The Incredible Life of Claude Shannon

last updated: October 5, 2020

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BookNotes on A Mind at Play: How Claude Shannon Invented the Information Age, by Jimmy Soni and Rob Goodman

Note: this is an excellent biography that pairs really well with "The Idea Factory" (

. It is a celebration of curious but serious play, and along with Gertner's book presents some of the most idea-dense pages that I've read. Here is a longer post by the authors themselves.

Claude Shannon, the father of the Information Age... and so much more (image
Claude Shannon, the father of the Information Age... and so much more (image link)

Who was Claude Shannon?

It’s true that, in most circles, this name is not well-known, even though Claude Shannon has been referred to as the Einstein of communication. Yet his ideas were foundational for generations of scientists and dreamers that built the Information Age - an age we still live in today. These two quotes begin to capture his ground-breaking contribution to our world:

“Before the two fields [computers, Boolean logic] melded in Shannon’s brain, it was hardly thought that they had anything in common. It was one thing to compare logic to a machine — it was another entirely to show that machines could do logic.”
“Of course, information existed before Shannon, just as objects had inertia before Newton. But before Shannon, there was precious little sense of information as an idea, a measurable quantity, an object fitted out for hard science. It was summed up in his recognition that all information, no matter the source, the sender, the recipient, or the meaning, could be efficiently represented by a sequence of bits: information’s fundamental unit.”

Below is a short summary of his life, his ideas, and some of the interesting insights that arise when considering the two. I've marked a few of my asides in blue and kept more biographical sections in black, for future reference and more efficient reading. In some areas, the authors (Soni and Goodman) do such a great job of illustrating a point that I don't even try to paraphrase - any uncited quotes are directly from them. I highly recommend reading straight from the source for those who are curious and can make the time.

Early childhood and family

Claude Shannon was born in Gaylord, Michigan in 1916. His father, owner of a successful furniture store, and his mother, a language teacher and later school principal, would be considered nothing if not ordinary. Indeed, there was little in his childhood to indicate the genius he would become - no overzealous parenting, no astounding feats as a boy.

The main marker was one of curiosity - above all, Claude loved to tinker. The early 20th century saw the magic that was radio spread across America, and it captivated him just as it did the rest of the country. One of Claude’s ‘inventions’ was a fence telegraph between his house and his friend’s - a common enough tool that some 3 million farmers used in rural areas where the phone company thought it unprofitable to build. His hero, Thomas Edison, would later turn out to be a distant cousin, a fact that would bring Claude much joy.

His only sibling and older sister, Catherine, was the over-achiever of the family, and set the example with high grades and matriculation at the University of Michigan. There was some degree of competition between the siblings, but Claude was never top of his class, though he showed early aptitude for math and science. One of the few highlights of his time in Gaylord, though, was a ‘human telegraph’ competition, where students were to use various body movements to communicate as quickly as possible in Morse code. Claude, with an interest in code-making and code-breaking, absolutely destroyed his competitors.

Two interesting ideas here: first, home radio assembly as a signal of curiosity and technical ability, which I write more about in

. Today's equivalent seems to be self-taught coding at an early age, although institutionalized coding programs may soon dull this signal ever so slightly. Second, a working DIY alternative to the phone grid, which popped up to fill gaps created by the profit-seeking large corporations of the time. The gap-stoppers were useful, but short-lived. The contemporary parallel appears to be the many companies bringing off-the-grid solar to East Africa, which has been hyped as a massive market opportunity (see here and here). However, the short-lived rural phone system of the early 1900s is a historical precedent that suggests these independent systems may not maintain market share for long (although history does not necessarily repeat itself).

College

Claude followed in his sister’s footsteps, enrolling at Ann Arbor with fortuitous and perfect timing. The university was just in the midst of transforming its engineering department, taking it from 30 students to over 2,000. He double-majored in engineering and mathematics, not out of outsized ambition, but because he could not decide between the two and realized the overlap in classes meant he only needed a few more credits to get both.

