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SUMMARY:Infinity Computing: Practical computations with numerical infiniti
 es and infinitesimals - Professor Yaroslav Sergeyev\, President of Interna
 tional Society of Global Optimization
DTSTART:20181115T110000Z
DTEND:20181115T130000Z
UID:TALK114250@talks.cam.ac.uk
CONTACT:Mari Huhtala
DESCRIPTION:In this lecture (that is self-contained\, does not require any
  special high level mathematical preparation and is oriented on a broad au
 dience)\, a recent computational methodology is described. It has been int
 roduced with the intention to allow one to work with infinities and infini
 tesimals numerically in a unique computational framework and in all the si
 tuations requiring these notions (recall that traditional approaches work 
 with infinities and infinitesimals only symbolically and different notions
  are used in different situations related to infinity\, e.g.\, infinity in
  mathematical analysis\, ordinals\, cardinals\, etc.). The methodology is 
 based on the Euclid’s Common Notion no. 5 “The whole is greater than t
 he part” applied to all quantities (finite\, infinite\, and infinitesima
 l) and to all sets and processes (finite and infinite). Using the separati
 on of mathematical objects from tools involved in their representation it 
 is shown that the new methodology does not contradict traditional Cantor
 ’s (and non-standard analysis) views on the subject and represents a fre
 sh independent way to look at infinity.\n\nOne of the strong advantages of
  this methodology consists of its computational power in practical applica
 tions. In fact\, the methodology uses as a computational device a new kind
  of supercomputer called the Infinity Computer patented in USA and EU. It 
 works numerically with a variety of infinite and infinitesimal numbers tha
 t can be written in a positional system with an infinite radix using float
 ing-point representation. Numbers written in this system can have several 
 infinite and infinitesimal parts. On a number of examples (numerical diffe
 rentiation and optimization\, divergent series\, measuring infinite sets\,
  ordinary differential equations\, fractals\, etc.) it is shown that the n
 ew approach can be useful from both computational and theoretical points o
 f view. In particular\, the accuracy of computations increases drastically
  and all kinds of indeterminate forms and divergences are avoided. The acc
 uracy of the obtained results is continuously compared with results obtain
 ed by traditional tools used to work with mathematical objects involving i
 nfinity. It is argued that traditional numeral systems involved in computa
 tions limit our capabilities to compute and lead to ambiguities in certain
  theoretical assertions\, as well.\n\nThe Infinity Calculator working with
  infinities and infinitesimals numerically is shown during the lecture. Su
 pporting materials\, videos of lectures\, more than 50 papers of authors f
 rom several research areas using this methodology in their applications\, 
 and a lot of additional information can be downloaded from the page http:/
 /www.theinfinitycomputer.com\n
LOCATION:Sir Arthur Marshall Room\, Engineering Design Centre\, CUED
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