The term J-curve is used in several different fields to refer to a variety of unrelated J-shaped diagrams where a curve initially falls, but then rises to higher than the starting point.

In private equity, the J curve is used to illustrate the historical tendency of private equity funds to deliver negative returns in early years and investment gains in the outlying years as the portfolios of companies mature.^[1][2]

In the early years of the fund, a number of factors contribute to negative returns including management fees, investment costs and under-performing investments that are identified early and written down. Over time the fund will begin to experience unrealized gains followed eventually by events in which gains are realized (e.g., IPOs, mergers and acquisitions, leveraged recapitalizations).^[3]

Historically, the J-Curve effect has been more pronounced in the US, where private equity firms tend to carry their investments at the lower of market value or investment cost and have been more aggressive in writing down investments than in writing up investments. As a result, the carrying value of any investment that is underperforming will be written down but the carrying value of investments that are performing well tend to be recognized only when there is some kind of event that forces the private equity firm to mark up the investment.^[4]

The steeper the positive part of the J curve, the quicker cash is returned to investors. A private equity firm that can make quick returns to investors provides investors with the opportunity to reinvest that cash elsewhere. Of course, with a tightening of credit markets, private equity firms have found it harder to sell businesses they previously invested in. Proceeds to investors have reduced. J curves have flattened dramatically. This leaves investors with less cash flow to invest elsewhere. For example, in other private equity firms. The implications for private equity could well be severe. Being unable to sell businesses to generate proceeds and fees means some in the industry have predicted consolidation amongst private equity firms.^[5]

Balance of trade model[link]

This unreferenced section requires citations to ensure verifiability.

In economics, the 'J curve' refers to the trend of a country’s trade balance following a devaluation or depreciation under a certain set of assumptions. A devalued currency means imports are more expensive, and on the assumption that the volume of imports and exports change little immediately, this causes a depreciation of the current account (a bigger deficit or smaller surplus). After some time, though, the volume of exports may start to rise because of their lower more competitive prices to foreign buyers, and domestic consumers may buy fewer of the costlier imports. Eventually, if this happens, the trade balance may improve on what it was before the devaluation. If there is a currency revaluation or appreciation the same reasoning leads to an inverted J-curve.

Immediately following the depreciation or devaluation of the currency, the volume of imports and exports may remain largely unchanged due in part to pre-existing trade contracts that have to be honoured. Moreover, in the short run, demand for the more expensive imports (and demand for exports, which are cheaper to foreign buyers using foreign currencies) remain price inelastic. This is due to time lags in the consumer's search for acceptable, cheaper alternatives (which might not exist).

Over the longer term a depreciation in the exchange rate can have the desired effect of improving the current account balance. Domestic consumers might switch their expenditure to domestic products and away from expensive imported goods and services, assuming equivalent domestic alternatives exist. Equally, many foreign consumers may switch to purchasing the products being exported into their country, which are now cheaper in the foreign currency, instead of their own domestically produced goods and services.

Empirical investigations of the J-curve have sometimes focused on the effect of exchange rate changes on the trade ratio, i.e. exports divided by imports, rather than the trade balance, exports minus imports. Unlike the trade balance, the trade ratio can be logged regardless of whether a trade deficit or trade surplus exists.^[6]

Country status model[link]

Another 'J-Curve' refers to the correlation between stability and openness. This theory was suggested initially by the author Ian Bremmer, in his book The J Curve: A New Way to Understand Why Nations Rise and Fall.

The x-axis of the political J-Curve graph measures the 'openness' of the economy in question and the y-axis measures the stability of that same state. It suggests that those states that are 'closed'/undemocratic/unfree (such as the Communist dictatorships of North Korea and Cuba) are very stable; however, as one progresses right, along the x-axis, it is evident that stability (for relatively short period of time in the lengthy life of nations) decreases, creating a dip in the graph, until beginning to pick up again as the 'openness' of a state increases; at the other end of the graph to closed states are the open states of the West, such as the United States of America or the United Kingdom. Thus, a J-shaped curve is formed.