It was at Ann Arbor that he had his first publication - his solution to an open problem posted on the back of a math journal, meant to be solved with undergraduate-level training. This showed the first hint of his desire to go above and beyond the usual burdens of college life and classes, out of ambition or perhaps just curiosity.

During sophomore year, Claude’s father passed away at the age of 71. Claude returned home briefly for the funeral, and after some altercation, he stopped talking to his mother altogether. It seems that the disagreement began when she baked some cookies and would only let Claude eat the burnt ones, saving the good ones for guests. They would never reconcile.

It was soon thereafter that he took on an internship at Bell Labs. Though he produced no work of record, it was there that he began to think deeply about circuit design. At the time, designing circuits was considered almost an art, dominated by good intuition and frequent testing. This will become relevant for what will soon become obvious reasons.

Vannevar Bush & Single Purpose Machines

Soon thereafter, Claude Shannon would begin his graduate studies in electrical engineering at MIT. There, Vannevar Bush (a scientific titan his own right) would take him under his wing, and had the young Claude work on his differential analyzer, an early analog computer.

Analog computers were the pre-digital revolution ancestors of computers today. The one at MIT was massive, requiring its own room, and could solve differential equations by performing integration that measured the literal area under a curve. In this sense, the machine literally ‘performed’ the equations in the process of solving them, by turning the equation into a physical operation and interacting with that representation. “As long as the machine was acting out the equations that shape an atom, it was, in a meaningful sense, a giant atom.”

These were ‘single purpose machines’ that answered only one specialized question apiece. In contrast to general purposes computers that we are familiar with, these were truly working models of the physical world, simplified down to their essence.

It is also interesting to note that this occurred during the Depression, and MIT’s budget was far from its peak. However, Bush’s ambitions were costly, and he was able to continue by securing a $265,000 grant ($4.1M in today's dollars) from the Rockefeller Foundation.

Analog machines were incredibly useful for their time, but merely as a stepping stone for what was to come. However, the idea of turning mathematical problems into solvable physical representations is not one that should be lightly dismissed. Physics lends itself naturally to this sort of dynamic, so experimentation is rampant. It would be interesting to see if more abstract fields could benefit from a similar anchoring in the physical space.

The world’s most influential graduate thesis

It was at MIT, aged 21, working with analog computers and thinking about circuit design, that Shannon had the insight to connect Boolean logic to electrical circuits. Until then, Boolean logic was a philosopher’s curiosity, with little practical value. Shannon had immediately fallen in love with it and, curiously, loved the way the word ‘Boolean’ sounded. In times of silence, he would say it to himself and chuckle: “Boo-o-o-lean” - a quirk that would lead to an entirely new understanding of computation. It was by connecting the two that Shannon would make his first mark as genius.

Context: Boolean logic was the brainchild of George Boole, a self-taught English mathematician whose cobbler father couldn’t afford to keep him in school beyond the age of sixteen. Nearly 25 years later, he would earn prodigy status when he published a book worthy of its presumptuous title: The Laws of Thought. Boole showed that these laws are founded on just a few foundational operations: AND, OR, NOT, and IF. Here is a good explanation of the basic operations, as well as the laws that follow from them. At a high level, Boolean Logic allows one to map logical statements into a sort of mathematical expression (ex: I want pizza that is hot AND NOT reheated, etc.).

Shannon realized that two things in series could be described by the word “and” in logic, so you would say this “and” this, while two things in parallel could be described by the word “or.” After Shannon, designing circuits was no longer an exercise in intuition. Circuit design was, for the first time, a science. And turning art into science would be the hallmark of Shannon’s career.

“I think I had more fun doing that than anything else in my life,” Shannon remembered fondly. An odd and wonkish sense of fun, maybe — but here was a young man, just twenty-one now, full of the thrill of knowing that he had looked into the box of switches and relays and seen something no one else had.

