why a Tao?

Metalogue: Why a Swan?

Daughter: Why a swan?

Father: Yes—and why a puppet in Petroushka?

D: No—that's different. After all a puppet is sort of hu­man—and that particular puppet is very human.
F: More human than the people?

D: Yes.

F:  But still only sort of human? And after all the swan is also sort of human.

D: Yes.

* * *

D: But what about the dancer? Is she human? Of course she really is, but, on the stage, she seems inhuman or impersonal—perhaps superhuman. I don't know.

F: You mean—that while the swan is only a sort of swan and has no webbing between her toes, the dancer seems only sort of human.

D: I don't know—perhaps it's something like that.

* * *

F: No—I get confused when I speak of the "swan" and the dancer as two different things. I would rather say that the thing I see on the stage—the swan figure—is both ^"sort of" human and "sort of" swan.

D: But then you would be using the word "sort of" in two senses.

F: Yes, that's so. But anyhow, when I say that the swan figure is "sort of" human, I don't mean that it (or she) is a member of that species or sort which we call human.
D: No, of course not.

F: Rather that she (or it) is a member of another subdivi­sion of a larger group which would include Petroushka puppets and ballet swans and people.

D: No, it's not like genera and species. Does your larger group include geese?

F: All right. Then I evidently do not know what the word "sort of" means. But I do know that the whole of fantasy, poetry, ballet, and art in general owes its meaning and importance to the relationship which I refer to when I say that the swan figure is a "sort of" swan—or a "pretend" swan.

D: Then we shall never know why the dancer is a swan or a puppet or whatever, and shall never be able to say what art or poetry is until someone says what is really meant by "sort of."

F:  Yes.

D:  But we don't have to avoid puns. In French the phrase espece de (literally "sort of") carries a special sort of punch. If one man calls another "a camel" the insult may be a friendly one. But if he calls him an espece de chameau—a sort of camel—that's bad. It's still worse to call a man an espece d'espece—a sort of a sort.
D: A sort of a sort of what?

F: No—just a sort of a sort. On the other hand, if you say of a man that he is a true camel, the insult carries a flavor of grudging admiration.

D: But when a Frenchman calls a man a sort of camel, is he using the phrase sort of in anything like the same way as I, when I say the swan is sort of human?

* * *

F:  It's like—there's a passage in Macbeth. Macbeth is talk­ing to the murderers whom he is sending out to kill Banquo. They claim to be men, and he tells them they are sort of men.

Ay—in the catalogue ye go for men.

as hounds and greyhounds, mongrels, spaniels, curs,

shoughs, water-rugs and demi-wolves are clept

all by the name of dogs.

(Macbeth, Act III, Scene 1)

D: No—that's what you said just now. What was it? "Another subdivision of a larger group?^" I don't think that's it at all.

F: No, it's not only that. Macbeth, after all, uses dogs in his simile. And "dogs" means either noble hounds or scav­engers. It would not be the same if he had used the domestic varieties of cats—or the subspecies of wild roses.

D: All right, all right. But what is the answer to my question? When a Frenchman calls a man a "sort of" camel, and I say that the swan is "sort of" human, do we both mean the same thing by "sort of"?

* * *

F: All right, let's try to analyze what "sort of" means. Let's take a single sentence and examine it. If I say "the puppet Petroushka is sort of human," I state a relation-ship.

D: Between what and what?

F:  Between ideas, I think.

D: Not between a puppet and people?

F:  No. Between some ideas that I have about a puppet and some ideas that I have about people.

D: Oh.

* * *

D: Well then, what sort of a relationship?

F:  I don't know. A metaphoric relationship?

* * *

F: And then there is that other relationship which is emphatically not "sort of." Many men have gone to the stake for the proposition that the bread and wine are not "sort of" the body and blood.

D: But is that the same thing? I mean—is the swan ballet a sacrament?

F:  Yes—I think so—at least for some people. In Protestant language we might say that the swanlike costume and movements of the dancer are "outward and visible signs of some inward and spiritual grace" of woman. But in Catholic language that would make the ballet into a mere metaphor and not a sacrament.

D: But you said that for some people it is a sacrament. You mean for Protestants?

F: No, no. I mean that if for some people the bread and wine are only a metaphor, while for others—Catholics —the bread and wine are a sacrament; then, if there be some for whom the ballet is a metaphor, there may be others for whom it is emphatically more than a metaphor—but rather a sacrament.

