Soeterbeeck programma 2006 ‘Het Onbegrensde Intellect’

1. Soeterbeeck programma 2006‘Het Onbegrensde Intellect’ Astrobiologie Lingua Cosmica Alexander Ollongren

2. Astrobiologie Leven in het universum: • Oorsprong • Evolutie • Waar? • Toekomst

3. Veronderstellingen I • existentie in de Melkweg van ‘aardse’ exo-planeten waarop • intelligente nieuwsgierige samenlevingen • technologisch ontwikkelingsniveau >> de onze

4. Veronderstellingen II • Niet universeel: - grammatica’s van talen • Wel universeel: - mathematica - logica

5. Communicatie met ETI ? • gemiddelde afstand • maximale snelheid info-overdracht • vorm info • inhoud info

6. Pioneer plaquette 1970-72

7. Karakteristieken van natuurlijke talen (op aarde) • In een natuurlijke taal • syntaxis en semantiek • gesproken / geschreven vorm • mogelijkheid van auto-interpretatie

8. Karakteristieken van Lingua Cosmica • Freudenthal (1960): symbolisch systeem • het uitdrukken van wiskundige relaties • voor aliens interpreteerbaar • traditie Lingua Characteristica • geen auto-interpretatie • waarheid via true en false

9. Karakteristieken van Lingua Cosmica • Ollongren (2006): multi level linguistisch systeem • basisniveau: tekst • toelichting op logische relaties • voor aliens interpreteerbaar • traditie Lingua Logica/Systematica • inclusief auto-interpretatie • waarheid via verificatie

10. LINGUA COSMICA (LINCOS)a Multilevel SystemLowest level: Text in Natural LanguageSecond level: Annotations in a Formal SystemLINCOS, Based on Logic, explains the logic contents of texts (sentences) written in ordinary language Sentences are split into constants, definitions conclusions in the form of facts

11. MARKERINGSSYMBOLEN CONSTANT A : Prop. In American Standard Code Information Interchange (ASCII) met markers spatie (20 = 0010 0000) punt (2E = 0010 1110) 43 4F 4E 53 54 41 4E 54 20 41 20 3A 20 50 72 0F 70 2E

12. Bits en Bytes 0100 0011 0100 1111 0100 1110 0101 0011 0101 0100 0100 0001 0100 1110 0101 0100 0010 0000 0100 0001 0010 0000 0011 1100 0010 0000 0101 0000 0111 0010 0000 1111 0111 0000 0010 1110 43 4F 4E 53 54 41 4E 54 20 41 20 3A 20 50 72 0F 70 2E

13. Tree Beard(J.R.R. Tolkien ‘The Lord of the Rings’, Part II) ‘Hm, but you are hasty folk, I see,’ said Treebeard. I a not going to tell you my name. For one thing it would take a long while: my name is growing all the time, my name is like a story. Real names tell you the story of the things they belong to in my language, in the Old Entish. It is a lovely language, but it takes a very long time to say anything in it, because we do not say anything in it, unless it is worth taking a long time to say, and to listen to.’

14. Introductie gehele positieve getallen CONSTANTS •,••,•••,••••,•••••,••••• •, ••••• ••,••••• •••, ••••• ••••, ••••• •••••, Etc. : Pos. DEFINE 0 = . DEFINE 1 = •. DEFINE 2 = ••. DEFINE 3 = •••. DEFINE 4 = ••••. DEFINE 5 = •••••. DEFINE 6 = ••••• •. DEFINE 7 = ••••• ••. DEFINE 8 = ••••• •••. DEFINE 9 = ••••• ••••. DEFINE 10 = ••••• •••••. DEFINE 11 = ••••• ••••• •. Etc.

15. Priemgetallen Een (onvolledige) lijst van ondeelbare getallen DEFINE Prime = 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, Etc.

16. Constanten en Variabelen CONSTANTS 0, 1, 2, 3, Etc. : Pos. CONSTANTS +, x : Pos  Pos  Pos. ( 2 argumenten, resultaat in Pos) Voorbeelden + 4 21 : Pos. (optelling) x 4 21 : Pos. (product) Variabelen a en b expliciet resp. impliciet VARIABLES a, b : Pos. [b : Pos](+ 4 b) : Pos  Pos. [a, b : Pos](+ a b) : Pos  Pos  Pos.

17. Proposities VARIABLES A, B : Prop. CONSTANT ¬ : Prop  Prop. (negatie) Conjunctie en disjunctie (en resp. of) CONSTANTS Λ, V : Prop  Prop  Prop. Voorbeelden ¬A : Prop. (Λ A) : Prop  Prop. (V A B) : Prop.

