Formal System

A site about formal logic, literature, philosophy and simulations. And formal systems!

The Carpet Makers: a brilliant analysis on the nature of power, religion and belief — February 5, 2012

The Carpet Makers: a brilliant analysis on the nature of power, religion and belief

There is a planet where everything revolves around making carpets. There are the actual makers, the merchants that transport them, the wives whose hair is taken to make the carpets, the concubines to “make” either a future carpet maker or future wives of carpet makers, etc. Each carpet maker makes one carpet but the whole process of making it takes a whole lifespan.

Using the money his father gave him, the young carpet maker buys the material he needs to make the carpet, marries a woman with nice hair and takes a concubine to produce future carpet makers or wives of carpet makers. Once the carpet is finished (usually when the carpet maker is an old man) he sells the carpet to a merchant (for the Emperor’s palace) and gives the money to his son who must consider take a wife soon. And this story is the neverending story of that planet.

Interesting thing is that the Emperor gets overthrown but the people in the planet are not aware of it and they keep making carpets for their God-like Emperor. Years later the rebels find the planet. And afterwards, they find another planet that does the same thing. And another… They find out an indefinite amount of planets spending their lives around carpet-making. And the carpets are not actually meant for the Emperor’s palace…

The book is about fundamentalism, religious beliefs, holding opposite beliefs (cognitive dissonance), the nature of power and the portrait of a man-made God that overthrows himself.

The Dice Man: Western Path to Freedom —

The Dice Man: Western Path to Freedom

George Cockroft. Luke Rhinehart. Who is who. Author or character, it does not matter.

Regarding social matters, this is one of the very very very few few books (I can count them with one hand) that is literally outspoken and seems to know no limits.

The character, Luke Rhinehart is a successful psychiatrist that is bored with his life. He complains about lack of novelty except by brief moments (he says isles) of “ectasis”. Luke is a psychiatrist but he is well-read in Western and Eastern philosophy, politics, comedy, history, religion and psychoanalysis amongst other areas. He concludes that the only way to gain novelty (uncertainty) and change is by giving up his freedom on some dices. Here’s is where things get really, really interesting.

Symbol of freedom

The premise is simple:

1 – Assign an action to every number of the dice.

2 – You MUST do any of the actions.

3- Roll some dice and if for example it turns out 3 and you assigned 3 to give hugs randomly you must do so.

Luke starts with “limited” within-the-box actions but he soon goes on for more “freedom” and things get out of control.

Maybe the most incredible thing is that the author is actually the first “Dice Man”. He wrote the story based on his first experiences and his explanation of the concept in a lecture to his horrified students.

Comparing the 70s (when the book was written) and our current age, I would state that few (if no works) have been written with the openness, simplicity, outspoken character, society-representative and originality that “The Dice Man” was written with.

“It is no measure of health to be well adjusted to a profoundly sick society.” Jiddu Krishnamurti .

You can read it here for free

Japanese Philosophy: Impermanence as a way of living and as art: Wabi-sabi — February 1, 2012

Japanese Philosophy: Impermanence as a way of living and as art: Wabi-sabi

As most elements in Eastern Philosophy, the definition of wabi-sabi is elusive and refuses to be contained in rigid definitions. It spills over. For this reason, my review of this highly unknown Japanese “view” will be based on analogies and metaphorical descriptions.

Wabi-sabi as art is dark, lacks symmetry, is rough. Not visually nice.

Wabi-sabi is humble, modest. It attracts no attention. It is difficult to see because it does not stand out. Because true beauty does not need to stand out. It is one with its surrounding. Simplicity.

Forget your perfect offering
There is a crack in everything
That’s how the light gets in. 
(Leonard Cohen)

Wabi-sabi as way of seeing the world, states that nothing is permanent but change (nothing new in Eastern philosophy) but Wabi-sabi’s variation is that things are evolving from or devolving towards nothingness. And beauty lies at the borders of nothingness. Imperfection is hailed as a virtue rather than a defect. It is admired.

Wabi-sabi is not about retaining, holding back. It is about accepting the fleeting nature of things. Things that come and go. Realization of that is the condition for a sense of  Wabi-sabi beauty.