D: In the Catholic sense?

F:  Yes.

* * *

F: I mean that if we could say clearly what is meant by the proposition "the bread and wine is not `sort of' the body and blood"; then we should know more about what we mean when we say either that the swan is "sort of" human or that the ballet is a sacrament.

D: Well—how do you tell the difference?

F:  Which difference?

D: Between a sacrament and a metaphor.

* * *

F: Wait a minute. We are, after all, talking about the per-former or the artist or the poet, or a given member of the audience. You ask me how I tell the difference between a sacrament and a metaphor. But my answer must deal with the person and not the message. You ask me how I would decide whether a certain dance on a certain day is or is not sacramental for the partic­ular dancer.

D: All right—but get on with it.

F: Well—I think it's a sort of a secret.

D: You mean you won't tell me?

F: No—it's not that sort of secret. It's not something that one must not tell. It's something that one cannot tell.

D: What do you mean? Why not?

F: Let us suppose I asked the dancer, "Miss X, tell me, that dance which you perform—is it for you a sacra­ment or a mere metaphor?" And let us imagine that I can make this question intelligible. She will perhaps put me off by saying, "You saw it—it is for you to de­cide, if you want to, whether or not it is sacramental for you." Or she might say, "Sometimes it is and sometimes it isn^'t.^" Or ^"How was I, last night?^" But in any case she can have no direct control over the matter.

* * *

D: Do you mean that anybody who knew this secret would have it in their power to be a great dancer or a great poet?

F: No, no, no. It isn't like that at all. I mean first that great art and religion and all the rest of it is about this secret; but knowing the secret in an ordinary conscious way would not give the knower control.

* * *

D: Daddy, what has happened? We were trying to find out what "sort of" means when we say that the swan is "sort of" human. I said that there must be two senses of "sort of." One in the phrase "the swan figure is a `sort of' swan, and another in the phrase "the swan figure is `sort of' human." And now you are talking about mys­terious secrets and control.

F: All right. I'll start again. The swan figure is not a real swan but a pretend swan. It is also a pretend-not hu­man being. It is also "really" a young lady wearing a white dress. And a real swan would resemble a young lady in certain ways.

D: But which of these is sacramental?

F: Oh Lord, here we go again. I can only say this: that it is not one of these statements but their combination which constitutes a sacrament. The "pretend" and the "pretend-not" and the "really" somehow get fused to­gether into a single meaning.

D: But we ought to keep them separate.

F: Yes. That is what the logicians and the scientists try to do. But they do not create ballets that way—nor sacra­ments.

Metalogue: Why a Swan?; Impulse 1954.

Tao level 5: Tao ecosystem

The hierarchical level 5 of ecosystem - both local and global - represents the highest degree of complexity of a system.

The term is attributed to the ecologist and botanist A.G. Tansley in 1935 to define the whole of living and non-living elements which are linked together and in equilibrium by a variety of complex relations of interdependence.

and, in detail, for the physical hierarchy:

and for the ecological ones:

A hierarchical description may be applied to specific parts of the ecosystems, for example for geopolitical systems:

 

the term ecosystem intends to describe the complexity of the biosphere integrating living species and environment at all levels:

The hierarchical description of an ecosystem may naturally be extended at higher levels over the global planetary one and to lower under the physical ones:

Hierarchical description levels from  space-time continuum to metagalaxies.
from: Ervin Laszlo, Introduction to Systems Philosophy, 1972

The global terrestrial ecosystem is in fact closed about biosphere but open for the physical level, where the main process is the radiation/reflection of the solar light.

The ecosystems represent the highest complexity level of systems with history and, as such, require for their comprehension the explicitation of their evolution in time or in other meaningful system variables; for example:

Global ecosystem evolution in terms of dimensions/complexity/bonding energy.
from: Ervin Laszlo, Evolution of complexity and the contemporary world order.

Similarly can be done by the sociocultural systems evolution:

Evolution steps of sociocultural systems.
from: Ervin Laszlo,  Evolution of complexity and the contemporary world order.

