Between 1580 and 2000, decision-makers learned to reason about what had not yet happened. Printed prices, an unfinished game of chance, a London coffee house, a margin of safety and the first venture fund turned records into forecasts. Part 2 follows the Age of Number, and the moment it discovered its own limits.

From Remembering to Calculating

In Part 1 we followed five thousand years of tools that made the basis of a decision outlast the moment of deciding: sealed envelopes, partnership archives, sea loans, ledgers. By 1600, Europe's merchants had all of them. What they lacked was a way to reason about what had not yet happened.

Over the next four centuries, three revolutions supplied it. Information became public and fast, through printed prices, stock exchanges and the telegraph. Chance became calculable, through probability and actuarial science. And value became a model, through present value, security analysis and portfolio theory. Alongside them came quieter inventions that mattered as much: logarithms, the footnote, standard time, the controlled experiment, the structured poll of experts.

We will keep tracking the five pillars of conviction introduced in Part 1: Memory, Evidence, Terms, Challenge and Consensus. The Age of Number extended that power more than any period before it. Its most important lesson, though, came at the end: learning exactly where the numbers stop. Keep the thread from Part 1 in hand as you read. Each invention here brought conviction faster, made the research behind it better, or gave the decision-maker a sharper instrument. The best did all three.

Era I. The Public Price: Print and the Amsterdam Exchange, c. 1580 to 1700

Prices on paper

Our second age opens not with a calculation but with a printing press. For most of history, a price was private knowledge, held by whoever had been in the market that morning. Print changed that. From at least 1585, Amsterdam brokers published weekly price currents, prijscouranten, listing the going rates for hundreds of commodities; the economic historian N.W. Posthumus counted some 12,000 issues between 1585 and 1813. In London, the broker John Castaing began his twice-weekly Course of the Exchange in the late 1690s, listing exchange rates, share prices and government annuities.

Where prices led, numbers followed. In 1582 the Flemish engineer Simon Stevin published Tafelen van Interest, interest tables that bankers had guarded as manuscripts, and three years later he offered "all kinds of merchants" decimal fractions. A printed price or a printed table can be checked by anyone who buys a copy. Print turned Evidence into a public good, and price currents became the market's shared Memory.

The first public company

Public prices invited a public market. In 1602 the Dutch East India Company (VOC) opened its share subscription to any resident of the Republic. In Amsterdam alone, 1,143 investors subscribed about 3.7 million guilders, part of a total capital of roughly 6.4 million. Lodewijk Petram's The World's First Stock Exchange (Columbia University Press, 2014) shows how trading in those shares built the institutions of a modern market, housed from 1611 in a purpose-built exchange on the Rokin.

The innovation that matters here is the continuous price. A tradable share is re-valued every day by everyone willing to buy or sell it. It is Consensus made liquid: a running, public estimate of what the enterprise is worth, revised as news arrives from Asia. No investor before had been able to update a view so quickly, or test it against so many others.

A handbook of confusions

A market that fast soon needed a guidebook. In 1688 Joseph Penso de la Vega, a Sephardic merchant in Amsterdam, published Confusión de Confusiones, a set of dialogues between a philosopher, a merchant and a shareholder. It describes options and forward contracts on VOC shares and, more unusually, the psychology of the traders who used them: their swings between hope and fear, their herding, their certainty.

The era's most famous episode needs correcting. The Dutch tulip mania of 1636 to 1637 is usually told as a ruinous national bubble. Anne Goldgar's archival study Tulipmania (2007) found a small circle of traders, very few bankruptcies and contracts that mostly went unpaid. The legend outlived the data, which is itself a lesson about decision-making: vivid stories travel faster than records.

Napier's shortcut, and the footnote

Two quieter tools complete the picture, one about speed and one about trust. In 1614 John Napier published his tables of logarithms, which turned multiplication into addition; Henry Briggs's base-10 tables followed, and by the 1620s the slide rule put the method in a pocket. Their main users were navigators and astronomers, but the principle reaches every analyst: when calculation becomes cheap, people ask questions they would not have dared to compute.

The second is the footnote. Anthony Grafton's The Footnote: A Curious History (1997) traces how early modern scholars learned to show their sources at the foot of the page, so a reader could follow a claim back to its origin. It is the bulla of Part 1 in a new medium, and the ancestor of every source link in a modern investment memo. Prices were now public and calculation cheap. The next question was harder: what about the things that had not happened yet?