One of the beauties of this system: as soon as switches are reduced to symbols, the switches no longer matter. The system could work in any medium, from clunky switches to microscopic arrays of molecules. The only thing needed was a “logic” gate capable of expressing "yes" and "no" — and the gate could be anything.

This was crucial — but the most radical result of Shannon’s thesis was largely implied, not stated, and its import only became clear with time. The implication gets clearer when we realize that Shannon, following Boole, treated the equal sign as a conditional: “if.”

Yet none of this could have been foreseen in 1937 by Vannevar Bush, planning ever more complex and capable versions of his differential analyzer, or even by Claude Shannon himself.

Looking back, it is quite beautiful that the finely engineered discs and gears of the analog computers would be replaced by simple switches no more complex than a telegraph key. However, it also highlights a key principle: the destruction of progress. The millions of man hours and dollars that funded Vannevar Bush's research were useful in that they primed Shannon's mind, but the machines themselves would be rendered absolutely useless as they were outclasses by digital computers. Indeed, one could say that the analog computer was, in a way, one of engineering's long, blind alleys. Of course, we cannot know which of today's engineering fronts will prove alleys, but it is helpful to realize that a great advance can easily render an entire field outdated. If we are to prioritize progress though, our job becomes to simply encourage those advances, no matter how costly previous progress was, and to try to decrease the number of alleys as soon as they seem vulnerable to obsolescence. I am not necessarily convinced that progress should be prioritized in every case, but it is helpful to be aware of the cost of doing so.

Short marriage to Norma

It was also at MIT that Claude met and married Norma Levor, a wealthy, Jewish, left-wing intellectual. They would only remain married for a year, as they found little in common to hold them together.

Brief genetic interlude

It was a matter of deep conviction for Bush that specialization was the death of genius. He therefore took it upon himself to find a dissertation project for Shannon in a completely new field - genetics. It was a field of which Shannon knew absolutely nothing. He would be learning about alleles, chromosomes, heterozygosity from scratch. He would also be conducting his research at one of America's great scientific embarrassments: the Eugenics Record Office.

Within a short year, though, he had more or less mastered the field and would publish original work: An Algebra for Theoretical Genetics. Everything in Shannon’s ground-breaking thesis flowed from his realization that circuits were poorly symbolized. What if genes were poorly symbolized, too? The main contribution of his thesis was a better form of notation, that allowed for more legible tracking of chromosomes. "Much of the power and elegance of any mathematical theory," Shannon wrote, "depends on use of a suitably compact and suggestive notation, which nevertheless completely describes the concepts involved."

This contribution was never truly embraced, and though some scientists say it may have accelerated the field considerably, it is still not clear how substantial his work was during that year. It is worth noting, too, that the rise of Nazi Germany made 'genetics' far less popular as well, which did nothing to encourage Shannon to stay within the field. It is also interesting to think that, without Nazi Germany, who took ideas of genetic selection to their extreme, eugenics may have continued to gain momentum within the United States, furthering ideas like selective breeding of the "fittest families" and the sterilization of "defective classes."

Superior notation still remains as one of Shannon's most powerful legacies. Several other examples come to mind: before the alphabet, there was no way to record thought. Before Arabic numerals, it was almost impossible for numbers to be calculated on paper. Before Leibniz, there was no simple way to engage with algebraic notation. In fact, in this example it was Leibniz's intuitive notation that won over Newton's, even though both had discovered calculus around the same time. In a way, notation automated the mental effort of a specific activity, by removing the strain of carrying information and relations in one's mind.

Today we think of many of these same principles are UI problems, and delegate designers to allow us to better engage with digital content. Steve Jobs understood notation better than most, and his shift to new interfaces (using a mouse and keyboard, then the iPod wheel, then the touch screen) was as paradigm-shifting as we're seen in the last few decades. Think of the 'pinch to zoom' action, or the press and hold - these 'shortcuts' shorten the distance between our minds and our ideas - with incredible consequences. For more on this topic, I highly recommend watching Bret Victor speak.