The high complexity of the global ecosystem, which integrates and encloses that at all the lower levels, leads to some relevant characteristics:

system Globality and Locality: zoom levels

At the ecosystem level is natural to perform zoom levels from different points of view over the underlying subsystems, not necessarily only dimensional. At any zoom level an ecosystem is observed the resulting will be always another ecosystem, a consequence of the hologrammatic principle proposed by Morin where "not only the part is in everything, but everything is in the part. Each cell is a part of everything, but everything in itself is in the part. The entire gene is present in each individual cell. The society is present in every individual."

Mental processes of ecosystems

From the formulation of Bateson's criteria of mental processes it follows that if in a system just an element or process has mental characteristics there all the system is mental. Any ecosystem has therefore - in a global sense - the maximum characteristics of mental type processes.

Invariance and Scalability of systemic complexity

The hologrammatic and fractal characteristics of ecosystems reflect on the fact that scaling in any ecosystem into some system variable, dimensions typically, the system complexity is invariant and scales with scaling dimension. In this sense the complexity of a single cell amounts to that of the entire planetary ecosystem, naturally on different elements and processes.

For example, one may consider the complexity of the interaction between the sociocultural ecosystem and the global ecosystem:

Sociocultural systems in interaction with ecosystems.
from: Ervin Laszlo,  Evolution of complexity and the contemporary world order.

in the sociocultural systems one may outline the economical system:

Schematics of the world economical system.

to arrive to the single individual metabolism:

portion of the metabolic system

to a single portion of a cell:

Front and back views of a 3D model of the Golgi region in an insulin-secreting, mammalian cell. Three serial 400-nm-thick sections cut from a high pressure frozen, freeze-substituted and plastic-embedded HIT-T15 cell were reconstructed by dual axis EM tomography.  The software package IMOD was used to model all visible objects within the resulting reconstructed volume (3.1 x 3.2 x 1.2 um3). The Golgi complex with seven cisternae (C1-C7) is at the center.  The color coding is as follows: C1, light blue; C2, pink; C3, cherry red; C4, green; C5, dark blue; C6, gold; C7, bright red. The Golgi is displayed in the context of all surrounding organelles, vesicles, ribosomes, and microtubules: endoplasmic reticulum (ER), yellow; membrane-bound ribosomes, blue; free ribosomes, orange; microtubules, bright green; dense core vesicles, bright blue; clathrin-negative vesicles, white; clathrin-positive compartments and vesicles, bright red; clathrin-negative compartments and vesicles, purple; mitochondria, dark green.
Bar, 500 nm.
Image courtesy of Dr. Brad Marsh, Institute for Molecular Bioscience
The University of Queensland, Brisbane, Australia.

in all these systems of extremely different types the preserved and invariant characteristic is the system complexity, which scales with the system dimensions.

Weaving of the complexity

The complexity invariance with dimension is well sketched by the etymology of the term complex, which comes from complexus, or "with texture". The "texture" or "weaving" of complexity becomes palpable scaling on zoom physical levels down to the subatomic one:

portion of texture of an iranian carpet; scale about 50 cm.

Optical microscope image by fluorescence and polarized light of carpet fibers; 20X zoom

colored SEM image of silk fibers; 220X zoom

I
colored SEM image of silk fibers; 1300X zoom

STM images of a single molecule before (left) and of a molecular chain (right) after the formation of intermolecular covalent bonds by “on-surface-synthesis”. The chemical structures of the initial building block and the chain are indicated. scale 2 nm
Fritz-Haber-Institut der Max-Planck-Gesellschaft- Department of Physical Chemistry

STM image of Silicon atoms; scale 2 nm

AFM image of Silicon atoms illustrating the atomic orbitals structure; scale 1 nm

from: Probing the shape of atoms in real space, Phys. Rev. B 68, (2003)

University of Augsburg, Institute of Physics, Center for Electronic Correlations and Magnetism

AFM image of subatomic structures inside a single Tungsten atom.
Resolution 77 pm, image size 500 × 500 pm2
University of Augsburg, Institute of Physics, Center for Electronic Correlations and Magnetism

Tao of form

The text of philosophical logic that historically was the foundation of the cybernetic epistemology is Laws of Form by G. Spencer-Brown, first published in 1969. Brown is a figure always surrounded by a shroud of mystery, he is considered an eclectic expert in various disciplines - a polymath - he associated and studied with figures like Russell, Wittgenstein and Laing and has strongly influenced with his work many authors of the systemic-cybernetic movement such Von Foerster, Maturana, Varela, Kauffman and Bateson himself. For example he is also novelist James Keys with his mystic vision of the "five levels of eternity":

A story by Bateson on a meeting with Spencer-Brown together with Heinz Von Foerster, from Keeney (1977), shows how Brown manages to keep his territory obscure: 

I talked to Von Foerster the morning before I met Brown to see if I was getting it right. I said these upside-down L-shaped symbols of this fellow are some sort of negative ... He said, "Yes, you've got it Gregory". At that moment Brown came into the room and Heinz turned to Brown and said, "Gregory has got it - those things are sort of negative". And Brown said, "They are not!".

