The Deficit Myth: The Biggest Lie in Politics

 

Free Market Ideology and Alternate Economic Systems

How does an ideological commitment to free market principles influence the consideration of alternative economic systems?

An ideological commitment to free market principles can significantly influence how alternative economic systems are considered. Here's a simple explanation using examples and quotes:

1. Emphasis on Market Efficiency: Ideological commitment to free market principles prioritizes market efficiency as a key driver of economic success. This perspective holds that the decentralized decision-making of individuals and businesses, guided by market forces, leads to efficient allocation of resources and optimal outcomes.

Example: "Advocates of free market principles argue that allowing market forces to determine prices, wages, and production levels leads to efficient resource allocation. They believe that alternative economic systems, such as central planning, may suffer from inefficiencies due to the lack of market signals."

2. Skepticism of State Intervention: A commitment to free market principles often fosters skepticism toward extensive state intervention in the economy. It emphasizes the belief that government interference can hinder market efficiency, impede individual freedom, and lead to unintended consequences.

Example: "Those who strongly support free markets view excessive government regulations and interventions as burdensome. They argue that alternative economic systems relying heavily on central planning may stifle innovation, discourage entrepreneurship, and limit individual choices."

Quotation: "The problem with socialism is that you eventually run out of other people's money." - Margaret Thatcher

This quote, attributed to former British Prime Minister Margaret Thatcher, reflects the skepticism toward alternative economic systems that rely heavily on state intervention. It implies that such systems may struggle to sustain themselves without adequate resources generated by market-oriented economies.

3. Focus on Individual Liberty and Choice: Ideological commitment to free market principles often places a strong emphasis on individual liberty, economic freedom, and the right to private property. It asserts that free markets provide individuals with the freedom to make their own economic decisions and engage in voluntary exchanges.

Example: "Supporters of free market principles argue that alternative economic systems, which involve greater government control, can infringe upon individual liberties and limit economic choices. They believe that market-oriented systems provide individuals with the opportunity to pursue their own goals and fulfill their economic aspirations."

An ideological commitment to free market principles can strongly influence the consideration of alternative economic systems, shaping the evaluation in several ways. However, it's essential to recognize both the strengths and weaknesses of this perspective:

Strengths:

1. Market Efficiency: The emphasis on market efficiency highlights the potential benefits of allowing market forces to guide resource allocation. Free market principles can incentivize competition, innovation, and productivity, leading to economic growth.

2. Individual Freedom: A commitment to free markets emphasizes individual liberty and economic freedom. It recognizes the importance of individual choices and the potential for entrepreneurship and self-determination.

3. Innovation and Adaptability: Free market systems often exhibit a high degree of innovation and adaptability, responding quickly to changing consumer demands and technological advancements.

Weaknesses:

1. Market Failures: An exclusive focus on free markets may overlook market failures, such as externalities, monopolies, or inadequate provision of public goods. These market failures can have adverse consequences and require government intervention to address.

2. Income Inequality: Unrestricted free markets can contribute to income inequality, as wealth accumulation is not distributed evenly. This disparity may result in social and economic divisions that require policy interventions to ensure fairness.

3. Systemic Risks: Unregulated markets can also be susceptible to systemic risks, such as financial crises or market instability. Some level of government oversight may be necessary to mitigate these risks and protect the broader economy.

Evaluation:

While an ideological commitment to free market principles brings several strengths, such as market efficiency and individual freedom, it's important to approach alternative economic systems with an open mind. Evaluating alternative systems should consider a range of factors, including economic efficiency, equity, stability, and the provision of public goods.

Quotation: "A system of free enterprise capitalism hinges on two main assumptions: rational individuals and efficient markets. Neither assumption is entirely realistic." - Alan S. Blinder

This quote highlights the importance of acknowledging the limitations of any economic system, including free markets. It suggests that a balanced evaluation should consider both the strengths and weaknesses of various economic models.

To ensure an effective evaluation, it is crucial to strike a balance between market mechanisms and appropriate government interventions. Recognizing the potential advantages of free markets while addressing their limitations through regulation and social safety nets can help achieve a more equitable and sustainable economic system.

Ultimately, a comprehensive evaluation should take into account the diverse needs and goals of society, balancing economic efficiency, social welfare, and the pursuit of individual freedoms within a broader framework of societal well-being.