Academia part 1

After his brief stint in genetics, Shannon transitioned to the Institute for Advanced Study at Princeton. There, he had great latitude to follow his curiosity across multiple disciplines and discuss with great minds like Von Neumann and Weyl. However, this time proved unhealthy for Shannon. For some, this island of knowledge, away from the typical worries of universities - teaching, deadlines, and the pressure to publish - was a curse rather than a blessing. Richard Feynman, then a PhD student at Princeton, observed of the IAS: "a kind of guilt or depression worms inside of you, and you begin to worry about not getting any ideas.... You’re not in contact with the experimental guys. You don’t have to think how to answer questions from the students. Nothing!"

WW2

This was, however, the late 1930s, and as World War 2 began, Shannon transitioned to Bell Labs to contribute to the war effort. And for scientists in the US, this would be a war like no other.

As Fred Kaplan, wartime science historian, would put it, "It was a war in which the talents of scientists were exploited to an unprecedented, almost extravagant degree." This was not just meant negatively - Vannevar Bush would say that "the scientists, burying their old professional competition in the demand of a common cause, have shared greatly and learned much." It is worth noting, too, that Bush would lead many of the scientific war efforts, and advise presidents and politicians for decades to come.

Wartime would interrupt the working lives of a whole generation — but as far as possible interruptions went, the convergence of some of the nation's brightest minds onto a singular mission could be quite a blessing. The war would also prove the most sophisticated in history and reframe the nature of military events. A naval battle at range was now a mathematical race, as captains competed to land precise strikes first, before the actions of their opponents could take them out.

Shannon was exempted from the draft and awarded $3,000 and a ten-month contract, for a project called "Mathematical Studies Relating to Fire Control." This meant he would be working on the study of moving targets. This project and others would pave the way for massive leaps of progress, birthing information theory, systems engineering, and classical control theory.

Galileo had a pendulum in Pisa. Newton had his falling apple. Einstein his beam of light. As for Shannon, the task of tracking evasive paths of aircraft would provide a rigorous course in probabilistic thinking. He would also get to use his childhood passion for cryptography at various times throughout the war. Crucially, he sometimes worked on projects so secret that he was never told the overall purpose. This allowed him to dive deep into the abstraction of things, and get a glimpse of encoded speech, communications, and cryptography.

It seems that one of the reasons WW2 accelerated science so much was the fact that top mathematicians, who once considered applicable problems as far too trivial and a waste of their time, suddenly agreed to work on necessary if unexciting issues. One wonders if such a dynamic would be repeatable, even if brought about by such dire circumstances as global warfare. Nevertheless, it confirms an interesting but important fact: there is always potential but untapped progress at hand. It is locked in the bright minds pushing the frontiers of knowledge, who might one day turn their focus to less esoteric but deeply applicable problems. As always, there is so much human value just waiting to be unlocked.

Joining the Bell Labs math group

Thornton Fry, founder of the Bell Labs math group, had seen Shannon's potential first hand in 1940. He soon offered him a full-time role to join Bell Labs as a research mathematician.

Context: We all take for granted that, in today's day and age, a mathematically gifted individual can easily profit from their abilities. Quant jobs at hedge funds, investment banks, or data analytics are high-paying and prestigious. However, this was not always the case. In the early 1900s, mathematic ability at the highest levels had very little application - and no societal recognition.

Thornton Fry, an applied researcher at Bell Labs, refused to believe that all mathematicians wanted tenure and more publications. By founding the Bell Labs math group, he bet on and created the "industrial mathematician," who could combine thinking with practical application. Initially, this group played an in-house consulting role, assisting engineers, physicists, and chemists in their problems. However, they were to avoid the messiness of timelines and massive industrial projects, limiting themselves to intellectual discovery and debate. Even so, they took pains to keep themselves stimulated, and as Henry Pollak said, "our principle was that we'll do anything once, but nothing twice."

