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\newcommand{\fpause}{\pause\vfill}

\title[]{
The artistry of discovery, and the shocking beauty of God's creation}
\author[]{Chris Staecker}
\institute[]{Fairfield University}
\date[]{Huntington United Methodist Church, Oct 18 2012}

\begin{document}
\frame{\titlepage}

\frame{
\frametitle{Words used last week which I will not use tonight}
\begin{itemize}
\item ontological \pause
\item kantianism \pause
\item meta-ethical \pause
\item hermeneutical \pause \only<8->{\textcolor{red}{$\leftarrow$ actually nobody said that}}
\item normative \pause
\item xanalogical \pause \only<9->{\textcolor{red}{$\leftarrow$ not a real word}}
\item de jure 
\pause\pause
\end{itemize}
}

\frame{
You're not going to talk about math, are you?
\fpause
It's all I know.
\fpause
My understanding of mathematics is a key motivator in my faith.
}

\frame{
What's interesting about this number?
\[ 1071048710934672908723598151\]
\fpause
Actually I'm not too interested in numbers.
\fpause
I'm interested in beautiful ideas. \pause In discovering them, \pause creating them, \pause thinking them, \pause describing them.
\fpause
It is the deepest level of God's created world that is accessible to us.
\fpause
This is worthwhile.
}

\frame{
\frametitle{Creation and discovery}
Creation vs discovery.
\fpause
Creation is about making things which did not exist before
\fpause
Discovery is about revealing and describing preexisting truths
\fpause
They seem like different concepts, but:

\begin{center}\bf Creation and discovery are on a spectrum\end{center}

\fpause
There is a sort of discovery in artistic creation, and an artistry in discovery
}

\frame{
\frametitle{A made up spectrum}
\begin{center}\it More creative\end{center}
\vfill
\uncover<2->{abstract visual arts, music, dance}
\vfill
\uncover<3->{representational visual arts, drama}
\vfill
\uncover<4->{photography, documentary cinema, journalism}
\vfill
\uncover<5->{physics, chemistry, biology}
\begin{center}\it More discoverive\end{center}
\pause\pause\pause\pause
}

\frame{
But even the most abstractly creative of these has elements of discovery and revelation to them
\fpause
It makes a lot of sense to say things like:
\fpause
``Jimi Hendrix discovered how to play electric guitar''
\fpause
``Walt Whitman discovered a new way to write poetry''
}

\frame{
Monumental acts of creativity seem in retrospect like discoveries.
\fpause
It's hard to imagine a world without novels. \pause Without rock and roll music.
\fpause
Music itself was created.
\fpause
But it seems like it was always bound to be created.
\fpause
Perhaps it's more proper to say music was discovered.
\fpause
It was both.
}

\frame{
One of the greatest creative achievements of humanity:\pause
\begin{center}\begin{tabular}{lr}
 &\only<3->{{\tiny 1}\phantom{1}} \\
&\tt 344 \\ 
+& \tt 217 \\
\hline
 &\only<5->{\tt5}\only<4->{\tt6}\only<3->{\tt1}
\end{tabular}\end{center}

\fpause\pause\pause\pause
You could probably even do this in your head, the same way.
\fpause
Awesome!
}

\frame{
This method for adding numbers did not always exist.
\fpause
If you traveled in the Roman empire and did this, you would amaze people.
\fpause
The method was invented by a person less than 1500 years ago.
\fpause
And we know his name.
}

\frame{
Actually it's not clear who originally invented it, but it's credited to Al-Kwarizmi (800s AD) who is best known for:
\fpause

\emph{Al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala}

``The Compendious Book on Calculation by Completion and Balancing'' 

\fpause

\emph{Kitab al-Jam' wa-l-tafriq bi-hisab al-Hind} 

``The Book of Addition and Subtraction According to the Hindu Calculation''

\fpause
This describes the method for arithmetic with Hindu-Arabic numerals. 