Era II. Taming Chance, 1654 to 1772

The unfinished game

The first answer came from a gaming table. In the summer of 1654, Blaise Pascal and Pierre de Fermat exchanged letters about an old gambling puzzle, the problem of points. Two players stake money on a game of several rounds, and the game is interrupted. How should the pot be split? For centuries, the answers had looked backwards, at the rounds already played. Pascal and Fermat looked forward: they enumerated every way the game could have finished and divided the stakes in proportion to each player's chances. Keith Devlin's The Unfinished Game (2008) calls the exchange the letter that made the world modern.

The shift is the foundation of all valuation. A position is worth what its possible futures are worth, weighted by their likelihood. Three years later Christiaan Huygens published De ratiociniis in ludo aleae (1657), the first printed treatise on the calculus of chance, built around a new concept: expectation.

Gravity and probability

The idea left the gaming table quickly. The Port-Royal Logic of 1662, a widely read textbook by Antoine Arnauld and Pierre Nicole, closed with a rule for everyday decisions: the fear of a harm should be proportional not only to its gravity but also to its probability. Every risk matrix in a modern diligence report, severity on one axis and likelihood on the other, descends from that sentence.

Counting the dead to price the living

The same year, a London haberdasher named John Graunt published Natural and Political Observations upon the Bills of Mortality (1662). From parish records of burials he built the first life table, estimating how many people out of a hundred survive to each age. In 1693 the astronomer Edmond Halley used records from Breslau to build a better table, and used it to price life annuities by age.

This is the birth of actuarial thinking: individual lives are unpredictable, populations are not. In 1762 the Equitable Life Assurance Society opened in London on the plan of the mathematician James Dodson, charging premiums graded by age; in 1775 it appointed William Morgan as its actuary. Risk had become a set of Terms derived from data rather than reputation.

Large numbers, utility and updating

Three more ideas completed the toolkit. Jacob Bernoulli's Ars Conjectandi (1713) proved the law of large numbers: with enough observations, frequencies converge on underlying probabilities. His nephew Daniel Bernoulli, in a 1738 paper on the St Petersburg paradox, argued that people value money by its usefulness to them, not its face amount, so that a rich and a poor man rationally price the same gamble differently. And an essay by the Reverend Thomas Bayes, read to the Royal Society by Richard Price in December 1763, showed how to update a belief as new evidence arrives.

Bayes matters most to investors. Conviction is not fixed at the first meeting; it should move, by a disciplined amount, with every finding in diligence. That is precisely what committees find hardest to do. Updating promptly, and by the right amount, is what speed to conviction really means.

Moral algebra

Not every tool of the era needed mathematics. In September 1772, Benjamin Franklin wrote to the chemist Joseph Priestley, who was agonising over a job offer. Franklin described his "moral or prudential algebra": divide a sheet into pros and cons, list reasons over several days, give each a weight, and strike out reasons of equal weight on opposite sides until the balance is clear. It is a decision tool for a single mind, and its two key moves still hold: spread the deliberation over time, and make the weights explicit. Calculation had arrived; now information had to move fast enough to feed it.

Era III. Networks of Information, 1688 to 1914

The coffee house

At first, information moved at the speed of conversation. In 1688 a coffee house kept by Edward Lloyd on Tower Street in London began to attract ship captains, merchants and the men who underwrote their voyages. It moved to Lombard Street in 1691, and from 1734 published Lloyd's List, a newsletter of shipping movements. Lloyd's own history makes the point plainly: underwriters gathered where the news arrived first.

The medieval underwriters of Part 1 had priced risk on rumour and reputation. Lloyd's industrialised that process. A room where information was shared, argued over and acted on became an institution, and the institution became a market. Shared Memory, made physical.

The Waterloo legend

Fast information breeds legends. Every history of financial information meets the story of Nathan Rothschild, who supposedly learned of Wellington's victory at Waterloo in 1815 before anyone else and made a fortune by misleading the market. Brian Cathcart's The News from Waterloo (2015) and the Rothschild Archive show that the tale grew out of an antisemitic pamphlet of 1846, and that Rothschild was neither first with the news nor made a spectacular profit. Myths of the decisive information edge are more common than the edges themselves. Real advantages were built more slowly, through systems.

