"By giving its support to these series, the Onassis Foundation wished to explore the links existing between the culture of ancient Greece and the world today." "It was never in it intention to associate itself to any opinion concerning the history and the political life of modern Greece." "The Onassis Foundation insists in clarfying that the choice of the themes as well as the selection of the interviewed persons are the sole responsibility of the director." "THE OWL'S LEGACY" "6 MATHEMATICS or the Empire counts back" "Famous throughout Greece" "Pythagoras, a young musician, wrote 5 centuries BC:" ""All things can be measured"." "Pythagoras was a great man." "A great initiate." "He was in the same league" " I may shock some people here - as Moses, Buddha and Jesus Christ." "He really was a Great Initiate." "The world could be expressed in harmonious balance of numbers and their perfect relationship is the Golden Number." "I used to believe that mathematics was a game invented by clever men like Pythagoras, Thales and others who invented a game like chess." "We know they disagreed." "Like Thales about the parallels" " the universe is curved, etc. " "I believed this most of my life." "Then some years ago in LA I started to look into myself and found something much simpler." "Numbers, hence mathematical laws are not Man's invention." "They are the basis of Creation." "Man didn't invent numbers." "He simply decoded them." "If mankind disappeared numbers would still exist." "Pythagoras used numbers in three ways." "First, on the material level which he called merchant's numbers." "So if a caveman goes hunting catches five rabbits, eats two, he would have three left." "He can barter rabbits for a goat, five goats for a camel, three camels for a wife, then he trades his wife, etc." "So merchant's numbers allowed man to evolve all over the planet." "Second level - scientific numbers, which allow all the rest." "We can do nothing without numbers." "No chemistry, physics, nothing." "They all need the law of numbers." "And the third level" "Pythagoras called divine numbers." "All physical phenomena, he said, can be defined in numerical terms." "This kicked off logical thinking." "Pythagoras never wrote a thing." "He was murdered, but two centuries later he found his own evangelist in Plato." "Read Plato and you read Pythagoras." "And Plato is full od numbers." "He wrote on his school's pediment 'Only geometricians may enter'." "There are many explanations for the birth of geometry." "Imagine these quarrelsome men endlessly arguing, their eternal polemic squabbles, the sound and fury we still hear in Plato's dialogues." "Imagine the inter-school fights." "And maybe in all this mess someone clutched his head, crying" ""Where can I think alone?"" "Maybe, to escape, he invented a totally pure space" " Utopia." "Historians say Utopia doesn't exist." "It does, it's the geometric space where everything is fully proven and universally accepted putting an end to noise, reality, and the stakes of any argument too." "So maybe he discovered in the middle of these squabbles a universal place of peace." "'Order and beauty':" "Two key-words which tell us of man's relentless quest." "Man, in grasping the universe, is going to translate into numbers, into equations, into formulas, the innumerable facets of Creation." "If we ever communicate with intelligent extra-terrestrials, it will be thanks to numbers." "The senses may not work." "Martians may not have our sight nor share our visual spectrum." "We may not be able to hear them." "But if we simply do this they understand that means One, twice means Two." "I can explain everything to them, the whole history of humanity." "Socrates, Plato and Aristotle posited that the rules of harmony apply to all forms of reasoning." "For them, numbers are ideas." "If a proposition is correct it is expressed in a balanced way, with harmonious relationship." "Euclid and Thales further posited the rules of logical reasoning and of mathematical proof." "Vocabulary can be classified." "For example, parallelogram, arithmetic, logarithm, topology are words of geometry, words of mathematics." "Democracy and aristocracy are political words." "Theology is a religious word." "When you classify vocabulary, since this is what you're doing, you realize we don't really know if the Greeks believed in the Gods." "And when we speak about democracy it's a false inheritance" "because Athenian democracy depended on huge numbers of slaves." "But in the case of parallelogram, arithmetic, logarithm, etc., a unique thing happened in history of which there is no other example." "When they say parallel, we mean exactly the same thing as Thales." "That is, we have today in 1987, the same thought contents as someone who lived between the 6th and 7th century BC." "Another peculiarity of vocabulary." "When I say parallelogram arithmetic, logarithm, am I speaking French?" "No." "It's the same in English, German, the same in Italian, Spanish, and the same, no doubt, in languages I don't know." "Consequently, this vocabulary when it comes to maths and science is invariable in all languages." "There was no Greek empire as such except in Alcibiades' plans, unlike the Roman or British empire." "But in a sense, the Greeks created an extraordinary empire because no matter where you live everybody learns the same words" "unchanged by time or space." "There is a re-setting of history a lifting of translation barriers" "I find this absolutely fascinating." "How did they impose this legacy which I cannot but accept?" "Greek philosophy has always pondered" "the meaning of words and their correct arrangement." "I think it was Aristotle who first posed the logic problem in almost contemporary terms." "Logic: the art of valid inference." "Definite valid inference regardless of the subject." "Hence: all tigers are ferocious this is a tiger - so it's ferocious." "Or all peas are green this is a pea - therefore it's green." "And to make this inference you don't even need to know what is a pea or a tiger." "Aristotle wanted to codify these rules of reasoning which don't depend on the subject." "So logic hardly evolved until the 19th century when it encountered mathematics." "On one hand, they created an algebra of logic." "On the other, they asked 'What language is best for science?" "'" "For the modern science of Galileo." "They sought a scientific language." "Then the subject of logic arose with renewed vigour." "Now they had mathematical tools to start treating logic as a mathematical object." "So there was a kind of threesome." "There was mathematics, there was the logic of Aristotle now revitalised with new ambition, and the science seeking a language," "a good, unified language." "Then late in the 19th century a German