Problem Solving with Claude Shannon
A great mind of the 20th Century and his unique approach to problem solving.
One of the great invention hotspots of modern history is the American Bell Labs which has a breathtaking list of world changing inventions. From the laser, communication satellites, mobile phones, solar cells and transistors just to name a few, our world is the product their existence.
Bell Labs, the curious mix of techniques, talent, culture, and scale had turned the modest R&D wing of the phone company into a powerhouse of discovery. It was an institution that churned out inventions and ideas at an unheard-of rate and of unimaginable variety. In Gertner’s words, “to consider what occurred at Bell Labs . . . is to consider the possibilities of what large human organizations might accomplish.” (Soni and Goodman)
Driving these inventions were some of the most impressive minds of our time, including 7 Nobel laureates.
Bell researchers were encouraged to think decades down the road, to imagine how technology could radically alter the character of everyday life, to wonder how Bell might “connect all of us, and all of our new machines, together.” One Bell employee of a later era summarized it like this: “When I first came there was the philosophy: look, what you’re doing might not be important for ten years or twenty years, but that’s fine, we’ll be there then.” (Soni and Goodman)
One of these was Claude Shannon.
There was a running joke of people working at Bell labs:
“There were two kinds of researchers at Bell Labs: those who are being paid for what they used to do, and those who are being paid for what they were going to do. Nobody was paid for what they were doing now.” (Soni and Goodman)
Claude Shannon , through his long career at Bell Labs inhibited both ends of this spectrum. He had many stunning inventions, related to information theory, artificial intelligence, computing and code breaking through WWII .
Shannon’s M.I.T. master’s thesis in electrical engineering has been called the most important MS thesis of the 20th century: in it the 22-year-old Shannon showed how the logical algebra of 19th-century mathematician George Boole could be implemented using electronic circuits of relays and switches. This most fundamental feature of digital computers’ design — the representation of “true” and “false” and “0” and “1” as open or closed switches, and the use of electronic logic gates to make decisions and to carry out arithmetic — can be traced back to the insights in Shannon’s thesis. (Sarkar, 2018)
Beyond this Shannon created the breakthroughs that has led to our modern communications advances. From the book “A Mind at Play”:
- First, communication is a war against noise. Noise is interference between telephone wires, or static that interrupts a radio transmission, or a telegraph signal corrupted by failing insulation and decaying on its way across an ocean. It is the randomness that creeps into our conversations, accidentally or deliberately, and blocks our understanding
- Second, there are limits to brute force. Applying more power, amplifying messages, strengthening signals… Yet there were high costs to shouting. In the best case, it was still expensive and energy-hungry. In the worst case, as with the undersea cable, it could destroy the medium of communication itself.
- Third, what hope there was of doing better lay in investigating the boundaries between the hard world of physics and the invisible world of messages. The object of study was the relationship between the qualities of messages — their susceptibility to noise, the density of their content, their speed, their accuracy — and the physical media that carried them
Whilst Shannon’s individual contributions was impressive, he also had a gift to work with others to get the best out of their ideas. Shannons approach to problem solving was unique as he outlined in a talk to colleagues as Bell Labs:
Claude Shannon Problem Solving technique
Simplification — attempt to eliminate everything from the problem except the essentials; that is, cut it down to size. Almost every problem that you come across is befuddled with all kinds of extraneous data of one sort or another; and if you can bring this problem down into the main issues, you can see more clearly what you’re trying to do and perhaps find a solution.
Seek similar known problems — You have a problem P here and there is a solution S which you do not know yet perhaps over here. If you have experience in the field represented, that you are working in, you may perhaps know of a somewhat similar problem, call it P’, which has already been solved and which has a solution, S’, all you need to do — all you may have to do is find the analogy from P’ here to P and the same analogy from S’ to S in order to get back to the solution of the given problem.
Try to restate the problem in just as many different forms as you can — Change the words. Change the viewpoint. Look at it from every possible angle. After you’ve done that, you can try to look at it from several angles at the same time and perhaps you can get an insight into the real basic issues of the problem, so that you can correlate the important factors and come out with the solution.
Generalization. — Another mental gimmick for aid in research work — ask yourself if you can generalize this anymore — can I make the same, make a broader statement which includes more — there, I think, in terms of engineering, the same thing should be kept in mind. As you see, if somebody comes along with a clever way of doing something, one should ask oneself °∞Can I apply the same principle in more general ways? Can I use this same clever idea represented here to solve a larger class of problems? Is there any place else that I can use this particular thing?
Structural analysis of a problem — If you can design a way of doing something which is obviously clumsy and cumbersome, uses too much equipment; but after you’ve really got something you can get a grip on, something you can hang on to, you can start cutting out components and seeing some parts were really superfluous. You really didn’t need them in the first place.
Inversion of the problem. You are trying to obtain the solution S on the basis of the premises P and then you can’t do it. Well, turn the problem over supposing that S were the given proposition, the given axioms, or the given numbers in the problem and what you are trying to obtain is P. Just imagine that that were the case. Then you will find that it is relatively easy to solve the problem in that direction. You find a fairly direct route. If so, it’s often possible to invent it in small batches
