writings on math, logic, philosophy and art

science shorts

On 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?

Hard things in computer science

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

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.

Science philosophy and mathematics

Science is just a subdiscipline of philosophy, the scientific method is an application to what philosophers call critical thinking.

Critical thinking is just asking yourself the question “What would be the consequence if a given thing that we accept as true is actually false?” over and over again.

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

Mathematics is another subdiscipline of philosophy that studies how far can you go once you accept a given set of postulates as true (while the rest of philosophy is mostly concerned with which things are true).

So science is mathematics + a little philosophy. 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.

On Godel-related strong AI refutations

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.”

This is 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).

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