States can travel both forward (right) and backwards (left) along this J-curve, and so stability and openness are never secure. The J is steeper on the left hand side, as it is easier for a leader in a failed state to create stability by closing the country than to build a civil society and establish accountable institutions; the curve is higher on the far right than left because states that prevail in opening their societies (Eastern Europe, for example) ultimately become more stable than authoritarian regimes.

Bremmer's entire curve can shift up or down depending on economic resources available to the government in question. So Saudi Arabia's relative stability at every point along the curve rises or falls depending on the price of oil; China's curve analogously depends on the country's economic growth.

Medicine[link]

In medicine, the 'J-curve' refers to a graph in which the x-axis measures either of two treatable symptoms (blood pressure or blood cholesterol level) while the y-axis measures the chance that a patient will develop cardiovascular disease (CVD). It is well known that high blood pressure or high cholesterol levels increase a patient's risk. What is less well known is that plots of large populations against CVD mortality often takes the shape of a J curve which indicates that patients with very low blood pressure and/or low cholesterol levels are also at increased risk.^[7]

Political science (Model of revolutions)[link]

In political science, the 'J-curve' is part of a model developed by James Chowning Davies to explain political revolutions. Davies asserts that revolutions are a subjective response to a sudden reversal in fortunes after a long period of economic growth, which is known as relative deprivation. Relative deprivation theory claims that frustrated expectations help overcome the collective action problem, which in this case may breed revolt. Frustrated expectations could result from several factors, including growing levels of inequality within a country, which may mean those who are increasingly poor relative to the rich are getting less than they expected, or a period of sustained economic development, lifting general expectations, followed by a crisis.

This model is often applied to explain social unrest and efforts by governments to contain this unrest. This is referred to as the Davies' J-Curve, because economic development followed by a depression would be modeled as an upside down and slightly skewed J.

References[link]

A parabola, a simple example of a curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature.^[1] Often curves in two-dimensional (plane curves) or three-dimensional (space curves) Euclidean space are of interest.

Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In every day language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields.

The term curve has several meanings in non-mathematical language as well. For example, it can be almost synonymous with mathematical function (as in learning curve), or graph of a function (as in Phillips curve).

An arc or segment of a curve is a part of a curve that is bounded by two distinct end points and contains every point on the curve between its end points. Depending on how the arc is defined, either of the two end points may or may not be part of it. When the arc is straight, it is typically called a line segment.

History[link]

Megalithic art from Newgrange showing an early interest in curves

Fascination with curves began long before they were the subject of mathematical study. This can be seen in numerous examples of their decorative use in art and on everyday objects dating back to prehistoric times.^[2] Curves, or at least their graphical representations, are simple to create, for example by a stick in the sand on a beach.

Historically, the term "line" was used in place of the more modern term "curve". Hence the phrases "straight line" and "right line" were used to distinguish what are today called lines from "curved lines". For example, in Book I of Euclid's Elements, a line is defined as a "breadthless length" (Def. 2), while a straight line is defined as "a line that lies evenly with the points on itself" (Def. 4). Euclid's idea of a line is perhaps clarified by the statement "The extremities of a line are points," (Def. 3).^[3] Later commentators further classified lines according to various schemes. For example:^[4]

• Composite lines (lines forming an angle)
• Incomposite lines
  • Determinate (lines that do not extend indefinitely, such as the circle)
  • Indeterminate (lines that extend indefinitely, such as the straight line and the parabola)

The curves created by slicing a cone (conic sections) were among the curves studied in ancient Greece.

The Greek geometers had studied many other kinds of curves. One reason was their interest in solving geometrical problems that could not be solved using standard compass and straightedge construction. These curves include:

• The conic sections, deeply studied by Apollonius of Perga
• The cissoid of Diocles, studied by Diocles and use a method to double the cube.^[5]
• The conchoid of Nicomedes, studied by Nicomedes as a method to both double the cube and to trisect an angle.^[6]
• The Archimedean spiral, studied by Archimedes as a method to trisect an angle and square the circle.^[7]
• The spiric sections, sections of tori studied by Perseus as sections of cones had been studied by Apollonius.

