Dear Krassimir and FIS Colleagues,
It is time for my second post this week.
First of all I am glad to participate in such very interesting
Thank you for the nice posts.
More than 25 years ago, working on the new theory, I had to solve the
problem with concept of entity which has information activity. There
many candidates for such concept: “robot”, “agent”, “intelligent
“interpreter”, “subject”, “information subject”, “intelligent
etc. Every such concept had its own history and many domains of
which caused many misunderstandings.
In the same time, if one had a single meaning then it couldn’t be
to all entities with information activity. For instance, concept
is not good to be used for a human.
Because of this, we had proposed a new word: “INFOS”, which had no
in advance and may be defined freely without misunderstandings. I
use it in my further posts.
I do not want to define it now. Step by step its meaning will arise
what I shall write. In many discussions till now, I had seen that this
approach is the best way to introduce a new concept.
I want specially to thank Bruno for his post from 18.10.2017 about
For me, it is very important it to be analyzed. I shall do this on the
basis of an example.
Not all kinds of self-reference concern information activity and
But, if at least one case exists, then we have to analyze it.
Such case, for instance, is the Barber paradox: A barber (who is a
shaves all and only those men who do not shave themselves. Does he
This paradox exists only in “3D” mathematical world based on triad
(x, y, f)
or, in other writings: (x, f, y), y=f(x), etc.
(there are several nice publications of Mark Burgin about triads !).
I.e. paradox exists only if we ignore the fact that the Barber is a
The paradox could not exist in the “4D” world of informatics where
quadruple (x, y, f, I) or, in other words, for Infos “I”, “y” is
information about “x” because of evidence “f”.
What is happen when the Barber shaves someone?
At the first place, it is a direct collecting, by eyes, the data
place where the razor has to be put to shave.
Have you ever seen a Blind barber?
NO! OK, this is a fundamental condition.
Not only Barber, but every human COULD NOT DIRECTLY COLLECT DATA about
his/her face, head, or back.
In another case, for instance, we have to have eye on the end of the
which has to be as long as the elephant trunk!
This means: the barber cannot shave himself because he could not see
to put the razor!
But every man can shave his beard! How he can do it?
Of course, everyone will say, by using a mirror!
But this is NOT DIRECT REFLECTION (data collecting).
It is TRANSITIVE SELF-REFLECTION via mirror!
Who does the barber shave: himself or the man in the mirror?
Of course, the second!!! Barber puts the razor on his own beard and
way he shaves the man in the mirror.
The Barber paradox does not exist if we take in account that the
a human (a kind of Infos) and needs data.
So, the answer of the question “Does he shave himself?“ is NO!, he
doesn’t, he shaves the man in the mirror who do not shave himself
the razor is in the hand of barber and no paradox exists.
Simple question: What we really see in the mirror?
Hmm... Let say a village exists where the barber shaves all and only
men who does not shave themselves (nor beard in that village!).
Then we have the logical paradox. If he does not shave himself he has
to shave himself, by definition, and if he shaves himself, he shaves
someone shaving himself, which he can't do.
The solution of the paradox is simple: there is no such village. (we
cannot solve so easily the paradox of the set of all set which do not
belong to themselves, though).
The idea of adding a "time parameter" is good though, and that is what
make the notion of enumeration of all partal computable functions
possible, but with the price that the one everywhere defined will be
sparsed in an non computable way, leading to incompleteness and
Yet, if we cannot build a machine comprehending its own semantics, we
can build a machine referring to any of its parts, including the whole
part of itself, by the use of the second recursion theorem of Kleene,
or Gödel self-reference.
The basic idea is elementary: you apply a duplicator to its self
description (in some universal machinery). If D'x' = 'x'x'', D'D'
gives 'D'D'' (with a reasonable notion of quoting). Similarly if D'x'
gives T('x'x''), D'D' gives T applied to itself T('D'D''). With the
term "human", you might have added a piece of non 3p communicable
insight, in which case you were referring, I guess, partially at
least, to the non nameable first person transported by that 3p self.
(in machines term: you have temporarily mixed p with p&p, which of
course looks quite alike for the ideally sound machine, but it still
obey different logics).
PS a more practical question: is this post my second post of last
week, or my first post of next week? To which week sunday belongs?
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