G. Bateson, quoted by Keeney, "Aesthetics of Change", 1983

Von Foerster saw Spencer-Brown as similar to Wittgenstein (of which he was the nephew) and Don Juan, Carlos Castaneda's teacher, in that all three shared "a state of melancholy that befalls those who know that they know".

The historical-logical base of the Brown text is the overcoming of the classical Logic (or Aristotelian) that the monumental work by Russell and Whitehead Principia Mathematica of 1910 sought to preserve against mathematical paradoxes and demonstrated impossible in 1931 by the Gödel's incompleteness theorems. Since 1931 any type of formal logic should explicitly take into account the existence of logical paradoxes since, as demonstrated by Gödel, in any formal system "powerful" enough - such arithmetic - one can derive undecidable propositions, which are neither true nor false but paradoxical: if they are true then they are false and back.
As stated by Brown in the preface: 

Recalling Russell's connexion with the Theory of Types, it was with some trepidation that I approached him in 1967 with the proof that it was unnecessary. To my relief he was delighted. The Theory was, he said, the most arbitrary thing he and Whitehead had ever had to do, not really a theory but a stopgap, and he was glad to have lived long enough to see the matter resolved.

The theory of logical types, though refuted in formal logic by the work of Gödel, has defined the fundamental idea of logical levels of meta- type, applied by Bateson on human and animal interaction and communication models, and fundamental to define meta-classes, meta-terms, meta-descriptions and meta-explanations in the theory of complexity.

The subject is introduced by Brown in his preface:

PREFACE TO THE FIRST AMERICAN EDITION

Apart from the standard university logic problems, which the calculus published in this text renders so easy that we need not trouble ourselves further with them, perhaps the most significant thing, from the mathematical angle, that it enables us to do is to use complex values in the algebra of logic. They are the analogs, in ordinary algebra, to complex numbers a + b √- 1 . My brother and I (*) had been using their Boolean counterparts in practical engineering for several years before realizing what they were. Of course, being what they are, they work perfectly well, but understandably we felt a bit guilty  about using them, just as the first mathematicians to use 'square roots of negative numbers' had felt guilty, because they too could see no plausible way of giving them a respectable academic meaning. All the same, we were quite sure there was a perfectly good theory that would support them, if only we could think of it.

The position is simply this. In ordinary algebra, complex values are accepted as a matter of course, and the more advanced techniques would be impossible without them. In Boolean algebra (and thus, for example, in all our reasoning processes) we disallow them. Whitehead and Russell introduced a special rule, which they called the Theory of Types, expressly to do so. Mistakenly, as it now turns out. So, in this field, the more advanced techniques, although not impossible, simply don't yet exist. At the present moment we are constrained, in our reasoning processes, to do it the way it was done in Aristotle's day. The poet Blake might have had some insight into this, for in 1788 he wrote that 'reason, or the ratio of all we have already known, is not the same that it shall be when we know more.'

Recalling Russell's connexion with the Theory of Types, it was with some trepidation that I approached him in 1967 with the proof that it was unnecessary. To my relief he was delighted. The Theory was, he said, the most arbitrary thing he and Whitehead had ever had to do, not really a theory but a stopgap, and he was glad to have lived long enough to see the matter resolved.

Put as simply as I can make it, the resolution is as follows. All we have to show is that the self-referential paradoxes, discarded with the Theory of Types, are no worse than similar self-referential paradoxes, which are considered quite acceptable, in the ordinary theory of equations.

The most famous such paradox in logic is in the statement, 'This statement is false.'

Suppose we assume that a statement falls into one of three categories, true, false, or meaningless, and that a meaningful statement that is not true must be false, and one that is not false must be true. The statement under consideration does not appear to be meaningless (some philosophers have claimed that it is, but it is easy to refute this), so it must be true or false. If it is true, it must be, as it says, false. But if it is false, since this is what it says, it must be true.

