Rabbi Lord Jonathan Sacks says: I have a friend in Washington. I asked him, what was it like being in America […]?
He said to me. Well, it was like the man sitting on the deck of the Titanic with a glass of whiskey in his hand, and he’s saying, “I know I asked for ice — but this is ridiculous.”
Edsger Dijkstra said once that Object-oriented programming is an exceptionally bad idea, which could only have originated in California.
It’s full of patterns and recipes that don’t help much in the way to deconstruct the domain and create a…
An interactive proof, informally, is a two-party protocol where an actor (the prover) can convince someone else (the verifier) of the validity of some statement. (The prover should be able to do so if and only if the proposition is indeed valid.)
The interactive proof system is zero-knowledge if the proofs, possibly in a convenient, polynomial-time, given by the Prover have the remarkable property of being both convincing and yielding nothing except that the assertions are indeed valid.
Let’s give a simple example that is not complex as the Feige-Fiat-Shamir Zero Knowledge Proof, let’s talk about Waldo.
Waldo, created by…
A proof in logic is a sequence of statements based on axioms, a set of propositions that are thought to be true.
This sequence is ordered, and it could comprise propositions or predicates, with variables.
Each statement is obtained through derivation rules. Very simple composition rules, like OR, AND, etc…
The first important thing to remember is that the proof is fixed, deterministic and that, anytime, anyone can read it, comprehend it and get convinced. At least if it holds the NON contradiction law recorded first by Aristotle.
But, in many other situations, a statement can be proved simply by…
On 4 June 1996, only about 40 seconds after initiation of the flight sequence, at an altitude of about 3700 m, the Ariane 5 broke up and exploded.
An independent Inquiry Board was appointed and gave out a complete report.
“ The failure of Ariane 501 was caused by the complete loss of guidance and attitude information 37 seconds after the start of the main engine ignition sequence (30 seconds after lift-off). This loss of information was due to specification and design errors in the software of the inertial reference system. …
Category Theory is a branch of mathematics. It’s the purest one since it’s all about abstraction. Well, it should not come as a surprise since many people think that math preexists human intelligence and it lives in the divine realm of ideas. So, if for any reason some particular resistant virus wiped the human race from the face of the earth, euclidean triangles just to say, would be always there to poke their angles into some other alien’s eyes. Math is innate, the universe is built on its order.
We got the main point in Category Theory: abstraction, we want…
Nature is working on creating unique individuals, whereas culture has invented a single blueprint to which all people should conform. It is madness. The problem with identity is that while you spend time creating a “persona,” a mask, at the very core nothing is there. Identity’s not a substitute for your individuality, that’s why it so hard to acquire and so hard to maintain.
In Category Theory identity it’s just an arrow that starts from the object and ends to it. Somehow the object and the subject are the same. And today we start with a simple scenario. We want…
When renowned philosopher U. G. Krishnamurti came to visit Ramana Maharshi he knew that uncountable people had experienced a tremendous peace in his presence.
But he felt nothing. So after a while, he asked: “Swami, are there any steps to reach the stage of liberation?”
And Ramana answered: “There are not such steps nor stages. If it’s there, it is absolute and unchangeable. On the other hand, if it’s not there, everything is missing.”
U. G. Krishnamurti seemed unsatisfied: “Sir, I’m asking can you give me what you have?”
Ramana Maharshi answered: “I can give it!” …
Natural languages and programming languages are often compared for a simple reason: they both try to define some meaning and the latter also procedural steps to achieve some goal.
Also, natural languages can be used to define a list of paces, the typical example being a todo list or a recipe. But a natural language has great limitations, it is:
That’s why we have poetry and literature!!!
The Sick Rose, written by William Blake, is abundant of ambiguities:
O Rose thou art sick.The invisible worm,That flies in the nightIn the howling storm:…
The Bongard problem is simple. The name comes from computer scientist Mikhail Moiseevich Bongard, the first to put in use a meta-rational approach to problem-solving.
It’s a drawing split into two parts. On both sides of it, usually, six geometrical pictures are drawn. The problem aims to find one, and only one solution that explains the similarity between the two pairs of six pictures.
The problem could look similar to any IQ logic test provided to students in the past decades. But, it’s not.
There are some elements characterizing the Bongard problem.
First, even if there are many parts of…
In programming languages, a type system is a logical system that comprises variables, expressions, functions, or modules. These types, every one in its own, form categories of sets. The main purpose of this system is, of course, to reduce possibilities for bugs defining interfaces and consistency checks.
The reason why we have objects in any category is to mark the origin and the end of morphisms.
Objects and morphisms are both primitive concepts. But somehow morphisms are more important. …