I'm a mathematician who has from time to time had to utilize computers to carry out certain thought experiments and who has been involved with various industrial projects based essentially around similar goals. I've had actual experience ``in the trenches'' regarding hardware, software, and system design.
I am now actively exploring the use of computers to carry out jobs in visualization (regarding graphs and also assemblages of geometric figures in 3-dimensional space). However, my background also includes psychophysics (especially visual perception) on one hand, with lasers and holography on the other. Currently, much of my research activity is concerned with the synthesis and analysis of neural networks.
With some colleagues, I have been studying quantum computing as well, and I believe that a particular mathematical theorem could be carried out algorithmically by machines based on these principles.
PCK 8/31/02;
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My computer experience stretches over 31 years. As an Assistant Prof. at Case Western Reserve University in 1970, I used Algol and punched cards as part of the calculus course which I was teaching. Just before leaving Case Western, I again used the computer. This time, instead of a mainframe Univac, it was a PDP-11 minicomputer. Two of my three Ph.D. students utilized computation in their theses. The first, Mark Thiel, used the PDP-11 (an early product by Digital Equipment) and Fortran code to carry out combinatorial experiments designed to test various lemmas and theorems from his thesis in topology. The second, Bomi Parakh, used the PDP-11 as a controller for a special-purpose peripheral device, the Evans and Sutherland LDS-2. His thesis demonstrated the feasibility of visual animation to show the output of statistical simulation for vehicle traffic flow on urban links, as a function of traffic signal timing.
Later in 1977 and 1978, at Bell Telephone Laboratories, I was a telecommuter by way of an acoustically-coupled modem, connecting to a ``time-share'' system. My 40-pound portable(!) terminal had paper output and used APL (Advanced Programming Language), a language which is specially designed for combinatorial and parallel formulations. In 1980, as part of a project, of which I was the technical coordinator, I used a mainframe computer, running PL1 and some JCL (IBM's infamous ``Job Control Language'') to read off the actual projected network growth statistics and compare the results of my new algorithm for deploying network multiplexors on the actual numbers with my heuristic estimates, which had been obtained using paper and pencil. By actually showing that my algorithm performed properly on the real data, I was able to convince the multi-organazational steering committee which was involved with the deployment problem for these new multiplexors to follow my algorithm instead of the original algorithm which it had been my assignment to ``fix''.
In the early 1980s, I experimented with an Atari 400 and learned to use 6502 machine code, as well as basic. This Atari, like most of its breed, was fundamentally a game machine, and I learned a bit about the issues which arise in human-interface design, as well as the technical problems of having fast-enough graphics and sound. Rather than mere color-table animation, such as I had used on the traffic simulation at Case, here one had ``sprites'' available, which amount to real-time graphical agents. Of course, with only 16K of memory and incredibly slow chips (by current standards) one had to be rather careful. I tried some psychophysical experiments using Fibonacci ratios to control the size and color of geometric display elements and the frequencies of notes. I also worked with lasers and with computer-controlled laser displays.
At TASC, around 1984, I had some opportunities to use the not-very-good ``AI'' machines of that era to explore expert systems for cartography and other applications. I gave seminars on neural network and object oriented software approaches, and reported on human-computer interactions and on image-understanding methodologies.
I had the requirement to develop a computer-aided production facility to print system engineering diagrams. Besides learning how to operate an IBM PC running suitable drafting software, I had to control a digitizing tablet and a flatbed-plotter via RS-232 cables. I chose AutoCAD, which turned out to be the company which went on to dominate the software market for PCs. To control the digitizing tablet (which included a pointing device called a ``puck'', like a hockey puck with cross-hairs), one suitably initialized the software, and in this way, one could have menus affixed to the tablet by which various software options could be invoked by a click - these actually invoked macros in AutoCAD's internal language. Eventually, I developed menus which enabled relatively untrained operators to use the system for drawing input. The plotter (Hewlett Packard models with four or sometimes eight different solenoid-controlled pens) was also controlled by AutoCAD but it sometimes needed special intercessions (via a kludge of DOS interrupts, Basic and HP plotter-control language) when, e.g., one of the solenoids would fail during an all-night rush job. The software hack, which I constructed early one morning, allowed all eight colors to still be used by having the machine pause to allow an operator to replace one color pen by another.
The computer monitor was an IBM Color Graphics display which was essentially the first (and lowest) of all color graphic screen resolutions. I did some experimentation with the possibility of using these techniques in softcopy form (i.e., with display tricks, as on the Atari). I was modeling in a simplified way the underlying process which the system engineering was designing: a means to digitally embody, via screen images, paper documentation traditionally displayed in charts. I also showed how it could be possible to design terminals with ``robust'' software that could adjust themselves to whoever was using them and remember what they were doing if they were suddenly turned off in the middle of a job.
After leaving TASC, I used computers again in the early 1990s. My MegaST Atari had a very nice black and white screen (with over 100 Hz) so it had essentially no flicker and it also had some quite sophisticated software. Rather than gaming, I used the machine for mathematical experiments (e.g., it could display rather complex two-dimensional surfaces in three-space) and especially as an Internet terminal. (I also had an IBM PC, XT variety, and it too functioned as a terminal for the net, and later a 386-PC, Toshiba, which still does.) I gave classes on how to use the Internet, including the very first occurence of the worldwide web, and I counseled the use of Internet technology within a proprietary environment, which is now called an ``Intranet''. The classes were using my Toshiba portable, a 1200-baud modem and a video projection system.
Around this time, I also organized a series of lectures for the Smithsonian Institution public education (Resident Associates) programs, including the use of computer-controlled displays and of multimedia. Set-up time was extremely limited but each week's presentation had different technical requirements. I also did some consulting regarding the feasibility of technological projects in the area of virtual reality for fashion design. The idea was to provide a VR-interface, via the Internet, for choosing the proper size clothing. I showed an enterprising group of young Foreign Service Officers how to use inexpensive (and rugged) available laptops and basic-grade modems (even via acoustic coupling) to access the Internet from anywhere in the world - e.g., by using e-mail interfaces to then-existing network services such as gopher, WAIS and the web. At seminars on busisness use of the Internet, I was an invited speaker on Internet protocol.
In the middle to late 1990s, my use of the web has, like most of us, grown geometrically and I now use it to stay in electronic touch with colleagues and coauthors, to write papers and to access and organize information. I have mostly managed to avoid using Windows. I have a Linux system and a Windows system at my office, and I am fluent in UNIX (as a user, not as the sysop or ``root''). I have some familiarity with neural network and genetic algorithm software simulations.
Over the years my theoretical work in mathematics has frequently been relevant to computer theory. For instance, my work on crossing numbers and various types of ``thickness'' parameters for graphs, is related to planarization - e.g., design of printed circuit boards and of VLSI chips. Color of graphs, another theme of my research, is related to the sharing of resources. More recently, my research on neural networks is involved with the approximation of functions by highly parallel networks of individual neuron-like processors and this is connected with pattern recognition and distributed control.
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