Direction Beats Diligence

The Core Insight

Richard Hamming spent 30 years in the Mathematics Research Department at Bell Telephone Laboratories. He then taught a graduate course at the Naval Postgraduate School with, by his own account, no technical content in it. Style of thinking was the center of the course, and everything technical was illustrative material.

Style is an art, so he copied how the other arts get taught. Style cannot be put into words, so he approached it from many sides and repeated himself on purpose.

Most engineers I know treat great work as a draw: raw brains, the right decade, and a problem that happened to be sitting there. Hamming argues for a learnable style instead, and he taught it as one. His evidence is bunching. Great results land on the same people too often for random luck to explain them.

The arithmetic under the course sets the stakes. Knowledge of the kind he cared about doubles about every 17 years, a rate he traces to Newton. The half-life of what an engineer learns in school runs about 15 years. Learning to learn is the subtitle and the only durable answer he offers.

The Framework

The course runs on a short list of claims about how a career adds up. The technical chapters carry them.

• A vision converts a random walk into a directed one, and the accuracy of the vision matters less than having one.
• Effort and knowledge compound, so one extra hour a day over a lifetime more than doubles total output.
• Important problems get worked on by people who believe they can do important things.
• Luck favors the prepared mind, and preparation is the work you did before the problem arrived.
• Selling the work is part of the work, in writing, in prepared talks, and in impromptu ones.
• The certainty of an expert is the block, because every impossibility proof rests on assumptions.

The vision claim has arithmetic under it. A drunken sailor taking n independent random steps ends about the square root of n from the start. Give him a reason to lean one way and the distance grows in proportion to n. A career of small choices runs the same way.

Two definitions run through the course. Science is the work you take on when you do not know what you are doing. Engineering is the work you must not start until you do.

Key Ideas

Most People Never Work On Important Problems

Direct observation and direct questioning gave Hamming his flattest finding. Most scientists spend most of their time on work they believe is neither important nor likely to lead to important things.

He ate for years with the Physics table at the Bell Telephone Laboratories restaurant. Fame, promotion, and hiring by other companies thinned the average quality, so he moved to the Chemistry table. He asked what the important problems in chemistry were, then what the table was working on. One day he asked why a person works on something he believes is neither important nor likely to lead anywhere. The table stopped welcoming him, so he moved to eat with the engineers.

That was the spring. In the fall one of the chemists stopped him in the hall and said the question had cost him a summer of thinking. He had changed no research, and he called the effort worth it. Within a few months he was made head of the group, and Hamming later saw him join the National Academy of Engineering. He never heard of anyone else from that table.

One qualifier gets dropped whenever the passage is quoted. The importance of the result is not the measure of the importance of the problem. Antigravity, teleportation, and time travel are seldom worked on because nobody has an attack on them. Fame runs the other way. Famous people come to believe they can only work on important problems, so they stop planting the small acorns.

The Open Door Correlates With The Right Problems

Hamming watched the doors at Bell Labs for decades. People who worked with the door closed got more done per year. People with open doors got less done and tended to work on the right problems, at the same level of effort.

He states the limit himself. He cannot prove the cause and effect relationship, and he observed the correlation only. He suspects that an open mind leads to the open door, and that the open door leads back, each reinforcing the other.

That sits inside a larger rule. The conditions a person picks for himself are usually not the conditions that produce his best work. The Institute for Advanced Study at Princeton is his example. By his count of what people did before and after going there, it ruined more great scientists than any place created. Contact with harsh reality pushes people into discoveries that private interests in a vacuum never reach.

Effort Compounds, And Direction Sets The Rate

Hamming worked with John Tukey for years before learning that Tukey was about his own age. He asked their mutual boss how a man his age knew so much. The boss leaned back, grinned, and said that working as hard as Tukey had for as many years produces that much knowledge.

The reading he took from it is compound interest applied to a mind. The more you do, the more you learn how to do, so the more you can do. He declines to name the rate and puts it well over 6 percent. One extra hour a day across a lifetime more than doubles total output.

The brake arrives in the next line. The race goes to the right problem, at the right time, in the right way, which is what he keeps calling style. Working hardest does not decide it.

The practice that ran the compounding was a standing appointment. Friday afternoons went to great thoughts. From lunch onward he thought only about what computing was and where it was heading. Ten percent of his time bought the direction the rest of the week ran in.

Luck Favors The Mind That Prepared Earlier

Pasteur supplies the spine, and Hamming returns to the line from the preface to the last chapter. Luck favors the prepared mind.

Hamming shared an office with Claude Shannon at Bell Telephone Laboratories. At about the same time Shannon created Information Theory and Hamming created Coding Theory. Both were in the air, and other people sat in the same building. The difference he names is preparation.

