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