It was while at Bell Labs that Shannon began to synthesize his thoughts on communication, eventually publishing "A Mathematical Theory of Communication" in 1948. It was this article that would become the foundation of Information Theory, the precursor to natural language processing and computational linguistics, and the beginning of an Age.

Information Theory

The paper itself is about 55 pages long and worth a read for the deeply curious. Shortly after it was published, another American Scientist, paired with Shannon to write a book titled, "The Mathematical Theory of Communication," which played a massive role in popularizing the work to the non-specialist. I will not attempt to summarize either, but instead will try to include some of the most impactful ideas I derived.

The model

source: Wikipedia
source: Wikipedia

It may be hard to grasp how groundbreaking this diagram was when first published. The pieces are rather self-explanatory, but the whole presented, for the first time, a universal way to understand communication. Along the theme of superior notation, this unlocked fields of communication not just in military applications or telecommunications, but in any area that involved transmitting information, from DNA to linguistics. For the first time, communication was understood as a topic that seeped into every aspect of human (and animal) life.

Signal, Noise, and Redundancy

Yes, the common trope of finding signal among the noise is something you should attribute to Shannon. Signal is what we intend to send, noise is the unintended static that the listener also receives. Before Shannon, it was assumed that the only way to beat the noise was by strengthening the signal. The first phone line across the Atlantic used incredible amounts of power in order to achieve this, at great waste and eventual failure.

And yet, there is another way to beat the noise: redundancy. Shannon realized that the same signal sent twice, with probabilistic noise each time, would lead to a clearer interpretation of the signal than more power. It was something that radio operators already understood, as they repeated common calls or lengthened them to make a dropped word less dangerous. By focusing on redundancy (also a common theme in cryptography, especially when the English language has words that appear far more than others), noise becomes an obstacle that can actually be overcome, in objective and definite ways.

Shannon proposed that every channel had a limit to the amount of information that could be sent reliably, which was defined by the length of the signal, the probabilistic amount of noise (which could be measured and thus predicted), the amount of redundancy needed to overcome it. For the first time, reliable communication across any channel was a real and attainable goal.

Redundancy is nothing new to us, nor to history. Great orators often have one key message (their signal), and a thousand ways to repeat the same thing (their redundancy). This is why some ideas, which could be conveyed in a short essay, are instead confined to books - the redundancy is part of what makes the message so powerful. Our challenge, then, is not just to find the signal among the noise, but to also accept the redundancy that comes along with it, and to know when to look for a new signal after the redundancy has done its job.

Information as Uncertainty Reduction (personal favorite)

Information is not defined by what is transmitted, but rather by what is not. More technically, the larger the alphabet, the more information is conveyed by a message of given length. To give an example, if my alphabet contains 3 letters (say a,b,c), then a 3 letter message is one of 9 possible messages (aaa, aab, aac, aba...). However, if my alphabet expanded to 6 letters, then a message of the same length becomes far more information-rich. This is because, in choosing specific messages, I communicate as much by the omission of letters (what I didn't say) as I do by what I sent (what I did say).

Of course, this has massive implications, because it defines all information as essentially uncertainty reduction. In that sense, we might as well rename the Information Age and call it "The Age of Uncertainty Reduction." It also provides a neat link between our obsession with information and our human instincts to reduce uncertainty (read

for more on the 'C' in SCARF). This was the clearest explanation I've ever found for the constant push of the last 70 years, as we continually decreased uncertainty far beyond our survival needs, unleashing a torrent of news, sharing personal information, and birthing the era of legibility that has defined so much of our business world.

Part of the usefulness of this definition was the separation of information from significance. This meant that Shannon, with his abstract mathematical thinking, could apply himself to communication usefully, while skipping entirely the complex and far more human conversation about what makes a conversation meaningful in the first place.

