The Size of the Bet

How Bell, Edison, Ford and Claude Shannon Led Us to the Mathematics of Uncertainty

In the United States of the 1870s, distance still imposed a tax on almost everything. A telegram could outrun a train, but ordinary speech could not. Gas and oil pushed back darkness, though illumination remained dirty, dangerous and local. Factories were becoming intricate organisms, but complex manufactured goods still moved through them at the pace of men carrying parts from station to station.

Then several bottlenecks began to give way.

Alexander Graham Bell came to communication through sound. He taught deaf students, studied speech and hearing, and worked with the machinist Thomas Watson on transmitting sound electrically. On March 7, 1876, Bell received U.S. Patent No. 174,465. Three days later Watson heard intelligible speech through the apparatus. Elisha Gray's lawyer filed a competing caveat on the same day Bell's application was filed, one reminder that invention usually emerges from a crowded field.

Bell, Gardiner Greene Hubbard, Thomas Sanders and Watson formed the Bell Telephone Company in 1877. In 1885 American Bell created the American Telephone and Telegraph Company as a subsidiary to build long-distance service. Theodore Newton Vail became its first president. In 1899 AT&T became the parent of the Bell System. Bell had helped invent the telephone; Vail and many others helped build the network, financing, standards and organization that made a telephone worth owning.

Thomas Edison confronted a similar problem in another domain. Electric lamps existed before him. What Edison and the Menlo Park team achieved in 1879 was a practical incandescent lamp embedded in a practical electrical system: generation, distribution, wiring, switches, meters and commercial deployment. The bulb mattered because the system around it made the bulb useful.

Edison's electrical companies were eventually consolidated into Edison General Electric. In 1892 J. P. Morgan organized its merger with Thomson-Houston, the company associated with the prolific inventor Elihu Thomson. Charles A. Coffin, Thomson-Houston's formidable executive, became the first president of the new General Electric. Once again, the invention had become an institution.

Several decades later, Henry Ford attacked a different constraint. Ford Motor Company was incorporated in 1903 after Ford's earlier automotive ventures had failed or proved short-lived. The Model T arrived in 1908. At Highland Park in 1913, Ford's team successfully integrated the moving assembly line into automobile production. They borrowed from a long inheritance of interchangeable parts, conveyor systems, slaughterhouse lines and continuous-flow manufacturing. Chassis assembly eventually fell from roughly 12.5 hours to about 1.5. The repetitive system produced severe turnover, and Ford's celebrated $5 workday in 1914 was partly an economic response to that labor problem.

Bell altered the economics of distance. Edison altered the economics of practical electric light. Ford altered the economics of production. Their deeper achievement was to turn technologies into systems that could scale.

What Survives a Century

Ford Motor Company is now more than 120 years old. The Bell corporate lineage reaches back nearly 150 years, although modern AT&T came through the 1984 breakup of the Bell System and the 2005 acquisition of AT&T Corp. by SBC, which then adopted the AT&T name. GE's lineage is more than 130 years old, although the old conglomerate completed its separation into GE HealthCare, GE Vernova and GE Aerospace in 2024, with GE Aerospace retaining the GE ticker.

Longevity therefore needs a careful definition. Some companies survive intact; others survive through institutions, brands, capabilities and descendants.

Coca-Cola offers a useful contrast. The drink dates to 1886 and The Coca-Cola Company to 1892. Its enduring product is conceptually simple, but the business around it never was. Bottling, distribution, advertising and local execution created a system capable of carrying the same basic promise across generations. Longevity can emerge from a durable consumer habit or repeated renewal around important technologies. Endurance belongs to the system surrounding the original object.

The Institution That Learned to Think

The Bell System's scale produced another remarkable institution. In 1925 AT&T and Western Electric created Bell Telephone Laboratories, consolidating thousands of scientists and engineers. It combined patient capital, practical constraints and unusually long intellectual horizons. The transistor emerged there. So did Unix. Its most consequential idea, however, concerned information itself.

Claude Elwood Shannon was born in 1916 and studied mathematics and electrical engineering at the University of Michigan. At MIT he worked on Vannevar Bush's differential analyzer, an enormous analog calculating machine. Shannon noticed that the machine's relays behaved like the true and false operations of Boolean algebra. His master's thesis showed that logical relationships could be designed as electrical switching circuits. Digital logic suddenly had a mathematical language.