Analytic geometry allowed curves, such as the Folium of Descartes, to be defined using equations instead of geometrical construction.

A fundamental advance in theory of curves was the advent of analytic geometry in the seventeenth century. This enabled a curve to be described using an equation rather than an elaborate geometrical construction. This not only allowed new curves to be defined and studied, but it enabled a formal distinction to be made between curves that can be defined using algebraic equations, algebraic curves, and those that cannot, transcendental curves. Previously, curves had been described as "geometrical" or "mechanical" according to how they were, or supposedly could be, generated.^[2]

Conic sections were applied in astronomy by Kepler. Newton also worked on an early example in the calculus of variations. Solutions to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways (in this case, the cycloid). The catenary gets its name as the solution to the problem of a hanging chain, the sort of question that became routinely accessible by means of differential calculus.

In the eighteenth century came the beginnings of the theory of plane algebraic curves, in general. Newton had studied the cubic curves, in the general description of the real points into 'ovals'. The statement of Bézout's theorem showed a number of aspects which were not directly accessible to the geometry of the time, to do with singular points and complex solutions.

From the nineteenth century there is not a separate curve theory, but rather the appearance of curves as the one-dimensional aspect of projective geometry, and differential geometry; and later topology, when for example the Jordan curve theorem was understood to lie quite deep, as well as being required in complex analysis. The era of the space-filling curves finally provoked the modern definitions of curve.

Topology[link]

Boundaries of hyperbolic components of Mandelbrot set as closed curves

In topology, a curve is defined as follows. Let Failed to parse (Missing texvc executable; please see math/README to configure.): I

be an interval of real numbers (i.e. a non-empty connected subset of Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{R}

). Then a curve Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma

is a continuous mapping Failed to parse (Missing texvc executable; please see math/README to configure.): \,\!\gamma : I \rightarrow X

, where Failed to parse (Missing texvc executable; please see math/README to configure.): X

is a topological space.

• The curve Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma

is said to be simple, or a Jordan arc, if it is injective, i.e. if for all Failed to parse (Missing texvc executable; please see math/README to configure.): x

, Failed to parse (Missing texvc executable; please see math/README to configure.): y

in Failed to parse (Missing texvc executable; please see math/README to configure.): I

, we have Failed to parse (Missing texvc executable; please see math/README to configure.): \,\!\gamma(x) = \gamma(y) \implies x = y . If Failed to parse (Missing texvc executable; please see math/README to configure.): I

is a closed bounded interval Failed to parse (Missing texvc executable; please see math/README to configure.): \,\![a, b]

, we also allow the possibility Failed to parse (Missing texvc executable; please see math/README to configure.): \,\!\gamma(a) = \gamma(b)

(this convention makes it possible to talk about "closed" simple curves, see below).

In other words this curve "does not cross itself and has no missing points".^[8]

• If Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma(x)=\gamma(y)

for some Failed to parse (Missing texvc executable; please see math/README to configure.): x\ne y
(other than the extremities of Failed to parse (Missing texvc executable; please see math/README to configure.): I

), then Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma(x)

is called a double (or multiple) point of the curve.

• A curve Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma

is said to be closed or a loop if Failed to parse (Missing texvc executable; please see math/README to configure.): \,\!I = [a, b]
and if Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma(a) = \gamma(b)

. A closed curve is thus a continuous mapping of the circle Failed to parse (Missing texvc executable; please see math/README to configure.): S^1

a simple closed curve is also called a Jordan curve. The Jordan curve theorem states that such curves divide the plane into an "interior" and an "exterior".