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Ideological biases can indeed undermine the examination of empirical evidence and case studies that challenge the supremacy of the market system. Here's an exploration using examples, quotes, and simple language:

1. Confirmation Bias: Ideological biases can lead individuals to seek and interpret evidence in a way that confirms their preexisting beliefs. This confirmation bias may prevent them from critically examining empirical evidence or case studies that challenge the supremacy of the market system.

Example: A staunch advocate of free markets may dismiss empirical studies highlighting market failures or negative consequences of unregulated capitalism, instead favoring evidence that supports their ideological position.

2. Dismissal of Alternative Models: Ideological biases can create a tendency to dismiss or downplay empirical evidence and case studies that demonstrate the effectiveness of alternative economic models. This can hinder a comprehensive examination of diverse approaches.

Example: A fervent supporter of market supremacy may reject case studies that showcase successful mixed economies or government interventions in achieving positive outcomes, undermining the examination of alternative models.

Quotation: "It is difficult to get a man to understand something when his salary depends on his not understanding it." - Upton Sinclair

This quote by Upton Sinclair highlights how personal interests and ideological biases can hinder individuals from objectively examining evidence that challenges their beliefs. In the context of economics, those whose livelihood or influence depends on the market system's supremacy may be more resistant to considering alternative models.

3. Cherry-picking Data: Ideological biases can lead to selective use of data, focusing only on information that supports the market system while ignoring or dismissing contradictory evidence. This cherry-picking approach undermines a balanced examination of empirical evidence.

Example: An ideologically biased individual may highlight economic success stories under free market systems while disregarding instances of market failures or negative social consequences associated with unregulated capitalism.

It's important to note that overcoming ideological biases and fostering a more open examination of empirical evidence and case studies is crucial for a robust and informed economic discourse. By considering a wide range of evidence, including studies and examples that challenge prevailing beliefs, we can gain a more nuanced understanding of economic systems and their real-world impacts.

The goal should be to approach empirical evidence and case studies with intellectual honesty and a willingness to critically evaluate findings, regardless of whether they align with our ideological biases. Only through this objective examination can we foster a more comprehensive understanding of economic systems and strive towards the development of effective and equitable economic policies.

Principles for Dealing with the Changing World Order

 

Time for a great reset of the financial system

A 30-year debt supercycle that has fuelled inequality illustrates the need for a new regime writes CHRIS WATLING in The FT 

On average international monetary systems last about 35 to 40 years before the tensions they create becomes too great and a new system is required. 

Prior to the first world war, major economies existed on a hard gold standard. Intra-wars, most economies returned to a “semi-hard” gold standard. At the end of the second world war, a new international system was designed — the Bretton Woods order — with the dollar tied to gold, and other key currencies tied to the dollar. 

When that broke down at the start of the 1970s, the world moved on to a fiat system where the dollar was not backed by a commodity, and was therefore not anchored. This system has now reached the end of its usefulness. 

An understanding of the drivers of the 30-year debt supercycle illustrates the system’s tiredness. These include the unending liquidity that has been created by the commercial and central banks under this anchorless international monetary system. That process has been aided and abetted by global regulators and central banks that have largely ignored monetary targets and money supply growth. 

The massive growth of mortgage debt across most of the world’s major economies is one key example of this. Rather than a shortage of housing supply, as is often postulated as the key reason for high house prices, it’s the abundant and rapid growth in mortgage debt that has been the key driver in recent decades. 

This is also, of course, one of the factors sitting at the heart of today’s inequality and generational divide. Solving it should contribute significantly to healing divisions in western societies. 

With a new US administration, and the end of the Covid battle in sight with the vaccination rollout under way, now is a good time for the major economies of the west (and ideally the world) to sit down and devise a new international monetary order. 

As part of that there should be widespread debt cancellation, especially the government debt held by central banks. We estimate that amounts to approximately $25tn of government debt in the major regions of the global economy. 

Whether debt cancellation extends beyond that should be central to the negotiations between policymakers as to the construct of the new system — ideally it should, a form of debt jubilee. 

The implications for bond yields, post-debt cancellation, need to be fully thought through and debated. A normalisation in yields, as liquidity levels normalise, is likely. 

High ownership of government debt in that environment by parts of the financial system such as banks and insurers could inflict significant losses. In that case, recapitalisation of parts of the financial system should be included as part of the establishment of the new international monetary order. Equally, the impact on pension assets also needs to be considered and prepared for. 