Pigeons, cables and tickers

Those systems arrived in quick succession. In April 1850 Paul Julius Reuter used 45 carrier pigeons to carry prices between Aachen and Brussels, bridging a gap in the telegraph line. A transatlantic telegraph cable worked for a few weeks in 1858; a permanent one landed in July 1866. In 1867 Edward Calahan introduced the stock ticker, printing prices on paper tape as they changed. On 18 November 1883, American railroads adopted standard time zones, a quiet coordination technology without which timetables, settlement and simultaneous prices made little sense.

On 26 May 1896, Charles Dow published an average of twelve industrial stocks, standing at 40.94. An index compresses a market into a single number that anyone can follow and compare over time: Evidence condensed to its most portable form.

Pricing character

Information about borrowers needed its own network. In 1841 Lewis Tappan founded the Mercantile Agency in New York, whose local correspondents reported on the character, capital and habits of merchants across the United States. Its ledgers, now held at Harvard's Baker Library, became the foundation of Dun & Bradstreet. Rowena Olegario's A Culture of Credit (2006) shows how such reports turned reputation from local gossip into a national, written record. Henry Varnum Poor's History of the Railroads and Canals of the United States (1860) did the same for the era's largest borrowers, and in 1909 John Moody began assigning letter ratings to railroad bonds.

Inside companies, a parallel revolution was under way. In 1914 Donaldson Brown, an engineer at DuPont, devised the return-on-investment formula that splits profitability into margin and asset turnover, and took it to General Motors in 1921. Alfred Chandler's The Visible Hand (1977) argues that such internal accounting let large firms allocate capital by numbers rather than by proximity to the founder. Capital allocation, for the first time, had a common language. Investors now had fast prices, ratings and accounts. What they lacked was a discipline for turning them into a judgment.

Era IV. The Analyst Is Born, 1921 to 1952

Risk is not uncertainty

That discipline began with a warning. In 1921 two economists drew the line that every investor still lives on. Frank Knight's Risk, Uncertainty and Profit distinguished risk, where outcomes can be assigned probabilities from experience, from uncertainty, where they cannot. Profit, Knight argued, is the reward for bearing the second kind. The same year John Maynard Keynes published A Treatise on Probability, and fifteen years later, in the General Theory (1936), described investors driven by "animal spirits", "a spontaneous urge to action rather than inaction", and markets as a beauty contest in which we "devote our intelligences to anticipating what average opinion expects the average opinion to be".

Knight's distinction is the clearest statement of why the power to decide cannot be handed to a formula. Where the future can be counted, numbers decide. Where it cannot, someone must.

Can forecasters forecast?

If the future could not always be counted, could the forecasters at least be tested? The 1920s produced the first systematic attempts to test investment claims against data. Edgar Lawrence Smith's Common Stocks as Long Term Investments (1924) compared stocks and bonds from 1866 to 1922 and found stocks had done better, a finding Keynes reviewed with interest. In 1933, after the crash, Alfred Cowles III asked a blunter question in the first volume of Econometrica: "Can Stock Market Forecasters Forecast?" He tested 16 financial services, 20 fire insurance companies and 24 publications. The best records, he concluded, could not definitely be attributed to skill.

Cowles had invented the track-record audit. It is the Shang verification inscription of Part 1, rebuilt with statistics, and it remains uncomfortable reading for anyone who forecasts for a living.

The margin of safety

The crash also produced the analyst. In 1934 Benjamin Graham and David Dodd, both teaching at Columbia, published Security Analysis. Its method was to anchor value in facts, in assets, earnings and the terms of each security, rather than in forecasts and market mood. Its central idea was the margin of safety: buy only when the price sits far enough below a conservative estimate of value that errors in the estimate can be absorbed.

The margin of safety is a decision tool disguised as a valuation rule. It admits, in advance, that the analyst's judgment will sometimes be wrong, and builds the error budget into the Terms of the purchase. In The Intelligent Investor (1949), Graham added Mr. Market, the moody partner who offers to buy or sell every day: an invitation to treat the price as information to evaluate, not an instruction to follow.