\fpause
This (and \emph{Al-Jabr}) was translated into Latin (12th century), and the method was referred to as ``Al-Kwarizmi's method'' \pause or ``Algorism's method'' \pause or eventually just ``The Algorism'' \pause or ``The Algorithm''.
}

\frame{
To say this changed the world would be an understatement
\fpause
It makes ordinary people capable of computing in their heads things which were impossible before.
\fpause
Our advantage today is a creative way of thinking
\fpause
But we feel like the method is universal or eternal, not Al-Kwarizmi's creation.
}

\frame{
In a sense things like this are eternal.
\fpause
God already knew about rock and roll before Chuck Berry played it.
\fpause
Maybe God already thought of numbers in the Hindu-Arabic system.
\fpause
In this sense, all of our artistic and creative works are discoveries. 
\fpause
This doesn't diminish our creativity!
\fpause
It's the same paradox as free will vs predestination.
}

\frame{
I don't try to resolve the paradox one way or another- this is a theological black hole. 
\fpause
The paradox itself is beautiful to me.
\fpause
It is inspiring to me to know that God desires us to be intensively creative, and also knows and forms the objects of our creation.
\fpause
It is a privilege that God allows us to participate in this sort of ``co-creation''.
}

\frame{
\frametitle{Artistry in Math?}
Where we're headed:
\begin{itemize}
\item Beauty and creativity in mathematics \pause
\item Unexpected complexity in mathematics \pause
\item So what?
\end{itemize}
}

\section{Beauty and creativity in mathematics}

\frame{
An example from my own research:\pause 
\begin{center}
\includegraphics[scale=.06]{sandwichuncut.JPG}
\end{center} 

\vfill

My lunch box.
}

\frame{
\begin{center}
\includegraphics[scale=.15]{sandwichoutline.JPG}
\end{center} 

\vfill
The area should fit, but it's the wrong shape.
}

\frame{
How to make it fit?
\fpause
Here's one method:
\begin{center}
\includegraphics[scale=.075]{sandwichsmashed.JPG}
\end{center} 
\fpause
We can do better.
}

\frame{
A better solution:
\fpause
\begin{center}
\includegraphics[scale=.12]{sandwichendcut1.JPG} \quad\pause
\includegraphics[scale=.12]{sandwichendcut2.JPG}
\end{center} 
\fpause
Better.
}

\frame{
A creative and elegant solution:
\fpause
\begin{center}
\includegraphics[scale=.15]{sandwichdiagcut1.JPG} \quad\pause
\includegraphics[scale=.15]{sandwichdiagcut2.JPG}
\end{center} 
}

\frame{
It works!
\begin{center}
\includegraphics[scale=.2]{sandwichdiagcut3.JPG}
\end{center} 
}

\frame{
It's creative, but really it's just a solution to a certain geometry problem.
\fpause
New research in mathematics is similar in character- hard problems which require creative solutions.
\fpause
Many of the answers to the deepest questions turn out to be more complicated than we thought.
}

\subsection{Beauty and complexity in numbers}

\frame{
\frametitle{Beauty and complexity in numbers}
Prime numbers:
\[ 2, 3, 5, 7, 11, 13, 17, 19, 23, 27, 31, 37, 41, 43, \dots \]

\fpause
One of the oldest and hardest themes in number theory has been to describe the distribution of prime numbers.

\fpause

There's still major unsolved problems in this area-- \emph{The Riemann Hypothesis} is one which gets you \$1 million.
}

\frame{
Make a line with dots on the prime numbers, gaps for the nonprimes.

\includegraphics{primeline.png} \fpause
Zoom out:

\includegraphics[scale=.5]{primeline.png} \fpause

Zoom out:
\includegraphics[scale=.25]{primeline.png}
\fpause
Hard to find any patterns at all- they seem almost randomly distributed.
}

\frame{
One day (1950s), Ulam was bored and wrote the numbers in a spiral like this:
\begin{center}
\includegraphics[scale=.4]{ulam1.png} \qquad
\pause
\includegraphics[scale=.4]{ulam2.png}
\end{center} 
\fpause
Ulam did not expect any patterns- this was just doodling.
}

\frame{
With the numbers in a spiral, this is what you see:
\begin{center}
\includegraphics[scale=3]{ulam3.png}
\end{center}
\hfill
{\tiny picture by User:Grontseca at Wikipedia, CC-BY-SA 3.0 }
\vfill
Black dots are primes, white dots are non-primes.
}

