PEOPLE are bad at judging the speed of large objects, especially those coming towards them. That is one reason why so many Indians die crossing Mumbai’s railway tracks. What is true of locomotives is also true of the world’s large, fast-moving countries. People struggle to wrap their heads around the size and speed of populous emerging economies so are taken aback by the impact as those countries come thundering on.

Among economists alert to the arrival of the emerging markets, none has tooted the horn louder than Jim O’Neill of Goldman Sachs. In 2001 he coined the “BRIC” acronym to describe four countries (Brazil, Russia, India and China) that would soon shake up the world economy. Ten years down the line, “The Growth Map” reflects on the idea’s successful career, now inseparable from his own.

The acronym provoked much excitement, some reflection and countless puns (see chart title and article rubric). The name was adopted by a bevy of investment funds, a leaders’ summit (which did not invite Mr O’Neill) and even an art exhibition (which did). The investment mania was interrupted by the financial crisis; the paronomasia seems unstoppable.

For this decade, Mr O’Neill has suggested another term, “growth markets”, defined as an emerging economy that accounts for more than 1% of global GDP. The BRICs qualify alongside Indonesia, Mexico, South Korea and Turkey. What sets them apart is not their size or their growth, but the combination of the two. That means the BRICs will make an outsize contribution to increases in global GDP. Between 2011 and 2020 their contribution will be twice that of the G7, Mr O’Neill predicts.

Such numbers are arresting. Indeed, what “really put BRICs on the map”, according to Mr O’Neill, were the audacious projections, first made by two of his colleagues, Dominic Wilson and Roopa Purushothaman, in 2003 and updated again this week, showing just how big the four economies could become by mid-century. They described the projections not as a forecast, but as a “dream” that the BRICs might fulfil.

But how credible is such fortune-telling? The scenarios may be bold but they rely on ideas that are reassuringly old. They assume that the BRICs will enjoy two kinds of economic convergence: of productivity and purchasing power. Poor countries grow faster than rich ones, because it is easier for them to imitate better techniques than it is to invent them. At the same time, prices and exchange rates tend to rise more quickly in “cheap” countries (like India, where a dollar’s worth of rupees stretches much further than a dollar in America), until things cost as much as they do in more expensive locations.

Thanks to both kinds of convergence, the combined GDP of the BRICs might exceed $95 trillion by 2050. That is more than six times the size of America’s economy but $35 trillion less than the bank calculated in its previous projection. This is not because it expects the BRICs to grow less quickly but because the bank now expects BRIC currencies to rise much less against the dollar. Brazil’s real, indeed, will even fall a little (see chart, left panel).

In painting these pictures, the economists from Goldman Sachs draw most directly on the work of Robert Barro of Harvard. He found that a poor country could expect to grow faster than a rich one, but only if the rule of law prevailed, the terms of trade were favourable, inflation and government profligacy remained in check and families were sufficiently small, healthy and educated. That list of factors has carried on growing. According to Steven Durlauf of the University of Wisconsin and his co-authors, economists have found almost as many “determinants of growth” (from coups to Confucianism) as there are countries with data.

Goldman Sachs takes the BRICs’ income per person, relative to that of America, as a proxy for their economic backwardness. The bigger the gap, the greater the potential for catch-up growth. The bank also assumes that countries differ in how well they exploit this potential. Some absorb know-how from abroad quicker than others. Their “convergence speeds” would vary, even if the distance they had to cover were the same.

These convergence speeds are the most important variables in the whole BRICs endeavour, and the hardest to pin down. Small tweaks produce vastly different outcomes. To make the choice less arbitrary, Goldman Sachs has drawn on 13 of the innumerable “growth determinants ” identified by Mr Barro and others. The bank now diligently rates and ranks emerging economies on such attributes as openness to trade, corruption, the diffusion of mobile phones and so on.

Tracking error

But a puzzle remains. Two of the BRICs, China and Russia, tend to grow much faster than their mediocre scores would suggest. They benefit from a “secret sauce”, as Goldman Sachs put it. Were it not for this ingredient, their 2050 GDPs would be $10.2 trillion and $1.9 trillion lower. That’s a lot of sauce.

In Mumbai, a consultancy called FinalMile has painted yellow lines at regular intervals across the tracks to help trespassers judge the speed of a train’s approach. Goldman Sachs also laid down markers to help track the BRICs’ progress. In 2003, it suggested that Brazil’s GDP would overtake Italy’s in 2025 and China’s would overtake Japan’s in 2015. In fact, both economies passed their markers last year. By 2008, the BRICs’ combined GDP was about 75% bigger than Goldman Sachs had suggested five years before. “My only regret”, writes Mr O’Neill, “is that we weren’t bolder.”

Of course no one can hope to look so far ahead with great accuracy. But, interestingly, the bank’s scenario for 2010 was a little closer to the mark. In other words, they did a better job of projecting seven years ahead than five. If the goal is to trace out long-term trends, forecasts may do better over the long run than the short. Predicting the distant future is forbiddingly difficult. Predicting the near future is no easier.