questions have evolved to making up new fields where their authors can work undisturbed, or producing theories of everything, which don’t explain anything more than their predecessors, all while voicing ridiculous opinions of philosophy and religion.

Formulas and text

Math is actually very far away from the universal language it should be and claims to be - read the formulas of some 200-year-old math paper - almost impossible to follow. Read the text - it reads like it was written yesterday.

Popper’s argument

The logical basis of Popper’s solution to the problem of induction - only with modus tollens we can make valid logical conclusions that proceed from specific to general, and we can make only negative such conclusions, e.g. “This swan is black, therefore not all swans are white.” Hence the only criteria for valid knowledge is fasifiability

Philosophy VS mathematics

Yesterday I was having fun imagining how would it look if people were bashing philosophical theories for being too impractical, in the way they are bashing mathematics. Like, for example someone attacking Wittgenstein’s Tractatus, saying “All too well, but what can you do with that theory?” And some philosopher sweating: “Well, it does have its applications is programming language theory…”

Instant gratification

Seeking instant gratification is not “living for the moment”, it’s a manifestation of our your fear of death (so kinda the opposite thing)

Converting others

The clearest sign that they do not feel content with themselves is their desire to convert others to be like them.

Kant’s discovery

The main discovery of Kant is that we are not “blank sheets”, but are born predisposed to certain modes of perception. This thought had profound influence on almost every intellectual discipline


Antinomy - an undecidable conflict between two thesis, none of which is true, simply because the question has no answer. (via Immanuel Kant)


Systematic learning (the way it’s done at schools) doesn’t work - the principal method of learning is being exposed to some new info which you connect to what you already know in a creative way, educational institutions always try to do the creative work for you and that’s why the process is bound to fail. Learning is always spontaneous and almost always comes from unserious and unusual channels.


I came to the world for the facts, but it turns out I can only have pictures of facts. This is some shit.

Wittgenstein VS Kierkegaard

Look how different philosophers are from one another:

Wittgenstein’s last words (upon hearing that friends are coming to visit him): “Tell them I’ve had a wonderful life”

Kierkegaard’s were “My life is a great, to others unknown and incomprehensible suffering.”

Seems that Wittgenstein and Kierkegaard are the modern version of the laughing and the crying philosopher.

The best of all possible worlds

And to think that we live in the best of all possible worlds, I mean, imagine what the rest of them look like.

Reading David Hume’s Treatise.

I find it fascinating how similar it is to the Critique of Pure Reason, though the backgrounds of the two authors are so different.

Kant and Hume embody the religious and scientific schools in philosophy, Kant seeing belief as a transformative force and Hume seeing it as a peculiarly of the human character.

The ultimate conclusion that you can reach when comparing their viewpoints is that causality is not a law, nor a meta law, but a belief which every thinking being must hold to some extend.

Science = Philosophy + Mathematics

This came because I learned that when writing “Principia Mathematica”, Newton was influenced by two books - “Principia Philosophiæ” by Rene Descartes, from which he took the subject matter (and the name) and “The Elements” by Euclid, from which he took the method of reasoning.

Deepest chapter of the Critique

At first I thought that the Transcendental Deduction was the heart of the matter of “The Critique of Pure Reason”, but upon rereading, it’s definitely not it. The deepest chapter is appropriately called “Systematic representation of All the Synthetic Principles of Pure Understanding” and is awesome. Especially the “Analogies of Experience” and the “Anticipation of Perception” are so deep that I did not understand a single word at first, but it all comes together with time.

Positive nihilism

Nothing that you say or do matters in the grand scheme of things, and this is pathetic, but more pathetic is the refusal to accept that fact, instead of conforming to it and thus making it the only thing you conform to:

Your achievements don’t matter, so no point in being dishonest.

You failures don’t matter, so no point in giving up.

Your strive to perfection is vain, so no point in pressuring yourself.

Rookie mistake

Top one rookie mistake made by analytic philosophers: thinking that just because X can be represented by Y therefore X is Y. So for example, just because a given phenomena can be represented by maths, does not mean that it is “mathematical” by nature.

The concept of self

Re-reading “I am a strange loop” and finding much stuff that I missed originally. I like the author’s idea of an organism’s concept of self as the central concept in an organism’s system of thought, and the one that binds all other concepts together.

Like, a concept is considered true and real by us only if it relates to our concept of ourselves. Our concept of ourselves is the realest thing there exists for us (although it in actuality is completely objective).


I wrote a very long article on capitalism and solarpunk which I did not publish anywhere, but the gist of it all was that when (if) we humans start fearing spiritual death more than we fear physical death, our society will arrive at the next stage.

Kant and Dogen

Dogen’s concept of a “myriad of things” is very similar to Kant’s concept of the “manifold of sensibility”, essentially both are trying to highlight the novel, flux-like aspect of reality, the fact that the concept of objects are subjective (no pun intended). It would be a really cool plot twist if it turned out that Kant had read Dogen (very highly unlikely in real life).


“The world is non-deterministic” bugs people so much because it is another way of saying that all science theories that are and that can ever be created are just abstractions that will never get to the heart of the matter.


Scientism isn’t a religion - it’s a cult.