Secondly, policymakers should negotiate some form of anchor — whether it’s tying each other’s currencies together, tying them to a central electronic currency or maybe electronic special drawing rights, the international reserve asset created by the IMF. 

As highlighted above, one of the key drivers of inequality in recent decades has been the ability of central and commercial banks to create unending amounts of liquidity and new debt.

This has created somewhat speculative economies, overly reliant on cheap money (whether mortgage debt or otherwise) that has then funded serial asset price bubbles. Whilst asset price bubbles are an ever-present feature throughout history, their size and frequency has picked up in recent decades. 

As the Fed reported in its 2018 survey, every major asset class over the 20 years from 1997 through to 2018 grew on average at an annual pace faster than nominal GDP. In the long term, this is neither healthy nor sustainable. 

With a liquidity anchor in place, the world economy will then move closer to a cleaner capitalist model where financial markets return to their primary role of price discovery and capital allocation based on perceived fundamentals (rather than liquidity levels). 

Growth should then become less reliant on debt creation and more reliant on gains from productivity, global trade and innovation. In that environment, income inequality should recede as the gains from productivity growth become more widely shared. 

The key reason that many western economies are now overly reliant on consumption, debt and house prices is because of the set-up of the domestic and international monetary and financial architecture. A Great Reset offers therefore opportunity to restore (some semblance of) economic fairness in western, and other, economies.

Are poor countries poor because of their poor people? Economic History in Small Doses 5

Girish Menon*

A bus driver in Mumbai gets paid around Rs.50 per hour whereas his equivalent in Cambridge gets paid £12 per hour. Using currency exchange rates, the Cambridge driver gets paid 24 times more than his Indian equivalent. Does that mean John the Cambridge driver is 24 times more productive than Om? If anything, Om would likely be a much more skilled driver than John because Om has to negotiate his way through bullock carts, rickshaws, bicycles and cows on the street.

The main reason why John is paid 24 times more than Om is because of protectionism. Some, British workers are protected from competition from workers in India, and soon from the EU, through immigration control.  (Technology has erased this protectionism in the relocation of many white collar jobs.) This form of protectionism goes unmentioned in the WTO (World Trade Organization) as countries raise their barriers to immigration of poor workers.

 Many people think that poor countries are poor because of their poor people. The rich people in poor countries typically blame their countries’ poverty on the ignorance, laziness and passivity of the poor. Arithmetically too, it is true that poor people pull down the national income average because of their large numbers.

 Little do the rich people in poor countries realize that their countries are poor not because of the poor but because of themselves. The primary reason why John is paid 24 times more than Om is because John works in a labour market with other people who are way more than 24 times more productive than their Indian counterparts. The top managers, scientists and engineers in the UK are hundreds of times more productive than their Indian equivalents, so the UK’s national productivity ends up being in the region of 24 times that of India.

In other words, poor people from poor countries are usually able to hold their own against counterparts in rich countries. It is the rich from the poor countries who cannot do that. It is their relative low productivity that makes their country poor. So, instead of blaming their own poor for dragging the country down, the rich of the poor countries should ask themselves why they cannot pull up the productivity and innovation in their own country,

Of course, the rich in rich countries need not get smug. They are beneficiaries of economies with better technology, better organized firms, better institutions and better physical infrastructure. Warren Buffet expressed it best:

 “I personally think that society is responsible for a very significant percentage of what I’ve earned. If you stick me down in the middle of Bangladesh or Peru or someplace, you’ll find out how much this talent is going to produce in the wrong kind of soil. I will be struggling thirty years later. I work in a system that happens to reward what I do well – disproportionately well.”

 

* Adapted from 23 Things they don’t tell you about Capitalism by Ha Joon Chang

India Business Role Models are Outed as System Manipulators

We tell ourselves we choose our own life course, but is this ever true? The role of universities and advertising explored

By abetting the ad industry, universities are leading us into temptation, when they should be enlightening us writes George Monbiot in The Guardian

 

To what extent do we decide? We tell ourselves we choose our own life course, but is this ever true? If you or I had lived 500 years ago, our worldview, and the decisions we made as a result, would have been utterly different. Our minds are shaped by our social environment, in particular the belief systems projected by those in power: monarchs, aristocrats and theologians then; corporations, billionaires and the media today.

