26 letters

This morning, I saw some interesting paintings of Jan Brueghel the older in the "Alte Pinakothek". I was drawn to a painting displaying a sermon including a large crowd of interested people. In the front, near the preacher, there were obviously some women, in the back there were some people with guns, maybe some soldiers or some hunters returning home. It was striking to me how peaceful the crowd of mixed people was standing there, listening to the words of the philosopher. That we see lectures like this also in our modern world might be related to our needs for hope, the hope for a better life, the hope to find better meaning of our existence, the hope to prevent disappointment, or the hope to solve conflicts between people. It is interesting to see how languages and words can unify or split groups of people so heavily. Words can be instruments for power or seduction, but equally, they can transport the most interesting secrets of the world we live in. All with 26 letters.




(another interesting picture concerning a Brueghel painting.... found somewhere on the internet by googling. besides the 26 letters of the alphabet for normal writing, it is interesting to think about the 4 letters of the DNA for writing the sources of life.)

Russell's Paradox

"Nothing contains everything", applied:

A man of Seville is shaved by the Barber of Seville if and only if the man does not shave himself. Does the barber shave himself ?

* If the barber does not shave himself, he must abide by the rule and shave himself.
* If he does shave himself, according to the rule he will not shave himself.

And, another one:

"One of themselves, even a prophet of their own, said, the Cretians are alway liars, evil beasts, slow bellies. This testimony is true."
Titus 1:12-14 (King James Version)

Automata

In the sense of this post, "automaton" is an abstract concept. It is not used such, that an element which can be explained by the automata concept, equals this concept. There is often large resistance to the idea that the working of minds or living processes in general can be explained by deductive reasoning, as by mathematical deduction of patterns. Still, it is my impression, that the concept of automata or virtual machines is very useful to predict certain patterns in our minds, or to explain the behavior of complicated, mechanical interactions, or to improve our use for processes in our "imagination" or learning. Daniel Dennett mentions that automata make the basic building blocks of our souls - although the resulting system is very complicated which maybe does not allow to use the automata concept for the soul itself. (Dennett: "Si, abbiamo un anima, ma e fatto di tanto picolo robots", "Yes, we have a soul, but is made from lots of tiny robots.") Marvin Minsky expresses the automata as agents or "ways to think" or "emotions".

Innovation !

Hello,

there is another quote by Alan Kay which I like:

"The best way of predicting the future is to invent it !"

It captures very clearly that aspect of creativity which we admire so much, breaking some mechanical routine which has been used in the past (= the way we do prediction), by replacing it with a new, interesting system (= the essence of an invention). It might help that someone does not know too much about a certain field to get this effect of discovery, on the other hand, experience teaches us, that it takes a careful, long, vertical approach of study to understand enough interactions and problems of a certain system. In his ACM Turing award, Alan Kays addresses this aspect when imitation of an existing solution is not possible:

"One of the most interesting characteristics of computing in the best universities of the 1960s was that the professors told the students that nothing much of importance was known, and it was the duty of all to try to invent a real computing science and software engineering."


...

"Just as "civilization" is not a place or state, but a process of people who are trying to be more civilized, real computing is the process of people trying to make a better notion of computing. The most progress will be made by young people who have been encouraged to criticize old conceptions and invent new ones with an elevated notion of what constitutes a high threshold for a good idea. "

Lambda calculus

Imagine, expression is based solely on algorithmic processes in our brain. How would we use this insight to reduce the complexity the modern information society provides, or how could we make learning difficult subjects such as physics or expression itself more effective ?

I am currently looking at lambda calculus, which is based on one transformation rule only: Substitution of variables. It is interesting to think on functions as basic components in expressions, and substitution of parts as one of the most simplest approaches to transform expression.

In lambda calculus, there are three possible forms to specify ideas:

(1) expressions := can be names, functions, applications
(2) functions := lambda name. expression
(3) application := expression expression


The idea of recurrence, expressions in terms of itself, simplifies tremendously the expression of repeating structures, or structures with so many details that make it impossible to keep track of everything. It also reminds me on the idea that mathematics is an artform, the art of expression, an artistic endeavour in itself.