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NEW YORK — Despite being in existence for more than 2,000 long time , the concept of eternity has run as an enigmatic , and oftentimes thought-provoking , idea for mathematician , physicists and philosophers . Does infinity really exist , or is it just part of the fabric of our imaginations ?
A dialog box of scientist and mathematicians gathered to discuss some of the profound questions and controversies surrounding theconcept of infinityhere Friday ( May 31 ) , as part of the World Science Festival , an one-year celebration and exploration of science .
The mathematical symbol that represents infinity.
Part of the difficulty in trying to solve some of the abstract questions related to infinity is that these problems fall down beyond the more established numerical theories , said William Hugh Woodin , a mathematician at the University of California , Berkeley . [ Watch : World Science Festival Highlights ]
" It ’s kind of like mathematics lives on a unchanging island — we ’ve built them a solid innovation , " Woodin said . " Then , there ’s the waste land out there . That ’s eternity . "
Where it all began
A philosopher named Zeno of Elea , who lived from 490 B.C. to 430 B.C , is credited with introducing the idea of infinity .
The construct was studied by ancient philosophers , includingAristotle , who questioned whether space could exist in a seemingly finite strong-arm world , articulate Philip Clayton , dean of the Claremont School of Theology at Claremont Lincoln University in Claremont , Calif. Theologians , let in Thomas Aquinas , used the space to explain the family relationship between humanity , God and the born earthly concern .
In the 1870s , a German mathematician call Georg Cantor pioneered work in a airfield that became known as set possibility . According to lay out hypothesis , whole number , which are numbers without a fraction or denary constituent ( such as 1 , 5 , -4 ) , make up an space set that is numerable . On the other hired man , actual numbers , which admit integers , fraction and so - phone irrational numbers , such as the square root of 2 , are part of an infinite readiness that is uncountable .
This led Cantor to question about different types ofinfinity .
" If there are now two kinds of infinity — the countable kind and this uninterrupted form , which is bigger — are there other infinity ? Is there some eternity that ’s sandwich in between them ? " pronounce Steven Strogatz , a mathematician at Cornell University in Ithaca , N.Y.
Cantor believe that no infinity exist between the band of integers and real bit , but he was never able to prove it . His command , however , became known as the continuum hypothesis , and mathematicians who take on the problem in Cantor ’s footsteps were label set theorists .
explore beyond
Woodin is a set theorist , and has drop his life story trying to work out the continuum hypothesis . To date , mathematicians have not been capable to demonstrate or confute Cantor ’s predication . Part of the problem is that the mind that there are more than two types of eternity is so nonfigurative , Woodin said .
" There ’s no artificial satellite you may build to go out and value the continuum theory , " he explain . " There ’s nothing in our world around us that will help us determine whether or not the continuum hypothesis is truthful or sour , as far as we know . " [ 5 gravely head - Boggling Math Facts ]
Trickier still is the fact that some mathematicians have dismiss the relevance of this eccentric of numerical oeuvre .
" These multitude in set theory strike us , even in mathematics , as sort of unusual , " Strogatz joked . But , he said he understands the importance of the work being done by set theorists , because if the continuum hypothesis is proven false , it could root out basic numerical principles in the same direction that controvert act theory would wipe out the basis for math andphysics .
" We know that they ’re doing really bass , important workplace , and in principle , it ’s foundational piece of work , " Strogatz explained . " They ’re shaking the understructure that we ’re all working on , up on the second and third floors . If they mess something up , it could tap us all over . "
The future of mathematics
Still , despite all of the uncertainties , the work done by define theorists could have positive ripple effects that serve to strengthen thefoundations of mathematics , Woodin say .
" By investigating infinity , and to the extent that we can be successful , I imagine we make the case for the consistency of arithmetical , " he explained . " That ’s a snatch of a fanatical instruction , but if infinity does n’t lead to a contradiction , sure the finite does n’t lead to a contradiction in terms . So , mayhap by exploring the stunned range to see if there is a contradiction , you profit some security system . "
The paradox that characterise the construct of infinity are perhaps well explained with thenumber pi , Strogatz said . Pi , one of the most recognisable mathematical constants , represents the ratio of a lot ’s perimeter to its diameter . Among its myriad app , pi can be used to find the region of a circle .
" Pi is distinctive of real numbers … in that it has this infinite amount of unpredictable data in it , and at the same time , is so entirely predictable , " Strogatz allege . " There ’s nothing more neat than a round , which shamus body forth — it ’s the very symbolic representation of parliamentary procedure and idol . So this coexistence of perfect predictability and lodge , with this tantalizing mystery of myriad enigma build into the same objective , is part of the pleasance of our content and , I suppose , of infinity itself . "