Value as a discounted future

Graham anchored value in today's facts; economists turned to tomorrow's cash. Irving Fisher's The Theory of Interest (1930) and John Burr Williams's The Theory of Investment Value (1938) formalised the idea Fibonacci had sketched for Pisan merchants in 1202: a security is worth the present value of the cash it will pay. With Pascal's expectation, it completes the logic of the discounted cash flow model. Its power is discipline: every assumption about growth, margins and risk must be written down, where someone else can challenge it.

Diversification as mathematics

One last piece completed the analyst's toolkit. In March 1952, a young University of Chicago graduate student named Harry Markowitz published "Portfolio Selection" in the Journal of Finance. He showed that an investor should judge each asset not alone but by how it moves with the others, and that diversification could be optimised, trading expected return against variance. Merchants had always spread cargo across ships. Markowitz turned the instinct into a calculation, and won the Nobel Prize for it in 1990. By mid-century, investment research had a method. The next challenge was to decide at scale, under uncertainty no method could remove.

Era V. Deciding at Scale, 1940 to 2000

The planes that did not return

The Second World War turned decision-making into a science. In 1942 Columbia University set up the Statistical Research Group to work on military problems, and one of its members, the mathematician Abraham Wald, analysed damage on bombers returning from missions. The intuitive move was to armour the places most often hit. Wald's insight was that the sample was biased: aircraft hit elsewhere had not come back. His memoranda, declassified and published in 1980, are the founding document of what we now call survivorship bias. (The familiar diagrams of bullet holes are later reconstructions; the logic is Wald's.)

For investors, the lesson is permanent. A deal library contains only the deals that reached you; a list of successful founders omits the ones who failed with the same traits. The most important evidence is often the evidence that is missing.

The controlled comparison

Another tool matured in the same decades: the controlled experiment. In 1747 the naval surgeon James Lind had compared six treatments for scurvy among twelve sailors. In 1908 William Gosset, a chemist at the Guinness brewery, published under the pen name "Student" the small-sample test he had devised to judge batches of hops. And in 1948 the British Medical Research Council published its trial of streptomycin for tuberculosis, the landmark randomised controlled trial of modern medicine. The randomised trial is Challenge institutionalised: a procedure designed to stop a researcher's conviction from contaminating the result.

Asking experts properly

Experiments disciplined the evidence; someone still had to discipline the experts. At the RAND Corporation in the early 1950s, Norman Dalkey and Olaf Helmer faced a problem familiar to every investment committee: how to combine expert opinions without letting the loudest or most senior voice dominate. Their answer, published in Management Science in 1963, was the Delphi method. Experts give estimates anonymously, see a summary of the group's answers and reasons, and revise over several rounds. Anonymity removes status. Iteration allows updating. Feedback shares reasoning without social pressure. It is Consensus engineered, rather than assumed. Yet even well-organised experts have limits, and one economist set out to name them.

Satisficing

In a 1955 paper in the Quarterly Journal of Economics, Herbert Simon challenged the economist's model of a perfectly rational chooser. Real decision-makers, he argued, have limited time, attention and computing power, so they search until they find an option that is good enough: they satisfice. Simon won the Nobel Prize in 1978 for his research on decision-making within organisations. In 1971 he added the line that best describes the modern deal team: a wealth of information creates a poverty of attention.

The first venture fund

The era's most consequential experiment in investment judgment began in Boston in 1946, when Georges Doriot, a professor at Harvard Business School, co-founded American Research and Development, the first publicly owned venture capital firm. In 1957 ARD put $70,000 of equity into Digital Equipment Corporation for roughly 70 percent of the company, plus a $30,000 loan. By the time ARD merged into Textron in 1972, the stake had returned more than $400 million. Spencer Ante's biography Creative Capital (2008) tells the story; Doriot's own summary, as Fortune quoted him in 1967, was "I am building men and companies."

Venture capital is Knight's uncertainty made into an asset class. A company with no history has no frequencies to count, and no model can price it alone. What Doriot and his successors built instead were processes: partner meetings, staged financing, reference calls, diligence on people. Arthur Rock financed Fairchild Semiconductor in 1957 and co-founded Davis & Rock in 1961; Sequoia and Kleiner Perkins followed in the early 1970s. Their tools were less mathematical than Markowitz's and no less deliberate: a process for reaching conviction quickly where the data ran out.