It has not hitherto been noticed that we have an equally vicious paradox in ordinary equation theory, because we have carefully guarded ourselves against expressing it this way. Let us now do so.
We will make assumptions analogous to those above. We assume that a number can be either positive, negative, or zero. We assume further that a nonzero number that is not positive must be negative, and one that is not negative must be positive.
We now consider the equation

x²+1=0

Transposing, we have 

x²=-1

and dividing both sides by x gives ,

x=-1/x

We can see that this (like the analogous statement in logic) is self-referential: the root-value of x that we seek must be put back into the expression from which we seek it.

Mere inspection shows us that x must be a form of unity, or the equation would not balance numerically. We have assumed only two forms of unity, +1 and — 1, so we may now try them each in turn. Set x = +1. This gives

+ 1= -1/+1= - 1

which is clearly paradoxical. So set x= -1. This time we have

- 1= -1/-1= + 1

and it is equally paradoxical.
Of course, as everybody knows, the paradox in this case is resolved by introducing a fourth class of number, called imaginary, so that we can say the roots of the equation above are ± i, where i is a new kind of unity that consists of a square root of minus one.
 

... 

G SPENCER-BROWN

Cambridge, England
Maundy Thursday 1972

(*): there are reasons to believe Spencer-Brown is only child.

Brown's epistemology is clearly stated in the beginning of text:

A NOTE ON THE MATHEMATICAL APPROACH

The theme of this book is that a universe comes into being when a space is severed or taken apart. The skin of a living organism cuts off an outside from an inside. So does the circumference of a circle in a plane. By tracing the way we represent such a severance, we can begin to reconstruct, with an accuracy and coverage that appear almost uncanny, the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance.
The act is itself already remembered, even if unconsciously, as our first attempt to distinguish different things in a world where, in the first place, the boundaries can be drawn anywhere we please. At this stage the universe cannot be distinguished from how we act upon it, and the world may seem like shifting sand beneath our feet.

Although all forms, and thus all universes, are possible, and any particular form is mutable, it becomes evident that the laws relating such forms are the same in any universe. It is this sameness, the idea that we can find a reality which is independent of how the universe actually appears, that lends such fascination to the study of mathematics. That mathematics, in common with other art forms, can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But mathematical texts generally begin the story somewhere in the middle, leaving the reader to pick up the thread as best he can. Here the story is traced from the beginning.

Unlike more superficial forms of expertise, mathematics is a way of saying less and less about more and more. A mathematical text is thus not an end in itself, but a key to a world beyond the compass of ordinary description.

An initial exploration of such a world is usually undertaken in the company of an experienced guide. To undertake it alone, although possible, is perhaps as difficult as to enter the world of music by attempting, without personal guidance, to read the score-sheets of a master composer, or to set out on a first solo flight in an aeroplane with no other preparation than a study of the pilots' manual.

In the first section Brown outlines what a form is:

T H E  F O R M

We take as given the idea of distinction and the idea of indication, and that we cannot make an indication without drawing a distinction. We take, therefore, the form of distinction for the form.

Definition
Distinction is perfect continence. 

That is to say, a distinction is drawn by arranging a boundary with separate sides so that a point on one side cannot reach the other side without crossing the boundary. For example,in a plane space a circle draws a distinction.
Once a distinction is drawn, the spaces, states, or contents on each side of the boundary, being distinct, can be indicated.
There can be no distinction without motive, and there can be no motive unless contents are seen to differ in value.
If a content is of value, a name can be taken to indicate this value.
Thus the calling of the name can be identified with the value of the content.

Axiom 1. The law of calling
The value of a call made again is the value of the call. 

That is to say, if a name is called and then is called again, the value indicated by the two calls taken together is the value indicated by one of them.
That is to say, for any name, to recall is to call.

Equally, if the content is of value, a motive or an intention or instruction to cross the boundary into the content can be taken to indicate this value.

Thus, also, the crossing of the boundary can be identified with the value of the content.

Axiom 2 . The law of crossing

The value of a crossing made again is not the value of the crossing. 

That is to say, if it is intended to cross a boundary and then it is intended to cross it again, the value indicated by the two intentions taken together is the value indicated by none of them.

That is to say, for any boundary, to recross is not to cross.

In the following he defines how forms are taken out of forms:

F O R M S  T A K E N  O U T  O F  T H E  F O RM

Construction
Draw a distinction.