A plane curve is a curve for which X is the Euclidean plane—these are the examples first encountered—or in some cases the projective plane. A space curve is a curve for which X is of three dimensions, usually Euclidean space; a skew curve is a space curve which lies in no plane. These definitions also apply to algebraic curves (see below). However, in the case of algebraic curves it is very common not to restrict the curve to having points only defined over the real numbers.

This definition of curve captures our intuitive notion of a curve as a connected, continuous geometric figure that is "like" a line, without thickness and drawn without interruption, although it also includes figures that can hardly be called curves in common usage. For example, the image of a curve can cover a square in the plane (space-filling curve). The image of simple plane curve can have Hausdorff dimension bigger than one (see Koch snowflake) and even positive Lebesgue measure^[9] (the last example can be obtained by small variation of the Peano curve construction). The dragon curve is another unusual example.

Conventions and terminology[link]

The distinction between a curve and its image is important. Two distinct curves may have the same image. For example, a line segment can be traced out at different speeds, or a circle can be traversed a different number of times. Many times, however, we are just interested in the image of the curve. It is important to pay attention to context and convention in reading.

Terminology is also not uniform. Often, topologists use the term "path" for what we are calling a curve, and "curve" for what we are calling the image of a curve. The term "curve" is more common in vector calculus and differential geometry.

Lengths of curves[link]

If Failed to parse (Missing texvc executable; please see math/README to configure.): X

is a metric space with metric Failed to parse (Missing texvc executable; please see math/README to configure.): d

, then we can define the length of a curve Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma : [a, b] \rightarrow X

by

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{length} (\gamma)=\sup \left\{ \sum_{i=1}^n d(\gamma(t_i),\gamma(t_{i-1})) : n \in \mathbb{N} \text{ and } a = t_0 < t_1 < \cdots < t_n = b \right\}.

where the sup is over all Failed to parse (Missing texvc executable; please see math/README to configure.): n

and all partitions Failed to parse (Missing texvc executable; please see math/README to configure.): t_0 < t_1 < \cdots < t_n
of Failed to parse (Missing texvc executable; please see math/README to configure.): [a, b]

.

A rectifiable curve is a curve with finite length. A parametrization of Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma

is called natural (or unit speed or parametrised by arc length) if for any Failed to parse (Missing texvc executable; please see math/README to configure.): t_1

, Failed to parse (Missing texvc executable; please see math/README to configure.): t_2

in Failed to parse (Missing texvc executable; please see math/README to configure.): [a, b]

, we have

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{length} (\gamma|_{[t_1,t_2]})=|t_2-t_1|.

If Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma

is a Lipschitz-continuous function, then it is automatically rectifiable.  Moreover, in this case, one can define the speed (or metric derivative) of Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma
at Failed to parse (Missing texvc executable; please see math/README to configure.): t_0
as

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{speed}(t_0)=\limsup_{t\to t_0} {d(\gamma(t),\gamma(t_0))\over |t-t_0|}

and then

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{length}(\gamma)=\int_a^b \text{speed}(t) \, dt.

In particular, if Failed to parse (Missing texvc executable; please see math/README to configure.): X = \mathbb{R}^n

is an Euclidean space and Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma : [a, b] \rightarrow \mathbb{R}^n
is differentiable then

Failed to parse (Missing texvc executable; please see math/README to configure.): \text{length}(\gamma)=\int_a^b \| \gamma '(t) \| \, dt.

Differential geometry[link]

While the first examples of curves that are met are mostly plane curves (that is, in everyday words, curved lines in two-dimensional space), there are obvious examples such as the helix which exist naturally in three dimensions. The needs of geometry, and also for example classical mechanics are to have a notion of curve in space of any number of dimensions. In general relativity, a world line is a curve in spacetime.

If Failed to parse (Missing texvc executable; please see math/README to configure.): X

is a differentiable manifold, then we can define the notion of differentiable curve in Failed to parse (Missing texvc executable; please see math/README to configure.): X

. This general idea is enough to cover many of the applications of curves in mathematics. From a local point of view one can take Failed to parse (Missing texvc executable; please see math/README to configure.): X

to be Euclidean space. On the other hand it is useful to be more general, in that (for example) it is possible to define the tangent vectors to Failed to parse (Missing texvc executable; please see math/README to configure.): X
by means of this notion of curve.

