Solve Hard Problems With Two Small Jumps, Not One Big Leap
Claude Shannon, who turned information into bits, left six practical moves for getting unstuck.
Founders · How Claude Shannon Invented The FutureClaude Shannon, who founded information theory with his 1948 paper, described information before that paper in everyday forms like telegrams, photographs, paragraphs, and songs, and showed all of them could be reduced to bits.
That work laid the foundation for the internet, data compression, and modern computing. For getting unstuck, he left practical advice: do not try one big leap.
Shannon favored reaching answers through short advances. As Shannon put it, "it seems to be much easier to make two small jumps than one big jump in any kind of mental thinking." The other moves help set up those smaller jumps.
First, simplify. Strip a cluttered problem down to its central issues so you can see what you are trying to do. Simplification, in his view, was the art of knowing what to throw out.
Second, encircle the problem. Collect answers to similar questions you already know, then look for what they share. Your unsolved problem often becomes the next short step from that common ground.
Third, phrase the problem differently. Swap vocabulary and viewpoint to loosen habits that lock in one way of looking, and do not let work you have already put in trap you. Fresh eyes help, because someone meeting a problem for the first time is not weighed down by earlier assumptions.
Fourth, divide a daunting task into smaller parts. Many mathematical proofs, he observed, emerge from winding detours, where a person establishes various separate results that appear aimless and then arrives unexpectedly at the answer from behind.
Fifth, invert. If you cannot get from your starting points to your endpoint, assume you have already arrived and work backward to see what must have come first.
Sixth, stretch an idea to see how far it will go. His advice was blunt: "Someone always comes along and starts generalizing it. So why not do it yourself?"
Questions people ask
Did Shannon actually use these moves himself?
The source does not show Shannon using these six moves by name. It describes eight years of scribbling, refining, and solitary night work on his 1948 paper, with ideas arriving in flashes rather than in a straight line.
What does encircling a problem look like in everyday work?
Pick two solved problems that resemble yours and write down their solutions side by side. Then ask what steps they share, what tools they both use, and what you could borrow. Your unsolved problem often becomes the next small jump from that common ground.
When should I try inverting instead of pushing forward?
Inversion helps when you are stuck moving forward. Instead of asking how to reach a goal, assume you already reached it and ask what must have been true just before. Working backward often reveals a premise you can actually prove or build.