Humans, the supremely social mammals, are ethical and intellectual sponges. We unconsciously absorb, for good or ill, the influences that surround us. Indeed, the very notion that we might form our own minds is a received idea that would have been quite alien to most people five centuries ago. This is not to suggest we have no capacity for independent thought. But to exercise it, we must – consciously and with great effort – swim against the social current that sweeps us along, mostly without our knowledge. 

----Also Watch

The Day The Universe Changed

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Surely, though, even if we are broadly shaped by the social environment, we control the small decisions we make? Sometimes. Perhaps. But here, too, we are subject to constant influence, some of which we see, much of which we don’t. And there is one major industry that seeks to decide on our behalf. Its techniques get more sophisticated every year, drawing on the latest findings in neuroscience and psychology. It is called advertising.
Every month, new books on the subject are published with titles like The Persuasion Code: How Neuromarketing Can Help You Persuade Anyone, Anywhere, Anytime. While many are doubtless overhyped, they describe a discipline that is rapidly closing in on our minds, making independent thought ever harder. More sophisticated advertising meshes with digital technologies designed to eliminate agency.

Earlier this year, the child psychologist Richard Freed explained how new psychological research has been used to develop social media, computer games and phones with genuinely addictive qualities. He quoted a technologist who boasts, with apparent justification: “We have the ability to twiddle some knobs in a machine learning dashboard we build, and around the world hundreds of thousands of people are going to quietly change their behaviour in ways that, unbeknownst to them, feel second-nature but are really by design.”

The purpose of this brain hacking is to create more effective platforms for advertising. But the effort is wasted if we retain our ability to resist it. Facebook, according to a leaked report, carried out research – shared with an advertiser – to determine when teenagers using its network feel insecure, worthless or stressed. These appear to be the optimum moments for hitting them with a micro-targeted promotion. Facebook denied that it offered “tools to target people based on their emotional state”.

We can expect commercial enterprises to attempt whatever lawful ruses they can pull off. It is up to society, represented by government, to stop them, through the kind of regulation that has so far been lacking. But what puzzles and disgusts me even more than this failure is the willingness of universities to host research that helps advertisers hack our minds. The Enlightenment ideal, which all universities claim to endorse, is that everyone should think for themselves. So why do they run departments in which researchers explore new means of blocking this capacity?

 ‘Facebook, according to a leaked report, developed tools to determine when teenagers using its network feel insecure, worthless or stressed.’ Photograph: Alamy Stock Photo

I ask because, while considering the frenzy of consumerism that rises beyond its usual planet-trashing levels at this time of year, I recently stumbled across a paper that astonished me. It was written by academics at public universities in the Netherlands and the US. Their purpose seemed to me starkly at odds with the public interest. They sought to identify “the different ways in which consumers resist advertising, and the tactics that can be used to counter or avoid such resistance”.

Among the “neutralising” techniques it highlighted were “disguising the persuasive intent of the message”; distracting our attention by using confusing phrases that make it harder to focus on the advertiser’s intentions; and “using cognitive depletion as a tactic for reducing consumers’ ability to contest messages”. This means hitting us with enough advertisements to exhaust our mental resources, breaking down our capacity to think.

Intrigued, I started looking for other academic papers on the same theme, and found an entire literature. There were articles on every imaginable aspect of resistance, and helpful tips on overcoming it. For example, I came across a paper that counsels advertisers on how to rebuild public trust when the celebrity they work with gets into trouble. Rather than dumping this lucrative asset, the researchers advised that the best means to enhance “the authentic persuasive appeal of a celebrity endorser” whose standing has slipped is to get them to display “a Duchenne smile”, otherwise known as “a genuine smile”. It precisely anatomised such smiles, showed how to spot them, and discussed the “construction” of sincerity and “genuineness”: a magnificent exercise in inauthentic authenticity.

Facebook told advertisers it can identify teens feeling 'insecure' and 'worthless'


Another paper considered how to persuade sceptical people to accept a company’s corporate social responsibility claims, especially when these claims conflict with the company’s overall objectives. (An obvious example is ExxonMobil’s attempts to convince people that it is environmentally responsible, because it is researching algal fuels that could one day reduce CO2 – even as it continues to pump millions of barrels of fossil oil a day). I hoped the paper would recommend that the best means of persuading people is for a company to change its practices. Instead, the authors’ research showed how images and statements could be cleverly combined to “minimise stakeholder scepticism”.

