We simply cannot doubt our consciousness. We know qualia---internally accessed qualities that make up the phenomenal character of experience. Understanding the nature of consciousness is the Philosophy of Mind's underlying impetus for sagacious study of unanswered questions. At the crux of these questions lies the Mind-Body problem: What is the relation between the mind and the body? Is our existence completely physical, completely mental, or a confluence of both realms? 


The personal computer was made with the vision of extending and improving the human mind and human condition: ``the ideal of the then-hypothetical personal computer was a brain supplement, enhancing human memory and amplifying human reasoning'' \cite[7]{victor}. If computers can bestow such raw augmentation such that software we write can act as extensions of our minds, then code is a manifestation of ideas that can interact!


\begin{quotation}
One of the major themes of the past century has been the growing replacement of human thought by computer programs. Whole areas of business, scientific, medical, and governmental activities are now computerized, including sectors that we humans had thought belonged exclusively to us. \cite[13]{artofcomp}.
\end{quotation}
Dr. Knuth delineates the fact that our lives are becoming enveloped by technology. Undoubtedly, you probably use a computer or smart device on a daily basis. Here are some thought-provoking questions for you:


\begin{enumerate}
\item does the computer expand your mind?
\item does the computer extend your physical life?
\end{enumerate}

Your consciousness is the sum of the neurological patterns and circuitry that embody the knowledge you've accumulated over your lifetime. Computers facilitate the transmission of ideas and concepts that are more complex than words. If software exists as representations of our consciousness, then through software we can express our ideas to others in ways that words may not have been able to otherwise.


\begin{quotation}
Every computer program is a model, hatched in the mind, of a real or mental process. These processes, arising from human experience and thought, are huge in number, intricate in detail, and at any time only partially understood. They are modeled to our permanent satisfaction rarely by our computer programs. Thus even though our programs are carefully handcrafted discrete collections of symbols, mosaics of interlocking functions, they continually evolve: we change them as our perception of the model deepens, enlarges, generalizes until the model ultimately attains a metastable place within still another model with which we struggle. The source of the exhilaration associated with computer programming is the continual unfolding within the mind and on the computer of mechanisms expressed as programs and the explosion of perception they generate. If art interprets our dreams, the computer executes them in the guise of programs! \cite[10]{sicp}
\end{quotation}


What Humans do with Computers

The transmission of information is not limited to text or language---the human visual system has capabilities that allow us to absorb large amounts of information in parallel \cite[9]{victor}. This channel for information thus implies that images are an important way for us to learn about our environment.


``To the thinking soul images serve as if they were contents of perception ... [t]hat is why the soul never thinks without an image'' \cite[60]{aristotle}. This quote from Aristotle describes a theory for how humans process information; simply, thought is not possible without images in his view. Humans harness an innate ability to process visual information---visualizations enable high-bandwidth communication of ideas between humans \cite[309]{kamat}.


Beyond images are \emph{diagrams}---a structured representation of a concept or object with graphical components laid out in a simplified way. The properties of diagrams present information in a manner that allows the human visual system to process the data in parallel \cite[2]{diagrams}. There exists systems where a diagram greatly improves transmission, or may even be required, for example, in representing a data structure in a programming language such as Lisp \cite[67]{diagrams}, or a the representation of a dynamical system in physics. To try and describe an environment diagram in a computer science class without a blackboard would be more than difficult.


\begin{quotation}
[P]roblem solvers in domains like physics and engineering make extensive use of diagrams, a form of pictures, in problem solving, and many distinguished scientists and mathematicians (e.g., Einstein, Hadamard) have denied that they ``think in words'' \cite[2]{10000words}
\end{quotation}
If images and diagrams are so important for the transmission of information, then it should be an important focus for the creation of academic works and documentation. 


The Human Visual System

When approaching the design of a system designed to author content for learning, we have to best attempt to allow the author to freely express their ideas. The author should be able to communicate their vision with clarity and a way that allows for impact. 


It has been shown that students learn more information through Web-based exercises than traditional tools \cite[12]{compare}, so how can we build these systems? Previous attempts at studying the design of learning systems has proven its difficulty: 


\begin{quotation}
It is difficult to establish a framework to symbolize and express learning contents design because the design of the target phenomenon, i.e. learning, is so abstract \cite[294]{learning}. 
\end{quotation}
Learning is too abstract! They key is to realize that \emph{it is too abstract to abstract} into a graphical user interface. The author of a learning system should use a generalized framework to support the authorship of learning concepts, and thus, a programming language, or language of the sorts should be used directly by the author. 


Their conclusion is a result of the fact that what they developed was simply {\it their own expression} of a system to design learning systems. For the last century, teachers and books have proven to work as a ``learning environment''. Any graphical interface is simply creating more distance between the idea of what needs to be expressed and the actual articulation. The existing instructional systems are working---if it's not broken, don't fix it. Language is what teachers and academics should be using to create books. 