The Bit: a Unit for Information

If information is uncertainty reduction, how can we measure it?

A simpler example of information transfer is that of flipping a coin. If both sides are heads, then flipping a head tells me nothing. But if one is heads and the other is tails, then the flip conveys information. Additionally, if the coin is weighted such that I will get heads 70% of the time, then landing on heads tell me little, while landing on tails tells me more. This same phenomenon applies to our conversations.

Say I get an email intro to a VC partner with a unisex name, like Jordan. Statistically, 91% of VCs are male. If I then get on a Zoom call with Jordan, and it turns out Jordan is indeed a man, I will have learned little. However, if Jordan is in fact one of the few and admirable women in the industry, then I will have learned a lot. In other words, learning Jordan's gender would have been more informational in the less likely case, and less informational in the more likely case.

The perfect balance, then, and the most informational coin is the one that is fairly weighted - when both options are equally likely. At the most abstract level, instead of a coin, I could have 2 numbers, with equal probability of choosing either one. For example, those numbers could be 0 and 1. And that, dear reader, is the fundamental unit of communication: the bit.

It is worth noting that Shannon himself did not invent the bit, and attributed the name to John Turkey, another Bell Labs researcher who focused on statistical methods. However, it was Shannon who connected the two seemingly disparate fields (his trademark move), by introducing the bit as not just a probability tool but also a unit to measure something that once was considered immeasurable.

For all of you who ever wondered why code boils down to binary... Well, now you know. Technically, there are ternary computers that use base-3 logic, and the real reason for binary is that it's easier to measure any voltage vs. zero voltage. But the fact remains that the 'bit' emerged a theoretical concept before it became as widely used as it is today.

Meeting Betty

After 1948, Shannon had earned the right to be non-productive. Shannon arrived at the office late, if at all, and often spent the day absorbed in games. It was at Bell Labs, though, that he met Betty (née Mary Elizabeth Moore).

With strong mutual interests (music and mathematics) and a shared sense of detachment from the world (the feeling that the world was always conspiring to make them chuckle), the two quickly charmed each other. They would get married in 1949 and go on to have three children together.

Betty was more than just a companion. "It wasn't just the joy he found in her company, though he did." She would partner with him professionally as well. As Mileva Maric was to Einstein, Betty would help Shannon by advising him on mathematic topics, keeping record of his thoughts, and editing his writing. It would become one of "the great mathematical marriages of our time: one that produced path-breaking work and lasted the rest of Claude's life."

Return to MIT

In 1956, Shannon returned to MIT as a professor. He was, by that point, more inspiration than instructor, but he proved an excellent bouncing board for the ideas and intuitions of others. With a great knack for asking questions, he would probe ideas instead of offering answers - often to the great benefit of all involved.

"Shannon’s favorite thing to do was to listen to what you had to say and then just say, ‘ What about... ’ and then follow with an approach you hadn’t thought of. That’s how he gave his advice. This was how Shannon preferred to teach: as a fellow traveler and problem solver, just as eager as his students to find a new route or a fresh approach to a standing puzzle."

I include this next anecdote in full, told by a graduate student under Shannon, because it does an excellent job of showcasing the professor's methods:

"I had what I thought was a really neat research idea, for a much better communication system than what other people were building, with all sorts of bells and whistles. I went in to talk to [Shannon] about it and I explained the problems I was having trying to analyze it. And he looked at it, sort of puzzled, and said, 'Well, do you really need this assumption?' And I said, 'well, I suppose we could look at the problem without that assumption.' And we went on for a while. And then he said, again, 'Do you need this other assumption?' And I saw immediately that that would simplify the problem, although it started looking a little impractical and a little like a toy problem. And he kept doing this, about five or six times. I don’t think he saw immediately that that’s how the problem should be solved; I think he was just groping his way along, except that he just had this instinct of which parts of the problem were fundamental and which were just details. At a certain point, I was getting upset, because I saw this neat research problem of mine had become almost trivial. But at a certain point, with all these pieces stripped out, we both saw how to solve it. And then we gradually put all these little assumptions back in and then, suddenly, we saw the solution to the whole problem. And that was just the way he worked. He would find the simplest example of something and then he would somehow sort out why that worked and why that was the right way of looking at it.”