Content
Call it the first distinction.
Call the space in which it is drawn the space severed or cloven by the distinction.
Call the parts of the space shaped by the severance or cleft the sides of the distinction or, alternatively, the spaces, states,or contents distinguished by the distinction.

Intent
Let any mark, token, or sign be taken in any way with or with regard to the distinction as a signal.
Call the use of any signal its intent.

First canon. Convention of intention
Let the intent of a signal be limited to the use allowed to it.
Call this the convention of intention. In general, what is not allowed is forbidden.

Knowledge
Let a state distinguished by the distinction be marked with a mark

of distinction.

Let the state be known by the mark.

Call the state the marked state.

Form

Call the space cloven by any distinction, together with the entire content of the space, the form of the distinction.

Call the form of the first distinction the form.

Name

Let there be a form distinct from the form.

Let the mark of distinction be copied out of the form into such another form.

Call any such copy of the mark a token of the mark.

Let any token of the mark be called as a name of the marked state.

Let the name indicate the state.

Arrangement

Call the form of a number of tokens considered with regard to one another (that is to say, considered in the same form) an arrangement.

Expression

Call any arrangement intended as an indicator an expression.

Value

Call a state indicated by an expression the value of the expression.

The mark or cross operator:

is the main symbol used by Brown.

The symbol represents the distinction between its inside and outside:

The inside state defined by the symbol is called marked state, the outside state unmarked state, meaning by state the two sides of a distinction, where the symbol itself represents the distinction between the two states:

with such definitions and axioms Brown derives a formal logical system for the description of primary arithmetic, primary algebra and second order equations.

the immanent Mind of Tao

The cybernetic epistemology ... would suggest a new approach. The individual mind is immanent but not only in the body. It is immanent also in pathways and messages outside the body; and there is a larger Mind of which the individual mind is only a sub-system. This larger Mind is comparable to God and is perhaps what some people mean by "God," but it is still immanent in the total interconnected social system and planetary ecology.
Freudian psychology expanded the concept of mind in-wards to include the whole communication system within the body—the autonomic, the habitual, and the vast range of unconscious process. What I am saying expands mind out-wards. And both of these changes reduce the scope of the conscious self. A certain humility becomes appropriate, tempered by the dignity or joy of being part of something much bigger. A part — if you will— of God.
If you put God outside and set him vis-à-vis his creation and if you have the idea that you are created in his image, you will logically and naturally see yourself as outside and against the things around you. And as you arrogate all mind to yourself, you will see the world around you as mindless and therefore not entitled to moral or ethical consideration. The environment will seem to be yours to exploit. Your survival unit will be you and your folks or conspecifics against the environment of other social units, other races and the brutes and vegetables.
If this is your estimate of your relation to nature and you have an advanced technology, your likelihood of survival will be that of a snowball in hell. You will die either of the toxic by-products of your own hate, or, simply, of over-population and overgrazing. The raw materials of the world are finite.
"Form, Substance, and Difference", January 9, 1970

The basic rule of systems theory is that, if you want to understand some phenomenon or appearance, you must consider that phenomenon within the context of all completed circuits which are relevant to it. The emphasis is on the concept of the completed communicational circuit and implicit in the theory is the expectation that all units containing completed circuits will show mental characteristics. The mind, in other words, is immanent in the circuitry. We are accustomed to thinking of the mind as somehow contained within the skin of an organism, but the circuitry is not contained within the skin.
"A Sacred Unity"

Honor to Tao: Alan Mathison Turing

A Blue Plaque marking Turing's home at Wilmslow, Cheshire, UK

Alan Turing was not only one of brightest mathematicians of the 900s and a genuine pioneer in the field of computer science, but also a hero of World War II for his decisive contribution to crack the Enigma code. 
Enigma was an electro-mechanical machine used in several versions by the Wehrmacht and Kriegsmarine, the german military navy, to cipher and decipher their messages.

Since the enormous importance to succeed in cracking the code produced by Enigma the english Government Communications Headquarters founded in 1939 at Bletchley Park a centre for uncoding war messages, particularly for the cryptanalysis of the Enigma in Hut 8, which was led by Turing for a certain time.

