Infinity
Author:
Ankur Srivastav
Last Updated:
7년 전
License:
Creative Commons CC BY 4.0
Abstract:
INFINITY: Finite Attempts to Capture The Infinite
\begin
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INFINITY: Finite Attempts to Capture The Infinite
\begin
Discover why over 20 million people worldwide trust Overleaf with their work.
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\title[Infinity] % [] is optional - is placed on the bottom of the sidebar on every slide
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\textbf{INFINITY}
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\subtitle[:Finite Attempts to Capture The Infinite]
{
\textbf{Finite Attempts to Capture The Infinite}
}
\author[\textbf{ANKUR SRIVASTAV}]
{ ANKUR SRIVASTAV\\
{\ttfamily (IPh-D $2^{nd}$ year) }
}
\institute[]
{
\textbf{ S.N. Bose National Centre for Basic Sciences\\
Block-JD, Sector-3, Kolkata (700106) \\ }
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\date{\textbf{May 21, 2018}}
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% THE BODY OF THE PRESENTATION
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\begin{document}
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% THE TITLEPAGE
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\vspace{20mm}
\begin{quote}
\textcolor{beamer@headercolor}{\textbf{\textit{\large``It is incumbent on the person who specializes\\ \vspace{2mm} in physics to discuss the infinite. And to \\ \vspace{2mm} inquire whether there is such a thing or not, \\ \vspace{2mm} and, if there is, what it is. ''}}}
\end{quote} \vspace{10mm}
\hspace{50mm} Aristotle, Physics III, 202b34
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\begin{frame}{Plan of Talk}{}
\tableofcontents
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\section{Introduction}
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\begin{frame}{Introduction}{}
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\begin{itemize}
\item The first recorded use of word ``Infinite'' is credited to Anaximander ( pre-Socratic Greek philosopher ).\vspace{3mm}
\item His term ``\textit{apeiron}'' can be translated as - limitless, boundless, indefinite, infinite. \vspace{3mm}
\item In 1655, the Oxford mathematician John Wallis \footnote{Famous for writing codes for both sides in the English Civil war.} first wrote down the `lazy eight'
symbol for Infinite - \LARGE$\infty$
\end{itemize}
\end{frame}
\begin{frame}{Zeno of Elea}{}
\begin{figure}
\includegraphics[scale=0.45]{Feathergraphics/Zeno}
\caption{Zeno of Elea (c. 490-430 BC) }
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\section{A Few Paradoxes}
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\subsection{The Dichotomy ( Zeno of Elea (c. 450 BC ) ) }
\begin{frame}{The Dichotomy}{}
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The Dichotomy paradox was put forward to show that motion is just an `illusion'.
\begin{figure}
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\caption{The Dichotomy}
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Because Zeno rejected the Infinite, he concluded that motion is not possible.\\
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\begin{frame}{Galileo Galilei}{}
\begin{figure}
\includegraphics[scale=0.65]{Feathergraphics/Galileo}
\caption{Galileo Galilei (1564-1642) }
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\subsection{Galileo's Paradox}
\begin{frame}{Galileo's Paradox}{}
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\begin{itemize}
\item Put the set of integers in one-to-one correspondence with the set of square of integers. \\ \vspace{2mm}
\item Galileo asked, which list is bigger? \\ \vspace{2mm}
\item Because set of squares is already subset of set of integers, does infinity come in different sizes? \\ \vspace{2mm}
\item Galileo never resolved this paradox. He only concluded - \\ \vspace{2mm}
``We cannot speak of infinite quantities as being the one greater or less than or equal to another.''
\end{itemize}
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\begin{frame}{Sir Edmund Halley}{}
\begin{figure}
\includegraphics[scale=0.65]{Feathergraphics/halley}
\caption{Sir Edmund Halley (1656-1736)}
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\subsection{Halley / Olber's Paradox}
\begin{frame}{Halley / Olber's Paradox}{}
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\begin{itemize}
\item Another interesting paradox arises if one considers an infinite Universe.
\item Sir Edmund Halley realized that a Universe containing infinite number of stars should shine like the surface of a star, day or night. But It Doesn't!
\end{itemize}
\begin{figure}
\includegraphics[scale=0.1]{Feathergraphics/Forest}
\caption{Looking into the woods. Everywhere your line of sight ends on a tree trunk. }
\end{figure}
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\section{Infinity in Modern Physics}
\subsection{Infinite Divisibility of Space}
\begin{frame}{Infinite Divisibility of Space }{Quanta of Space}
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\begin{itemize}
\item Two most powerful theories of $20^{th}$ century are General Relativity \\ \vspace{1mm} and Quantum Theory. \vspace{2mm}
\item If we rely on these theories, taken together, we are forced to \\ \vspace{1mm} accept that space is not infinitely divisible. \textbf{Space itself can be \\ \vspace{1mm} thought of as an ensemble of \textit{atoms of space}}.\vspace{2mm}
\item Notice that Zeno's Dichotomy paradox is resolved if space is not \\ \vspace{1mm} infinitely divisible. \vspace{2mm}
\item There is no necessarily infinite toward the small.\footnote{Carlo Rovelli}
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\subsection{Infinite Extension of Space}
\begin{frame}{Infinite Extension of Space}{Is Universe Infinite?}
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\begin{itemize}
\item Archytas of Tarentum was a $5^{th}$ century Greek thinker.\\ \vspace{2mm}
\item Archytas claimed that the Universe must be infinitely extended \\
\vspace{1mm} because of the following: \\ \vspace{1mm}
\textcolor{beamer@headercolor}{``If I arrived at the outermost edge of the heaven, could I extend \\ \vspace{1mm} my hand or staff into what is outside or not? It would be \\ \vspace{1mm} paradoxical not to be able to extend it.''} \vspace{2mm}
\item Aristotle considered this argument to be ``most important'' reason \\ \vspace{1mm} why people believe in the existence of the infinite.
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\begin{frame}{Dante Alighieri}{}
\begin{figure}
\includegraphics[scale=0.55]{Feathergraphics/Dante}
\caption{Dante Alighieri (1265-1321)}
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\subsection{Dante's Universe}
\begin{frame}{Dante's Universe}{Finite Universe Without Boundary}
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\begin{itemize}
\item Middle Age poet, Dante, solved above problem by imagining geometry of Universe as a 3-sphere. \vspace{1mm}
\item This is precisely a geometry of Universe that emerges from Einstein's equations. \footnote{Carlo Rovelli}
\end{itemize}
\begin{figure}
\includegraphics[scale=0.25]{Feathergraphics/DanteUniverse}
\caption{Dante Alighieri (1265-1321)}
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\section{Conclusion}
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We don't really know what infinity is, but there are strong reasons to believe that physical infinities are less likely.
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\section{References and Bibliography}
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\begin{itemize}
\item Rovelli, Carlo - 2011 - In Michal Heller and W. H. Woodin (eds.),\\ \vspace{1mm} Infinity: New Research Frontiers. Cambridge University Press. \\ \vspace{1mm} pp. 167--175. \vspace{2mm}
\item Clegg, Brian - 2012 - Introducing Infinity: A Graphic Guide \vspace{2mm}
\item Stewart, Ian - 2017 - Infinity: A Very Short Introduction \vspace{2mm}
\item Barrow, John D. - 2005 - The Infinite Book \vspace{2mm}
\item Rovelli, Carlo - 2014 - Seven Brief Lessons On Physics \vspace{2mm}
\end{itemize}
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\finalpage{\textbf{\LARGE Thank you!}}
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