called Frege created to a certain point modern logic," "the logic on which we work today, on which logicians work." "Logicians took another direction in the 1930s following Frege's example." "They pondered the idea of effective procedures." "There are two ways of seeing things, two ways of answering any question such as 'Do unicorns exist?" "'." "You can answer abstractly following very general principles and conclude that they exist without being able to construct them." "Or you can construct a unicorn display it, pull one out of a hat" "'I can show it, so it exists'." "This is a central problem in maths to generally define the procedures which enable us to exhibit a being be it abstract, like a function." "To exhibit it, pull it from a hat, and to say 'This object is what you were looking for'." "This reflexion on the production of abstract objects led us to the idea of the computer." "As we go on inventing mathematics" "Greekness is always present." "But something new has just happened which I am begining to understand and which I can put like this," "Greeks invented mathematics, we've inherited it, like it or not." "Consequently, before the Greeks in the Babylonian or Egyptian eras mathematics didn't exist." "Suddently my generation discovered something incredibly new." "Now that we are aware of a new kind of mathematics we re-read these manuscripts written in Egyptian hieroglyphics" "or cuneiform writing from Babylon and find that the formulas, which we had slightly spurned for the invention of geometry," "are absolutely codified formulas and punctuated in a certain manner." "And now that we can read them we realize they are algorithms." "We talked earlier about vocabulary." "You may think 'algorithm' is a Greek word, but it isn't." "It's half-Arabic, half-Persian." "It comes from a person's name." "Al Khawarizmi and he gave his name" " Algorithm to numbers as a whole" "PLUS the nought: zero." "We now see the Greek source in a different light not as an 'ex nihilo' miracle pulling maths out of nothing" "but as a sort of tension or difficulty." "Greek mathematics was born of quarrel with the old thinking which came from Egypt or Babylon." "We inherited not one mathematics but two forms." "That which we took as the only one which I mentioned earlier and also a kind of undercurrent flowing from an archaic period more archaic than the Greeks." "It exploded into our modern world and with artificial intelligence, comupters, for example, algorithm becomes more significant." "I can't help thinking that when we talk of legacy," "Greekness or Greece has leant a little on this legacy slowed its development whilst giving more weight" "to an invented Smooth Abstraction." "The idea of imperfection of uncertainty, etc., is essential to the programme" "of artificial intelligence, essential to cognitive science which is a 20th century science, the century of uncertainty, of Heisenberg's unvcertainty, of quantum intedetermination, etc." "It's evidently an idea that attract us," "an idea fundamentally embedded in our contemporary approach." "So there is a departure in this development of uncertainty," "of imperfection, there's maybe a departure from the Greek reasoning." "Once you accept uncertainty you try to dominate and control it." "The fuzzy logics for instance are being actively researched." "They are effectively a way of linking eternal perfect logic" "which doesn't admit uncertainty with this universe of phenomena which brings you close to despair." "Nothing is clearly defined..." "We don't know how to deal with it..." "so we let it go." "Attempts to link cognitive science and artificial intelligence are not simply theoretical not purely technological." "They are based on the idea that man and other animals are able to deal with uncertainty in a relatively effective manner." "They get by well enough." "For example, in the countryside owls live off mice and rodents." "What do owls eat in Paris today?" "They have to eat small birds." "Why?" "Because there are no mice in Paris." "The owl managed to get by in conditions of uncertainty in an unpredictable situation." "Owls don't have a fixed definition of what is actually edible." "They used to eat mice, well now it's small birds." "The idea that the living world is build around unpredictability," "survive in uncertainty, isn't the philosophers' idea." "It simply works." "But we are not going to stop there." "We are not going to simply say 'Great, it works, leave well alone'." "It may well be God's good work but we must be able to explain it." "Armed with technical tools like the new computers, theoretical tools, we attack the work with gusto." "People said to themselves" "'This world of living systems that get by, interact, reproduce, is open, ultimately, to analysis'." "It may give us new ideas, ideas for new machines, to help us learn, cure" "or change people's mode of thought." "The pre-Socratics were not from Athens but from the opposite Aegean coast in Greek Asia Minor." "Some of them had fled to Sicily." "The pre-Socratics, in my opinion, are the philosophers of the future because they discovered computers and the immaterialism of matter." "As you quite rightly said they derived the abolition of the Law of Entropy, entropy, the decay of matter, with the 2nd law of thermodynamics, all the Greek words again." "And they are now at the forefront because they invented the indestructibility of matter, which is non-matter." "It's a pity that some philosophers interpret pre-Socratics as poets or as very erudite philosophers, atheists or political philosophers." "While others interpret them, with as much justification, as the founding fathers of arithmetic, geometry, physics," "physics is a very early word." "It's a pity that we are so limp, so feeble and divided that we pull their work apart so that it can only be understood in one ear by the scientists and in the other by the humanists." "We can't reform the whole body from the two separate parts, the body made by ancient Greeks." "When the pre-Socratics, with a single voice, pronounce the word logos they mean logos as understood by those educated in philosophy" "and in religion." "But they also mean relation, proportion and analogy, mathematical principles." "It's all the same thing for them, one single utterance." "For them, science and philosophy," "I was going to say 'are mixed' but it is us who mixed them." "For the Greeks, it was one entity." "My fervent hope is to rediscover Greek heritage." "We have lost it and yet" "it is present almost without trying." "I wish the scientific heritage could recover its humanistic trail." "I wish the humanistic heritage, also a bit lost at the moment, could recover its scientific trail." "It's one and the same heritage but we are mediocre inheritors."