18. Proposities, vervolg [x : Prop](Λ x) : Prop  Prop  Prop. [x : Prop](Λ x B) : Prop  Prop. ([x : Prop](Λ x B)). toepassen op A (applicatie) ([x : Prop](Λ x B))A. reduceert tot (Λ A B) : Prop.

19. ModusPonens • CONSTANTS A, B : Prop. zodat (A /\ (A  B))  B : Prop. • FACT MP : (A /\ (A  B))  B.

20. Example all men are human, all women are humanSusan is a woman so Susan is human John is a man so John is human CONSTANTS Susan, John : Prop.CONSTANTS is-woman, is-man : Prop  Prop. DEFINE is-human : Prop = m : (ALL x : Prop)(is-man x)  (is-human x) | w : (ALL y : Prop)(is-woman y)  (is-human y). FACT (w Susan) : (is-woman Susan)  (is-human Susan). FACT (m John) : (is-man John)  (is-human John). Opm. Susan is een zgn. singulier vlgs. Aristoteles

21. Aristotelian syllogism, universal case (all) Sentences with a single subject S and a single predicate P, all S is P (no singular). Example: if all humans are mortal, if all Greeks are humans, then all Greeks are mortal CONSTANTS is-human, is-Greek, is-mortal : Prop  Prop. HYPOTHESES 1,2 : (ALL x : Prop)(is-human x)  (is-mortal x), (ALL x : Prop)(is-Greek x)  (is-human x). FACT 3 : (ALL x : Prop)(is-Greek x)  (is-mortal x).

22. Aristotelian syllogisms (general) subject S is predicated by P all S is P (ALL x : Prop) (is-S x)  (is-P . . .) some S is P (EXISTS x : Prop) (is-S x)  (is-P . . .) no S is P (NOT (EXISTS x : Prop) (is-S x)  (is-P . . .)) not every S is P (NOT (ALL x : Prop) (is-S x)  (is-P . . .))

23. Uit ‘Alice in Wonderland’ • “You are sad,” the knight said in an anxious tone: “let me sing you a song to comfort you.” • “Is it very long?” Alice asked for she had heard a good deal of poetry that day. • “It’s long ,” said the knight, “but it’s very, very beautiful. Everybody that hears me sing it – either it brings the tears into their eyes, or else –“ • “Or else what?” said Alice, for the knight had made a sudden pause. • “Or else it doesn’t, you know. The name of the song is called ‘Haddocks’ Eyes.’ ” • “Oh, that’s the name of the song, is it?” Alice said, trying to feel interested.

24. “No, you don’t understand,” the Knight said, looking a little vexed. • “ That’s what the name is called. The name really is ‘The Aged Aged Man.’ ” • “Then I ought to have said ‘that’s what the song is called’? “ Alice corrected herself. • “No, you oughtn’t: that’s quite another thing! The song is called ‘Ways and means’; but that is only what it’s called, you know!” • “Well, what is the song, then?” said Alice, who was by this time completely bewildered. • “I was coming to that,” the Knight said. “The song really is ‘A-sitting on AGate’: and the tune’s my own invention.”

25. Logic structure of the story *Knight’s song ‘A-sitting on AGate’ ** song’s name ** call name of song ‘The Aged Aged Man ’ ‘Ways and means’ *** call name of song’s name ‘Haddocks’ Eyes’

27. Formal logic structure of the story *Knight’s song DEFINE Knight’s song = ‘A-sitting on AGate’ **DEFINE song’s name = **DEFINE call name of song = ‘The Aged Aged Man’ ‘Ways and means’ ***DEFINE call name of song’s name = ‘Haddocks’ Eyes’

28. Logic of the story in LINCOS *DEFINE Knight’s-song [song’s-name, call-name-of-song : Prop] : Prop = ‘A-sitting On A Gate’**(DEFINE song’s-name [call-name-of-song’s-name] : Prop = ‘The Aged Aged Man’***(DEFINE call-name-of-song’s-name : Prop = ‘Haddocks’ Eyes’) )**(DEFINE call-name-of-song : Prop = ‘Ways and Means’)  (Knight’s-song song’s-name call-name-of-song).

29. Mensenrechten Preambule • Whereas recognition of the inherent dignity and of the equal and inalienable rights of all members of the human family is the foundation of freedom, justice and peace in the world, • Whereas it is essential, if man is not to be compelled to have recourse, as a last resort, to rebellion against tyranny and oppression, that human rights should be protected by the rule of law, • Whereas it is essential to promote the development of friendly relations between nations,

30. Universal Declaration of Human Rights (UN 1948) 30 articles • Article 1. • All human beings are born free and equal in dignity and rights. They are endowed with reason and conscience and should act towards one another in a spirit of brotherhood.

31. PIONEER PLAQUETTE

32. EINDE