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Menno Ekkelboom Phänomen und Paradigma Seite

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"Was, wer, wo - von wem hast du das?"


NL; Van Dale Dictionary [[1]]

fe·no·meen het; o -menen 1 ieder waarneembaar (natuur)verschijnsel 2 zeldzaam verschijnsel

(1 every observable (natural)appearance 2 rare appaerance)

UK; Oxford Dictionary [[2]]

Pronunciation: /fɪˈnɒmɪnən/ noun (plural phenomena /-nə/) 1a fact or situation that is observed to exist or happen, especially one whose cause or explanation is in question: glaciers are interesting natural phenomena 2 Philosophy the object of a person’s perception. 3a remarkable person or thing: the band was a pop phenomenon just for their sales figures alone Origin: late 16th century: via late Latin from Greek phainomenon 'thing appearing to view', based on phainein 'to show'


UK; Oxford Dictionary [[3]]

Pronunciation: /ˈparədʌɪm/ noun 1a typical example or pattern of something; a pattern or model: society’s paradigm of the ‘ideal woman’ a world view underlying the theories and methodology of a particular scientific subject: the discovery of universal gravitation became the paradigm of successful science 2 Linguistics a set of linguistic items that form mutually exclusive choices in particular syntactic roles: English determiners form a paradigm: we can say ‘a book’ or ‘his book’ but not ‘a his book’Often contrasted with syntagm. 3(in the traditional grammar of Latin, Greek, and other inflected languages) a table of all the inflected forms of a particular verb, noun, or adjective, serving as a model for other words of the same conjugation or declension.

Origin: late 15th century: via late Latin from Greek paradeigma, from paradeiknunai 'show side by side', from para- 'beside' + deiknunai 'to show'


NL; Van Dale Dictionary http://www.vandale.nl/

di·gi·taal bn, bw in cijfers, cijfer-; werkend op basis vh binaire stelsel: ~ vastgelegde databestanden; -tale klok met cijfers, niet met wijzers (tegenst analoog)

(Cypher-; functioning on basis of the binary system: ~ established databases; -tal clock with numbers, not with pointers (antithesis analog))

UK; Oxford Dictionary http://oxforddictionaries.com/

Pronunciation: /ˈdɪdʒɪt(ə)l/ adjective 1(of signals or data) expressed as series of the digits 0 and 1, typically represented by values of a physical quantity such as voltage or magnetic polarization. Often contrasted with analogue. relating to, using, or storing data or information in the form of digital signals: digital TV a digital recording involving or relating to the use of computer technology: the digital revolution 2(of a clock or watch) showing the time by means of displayed digits rather than hands or a pointer. 3relating to a finger or fingers. Derivatives digitally adverb Origin: late 15th century: from Latin digitalis, from digitus 'finger, toe'

footnote: I have to argue that in the Oxford dictionary 'digital' discribes with the numbers 0 and 1. Jan Sloot [4] invented the Sloot Digital Coding System that did not work on with the binair system.

Aufgabe 2: Phenomenon

I tried to look for the most universal known phenomenon, something that has the same meaning in any part of the world, in any kind of religion. Counting, numbers or simple mathematics seems to be the most universal known phenomenon. Numbers: the phenomenon numbers or cyphers would at first sight seem to be a very clear and easy to understand phenomenon. You have the cyphers 0 to 9 or in roman I, V, X, C, M and with these symbols you can make combinations to get a certain number. It seems to be a universal acknowledged phenomenon, everybody knows what you mean and it is a universal language. Or is it? The Pirahã tribe in the Brazilian Amazon only knows (about) one, (about) two and many, or small amount and large amount. So if a phenomenon is only known to a “limited” amount of people is it still a phenomenon?

Aufgabe 3: Mathematics (a universal language?)

Mathematics; Oxford dictionaries: “a science of numbers, quantity, and space, either as abstract or applied concepts”

To summarise mathematics can be understood as a understanding of numbers.

Does everyone have this understanding of numbers, quantity and space? Is it a innate skill?

Is mathematics innate?

“Children enter the world with a head for numbers. Veronique Izard, a cognitive psychologist at Harvard University, demonstrated this in a recent study of newborns.”

“Mathematical intuition develops as we grow up,...”

“From infancy to old age, mathematical intuition consistently follows two rules. One is that people score better when the numbers are small than when they are large. The other is that people score better when the ratio of the bigger number to the smaller one is greater.”

“Neuroscientists have found that when people do mathematical intuition problems, a strip of neurons near the top of the brain, surrounding a fold called the intraparietal sulcus, consistently becomes active. And when we confront more difficult problems—when the numbers are bigger or closer together—this region becomes more active.”

“...recent research indicates that our forebears possessed such an intuition long before they could walk upright. Scientists have found that many primates, including rhesus monkeys, can solve some of the same mathematical problems we can. Since monkeys and humans diverged 30 million years ago, mathematical intuition presumably is at least that old.”

“...what makes humans so much better with numbers than other animals. Nieder and Cantlon have both speculated that the difference lies in our ability to understand symbols, which enables us to transform our approximate intuition of numbers into a precise understanding.”

“...once our ancestors began to link their natural instinct for numbers with a new ability to understand symbols, everything changed. Math became a language of ideas, of measurements, and of engineering possibilities.”

http://discovermagazine.com The Brain Humanity's Other Basic Instinct: Math by Carl Zimmer

The answer is; yes, mathematics is innate, and we develop it to a higher level as we grow older (at least for most of us).

When we look at the evolution of mathematics we see that it has been developing drastic over the last centuries and still is.

“Numbers make modern life possible ... University of Rochester neuroscientist Jessica Cantlon and her colleagues recently observed in the journal Trends in Cognitive Sciences, “we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market.” ” http://discovermagazine.com The Brain Humanity's Other Basic Instinct: Math by Carl Zimmer

So what are the boundaries of mathematics?

In the hitchhiker's guide of the galaxy mathematics can even be used to solve "The Answer to the Great Question, of Life, the Universe and Everything", which is: 42

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