# Aristotle and Hypathia

\chapter{Aristotle and Hypatia: Mathematicians}

\begin{quote} Reserve your right to think, for even to think wrongly is better than not to think at all.

(Hypathia)

\end{quote}

\begin{quote} Humor is the only test of gravity, and gravity of humor; for a subject which will not bear raillery is suspicious, and a jest which will not bear serious examination is false wit. (Aristotle)

\end{quote}

As a formidable student, researcher, teacher, and philosopher in virtually all scientific disciplines,

way science and mathematics is practiced and

investigated today. His analytical

method, now known as Aristotelian logic, is the backbone of not only mathematics,

but of all the natural sciences.

\begin{figure}

\begin{center}

\epsfig{file=aristotle.eps, width=6cm}

\end{center}

\caption{Aristotle: Philosopher and Mathematician}

\end{figure}

%\section{Hypatia: Mathematician}

\href{http://www.youtube.com/watch?v=cbskP9utQ0M}{Hypatia of Alexandria} (born between 350 and 370; died 415) was a Greek scholar from Alexandria in Egypt,

considered the first notable woman in mathematics, who also taught philosophy and astronomy. She lived in

Roman Egypt, and was killed by a Christian mob who falsely blamed her for religious turmoil, see the recent film

%Some suggest

%that her murder marked the end of what is traditionally known as Classical antiquity, although others such as

%Christian Wildberg observe that Hellenistic philosophy continued to flourish until the age of Justinian in the

%sixth century.

A Neoplatonist philosopher, she belonged to the mathematical tradition of the Academy of Athens represented by

Eudoxus of Cnidus; she followed the school of the 3rd century thinker Plotinus, discouraging empirical

enquiry and encouraging logical and mathematical studies.

\begin{figure}

\begin{center}

\epsfig{file=darkage.eps, width=5cm}

\end{center}

\caption{Destruction of Library of Alexandria: In 391, Christian Emperor Theodosius I ordered the destruction of all “pagan” (non-Christian) temples, and the Christian Patriarch Theophilus of Alexandria complied with this request.}

\end{figure}

John of Nikiu (7th century) writes;

\begin{itemize}

\item \emph{And in those days there appeared in Alexandria a female philosopher, a pagan named Hypatia, and she was devoted at all times to magic, astrolabes and instruments of music, and she beguiled many people through Satanic wiles…A multitude of believers in God arose under the guidance of Peter the magistrate…and they proceeded to seek for the pagan woman who had beguiled the people of the city and the prefect through her enchantments. And when they learnt the place where she was, they proceeded to her and found her…they dragged her along till they brought her to the great church, named Caesareum. Now this was in the days of the fast. And they tore off her clothing and dragged her…through the streets of the city till she died. And they carried her to a place named Cinaron, and they burned her body with fire.}

\end{itemize}

\begin{figure}

\begin{center}

\epsfig{file=Hypatia.eps, width=8cm}

\end{center}

\caption{Hypatia from Alexandria 350-415: Mathematician and Scientist.}

\end{figure}

\section{Integers and Rational Numbers}

Of course you know about natural numbers $0,1,2,3,…,$ and integers $0,\pm 1,\pm 2,\pm 3,…$ and rational numbers

as quotients $\frac{p}{q}$ of integers with $q\neq 0$. You may also know that rational numbers have ending (finite)

or periodic (non-ending) decimal expansions. You can refresh your conception of rational numbers by reading

\begin{itemize}

\item \hyperref[integers]{Integers.}

\item \hyperref[rationalnumbers]{Rational numbers.}

\end{itemize}

Remember that numbers is the basis of the digital world or IT-world.

\begin{itemize}

\item \href{http://hanskayser.com/EZ/kayser2/kayser2/index.php}{Hans Kayser, 20th Century Pythagorean Master}.

\end{itemize}

\begin{figure}

\begin{center}

\epsfig{file=pythagoreanharmonics.eps, width=10cm}

\end{center}

\caption{Man’s Constitution and the World’s Constitution.}

\end{figure}

%\section{The Game of Icarus}

%Deadalus is the mythical father of engineering.

%As you plunge into your studies you will be accompanied by Icarus and Deadalus in the computer game

%The Flight of Icarus. The starting point is the following following formulas discovered by Icarus

%on a piece of paper hidden in a glitch of the Labyrinth wall:

%

%\begin{array}{rcl}

%R_\rho (\hat u)\equiv

%\dot \rho +\nabla\cdot (\rho u )&=& 0 \\

%R_m(\hat u)\equiv

%\dot m +\nabla\cdot (mu +p)&=& f \\

%R_e(\hat u)\equiv

%\dot\epsilon +\nabla\cdot (\epsilon u +pu)&=& 0 \\

%u\cdot n&=&0\quad \mbox{on } \Gamma_I\equiv\cup_{t\in I} \Gamma (t)\\

%\hat u(\cdot ,0)&=&\hat u^0\quad \mbox{in } \Omega (0) ,

%\end{array}

%

%idea is to follow Icarus and Daedalus as they prepare to escape from the Labyrinth.

%The only possiblity is the flee by flying over the walls of the Labyrinth, 20 feet tall.

%How to get out? Impossible to climb the walls; vertical and smooth 40 feet high.

%This gives the first clue, and now it is up to you to continue.

%\section{The Symbolic Meaning of the Myth of Icarus and Daedalus}

%\part{Icarus and Daedalus}