Bush then did something equally important. He pushed Shannon toward genetics, a field Shannon barely knew. Shannon spent time at Cold Spring Harbor and completed a 1940 doctorate, An Algebra for Theoretical Genetics. He never became a geneticist. The value of the exercise lay in forcing a powerful set of tools into unfamiliar territory.

That is generalism in its demanding form: depth somewhere, transferable structure everywhere.

Shannon joined Bell Labs in 1941. During the war he worked on fire-control problems, cryptography and secure communications, including work connected to secure high-level Allied links used by Roosevelt and Churchill. He met Alan Turing when Turing visited Bell Labs in 1943, but they did not form an Enigma-cracking partnership. Shannon's wartime work instead sharpened his thinking about secrecy, coding, signal and noise. His 1949 paper, Communication Theory of Secrecy Systems, grew from a classified 1945 report and helped place cryptography on a rigorous mathematical foundation.

A year earlier came the paper that made Shannon immortal.

In A Mathematical Theory of Communication, Shannon asked an austere question: how much information can a channel carry, and under what conditions can it be transmitted reliably? Building on Harry Nyquist and Ralph Hartley, he formalized information in terms of choices, gave binary information its natural unit, the bit, and used entropy to measure uncertainty. Noise could corrupt a signal. Channel capacity described a limit. Coding could approach that limit.

The meaning of a message was deliberately set aside. A poem, photograph, telephone call and stream of numbers could all be treated as information. That abstraction became foundational to computing, compression, storage, telecommunications, cryptography, the internet and, eventually, modern artificial intelligence.

There is a small modern echo. Reporting in The New Yorker describes it as Anthropic company lore that its model Claude is named partly for Claude Shannon, while also being chosen because Claude sounded like an approachable human name. That degree of uncertainty is worth preserving.

When Information Meets Money

In 1956, Bell Labs physicist John L. Kelly Jr. took Shannon's framework somewhere unexpected. His paper A New Interpretation of Information Rate considered a gambler receiving imperfect information about a favorable wager. The problem was no longer only whether the gambler possessed an edge. It was how much of the bankroll should be committed.

For a simple binary wager, the Kelly fraction can be written as f∗=(bp−q)/bf^*=(bp-q)/b, where pp is the probability of winning, qq the probability of losing and bb the net payoff per unit wagered. With even-money odds and a genuine 60 percent chance of winning, full Kelly would risk 20 percent of capital.

The mathematics points toward a broader discipline. Bet too little and an edge compounds slowly. Bet too much and volatility destroys geometric growth. Extreme overbetting can end the game.

Edward O. Thorp carried the idea from mathematics into casinos and markets. He and Shannon even constructed an early wearable analog computer intended to exploit predictable roulette physics. Thorp later became a pioneering quantitative investor.

Shannon also invested. William Poundstone's Fortune's Formula reports a retrospective estimate of roughly 28 percent annualized for Shannon's stock portfolio from the late 1950s through 1986. That number is a reconstruction, not an audited fund record. A narrower figure is better grounded: Shannon's Teledyne investment is reported to have compounded at about 27 percent annually for 25 years. When asked about Teledyne, Shannon emphasized his judgment of Henry Singleton, his friend and Teledyne's extraordinary capital allocator. The mathematician's explanation came down partly to the quality of a person.

Quantitative sophistication had not eliminated qualitative judgment.

Knight Meets Kelly

Frank Knight had supplied the missing distinction in 1921. In Risk, Uncertainty and Profit, he separated measurable risk from genuine uncertainty, where the probabilities themselves cannot be known with confidence.

In a 2026 Konversation with Kushal episode, Morgan Stanley India's Ridham Desai connected Knight, Shannon and Kelly to an investing idea he has used for years: maximum prospective return can appear near maximum uncertainty. He recalled buying during March 2020, when the pandemic made the range of outcomes unusually wide, then buying more as prices fell.

The phrase belongs to Desai's investing interpretation rather than to Knight as a theorem. Uncertainty can create opportunity because frightened or forced sellers withdraw capital and prices can move farther than long-run business value. It can also accompany permanent destruction. Uncertainty alone offers no edge.