If Failed to parse (Missing texvc executable; please see math/README to configure.): X

is a smooth manifold, a smooth curve in Failed to parse (Missing texvc executable; please see math/README to configure.): X
is a smooth map

Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma : I \rightarrow X.

This is a basic notion. There are less and more restricted ideas, too. If Failed to parse (Missing texvc executable; please see math/README to configure.): X

is a Failed to parse (Missing texvc executable; please see math/README to configure.): C^k
manifold (i.e., a manifold whose charts are Failed to parse (Missing texvc executable; please see math/README to configure.): k
times continuously differentiable), then a Failed to parse (Missing texvc executable; please see math/README to configure.): C^k
curve in Failed to parse (Missing texvc executable; please see math/README to configure.): X
is such a curve which is only assumed to be  Failed to parse (Missing texvc executable; please see math/README to configure.): C^k
(i.e. Failed to parse (Missing texvc executable; please see math/README to configure.): k
times continuously differentiable).  If Failed to parse (Missing texvc executable; please see math/README to configure.): X
is an analytic manifold (i.e. infinitely differentiable and charts are expressible as power series), and Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma
is an analytic map, then Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma
is said to be an analytic curve.

A differentiable curve is said to be regular if its derivative never vanishes. (In words, a regular curve never slows to a stop or backtracks on itself.) Two Failed to parse (Missing texvc executable; please see math/README to configure.): C^k

differentiable curves

Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma_1 :I \rightarrow X

and

Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma_2 : J \rightarrow X

are said to be equivalent if there is a bijective Failed to parse (Missing texvc executable; please see math/README to configure.): C^k

map

Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,p : J \rightarrow I

such that the inverse map

Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,p^{-1} : I \rightarrow J

is also Failed to parse (Missing texvc executable; please see math/README to configure.): C^k , and

Failed to parse (Missing texvc executable; please see math/README to configure.): \!\,\gamma_{2}(t) = \gamma_{1}(p(t))

for all Failed to parse (Missing texvc executable; please see math/README to configure.): t . The map Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma_2

is called a reparametrisation of Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma_1

and this makes an equivalence relation on the set of all Failed to parse (Missing texvc executable; please see math/README to configure.): C^k

differentiable curves in Failed to parse (Missing texvc executable; please see math/README to configure.): X

. A Failed to parse (Missing texvc executable; please see math/README to configure.): C^k

arc is an equivalence class of Failed to parse (Missing texvc executable; please see math/README to configure.): C^k
curves under the relation of reparametrisation.

Algebraic curve[link]

Algebraic curves are the curves considered in algebraic geometry. A plane algebraic curve is the locus of the points of coordinates x, y such that f(x, y) = 0, where f is a polynomial in two variables defined over some field F. Algebraic geometry normally looks not only on points with coordinates in F but on all the points with coordinates in an algebraically closed field K. If C is a curve defined by a polynomial f with coefficients in F, the curve is said defined over F. The points of the curve C with coordinates in a field G are said rational over G and can be denoted C(G)); thus the full curve C = C(K).

Algebraic curves can also be space curves, or curves in even higher dimension, obtained as the intersection (common solution set) of more than one polynomial equation in more than two variables. By eliminating variables (by any tool of elimination theory), an algebraic curve may be projected onto a plane algebraic curve, which however may introduce singularities such as cusps or double points.