Games and Artificial Intelligence

Shannon would spent a disproportionate amount of time making little toys and gimmicky devices. Some even considered this a waste of such great talent. But his games served as fun mental experiments for how something might be done, or if something might even be possible at all.

One of Shannon's most famous inventions, created while still at Bell, was Theseus, the mechanical mouse. Theseus was special in that it could 'learn' its way through a maze to a piece of 'cheese,' and go through the maze faster the next time round.

But solving such a problem required remembering facts, and somehow processing them. In other words, Theseus had the rough equivalent of a brain. Of course, this was not real intelligence, but it was the an imperfect model of how an animal could learn. And it created, for the first time, a real glimpse at a machine that could learn.

Artificial intelligence was not a new thought, but it was one that Shannon took seriously. To him, it was not some fantasy, but a step of innovation that he very much expected to see within his lifetime - and a very positive one at that. "In the long run [the machines] will be a boon to humanity, and the point is to make them so as rapidly as possible."

Nor was the impact of true artificial intelligence lost upon him. "I believe that [...] we are going to invent something. It's not going to be the biological process of evolution anymore, it's going to be the inventive process whereby we invent machines which are smarter than we are and so we're no longer useful. Not only smarter but they last longer and have replaceable parts and they're so much better." With a smirk, he would half-joke that humans were preparing their own extinction. But to Shannon, the logical, energy conserving, friendly computer was not such a bad alternative to people.

There were three central questions that needed to be answered first: how can we give computers better sensory knowledge of the real world? How can they better tell us what they know, besides printing out information? And finally, how can we get them to react upon the real world?

Shannon was careful not to advocate for fully machine solutions. For example, within the realm of chess, he was adamant that the inanimate had certain advantages, but not every advantage. Processing speed, attitude, and ego - those were best left to computers. But the flexibility, imagination, and continual learning was something that no chess-playing machine could ever optimize. In this sense, the ultimate chess-playing machine was not one created in man's image, but rather one designed to bolster his weaknesses.

Regardless, his theories on chess-machines (it was not until 1996 that Deep Blue would beat Kasparov) solidified a new and dangerous thought: in some arenas, computers were undoubtedly smarter than humans. This seems fairly obvious to us now, but it is quite a testament to Shannon's imagination that he was able to see this so clearly decades before the rest of the world.

It was this section that started my grappling with our understanding of intelligence. By all accounts, a large part of our brains is simply information processing. There is input, a black box, then output. Then again, when the steam engine was invented we began to think of people as energy machines. Today we have computers, so we naturally compare ourselves to them. Without being too narrow-minded in our current circumstances, I think that artificial intelligence (true general intelligence, not the buzzword of today) can shed a valuable light on how we understand ourselves and find meaning in that understanding.

It is also unfortunate that Shannon's attitude towards the advance of the field was misguided, and far too optimistic. Nevertheless, I do look forward to when the Shannons of today take us leaps and bounds towards empowering man-machine pairings. I suspect that these actors will not be the lauded nor the celebrated, but rather the quiet, the curious, and the playful. Time will tell if my optimism is any better placed than Shannon's.

Angel Investing

Another surprising facet of Shannon's life was his self-made status as multi-millionaire. Still on payroll at Bell Labs, and with an MIT salary, he was certainly well-off, but it was his prolific angel investing that would make his fortune.

As many investors do, he would admit that fortune played a large hand, in addition to his privileged position alongside brilliant founders and solid companies. But it was his reputation and previous work that opened those doors, allowing him to get in early in Teledyne, Motorola, HP, and others.