I don’t usually recommend books, but I will make an exception:

Ted Chiang Series 4 (Part 2) – Understanding of God: Its Presence, Its Absence — January 29, 2012

Ted Chiang Series 4 (Part 2) – Understanding of God: Its Presence, Its Absence

As I already said, with this second part, the Ted Chiang Series come to an end.

Part 1 stories were about scientific understanding (emergence of patterns and determinism in the scientific method).  The next two stories come from a religious standpoint where God is an axiom, or rather, understanding of God is the core topic.

The are three differences in both stories: one is, the nature of the realization about a God-related truth, in the first story, this revelation is metaphorical while in the second is literal, the second difference is the presence of God, in the first story, God is absent but in the second story God is present (through his avatars, the vengeful and frightening angels), the third difference is the degree of the revelation, it is more general in the first story and more drastic and absolute in the second one.

Ancient model of the universe

1 – Tower of Babylon

French cover
Extract of "Tower of Babylon"

can be summed up as an attempt by the ancient Babylonian men to reach the sky, or rather, God’s kingdom in Heaven. Ted Chiang’s model of the world is based on the Babylonian geocentric model of the universe where all the celestial spheres orbit around Earth.

Read it here for free







2 – Hell is the absence of God

Extract from "Hell is the Absence of God"

It is a world where God, his angels, Heaven and Hell are literally real. Angels spread the Word through “visitations” where supernatural “miracles” (not always good) occur. The story is not about believing in God (there is no point) but about devotion and the eternal question of why righteous people suffer. Only those who love God can go to Heaven, the rest go to Hell, a place below our world where God is absent (hence the title). There are two interesting aspects of this story:

1- There are not non-believers but there are non-religious people. The protagonist is the latter.

2-  Most readers (me included) made the assumption that the religion in the story is Christianity. Ted has even been criticized for  “trite antichristian propaganda” and his story described as  “God’s a jerk” story, big deal”. The fact is that the word Christianity or Christ is not  even in the story (I searched).

The background of this story is the Book of Job. Ted thought that the end was not fair and that it missed the point of teaching that sometimes bad things happen to good people.  The end of  “Hell is the absence of God” is a direct response to the last part of the Book of Job.

Read the story here for free.





Story of Your Life and Other Stories (covers)

Is the title of the book that collected most of  Ted Chiang’s short stories.  Below I post some of the different covers of the book.

My favourite one
Variation of the earlier cover
Polish version of "Story of your Life and others"
Unexpected Examination Paradox —

Unexpected Examination Paradox

A teacher announces in class that an examination will be held on some day during the following week,

and moreover that the examination will be a surprise. The students argue that a surprise exam cannot occur. Because of a simple induction inference:

Friday: if by Thursday evening there is no exam, then it will be Friday. But since it would then be expected, it cannot be the Friday.

Thursday: if by Wednesday evening there is no exam, then it will be Thursday. But since it would then be expected, it cannot be the Thursday nor Friday.

Wednesday: if by Tuesday evening there is no exam, then it will be Wednesday. But since it would then be expected, it cannot be the Wednesday nor Thursday nor Friday.

Tuesday: if by Monday evening there is no exam, then it will be Tuesday. But since it would then be expected, it cannot be the Tuesday nor Wednesday nor Thursday  nor Friday.

Monday: it can only be the Monday but then if it is expected on Monday it cannot, because of the expectancy, happen on Monday.

Condent in this conclusion, they are of course totally surprised when the exam occurs (on Wednesday, say).

What is wrong with the students’ line of reasoning?

Let us try to solve the paradox:

1: the exam is expected any of the five days.

2: since it is expected, it cannot happen.

3: line 2 itself is expected.

4: the teacher hands over the exam on monday.

5: the exam is expected any day (see step 1) => it is not not expected to happen any day ( because it cannot happen)

6: since it is not expected to happen, it can happen and happens.

7: go to line 1 and replace Monday with any other of the 5 days.

The backwards reasoning seems to fully cover any hole and assure the student that the exam cannot happen on the basis of the student’s current knowledge but this knowledge is based on probability.

About free will, evil and love: Dialogue with an amoralist God — January 27, 2012

About free will, evil and love: Dialogue with an amoralist God

Smullyan is quite an off-beat person. Why?

