I would like to say a few remarks about my own career and my own life in order to show my perspective on these things. First of all I am an engineer, secondarily I may be a physicist, and only thirdly a mathematician. So, I see things from a different perspective than those people in the room who are mathemati- cians.

When I was much younger, I looked around rooms such as this, or looked around the world, and I saw that information was everywhere. Information is in every corner of this room. Chemical and biological informa- tion is flowing through our bodies. There are microwaves passing through the room that are carrying information. There are radio signals going through the room carrying information. Besides the information that is embedded into those signals intentionally, there is information about reflections and the propagation path and so on. The air molecules contain information about the environment. There are complex patterns of communications among the panel and the audience. These are multiway communications that we do not understand.

As I looked at such things, I saw something about the future that is evolving into the era of information. So this is the direction I went in my career. I nev- er really looked back, nor regretted it in the least. It has taken me into many exciting problems and many exciting to- pics and many exciting places. I do not think that there is any other career that I could have chosen that touches on algebraic geometry and physics and magnetic recording and integrated cir- cuits and deep space communications and radar design and economics and many other things. Information theory touches many topics and it is a rewarding place in which to spend one's life.

If we look back to the nineteenth century, we now think of it as the age of energy. This was the time when technologists developed steam engines and automata and devices. In the background of that whole culture developed the subject of thermodynamics. I am sure that thermodynamics was developed by a small group of people as the intellectual underpinnings of the age of energy. It was not developed by the world at large. I am sure that that small group of people felt in some ways insulated from the engineers at large. But, nevertheless, thermodynamics is a very important, very successful subject. I see infor- mation theory is to the age of information as thermo- dynamics is the age of energy.

We are creating something that touches on a lot of topics and it is important in that way. I have always been happy working in this field and, and as I say, it has taken me many places. In some ways I see some regret that we have a tendency to identify or isolate very narrowly de- fined problems, very difficult problems and then continue to work on those problems. Maybe idealizing or abstracting those problems to such a degree that those idealizations are no longer useful.

I was thinking about an article that Peter Elias wrote. Peter Elias wrote an edi- torial in the Information Theory Transactions about thirty years ago, a one page editorial. My memory says the title of that article was "Photosynthesis, Information Theory, and Religion." In that article, Peter Elias warned about writ- ing papers that are very abstract papers on very arcane subjects that are not necessarily related to any- thing at all. I think we have a tendency to do that.

As several people have already said here, the development of waveforms for the additive Gaussian noise channel has been an absolutely remarkable story over the last twenty years or so. In Shannon's paper, already he had computed a formula or given a formula for the capacity of a bandlimited white noise Gaussian channel. But at that time the point of view was that this was a very theoretical formula by Shannon and it really did not have any relevance to our communication indus- try. Yet after twenty or twenty-five years, we have now essentially achieved the capacity of the additive white Gaussian noise channel. We know how to do that and modems now come close to achieving the capacity and are available in the marketplace. It is a very impressive success story. But, as we worked on that channel there are other channels of a practical nature that I think we somehow have neglect- ed.

We like to study discrete channels, but there are con- tinuous channels with continuous time that are not well understood. The hard limited passband channel is an elementa- ry model of the magnetic recording channel. The channel in- puts are waveforms that can only take values of plus and minus 1. Those functions are viewed at the output of the channel after being passed through a filter. So the waveforms themselves are not observed, but a filtered ver- sion in additive Gaussian noise. We still do not know the capacity of that simple channel. We do not know how to achieve the capacity of that channel, although it seems we are rapidly working towards achieving its capacity without knowing what its capacity is. Information theory is now making very substantial strides towards very sophisticated waveforms for magnetic recording and optical recording.

Another topic that I have interested myself in lately is algebraic geometry codes, trying to understand these codes from an engineering point of view. The nature of our subject is that the period of gestation between the theoretical work and the time it reaches some useful application is measured more on the order of two or three decades than on the order of months. This leads some outside observers to view what we are doing as not necessarily relevant in the world because such observers fail to take a long enough view to see over a period of decades. I will take a wager with anyone in the room, a wager of $1,000 right now, that the Hermetian codes are going to be widely used in an applica- tion within twenty years from today. I am not a gambling man, but I don't regard this as a gamble. I propose it to indicate my view that these things are developed over the long term. The area of noiseless data compression, or I like to call it data compaction, the Lempel-Ziv algorithm, reached journal stage about fifteen years ago but it took years for people to actually notice it and put it into ap- plication. Now, there are companies whose only product is Lempel-Ziv data compression algorithms. So, to see the future, to take whatever we are doing today, we have to see the outcome of that at some distant time in the future.