\frame{
Clearer if we put dots on the non-primes, bigger dots for more factors:
\pause
\begin{center}
\includegraphics[scale=.4]{ulam5}
\end{center}
\fpause
Most definitely not random! 
}

\frame{
\begin{center}
\includegraphics[scale=.3]{ulam5}
\end{center}
The patterns here are still not fully understood.
\fpause
We'd go a long way toward explaining them if somebody could prove:
\[ P(n)\sim A\frac{1}{\sqrt{a}}\frac{\sqrt{n}}{\log n} \]
This is Hardy \& Littlewood's ``Conjecture F'' (1923).
}

\frame{
A big question: \pause Why should there be structure where we expect only randomness?
\fpause
Numbers serve a very specific and fairly simple purpose.
\fpause
But why is there so much to say about them?
\fpause
They turned out to be more complicated than we thought.
\fpause
But we invented them, didn't we?
}

\frame{
If we created mathematics, then how could it surprise us? \pause Maybe we didn't really create it.
\fpause
The feel of ``intelligent design'' is inescapable for mathematicians.  
\fpause
Science offers no alternative here-- the question of why mathematics exists in the way it does is unanswerable to science.
\fpause
These mysteries are beautiful for mathematicians.
}

\begin{comment}
\subsection{Beauty in $\infty$}
\frame{
A surprising idea: you can compare sizes of infinite things (Cantor, 1870s).
\fpause
E.g. there are the same number of even numbers as odd numbers, since:
\begin{eqnarray*}
1 & 3 & 5  \dots \\
\updownarrow & \updownarrow & \updownarrow \\
2 & 4 & 6 \dots
\end{eqnarray*}

It's a great idea, but a big surprise:
\fpause
Not all infinite things have the same size.
\fpause
There are different sizes of infinity.
}

\frame{
Cantor showed the amount of whole numbers is different than the amount of real numbers. The first amount he called $\aleph_0$, the next is $\aleph_1$, and 
\[ \aleph_0 < \aleph_1, \]
though both are infinite.

\fpause

Are there other sizes of $\infty$? \pause Yes.
\fpause
There's $\aleph_2$, \pause $\aleph_3$, \dots, \pause also $\aleph_{\aleph_0}$, etc.
\fpause
Actually there's infinitely many different sizes of infinity!
}

\frame{
Infinitely many different infinities?
\fpause
How many?
\fpause
This question is unanswerable in the theory developed by Cantor. (The set of infinities is too large to be corresponded with any other set.)
}
\end{comment}

\frame{
One other example of unexpected complexity and beauty: \pause truth itself.
}

\subsection{Surprises in truth itself}

\frame{
A fact about ordinary language: \pause not every statement is absolutely either ``true'' or ``false''. 
\fpause
Like: ``Methodists are better than Catholics.'' (subjective, ambiguous)
\fpause
``You never know when I'm hammering, because I'm hammering now'' (nonsensical)
\fpause
This is the difference between mathematics and ordinary language: mathematical statements are always either provably true or provably false. 
\fpause
Students love this.
}

\frame{
``Mathematical statements are always either provably true or provably false.''
\fpause
This turns out to be incorrect.
\fpause
In 1930s, G\"odel proved that some mathematical statements are unprovable.
\fpause
Turns out this is a basic feature of any logical system.
\fpause
Any consistent logical system has statements which cannot be proven true or false.
\fpause
Logical statements can be true, false, or ``undecidable''.
}

\frame{
This was shocking and upsetting to mathematicians. 
\fpause
By 1960s, ``The Continuum Hypothesis'' was shown to be undecidable.
\fpause
Erd\H os: \pause ``When I meet God, the first thing I'll ask him is: is the continuum hypothesis true?''
\fpause
Some things are simply inaccessible with the tools of pure logic.
\fpause
!
}

\section{Photo break}
\frame{
\begin{center}
\includegraphics[scale=.15]{josie}
\end{center}
Start paying attention again!
}

\section{}
\frame{
\frametitle{Recap}
God participates with us in creating and discovering our complex world
\fpause
There is surprising beauty and complexity at the foundations of our natural world \pause even in the nature of truth itself
\fpause
Complexity is the norm, not the exception
}

\section{So What?}
\frame{
\frametitle{So What?}
The big idea:

\begin{center}
\bf God loves complexity
\end{center}
}

\subsection{God loves complexity}
\frame{
\frametitle{God loves complexity}
God has made things complex which might as well have been simple.
\fpause
\begin{itemize}
\item Our environment \pause
\item The structure of physical laws \pause
\item Mathematics \pause
\item People
\end{itemize}
\fpause

God loves complexity, and we should too.