He started as magician and later on went to become a logician. The most incredible part is that he also became a Taoist (for details of the core ideas of this eastern philosophy click here). It is no secret that Taoist views are rooted on profound paradoxes nor it is secret that Western logicians have been battling against paradoxes like doctors a disease. It should seem that both logic and Taoism are conflicting but apparently, this fellow has managed to keep inner peace.

“Is God a Taoist?” is a dialogue between God and a theist where the latter asks the former why did he bestow free will on humans.  What follows is an explanation of quite a laid-back God who describes the problem of evil, his love for humans as well as a surprisingly simple idea to show why humans need free will.

P.S. Taoists do not believe in divine entities so the title of the dialogue itself can be taken as a sort of paradox, making the title a subtle reference to a core paradox surrounding the idea of free will (this core paradox happens to be mentioned in the dialogue).

You can read it here for free.

Artificial Intelligence: Soul Searching and views of an A.I. advocate. — January 26, 2012

Artificial Intelligence: Soul Searching and views of an A.I. advocate.

I will just put down common objections against the idea that machines can, someday, think and I will reply to them in a systematic manner. If you want your question to be added (and replied) write the question in the comments and I will add it to the list of objections. 😉

First of all, I shall make clear that I don’t think that our “modern” machines can support full human cognition as they are not complex nor flexible enough, but I do think that the period of time to get the complexity required to achieve a decent level of flexibility is finite even though it is going to take several computer science revolutions to get to that point.

1 – Machines can only do what you tell them to do.

The above statement implies predictability (and thus, full knowledge) of the actions of the machine. But as programming languages go farer and farer from the original machine language this predictability is gradually being lost. This means that eventually there will be a time when our predictions about what a machine can do from what we told them to do will be approximate. We will only know the “space” in which the machine’s actions will fall. As simple analogy: when we tell the computer to calculate the first million digits of Pi, we don’t know which digits will be, we only know that it is exactly one million digits.


2 – Machines cannot feel thus they cannot think in a human way (intelligent).

As far as I am (and most psychologists) concerned, emotions are a by-product of intelligence.


3- Humans are sometimes irrational beings, machines are always rational beings. Moreover, machines cannot be irrational beings because they are mechanic beings.

Look at this picture:

The brain is rational, the mind might not be.

The problem with the above statement (machines are always rational and humans sometimes are irrational) is that it mistakes levels.

To simplify, there are two levels, low rigid level and high flexible level.

Now, let us do some analogies:

Brain <=> Hardware of the machine <=> Low level (rigid)

Mind <=> Software of the machine <=> High level (flexible)

Now, are humans sometimes irrational? Yes. Are human brains sometimes irrational? No. Neurons either fire or not. There is no paradox there. Are humans irrational? Yes. Are human minds sometimes irrational? Yes. BUT, this flexibility of being able to switch between irrational and rational is the consequence of the complexity of a rigid system (the brain). When people say “machines cannot be irrational” they talk about a machines low level (their hardware) but they do refer to humans high level when they say “humans can be irrational”. So the problem with that statement is a lack of differentiation between levels of description. So the hardware of a machine is as rigid as a human’s brain and computer software is (potentially) as flexible as the human mind.


4 – How can you program thinking if you do not know what it is?

See my earlier post about the Turing Test.


5 – Okay, let us say that in some future, we get some machines thinking like humans, wouldn’t the machine be simulating thinking rather than actually thinking? Simulated thoughts are not actual thoughts. If I simulate milk, regardless of how complex the simulation is, I will never be able to drink it. Simulations are not real.

First, I recommend you to read this and this, since they explain my view quite nicely.


Axiom 1 – Simulation of concrete objects is never complete regardless of the complexity of the simulation.

Axiom 2 – Simulation of abstract objects can be complete.

Regarding Axiom 2, then: what is the difference between a simulated song and a real song? There is no difference because:

First: Simulations are data.

Second: Abstract objects are data

Third: Songs are abstract objects.

And the above holds even truer for a complex and abstract “object” as the human mind.


If you want your question to be added (and replied) write the question in the comments and I will add it to the list of objections. 😉