Here Knight and Kelly fit together. Knight describes the world in which probabilities become unreliable. Kelly asks how much to commit when some edge nevertheless exists. Real markets make Kelly especially dangerous because the inputs are estimates. Fat tails, changing correlations, leverage, liquidity and simple human error argue for conservatism, which is why sophisticated practitioners often think in terms of fractional Kelly rather than blindly applying the full formula.

Charlie Munger's latticework of mental models supplies the intellectual architecture. Shannon moved among mathematics, engineering, logic, genetics, cryptography, machines, gambling and investing without becoming a tourist in any of them. Munger's habit of inversion supplies the survival rule: before asking how much can be made, ask what can permanently end the compounding process.

The Founder and the Investor

For a founder, Bell, Edison and Ford suggest three questions before another feature is built. What network makes the product more valuable? What complementary infrastructure must exist for adoption? What part of production or distribution actually constrains scale?

Shannon adds another: what is the deepest bottleneck beneath the visible problem?

Kelly then enters the boardroom. A startup has a finite bankroll. Every hire, launch, acquisition and expansion is a wager made before certainty.

Kelly's business lesson is qualitative: increase commitment as evidence of an edge strengthens, preserve enough capital to survive mistakes, and avoid wagers whose failure eliminates the opportunity to learn. Runway buys experiments; experiments buy information; information can create edge.

For an investor, the discipline can be reduced to four questions: What is the edge? What are the odds? How much should be committed? What happens if the thesis is wrong?

Position sizing can matter as much as security selection. Concentration amplifies genuine insight and mistaken confidence alike. Diversification protects against errors in the estimate of one's own edge. Cash preserves future choices. Rebalancing disciplines exposure. Leverage can remove the time required for a correct thesis to become profitable.

A casino game has written rules and often knowable odds. A company has competitors, management, refinancing risk, technological change and a future that refuses to stay inside a probability table. The presence of fear does not prove undervaluation. Severe uncertainty becomes interesting only when combined with price, financial resilience, business quality, balance-sheet strength, time and some defensible informational or analytical advantage.

The story began with engineers learning to send a voice farther, keep a lamp burning and move a chassis faster. Their institutions eventually produced a man who learned to measure information, and another who asked how much capital an informational advantage deserved.

The question has survived every technology that followed. When the signal is incomplete and the future refuses to become clear, how much can be bet without surrendering the right to hear the next signal?

References and Further Reading:

• Alexander Graham Bell Family Papers, Library of Congress, especially the 1870 to 1879 chronology. Archival material used to verify Bell's patent chronology, the March 10, 1876 call, Elisha Gray's competing filing, Bell's financial backers and the formation of the Bell Telephone Company. Library of Congress Bell chronology

• “Studying Sound: Alexander Graham Bell,” Smithsonian National Museum of American History. Useful institutional history for Bell's work on speech, hearing and the experimental development of the telephone. Smithsonian Bell material

• “History of AT&T Brands,” AT&T. Used for the Bell corporate genealogy, AT&T's creation in 1885, the Bell System breakup and the 2005 SBC acquisition of AT&T Corp. AT&T corporate history

• “Edison Biography,” Thomas Edison National Historical Park, National Park Service. Establishes the distinction between earlier electric lighting experiments and Edison's commercially practical lamp plus integrated electrical system. National Park Service Edison biography

• General Electric historical material on the Edison General Electric and Thomson-Houston merger. Used for the 1892 formation of GE, J. P. Morgan's role, Elihu Thomson and Charles A. Coffin. GE historical account

• GE, 2024 separation materials. Used to distinguish the historical General Electric lineage from today's three independent companies, GE Aerospace, GE Vernova and GE HealthCare. GE Aerospace launch and separation history

• Ford Motor Company historical timeline and “The Moving Assembly Line and the Five-Dollar Workday.” Used to verify Ford Motor Company's 1903 formation, the Model T in 1908, Highland Park's 1913 moving assembly line, assembly-time reductions and the labor context surrounding the $5 day. Ford company timeline

• The Coca-Cola Company historical archive. Used to verify the drink's introduction in 1886, the company's 1892 incorporation and the importance of the later bottling and distribution system. Coca-Cola history

• Nokia Bell Labs, “Our History.” Institutional source for Bell Labs' formal creation in 1925, its research structure and its history of combining fundamental science with communications engineering. Nokia Bell Labs history