Turing joined the Bletchley Park centre at the beginning of the war, working mainly on the naval version of, developing a number of techniques of analysis and deciphering, using a refined version of a computing machine called the "Bombe" already used in the past with success by the Polish Cipher Bureau which, at the outbreak of war, passed the results to english. The techniques which developed are named Banburismus for the Enigma machine and Turingery (or Turing's Method) for the Lorenz machine. Since 1941 the Enigma decoding projectil was known as Ultra and shared with the Allies. Turing contributed decisively to break the Enigma machine code of the navy version, resulting in a turning point for the Atlantic naval war.

In 1945 Turing was awarded the OBE for his wartime services, though his work remained secret for many years.

---

In 1952 Turing reported to the police for a break into his house by an his friend's accomplice. During the investigation he admitted to be homosexual and acknowledged a sexual relationship with that friend, saying "What's wrong?".
Homosexual acts were illegal at that time in the respectable, repressive and homophobic U.K. and Turing was charged with gross indecency under Section 11 of the Criminal Law Amendment Act 1885, the same crime for which Oscar Wilde had been convicted more then fifty years earlier.
Turing was given a choice between imprisonment or probation conditional on his agreement to undergo chemical castration, which he accepted.

Turing was a playful figure, he invented a way to play chess called "turn around the house": when a player moved he ran around the house, if the other player had still to move, he could make a further move.

Even in the implementation of his suicide Turing did not miss to get an humor's touch: as in the Snow White fairy tale, one of his favourite, on June 8, 1954 he injected cyanide poisoning into an apple and ate it.

---

The story of the treatment to which Alan Turing was subjected is one of the most infamous in British history.

Only on September 10, 2009, acknowledging an internet e-petition started by John Graham-Cumming, the former prime minister Gordon Brown released on the official site a public and personal statement, apologising and describing Turing's homophobic treatment as "appaling":

Text of Gordon Brown's statement on Alan Turing

Prime Minister: 2009 has been a year of deep reflection – a chance for Britain, as a nation, to commemorate the profound debts we owe to those who came before. ... So I am both pleased and proud that, thanks to a coalition of computer scientists, historians and LGBT activists, we have this year a chance to mark and celebrate another contribution to Britain’s fight against the darkness of dictatorship; that of code-breaker Alan Turing.

Turing was a quite brilliant mathematician, most famous for his work on breaking the German Enigma codes. It is no exaggeration to say that, without his outstanding contribution, the history of World War Two could well have been very different. He truly was one of those individuals we can point to whose unique contribution helped to turn the tide of war. The debt of gratitude he is owed makes it all the more horrifying, therefore, that he was treated so inhumanely. In 1952, he was convicted of ‘gross indecency’ – in effect, tried for being gay. His sentence – and he was faced with the miserable choice of this or prison - was chemical castration by a series of injections of female hormones. He took his own life just two years later.

Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling way he was treated. While Turing was dealt with under the law of the time and we can't put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him. Alan and the many thousands of other gay men who were convicted as he was convicted under homophobic laws were treated terribly. Over the years millions more lived in fear of conviction.

I am proud that those days are gone and that in the last 12 years this government has done so much to make life fairer and more equal for our LGBT community. This recognition of Alan’s status as one of Britain’s most famous victims of homophobia is another step towards equality and long overdue.

But even more than that, Alan deserves recognition for his contribution to humankind. For those of us born after 1945, into a Europe which is united, democratic and at peace, it is hard to imagine that our continent was once the theatre of mankind’s darkest hour. It is difficult to believe that in living memory, people could become so consumed by hate – by anti-Semitism, by homophobia, by xenophobia and other murderous prejudices – that the gas chambers and crematoria became a piece of the European landscape as surely as the galleries and universities and concert halls which had marked out the European civilisation for hundreds of years. It is thanks to men and women who were totally committed to fighting fascism, people like Alan Turing, that the horrors of the Holocaust and of total war are part of Europe’s history and not Europe’s present.

So on behalf of the British Government, and all those who live freely thanks to Alan’s work I am very proud to say: we’re sorry, you deserved so much better.

Alan Turing memorial statue in Sackville Park, Manchester

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Since 1966 by ACM - Association for Computing Machinery a Turing award has been given annualy to honor his memory. It is widely considered as the computing world's highest honour in the fields of computer science, intelligent systems and artificial intelligence.

Statue of Turing by Stephen Kettle at Bletchley Park

The Alan Turing Home Page

A. M. Turing Award

The Turing Digital Archive