Design of Learning Systems

Perhaps we've all played the game ``telephone'' when we were kids. By the end of the transmission, the sentence was completely changed form its original form! When building a system to facilitate the conduction of ideas between humans, it is important to cause as little distortion as possible---an important concept in design known as \emph{direct manipulation} mitigates this issue.


\begin{quotation}
Here the critical issues involve minimizing the effort required to bridge the gulf between the user's goals and the way they must be specified to the system \cite[318]{directmanipulation}.
\end{quotation}
Imagine our world sometime in the future, and digital textbooks are ubiquitous. However, the mathematicians and physicists who author these textbooks must outsource the design of the diagrams and interactivity to programmers and engineers. Is it possible for the goals of the author to met with accuracy? 


\begin{quotation}
Alternately, a designer can draw a series of mockups, snapshots of how the graphic should look for various data sets, and present these to an engineer along with a verbal description of what they mean. The engineer, who is skilled in manipulating textual abstractions, then implements the behavior with a programming language. This results in ridiculously large feedback loops—--seeing the effect of a change might take a day instead of a second. It involves coordination and communication between at least two people, and requires that the designer justify herself---she must convince the engineer and possibly layers of management that each change is worth the engineer’s time. This is no environment for creative exploration \cite[43]{victor}.
\end{quotation}
As Bret Victor's argument is laid out, this solution poses many issues, and ultimately people should render their own ideas if they want them to be expressed as close as possible to the representation in their minds. 


\begin{quotation}
Historically, most interfaces have been built on the conversation metaphor. There is power in the abstractions that language provides (we discuss some of this later), but the implicit role of interface as an intermediary to a hidden world denies the user direct engagement with the objects of interest. Instead, the user is in direct contact with linguistic structures, structures that can be interpreted as referring to the objects of interest, but that are not those objects themselves. \cite[319]{directmanipulation}
\end{quotation}

A famous paper describes to main important points regarding {\it semantic distance} \cite[321]{directmanipulation}: 

\begin{enumerate} 
\item ``Is it possible to say what one wants to say in this language?''
\item ``Can the things of interest be said concisely?''
\end{enumerate}

Below are graphics re-interpreted and reproduced version of the graphic from the paper:

\begin{center}
\begin{pspicture}(0,-3.5)(8,2)
\psline{<->}(3.5,-2)(3.5,0)
\rput(3.5,0.5){Meaning of Expression}
\rput(3.5,-2.5){Form of Expression}
\rput(5.5,-0.75){Articulatory Distance}
\end{pspicture}
\end{center}

``Semantic distance concerns the relation of the meaning of an expression in the interface language to what the user wants to say'' \cite[321]{directmanipulation}. The diagram below describes \emph{semantic distance}, 

\begin{center}
\begin{pspicture}(-2,-2)(7,2)
\psline{<->}(1,0)(4,0)
\rput(6,0){Meaning of Expression}
\rput(-0.5,0){Goals}
\rput(2.5,-0.75){Semantic Distance}
\end{pspicture}
\end{center}

\begin{quotation}
The gulfs of execution and evaluation. Each gulf is unidirectional: The gulf of execution goes from goals to system state; the gulf of evaluation goes from system state to goals \cite[319]{directmanipulation}.
\end{quotation}

\begin{center}
\begin{pspicture}(0,0)(11,6)
\psline(0,0)(4,0)
\psline(0,1)(4,1)
\psline(4,0)(4,1)
\rput(1.1,2.4){Physical System}
\psline(4,1)(1,4)
\psline(1,4)(0,4)


\psline(10,0)(11,0)
\psline(10,0)(10,1)
\psline(10,1)(11,1)
\rput(9.4,2.5){Goals}
\pspolygon(10,1)(6,4)(6,3)(10,0)
\psline(6,4)(11,4)

\rput(4,3.25){Gulf of Execution}
\psline{<-}(2,3)(6.5,3)

\rput(5,1.75){Gulf of Evaluation}
\psline{->}(3.5,1.5)(8.5,1.5)


\end{pspicture}
\end{center}

We need to minimize the distance between the concepts in science and math and the articulation of these ideas, and especially these expressions on the Web and interactive devices. As technology advances, the technical knowledge required to produce interactivity is domain expertise to that of an engineer---to minimize the distance means enabling the professor or academician to express interactive ideas through an expressive language that is close as possible to the actual content they are describing.  

Some Principles of Design

``[E]thnographers are interested in gaining an insider's view of a situation'' \cite[967]{ethnographic}. We can use \emph{ethnographic design} to build a system around the existing behavior of a ``user'', so that they can use the system in their natural state, and it adapts to their natural behavior. 


When looking to build a digital system for expressing diagrams in the realm of mathematics, how can we adapt to their existing behavior? Given than the goal of this project is to support academics, using \TeX\ as a basis makes sense from an ethnographic standpoint, given that it has been around for over 30 years and still remains the {\it de facto standard}. Now, not all of the academic population knows \TeX, however, not all people are authors, either. It only takes one good book to propagate information to thousands of minds.


Going forward with a digital system using \TeX\ as its syntax, it's of paramount importance to understand not only the language of \TeX\ and its syntax, but also how it is structured. This can provide a technology that is engaging and productive for authors. 


This system was genuinely designed to optimize development of structured documents in \TeX. The structure was developed from my experience in authoring \TeX. This project is just as much a project for other \TeX\ people as it is for myself. I strive to be a part of my community, and I am a strong believer that we can use technology for learning. For example, I wrote a database application during my undergraduate years at Berkeley to categorize and store my entire lecture notes and output a structured version in \TeX. I used this program to write a series of useful academic material---a 55-page reference manual for CS61A (The Structure and Interpretation of Programming Languages), a 35-page review for Math 55 (Discrete Mathematics), lecture notes for Math 54 (Linear Algebra), final and midterm papers for a series of liberal arts courses, and later used it to author over 300 pages of signal processing documentation for EE20 and EE120 in the EECS department. 


Admittedly, much of this product was built while authoring textbooks within the platform itself (including \emph{this} text). It was a symbiotic process where I stuck to using \TeX\ as the standard, and even if it made programming more painful, I forced myself to implement it in a way that made sense for typesetting. In fact, the original diagrams were much more interactive in the Objective-C and JavaScript versions of the authorship interface than this current implementation, but they required the knowledge of programming! I believe the success of this platform solely lies on the adherence to \TeX\ as the syntax for expression. My goal with this platform is to deliver tools that will accelerate education from both directions---the professors teaching, and the students learning---so that it stays in step with technology.


4 The Human Element