Teledyne, an industrial conglomerate still in action today, was one of his early advising/investing plays. Over the course of the next 25 years, it would yield an annual compound return of almost 27 percent.

This was one of the arenas where both Shannon and Betty thrived. They would both take every opportunity to meet founders in person and size them. New products and prototypes would regularly grace their home. When considering whether to invest in a new food venture, Kentucky Friend Chicken, they ordered several buckets for a festive taste test with friends.

Their interest would also extend to the public markets, as stock trading became one of the stranger Shannon obsessions. Neither spouse cared much for what the money could buy, but more for the interesting games that money made possible.

This is perhaps my favorite argument for video games (it is also entertaining to imagine Shannon's life had Xbox and Steam been around during his childhood). Clearly, a game-winning mentality carries far beyond the confines of any specific game. Even the real world has similar rules, winners, and losers - after all, games were first modelled off our own lives.

Secondly, the advantage of brilliance is compounding. Shannon, by being brilliant, was surrounded by brilliant people who valued his opinion. This is the core of why he was able to make his investments, and eventually his fortune. This is also why wealth, even in meritocratic settings, follows a Pareto distribution. Taxes, foundations, and stupidity are the only reason why this is not an even more prominent feature of our society than it is today.

Juggling

No biography of Claude Shannon would be complete without a nod to his juggling.

Until he arrived on scene, no one had ever considered the mathematical side of it. And yet, by slowing the act of juggling down, one begins to see a series of predictable parabolas. Each ball has its own arc, and together these arcs form a consistent and predictable pattern.

In order to study these phenomena more closely, Shannon titled a table and let the ball roll from one end to other. As the incline became steeper, the vertical acceleration would play more strongly into the ball's trajectory. And, conversely, with a more flat surface, the ball would travel more slowly. In this way, Shannon was able to more finely study the patterns of juggling, as well as refine his own technique, in his own version of slow motion.

An interesting tie-in: Gene Krupa, an American jazz drummer, once called the cross rhythm of 3 against 2 "one of the most seductive rhythms known to man." It is also the rhythm by which most people first learn to juggle: three balls, and only two hands. This connection was not left unnoticed by Shannon, who opened his (and the very first) mathematical paper with a reference to Krupa's quote.

But please, by all means, read the paper yourself if this piques your curiosity in any way.

Final notes on his personality

Hopefully some of these anecdotes make clear that Claude was distinguished by his mastery of model making more so than his quantitative horsepower. His true talent was reducing big problems to their essential core, in a most playful manner.

This power for abstraction had, in his twenties, driven him to shyness and withdrawal. But it would also grant him a lifelong obsession with play, for the core of abstraction is understanding that "the world we see merely stands for something else." To someone who saw the physical world - valuable as it was - as a stand-in for the reality of numbers, logic, and theorems, everything may have seemed at times like a permanent joke.

Shannon would himself try to distill his thoughts about where great ideas come from. I've compiled some of my notes in

, which you may find interesting.

Claude would gain quite the reputation when he gave his occasional talk, by sometimes discussing his published work, sometimes rambling about stock dynamics, and other times juggling silently on stage. But despite his heavily quantitative life, he always made time for music, and especially improvisational jazz, which he would call "unpredictable" and "irrational." This was just one of the many facets that would define his multidisciplinary career, as he brought disparate topics, from Boolean logic and circuit design, to juggling and mathematics, into focus and clarity for the first time.

There is in this essay, and in this book, a marvelous and beautiful glimpse at genius. It was neither the brute brainpower nor sheer determination that are so often lauded in schools, shows, and newspapers. Rather, Shannon's main superpower was simply his curiosity, coupled with his power for abstraction. By living in his own abstracted world, he was free to connect fields in ways no one had ever conceived. In this sense, Shannon is a titan in his own right, but still a figure that we can aspire to emulate in our own way.

Obviously, tackle big and hard questions. Stay multidisciplinary. Stay creative. Stay playful. But above all, stay curious.