A plane curve may also may also be completed in a curve in the projective plane: if a curve is defined by a polynomial f of total degree d, then w^df(u/w, v/w) simplifies to a homogeneous polynomial g(u, v, w) of degree d. The values of u, v, w such that g(u, v, w) = 0 are the homogeneous coordinates of the points of the completion of the curve in the projective plane and the points of the initial curve are those such w is not zero. An example is the Fermat curve uⁿ + vⁿ = wⁿ, which has an affine form xⁿ + yⁿ = 1. A similar process of homogenization may be defined for curves in higher dimensional spaces

Important examples of algebraic curves are the conics, which are nonsingular curves of degree two and genus zero, and elliptic curves, which are nonsingular curves of genus one studied in number theory and which have important applications to cryptography. Because algebraic curves in fields of characteristic zero are most often studied over the complex numbers, algebraic curves in algebraic geometry may be considered as real surfaces. In particular, the non-singular complex projective algebraic curves are called Riemann surfaces.

See also[link]

Notes[link]

Wikimedia Commons has media related to: Curves

1. ^ In current language, a line is typically required to be straight. Historically, however, lines could be "curved" or "straight".
2. ^ ^{a b} Lockwood p. ix
3. ^ Heath p. 153
4. ^ Heath p. 160
5. ^ Lockwood p. 132
6. ^ Lockwood p. 129
7. ^ O'Connor, John J.; Robertson, Edmund F., "Spiral of Archimedes", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Curves/Spiral.html .
8. ^ "Jordan arc definition at Dictionary.com. Dictionary.com Unabridged. Random House, Inc". Dictionary.reference.com. http://dictionary.reference.com/browse/jordan%20arc. Retrieved 2012-03-14. 
9. ^ Osgood, William F. (January 1903). "A Jordan Curve of Positive Area". Transactions of the American Mathematical Society (American Mathematical Society) 4 (1): 107–112. DOI:10.2307/1986455. ISSN 0002-9947. JSTOR 1986455. 

References[link]

• A.S. Parkhomenko (2001), "Line (curve)", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4, http://www.encyclopediaofmath.org/index.php?title=l/l059020 
• B.I. Golubov (2001), "Rectifiable curve", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4, http://www.encyclopediaofmath.org/index.php?title=r/r080130 
• Euclid, commentary and trans. by T. L. Heath Elements Vol. 1 (1908 Cambridge) Google Books
• E. H. Lockwood A Book of Curves (1961 Cambridge)

External links[link]

• Famous Curves Index, School of Mathematics and Statistics, University of St Andrews, Scotland
• Mathematical curves A collection of 874 two-dimensional mathematical curves
• Gallery of Space Curves Made from Circles, includes animations by Peter Moses
• Gallery of Bishop Curves and Other Sperical Curves, includes animations by Peter Moses
• YAN Kun. Research on adaptive connection equation in discontinuous area of data curve. doi:10.3969/j.issn.1004-2903.2011.01.018

Ian Bremmer
Ian Bremmer
Born	(1969-11-12) November 12, 1969 (age 42) United States
Occupation	Political scientist, author, entrepreneur
Nationality	United States
Education	B.A., Tulane University M.A., Ph.D., Stanford University

Ian Bremmer (born November 12, 1969) is an American political scientist specializing in US foreign policy, states in transition, and global political risk. He is the president and founder of Eurasia Group, a leading global political risk research and consulting firm, and a professor at Columbia University. Eurasia Group provides financial, corporate, and government clients with information and insight on how political developments move markets. Bremmer is of Armenian and German descent.^[1]

Bremmer has authored/published eight books, including the national bestsellers Every Nation for Itself: Winners and Losers in a G-Zero World (Portfolio, May 2012), which details risks and opportunities in a world without global leadership, and The End of the Free Market: Who Wins the War Between States and Corporations (Portfolio, May 2010), which describes the global phenomenon of state capitalism and its implications for economics and politics. He also wrote The J Curve: A New Way to Understand Why Nations Rise and Fall (Simon & Schuster, 2006), selected by The Economist as one of the best books of 2006.^[2]

Bremmer is a frequent writer and commentator in the media. He is a contributor for the Financial Times A-List,^[3] and writes an opinion blog for Reuters.com as well as "The Call" blog on ForeignPolicy.com. He has also published articles in the Washington Post, the New York Times, The Wall Street Journal, Newsweek, Harvard Business Review, and Foreign Affairs. He is a panelist for CNN International's "Connect the World" and appears regularly on CNBC, Fox News Channel, National Public Radio, and other networks.