What the Age of Number Taught Us

Four centuries of numbers gave the power to decide new instruments at every pillar, and made each of them faster, better researched and easier to share.

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The era also created two new ways to fail. The first was false precision: a model can be so elegant that its users forget it rests on assumptions, and that Knight's uncertainty lies outside it. The second was the forgotten decision-maker. From Bernoulli to Markowitz, the theories assumed a rational chooser who weighs probabilities and utilities consistently. Simon had warned that real people do not. Nobody yet knew how far they departed, or in which direction.

In September 1974, two Israeli psychologists, Amos Tversky and Daniel Kahneman, published a short article in Science titled "Judgment under Uncertainty: Heuristics and Biases". It turned the scientific instruments of the Age of Number on the people using them. The question was no longer only how to calculate the future, but how to protect the power to decide from its own systematic errors. That is where Part 3, The Age of Judgment, begins.

References and Further Reading

Print, prices and the Amsterdam exchange

1. Posthumus, N.W. Nederlandsche Prijsgeschiedenis (1943); dataset: Posthumus commodity prices, Rutgers MEMDB
2. John Castaing, Huguenots of Spitalfields
3. MacTutor. Simon Stevin, University of St Andrews
4. Petram, L. The World's First Stock Exchange (Columbia University Press, 2014)
5. Cardoso, J.L. "Confusión de Confusiones: Ethics and Options on Seventeenth-Century Stock Exchange Markets", Financial History Review 9(2), 2002
6. Goldgar, A. Tulipmania (University of Chicago Press, 2007); review, IHR Reviews in History
7. Logarithms celebrate their 400th birthday, Science News, 2014
8. Grafton, A. The Footnote: A Curious History (Harvard University Press, 1997)

Probability and actuarial science

9. Devlin, K. The Unfinished Game (Basic Books, 2008)
10. Encyclopedia of Mathematics. Christiaan Huygens
11. Stanford Encyclopedia of Philosophy. Port Royal Logic
12. Britannica. John Graunt
13. University of Glasgow. Equitable Life and early actuarial records
14. Bernoulli, D. "Specimen theoriae novae de mensura sortis" (1738)
15. Franklin, B. Letter to Joseph Priestley, 19 September 1772, Founders Online

Information networks

16. Lloyd's. History, Chapter One
17. Cathcart, B. The News from Waterloo (Faber, 2015); Nathan Rothschild and Waterloo, The Rothschild Archive
18. Reuters history, The Baron
19. Union Pacific Railroad Museum. Standard Time
20. Dow Jones Industrial Average first published, HistoryofInformation.com
21. Baker Library, Harvard Business School. R.G. Dun & Co. credit report volumes; Olegario, R. A Culture of Credit (Harvard University Press, 2006)
22. Hagley Museum and Library. The father of ROI: Donaldson Brown; Chandler, A.D. The Visible Hand (Harvard University Press, 1977)

The analyst

23. Knight, F. Risk, Uncertainty and Profit (1921)
24. Keynes, J.M. The General Theory, chapter 12 (1936)
25. Cowles, A. "Can Stock Market Forecasters Forecast?", Econometrica 1(3), 1933
26. Columbia Business School, Heilbrunn Center. History of value investing; Graham, B. and Dodd, D. Security Analysis (1934)
27. Rubinstein, M. "Great Moments in Financial Economics: I. Present Value", Journal of Investment Management, 2003
28. Nobel Prize. Economic Sciences 1990 press release (Markowitz, Miller, Sharpe)

Deciding at scale

29. American Mathematical Society. "The Legend of Abraham Wald", Feature Column, 2016
30. The genius at Guinness and his statistical legacy, The Conversation
31. James Lind Library. MRC streptomycin trial, 1948
32. Dalkey, N. and Helmer, O. "An Experimental Application of the Delphi Method to the Use of Experts", Management Science 9(3), 1963
33. Simon, H.A. "A Behavioral Model of Rational Choice", Quarterly Journal of Economics 69(1), 1955
34. Baker Library, Harvard Business School. Doriot and DEC; Ante, S. Creative Capital (Harvard Business Press, 2008)
35. Computer History Museum. Fairchild and the Fairchildren

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