A further paper discussed advertisements that work by stimulating Fomo – fear of missing out. It noted that such ads work through “controlled motivation”, which is “anathema to wellbeing”. Fomo ads, the paper explained, tend to cause significant discomfort to those who notice them. It then went on to show how an improved understanding of people’s responses “provides the opportunity to enhance the effectiveness of Fomo as a purchase trigger”. One tactic it proposed is to keep stimulating the fear of missing out, during and after the decision to buy. This, it suggested, will make people more susceptible to further ads on the same lines.

Yes, I know: I work in an industry that receives most of its income from advertising, so I am complicit in this too. But so are we all. Advertising – with its destructive impacts on the living planet, our peace of mind and our free will – sits at the heart of our growth-based economy. This gives us all the more reason to challenge it. Among the places in which the challenge should begin are universities, and the academic societies that are supposed to set and uphold ethical standards. If they cannot swim against the currents of constructed desire and constructed thought, who can?

Narendra Modi is a fraud

Markandey Katju - former Indian Supreme Court judge

Risk models must be torn up, says Bank of England's Haldane

Financial risk models that underpin market behaviour, economic theory and bank regulation dangerously underestimate the threat to taxpayers and must be completely redrawn to prevent a repeat of the financial crisis, a leading policymaker has warned.
 

The Bank of England's Andrew Haldane has called for economists to re-think what they mean by "normal" 

 

By Philip Aldrick, Economics Editor

11:46AM BST 08 Jun 2012

57 Comments

 

Andrew Haldane, executive director for financial stability at the Bank of England, said the crisis provided compelling proof that “catastrophe risk” has been totally mis-priced. “That was a key fault-line during the crisis and, as recent experience attests, remains a key fault-line today,” he said in a paper at the University of Edinburgh Business School.

If taxpayers are to be protected in future, financial regulators must put “in place robust fail-safes to stop chaos emerging”, such as UK plans to ringfence banks’ retail operations or US proposals to ban casino-like proprietary trading.

Such “structural safeguards on worst-case outcomes” need to be accompanied by a massive increase in the “array of financial data available to regulators” provided by banks, he added. The extra information would allow regulators to build a “systemic risk map” not unlike a weather forecast that could “provide early warnings to enable defensive actions to be taken”.

“In a complex, uncertain environment, the only fail-safe way of protecting against systemic collapse is to act on the structure of the overall system, rather than the behaviour of each individual within it,” he said. “Until then, normal service is unlikely to resume.”

In a wide-ranging piece of research that sourced evidence not just from economics but from physics, biology and even behaviour on Twitter, Mr Haldane argued that the orthodox models used to measure risk overstate “normality” and underestimate the costs and probability of “catastrophe”.

To make the financial system safer, they need to be torn up, he said in the paper, co-authored with Bank economist Benjamin Nelson.

“The economics profession has for much of the 20th century been bewitched by normality. Real business cycle theory in economics and efficient markets theory in finance bear the tell-tale signs of this intellectual infatuation,” he said. “Over the past five years, the real world has behaved in ways which make a monkey of these theories.”

Changing the dangerous consensus “will require a fairly fundamental re-think of the foundations of modern-day economics, finance and econometrics”, Mr Haldane added.

Popular models that underpin banks’ risk management, such as Value-at-Risk (VaR), Black-Scholes and Vasicek, underprepare directors and regulators for a “fat tail”, or catastrophe event.

Citing studies of actuarial models used in insurance, Mr Haldane said “fat tails... would be expected to occur approximately once every 800 years for GDP and once every 64 years for equities”. “In reality, for GDP it appears to occur roughly once every century, for equities once every eight years.”

Regulatory risk measurements using the Vasicek model underestimate capital requirements by between 20pc and 85pc compared with a proper analysis of the past three centuries, he added. He cited JP Morgan’s recent $2bn trading loss as an example of the failure of VaR.

Changing the accepted wisdom on how to calculate risk is more important now than ever before, he added. “As the world becomes increasingly integrated – financially, economically, socially – interactions among the moving parts may make for potentially fatter tails. Catastrophe risk may be on the rise."

