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CATEGORIES:Engineering Design Centre Seminars
SUMMARY:Infinity Computing: Practical computations with nu
merical infinities and infinitesimals - Professor
Yaroslav Sergeyev\, President of International Soc
iety of Global Optimization
DTSTART;TZID=Europe/London:20181115T110000
DTEND;TZID=Europe/London:20181115T130000
UID:TALK114250AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/114250
DESCRIPTION:In this lecture (that is self-contained\, does not
require any special high level mathematical prepa
ration and is oriented on a broad audience)\, a re
cent computational methodology is described. It ha
s been introduced with the intention to allow one
to work with infinities and infinitesimals numeric
ally in a unique computational framework and in al
l the situations requiring these notions (recall t
hat traditional approaches work with infinities an
d infinitesimals only symbolically and different n
otions are used in different situations related to
infinity\, e.g.\, infinity in mathematical analys
is\, ordinals\, cardinals\, etc.). The methodology
is based on the Euclid’s Common Notion no. 5 “The
whole is greater than the part” applied to all qu
antities (finite\, infinite\, and infinitesimal) a
nd to all sets and processes (finite and infinite)
. Using the separation of mathematical objects fro
m tools involved in their representation it is sho
wn that the new methodology does not contradict tr
aditional Cantor’s (and non-standard analysis) vie
ws on the subject and represents a fresh independe
nt way to look at infinity.\n\nOne of the strong a
dvantages of this methodology consists of its comp
utational power in practical applications. In fact
\, the methodology uses as a computational device
a new kind of supercomputer called the Infinity Co
mputer patented in USA and EU. It works numericall
y with a variety of infinite and infinitesimal num
bers that can be written in a positional system wi
th an infinite radix using floating-point represen
tation. Numbers written in this system can have se
veral infinite and infinitesimal parts. On a numbe
r of examples (numerical differentiation and optim
ization\, divergent series\, measuring infinite se
ts\, ordinary differential equations\, fractals\,
etc.) it is shown that the new approach can be use
ful from both computational and theoretical points
of view. In particular\, the accuracy of computat
ions increases drastically and all kinds of indete
rminate forms and divergences are avoided. The acc
uracy of the obtained results is continuously comp
ared with results obtained by traditional tools us
ed to work with mathematical objects involving inf
inity. It is argued that traditional numeral syste
ms involved in computations limit our capabilities
to compute and lead to ambiguities in certain the
oretical assertions\, as well.\n\nThe Infinity Cal
culator working with infinities and infinitesimals
numerically is shown during the lecture. Supporti
ng materials\, videos of lectures\, more than 50 p
apers of authors from several research areas using
this methodology in their applications\, and a lo
t of additional information can be downloaded from
the page http://www.theinfinitycomputer.com\n
LOCATION:Sir Arthur Marshall Room\, Engineering Design Cent
re\, CUED
CONTACT:Mari Huhtala
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