The error-correcting code came out of a bad weekend. As low man on the totem pole he got free time on the Model 5 relay computer from Friday evening to Monday morning. Twice in a row the machine failed and he got nothing back. Angry, he asked why a machine that finds an error cannot find where the error is and flip the bit.

He flags the mechanism twice. The step happened under real emotional stress, and he says most great discoveries work the same way. Calm work elaborates and extends. Breakthroughs arrive after frustration and involvement. Preparation supplied the rest, because he already knew the 2-out-of-5 codes and the implications of a parity check.

Selling The Work Is Part Of The Work

By the 1950s Hamming was frightened of large audiences, after years of college teaching. He treated that as a defect he had to remove. A scientist owes the field three forms of communication: written papers and books, prepared public talks, and impromptu talks. Missing any one of the three drags on a career.

The fix was volume, aimed on purpose. Asked to give an evening talk to IBM customers, he accepted at once and set out to be invited back. So he picked what the audience wanted over what was dear to him. The result was The History of Computing to the Year 2000, given around 1960.

Good ideas do not win on merit. Many a good idea had to be rediscovered because nobody presented it well the first time. Clear presentation does the selling, and propaganda has no part in it.

Two adjacent rules travel with it. Do the job so other people can build on it, and refuse to make yourself indispensable, because the indispensable person never gets promoted. The second is to recast finished work into its basic form. Hamming did that with an integration method he had improvised on an IBM 701, and it ran for years under his name.

The Best Forecasts Rest On The Underlying Forces

Hamming read that 76 methods of predicting the future exist, and took the number itself as proof that none is widely accepted. Two cheap methods start the discussion: tomorrow looks exactly like today, or extrapolate the current rate.

His own method rests on understanding the fundamental forces in play. Physical limits often matter less than human-made laws, habits, organizational rules, egos, and inertia. Three questions get separated before planning starts: what is possible, what is likely to happen, and what is desirable. The first is science, the second is engineering, and the third is ethics.

The doubling number carries three supports. Libraries must double their holdings every 17 years to hold position. Bell Telephone Laboratories doubled employees every 17 years across his 30 years there, through hiring freezes. And almost 90 percent of the scientists who ever lived are alive now.

He checks the last two claims against each other on the back of an envelope. Assume scientists grow exponentially and knowledge production runs proportional to the number alive. Take a working lifetime as 55 years, and the model returns very close to 90 percent. The general version with a 17-year doubling period gives 56.47 years, against the 55 assumed.

The table he prints turns years into a factor. Seventeen years doubles current knowledge, 34 years gives four times, and 51 years gives eight. Pick your years to retirement and read the factor you will stand in front of. Set the half-life beside it, because technical knowledge from school goes stale in about 15 years.

Practical Applications

Book one afternoon a week and defend it. Hamming spent ten percent of his week on where computing was heading, and that share set the direction for the rest.

Keep a written list of 10 to 20 problems you regard as basic and cannot solve. When a clue arrives out of work you are doing for other reasons, drop the current task and go.

Practice the three forms of selling on a schedule. Produce one written report, one prepared talk, and one impromptu answer each quarter. Critique every talk you attend in private and take the parts that fit your style.

Run the back-of-the-envelope check on quantitative claims before you repeat them. The value is in seeing which factors you were inclined to leave out.

Take the door observation as a test rather than a rule. Hamming reports a correlation and refuses to claim the cause. Run a quarter with the interruptions accepted, record which problems arrive through the door, and decide from your own record.

Who This Is For

Engineers and founders early enough in a career for compounding to pay get the most from it. The book answers what to work on and how a career adds up, and it leaves the how-to alone.

Skip the technical chapters unless you want them for their own sake. Coding theory, information theory, digital filters, and n-dimensional geometry run to a graduate course. Hamming says outright that the content is illustrative, and the method survives without a line of it.

Read the evidence for what it is. This is a lecture course written up from a Bell Telephone Laboratories and Naval Postgraduate School vantage. The research era behind it had corporate labs, long horizons, and free weekend machine time. The evidence is what one distinguished career observed. No dataset sits behind it. Survivorship runs through every example. Shannon, Tukey, and Hamming all won, and the people who kept the door open and produced nothing never enter the count. He states the door finding as a correlation and declines to claim the cause, which is the most careful sentence in the book. The reader has to supply the same care everywhere else.

The Decision

Write two lists this week. The important problems in your field, as far as you can name them today. Then what you worked on over the last month, line by line.

Hold them side by side. A gap between the lists is the finding, and its size is readable.

One condition governs which problems from the first list are yours. A problem is important partly because a way in exists, so the ones worth your time are the ones where you see an attack.

Pick one and give it the next Friday afternoon.