Why we need more banker bashing

Banks are the biggest scroungers of public money – solutions will not simply materialise if we don't keep up the pressure

• 
• • Sunny Hundal
  • guardian.co.uk, Tuesday 7 February 2012 10.15 GMT

Bank-bashing is in its third year and has become even more vociferous. Photograph: Martin Godwin

 

I have a confession to make: I wanted to be a banker once. While arming myself with a degree in economics, I dreamed of working at an investment bank arranging mergers and acquisitions. The growing size of M&A activity got us budding economists excited and I wanted a part of the action. But the dotcom boom of the late 90s lured me in instead and I missed out on the opportunity to ruin the world's economy. In a sign of the times, when I asked a university mate recently where he worked now, he replied: "Goldm- *cough* -acks" rather haphazardly. It seems not many want to be associated with the "great vampire squid" any more.

Banker bashing has now entered its third year and become even more vociferous, spreading to bonus bashing thanks to Network Rail. Last week columnists at the Times and Financial Times wailed that all this a) was hurting UK's economic prospects and b) would have limited traction with the public. The second excuse is easy to dismiss: actually there is plenty of public appetite for banker bashing to continue. They want more and they don't think it damages our economic prospects. But is it right to continue this, ask critics? Who will think of the [privately educated] children? Let me offer several reasons to continue banker bashing.

First, banking reform has been pitifully weak. If the crash were to happen again tomorrow, the government would have to bail them out again. They remain leveraged up to their eyeballs; remain "too big to fail" and too inter-connected to each other so most can't be allowed to go bust. Without public anger there is no impetus to push banking reforms further, which the Conservatives are stridently resisting and Labour is still reluctant to push too far.

Secondly, the banker bashing begs a wider question – if finance has become the life-blood of modern economies, why can't we exercise more control over such a vital industry? Consider this: we pretend that banks are private businesses that should be allowed to run their own affairs. But they are the biggest scroungers of public money of our time. Banks are lent vast sums of money by central banks at near-zero interest. They lend that money to us or back to the government at higher rates and rake in the difference by the billion. They don't even have to make clever investments to make huge profits.
At the height of the crash, US banks were simply given $13bn overnight. No repayment needed. We don't know what happened, because the details are kept secret. The entire industry is underwritten by guarantees from central banks. If threatened with systematic failure, which is becoming increasingly common, governments have no option but to bail them out. The financial system rules over our lives too, through our credit history. Everything could be choked off at a whim, through administrative error or for political reasons, and we wouldn't have democratic recourse. Organisations such as WikiLeaks were simply frozen out of the global financial system at the click of a button. Banks get special preferences like no other industry, and yet we don't even ask why these publicly subsidised yacht owners have so much control over our lives. Why not?

Far from being the pinnacle of free market capitalism, banking is full of sorry executives who keep asking for more handouts to protect their deliberately bloated businesses. The solutions won't materialise if we go back to how things were. Public anger has grown because it is starting to dawn on middle England that while the rest of us are paying for the crisis, the people who caused the crash want to go back to 2007. Even the Daily Mail is starting to reflect this impatience. This recession is already longer than the 1930s and the stagnation will continue for maybe a decade. For from being over, the nightmare for the Goodwins and Hesters is just getting started. And quite rightly too.

Pick a Card, Any Card

• DECEMBER 10, 2011 The Wall Street Journal

By ALEX STONE

The standard way to mix a deck of playing cards—the one used everywhere from casinos to rec rooms—is what is known as a riffle (or "dovetail") shuffle. You begin by splitting the deck into two roughly equal stacks. Then you flick the cards with your thumbs off the bottoms of the piles in alternating fashion, interleaving the two stacks.

For games like blackjack or poker to be truly fair, the order of the cards must be completely random when the game begins. Otherwise a skilled cheat can exploit the lack of randomness to gain an advantage over other players.

How many riffle shuffles does it take to adequately mix a deck of 52 playing cards?

Francesco Abrignani/Alamy

As it turns out, you have to shuffle seven times before a deck becomes truly scrambled. Not only that, the cards become mixed in a highly unusual way: The amount of randomness in the deck does not increase smoothly. The first few shuffles do little to disturb the original order, and even after six shuffles, you can still pick out distinctly non-random patches.

But right around the seventh shuffle something remarkable happens. Shuffling hits its tipping point, and the cards rapidly decay into chaos.