• A Mind at Play: How Claude Shannon Invented the Information Age, Jimmy Soni and Rob Goodman, 2017. The principal modern biography used for Shannon's character, intellectual habits, relationship with Vannevar Bush, Bell Labs years and multidisciplinary style. Publisher page for A Mind at Play

• MIT material on Claude E. Shannon, including his biography and doctoral work. Used for Shannon's education, work on Bush's differential analyzer, switching-circuit thesis and subsequent career. MIT News biography of Shannon

• An Algebra for Theoretical Genetics, Claude E. Shannon, MIT doctoral dissertation, 1940. Primary evidence for the surprising genetics episode that followed Bush's encouragement to carry Shannon's mathematical tools into another discipline. MIT archival record of Shannon's dissertation

• “A Mathematical Theory of Communication,” Claude E. Shannon, 1948, Bell System Technical Journal. Primary source. The foundational paper for the article's treatment of information, entropy, channel capacity, noise and coding. Shannon's 1948 paper, Part I

• “Communication Theory of Secrecy Systems,” Claude E. Shannon, 1949, Bell System Technical Journal. Primary source. Used for Shannon's mathematical treatment of cryptography and the connection to his classified wartime research. Shannon's 1949 cryptography paper

• “A New Interpretation of Information Rate,” John L. Kelly Jr., 1956, Bell System Technical Journal. Primary source. The original paper connecting information theory with optimal long-run capital growth under repeated favorable wagers. Kelly's 1956 paper

• “The Invention of the First Wearable Computer,” Edward O. Thorp, 1998. Thorp's own account of his work with Shannon on a miniature roulette-prediction computer and an important bridge from information theory to gambling and quantitative finance. Thorp's paper at UC eScholarship

• Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, William Poundstone, 2005; expanded twentieth-anniversary edition, 2025. Central secondary source for Kelly, Shannon, Thorp, the migration of growth-optimal betting into finance and the retrospective estimate of Shannon's investment record. Macmillan page for Fortune's Formula

• Shannon interviews and profiles from his later life, including the 1987 Omni profile. Used cautiously for Shannon's comments about Teledyne, Henry Singleton and the mixture of mathematical knowledge and personal judgment in his investing. Archived 1987 Shannon profile

• Founders episode #95, “Claude Shannon,” David Senra, October 27, 2019. Senra's reading of A Mind at Play helped illuminate Shannon's working habits, Bush's influence and the practical character of his generalism. Founders episode #95

• Founders episode #428, “How Claude Shannon Worked,” David Senra, August 9, 2026. A later examination of Shannon as both abstract thinker and builder, with particular attention to his habit of reducing difficult problems to their essential structure and moving ideas across disciplines. Founders episode #428

• Risk, Uncertainty and Profit, Frank H. Knight, 1921. Primary source. The intellectual foundation for the distinction between measurable risk and situations in which probabilities themselves cannot be confidently specified. Library of Congress edition of Risk, Uncertainty and Profit

• Konversation with Kushal, episode #333, Kushal Lodha with Ridham Desai, May 22, 2026. Used for Desai's discussion of Shannon, Kelly, position sizing, Knightian uncertainty and the idea that unusually high prospective returns can coexist with maximum uncertainty. Konversation with Kushal episode #333

• Ridham Desai interviews discussing March 2020 and uncertainty, including NDTV Profit, 2026. Used to check Desai's recollection of buying during the pandemic collapse and to separate his formulation about maximum uncertainty from Frank Knight's original language. Ridham Desai interview on uncertainty and markets

• “A Lesson on Elementary, Worldly Wisdom,” Charlie Munger, USC Business School, 1994, and Poor Charlie's Almanack, 2005. Sources for Munger's latticework of mental models and the habit of inversion, used here to connect multidisciplinary reasoning with survival and compounding. Archive of Munger's 1994 worldly wisdom lecture

• Gideon Lewis-Kraus, “What Is Claude? Anthropic Doesn't Know, Either,” The New Yorker, February 2026. The basis for the carefully qualified account that Anthropic company lore partly associates the Claude name with Claude Shannon while also emphasizing its approachable human quality. The New Yorker on Anthropic and the Claude name

p.s. Drafted with assistance from OpenAI. The image was generated using OpenAI as well.