\fpause
But this is hard.
}

\begin{comment}
\frame{
\frametitle{and we should too}
God also made us with limited understanding. 
\fpause
God wants us to be confronted by complexity. \pause Otherwise he would have made us a lot smarter.
\fpause
Actually it's not about smarts- \pause there are always unprovable statements, regardless of how smart we are.
\fpause
We inhabit a universe in which even the smartest imaginable creature will never be able to understand everything.
\fpause
So we might as well get used to complexity.
}
\end{comment}

\frame{
Complexity confuses us:
\fpause
Mk 6:48 (NASB): ``He came to them, walking on the sea; and He intended to pass by them.''
\fpause
Mt 9:30 (NASB): ``Jesus sternly warned them: See that no one knows about this!''
\fpause
We should not view these as ``problem verses'' which need to be solved.
\fpause
A picture is painted of Jesus as a complex human being with sometimes obscure motivations.
\fpause
This is the kind of Jesus I want to follow.
}

\frame{
My favorite Bible verse:
\fpause
Jn 1:1: ``In the beginning was the Word, and the Word was with God, and the Word was God.''
\fpause
Apparently ``the Word'' is Jesus. 
\fpause
But what does that really mean?
\fpause
It is deep and mysterious and beautiful. \pause What more do you need?
}

\frame{
Christians must be willing to accept complexity when we encounter it.
\fpause
As people of faith we care about the truth. \pause The truth is often complex.
\fpause
If Christianity is a faith based in truth, it must never become a faith of easy answers.
\fpause
American Christians today have become identified with simple answers and denial of subtlety.
\fpause
This is tragic.
}

\frame{
Even in our faith, embrace complexity.
\fpause
``Confusing'' or ``strange'' should be part of our discourse when discussing our faith.
\fpause
There's no shame in lacking answers.
\fpause
This is misunderstood, so be careful.
}

\frame{
We must fully embrace the truth, whatever it may be.
\fpause
The truth, no matter how mysterious or complex, will never defeat our faith.
\fpause
Complexity sometimes feels like a burden- it is easier to cling to simple ideas, and complexity forces us to change our perspective.
\fpause 
But the truth sets us free.
}

\frame{
One more verse:

1 Cor 13:11: ``When I was a child, I used to speak like a child, think like a child, reason like a child; when I became a man, I did away with childish things.''
\fpause
We can have faith like a child, and still reason like an adult.
\fpause
This is what God wants from us.
}

\frame{
\frametitle{Last words}
\pause
Never be afraid:
\begin{itemize}
\item to look more closely \pause
\item to turn from easy answers \pause
\item to ask bigger questions \pause
\item to embrace the unknowable \pause
\item to dream deeper dreams 
\end{itemize}
}

\begin{comment}
\frame{
Some simple affirmations by Christians:
\begin{itemize}
\item The Earth is the center of the universe \pause
\item Sex outside of marriage is bad \pause
\item Homosexuality is a choice \pause
\item Life begins at conception \pause
\end{itemize}
I'm not suggesting these are all wrong. \pause (I more or less agree with \#2.)
\fpause
All are based on simplistic readings of verses or ideas from the Bible
\fpause
But the Bible doesn't actually say any of these things specifically
}

\frame{
I'm not saying these simple ideas are all false. 
\fpause
But Christians need to be open to complexity.
\fpause
Christians should never project simplicity into the Bible where it does not exist.
\fpause
This takes our own values and attributes them to God, which is very bad.
}

\frame{
But Christians need to stand firm in our beliefs!
\fpause
Our core doctrines are constantly undermined by the world around us, and we need to hold fast to the truth.
\fpause
Sometimes we need to draw lines and plant our feet on God's truth.
\fpause
When we do this, we as Christians become identified and defined by those truths we loudly affirm.
}
\end{comment}

\section{}
\frame{
\begin{center}The end!\end{center}
}





\end{document}