Magical Mathematics

By Persi Diaconis and Ron Graham
Princeton, 244 pages, $29.95

The seven-shuffles finding applies to messy, imperfect riffle shuffles. The deck might not be divided exactly in half, for instance, or the cards might be riffled together in a haphazard way. Far from undesirable, a little sloppiness is actually the key to a random shuffle.

A perfect (or "faro") shuffle, meanwhile, wherein the deck is split precisely in half and the two halves are zippered together in perfect alternation, isn't random at all. In fact, it's completely predictable. Eight perfect shuffles will return a 52-card deck to its original order, with every card cycling back to its starting position.
And this doesn't just work for 52 cards. A deck of any size will eventually return to its starting order after a finite sequence of faro shuffles, although the number of faros required isn't always eight—and doesn't increase linearly. If you have 104 cards, for instance, it takes 51 faros to restore the deck. For a thousand cards, it takes 36.

These findings are among the many fascinating results explored in "Magical Mathematics," a dazzling tour of math-based magic tricks. The authors, Persi Diaconis and Ron Graham, are distinguished mathematicians with high-powered academic pedigrees. Both are also accomplished magicians who have taught courses on mathematical magic at Harvard and Stanford.

Mr. Diaconis has an especially unusual résumé for a mathematician. In 1959, at age 14, he ran away from home to study with the great 20th-century sleight-of-hand master Dai Vernon—a man who once fooled Harry Houdini with a card trick. After spending 10 years under Vernon's tutelage, Mr. Diaconis returned home to New York and enrolled in night school, eventually earning a full ride to a Ph.D. program in mathematics at Harvard.

The book's title may strike some people as odd in its pairing of magic and math, but the two subjects share a common lineage that goes back centuries. In fact, some of the earliest recorded magic tricks were based in math. Fibonacci's 1202 manuscript "Liber Abaci," the foundation of modern arithmetic, contains a number of magic tricks, including several versions of the famous three-object divination, wherein a spectator mentally selects one of three objects and the magician correctly identifies the spectator's choice.

The earliest recorded card tricks, meanwhile, appear in a math text written around 1500 by a Tuscan friar who was close friends with Leonardo da Vinci. And one of the first magic manuals was compiled in the 17th century by Claude Gaspard Bachet de Méziriac, an early number theorist.

Player/Alamy

But mathematical magic truly came of age in the 20th century, with the growth of magic as a mainstream hobby. "In the past hundred years, a revolution has taken place," the authors write, citing the thousands of math-based magic tricks now in circulation.

In their breezy yet authoritative book, Messrs. Diaconis and Graham showcase some of the genre's best creations as well as many new ones of their own devising. Included are tricks with coins and cards (the reader will want to have a deck handy), a divination routine that employs the I Ching—the 5,000-year-old Chinese fortune-telling book—and, my personal favorite, a gambling demonstration in which the spectator shuffles a deck of cards but somehow still manages to deal himself a royal flush in spades.

This last effect exploits something known as the Gilbreath Principle, a beautiful property discovered in the 1950s by a mathematician who worked for many years at the Rand Corp. Take a deck of cards and arrange it in alternating red-black order. Now deal half of the deck facedown into a pile—thus reversing its order—and riffle shuffle the two piles together. Finally, deal the cards face up in pairs.

Each pair will contain one red and one black card (though not necessarily in alternating order). This is the Gilbreath Principle. This same idea applies to any repeating pattern of cards. If, for instance, the deck is arranged so that the cards cycle through the four suits—clubs, hearts, spades, diamonds, clubs, hearts, spades, diamonds, and so on throughout the deck—and the same procedure is executed, then every four cards dealt off the top will contain a complete set of suits. This result, combined with a few clever subtleties, is the basis of the royal-flush effect.

All the tricks in "Magical Mathematics" are of the "self-working" variety—meaning they require little or no physical skill—and while a grasp of the underlying mathematics is helpful, it is by no means a necessity. Even math-phobes will be able to astound audiences by simply following the directions and consulting the many full-color illustrations provided throughout the text.

The mixing of magic and math is more than just a means to new tricks. It has also spawned a host of major mathematical breakthroughs. "Some magic tricks use 'real mathematics' and lead to questions beyond the limits of modern mathematics," the authors write. "Sometimes, we have been able to solve the math problems."

The seven-shuffles result is one such solution. Mr. Diaconis became interested in the math of shuffling after he encountered a card trick published in the early part of the 20th century by Charles Jordan, a chicken farmer and champion puzzle solver who invented several groundbreaking card tricks. In this particular effect—called "Long Distance Mind Reading," because it could be performed through the mail—the spectator shuffles before and after picking a card, but the magician still finds his selection.

Mr. Diaconis realized that for the trick to work shuffling had to be less effective than people generally assumed. While at Harvard, he teamed up with a mathematician named David Bayer and the two undertook a theoretical analysis, building on work done at Bell Labs in the 1950s. Their landmark 1992 paper—"Trailing the Dovetail Shuffle to its Lair"—rigorously proved that anything less than seven shuffles is inadequate. Not only that, their results had implications for a wide class of "mixing" phenomena—from stirring cake batter to compounding chemicals.

Similarly, the remarkable "looping" property of perfect shuffles is a facet of group theory—a branch of abstract mathematics that deals with, among other things, symmetric structures. Group theory has applications to chemistry, biology and, most notably, physics, where it provides the mathematical framework for the Standard Model—the overarching theory of subatomic particles and forces.

There's also a deep link between the perfect shuffle and the binary number system—the universal language of modern computing. To appreciate the connection, you first have to understand that there are two ways to do a faro. You can either weave the cards together so that the top and bottom cards stay in place—this is called an "out-faro"—or you can do what is known as an in-faro, in which the top and bottom cards each move inward by one card.

Now let's say that the ace of spades is on top, and you want to move 25 cards above it, so that the ace will be 26th from the top. The sequence of faros required to bring about this arrangement can be found by writing the number 25 in binary notation, like this: 11001. For each 1, you do an in-faro, and for each 0 you perform an out-faro. In this case, you would do two in-faros (11), followed by two outs (00) and, lastly, one more in (1).

Shuffling is one example of something seemingly ordinary that subtends an elegant mathematical structure. Juggling is another. "Mathematics is often described as the science of patterns," Messrs. Diaconis and Graham (a former president of the International Jugglers' Association) write. "Juggling can be thought of as the art of controlling patterns in time and space. Both activities offer unbounded challenges."

The central challenge in the mathematical study of juggling is to figure out which sequences of throws are possible and to categorize them according to the number of balls they require and their length—or period. Toward that end, mathematicians have developed a notation, called "siteswap," that uniquely describes all possible throwing sequences.

A siteswap pattern consists of a string of numbers, each of which specifies how much time one ball—or club, or chainsaw, or banana—spends in the air. The classic three-ball cascade, for instance, is denoted 333, because each ball is aloft for the same amount of time (three beats), and the sequence repeats after every third throw.

The remarkable thing about siteswap is that it allows jugglers to devise new patterns on paper and determine whether they're juggleable with a few simple calculations, all without tossing a single ball. What's more, the average of the digits in a pattern tells you the number of objects needed to juggle it—3 in the case of 441, for example, since the average of 4, 4 and 1 is 3.

Siteswap has led to the discovery of hundreds of unknown throwing sequences, many with just three or four balls. "Once the connection has been made between juggling (sequences) and mathematics, all kinds of doors, both mathematical as well as juggling, are thrown wide open," the authors note. "Many jugglers have been working hard to master the almost unlimited number of new patterns suggested by siteswaps."

Throughout the book, Messrs. Diaconis and Graham shuttle back and forth between magic and math, probing each trick for hidden mathematical insights and developing new magic based on what they find. In the process, they encounter a number of unsolved problems, some of which have prize money attached to them. It's a fun ride, even if you don't follow the nuances of every theorem and proof, and a refreshing change from the bombastic sort of magic one typically encounters on television.

Lovers of recreational mathematics, and especially fans of the late Martin Gardner, who contributed the foreword, will find many pleasures in "Magical Mathematics." And while exposing magic secrets in a book intended for the general public may raise hackles among some old-guard magicians, exploring the math behind these tricks will, in truth, only deepen the mystery. For, as the authors remind us, sometimes the methods are as magical as the tricks themselves.
 

—Mr. Stone is the author of the forthcoming "Fooling Houdini: Magicians, Mentalists, Math Geeks, and the Hidden Powers of the Mind."