Bremmer is most widely known for advances in political risk; called the "rising guru" in the field by the Economist^[4] and, more directly, bringing political science as a discipline to the financial markets.^[5] In 2001, Bremmer created Wall Street’s first global political risk index, now the GPRI (Global Political Risk Index) —a joint venture with investment bank Citigroup. Bremmer's definition of an emerging market as "a country where politics matters at least as much as economics to the market"^[6] is a standard reference in the political risk field.

Among his professional appointments, Bremmer serves on the Board of Trustees of the Carnegie Council for Ethics in International Affairs and the Advisory Board of the Westport Public Library. In 2007, he was named as a 'Young Global Leader' of the World Economic Forum, and in 2010 was appointed Chair of the Forum's Global Agenda Council for Geopolitical Risk.

Bremmer received his B.A. at Tulane University, and his M.A. and Ph.D. in political science from Stanford University in 1994. He then served on the faculty of the Hoover Institution where, at 25, he became the Institution’s youngest ever National Fellow. He has held research and faculty positions at Columbia University (where he presently teaches), the EastWest Institute, Lawrence Livermore National Laboratory, and the World Policy Institute, where he has served as Senior Fellow since 1997.

Key concepts[link]

The J-Curve[link]

Bremmer's J curve outlines the link between a country's openness and its stability. While many countries are stable because they are open (the United States, France, Japan), others are stable because they are closed (North Korea, Cuba, Iraq under Saddam Hussein). States can travel both forward (right) and backwards (left) along this J curve, so stability and openness are never secure. The J is steeper on the left hand side, as it is easier for a leader in a failed state to create stability by closing the country than to build a civil society and establish accountable institutions; the curve is higher on the far right than left because states that prevail in opening their societies (Eastern Europe, for example) ultimately become more stable than authoritarian regimes.

State Capitalism[link]

Ian Bremmer describes state capitalism as a system in which the state dominates markets primarily for political gain. In his book, The End of the Free Market: Who Wins the War Between States and Corporations (New York: Portfolio, 2010), Bremmer describes China as the primary driver for the rise of state capitalism as a challenge to the free market economies of the developed world, particularly in the aftermath of the financial crisis.^[7]

G-Zero[link]

The term G-Zero refers to a breakdown in global leadership brought about by a decline of Western influence and the inability of other nations to fill the void.^[8][9] It is a reference to a perceived shift away from the pre-eminence of the Group of Seven industrialized countries and the expanded Group of Twenty, which includes major emerging powers like China, India, Brazil, Turkey, and others. In his book, Every Nation for Itself: Winners and Losers in a G-Zero World (New York: Portfolio, 2012), Bremmer explains that, in the G-Zero, no country or group of countries has the political and economic leverage to drive an international agenda or provide global public goods.^[10][11]

Pivot State[link]

Bremmer uses 'pivot state' to describe a nation that is able to build profitable relationships with multiple other major powers without becoming overly reliant on any one of them. This ability to hedge allows a pivot state to avoid capture--in terms of security or economy-- at the hands of a single country. In his book, Every Nation for Itself: Winners and Losers in a G-Zero World (New York: Portfolio, 2012), Bremmer explains how, in a volatile G-Zero world, the ability to pivot will take on increased importance. At the opposite end of the spectrum are shadow states that are frozen within the influence of a single power. The United States' neighbors illustrate the terms very well. With significant trade ties with both the United States and Asia and formal security ties with NATO, Canada is a good example of a pivot state that is hedged against a slowdown in or conflict with any single major power. Mexico, on the other hand, is a shadow state due to its overwhelming reliance on the US economy.

Selected bibliography[link]

Books[link]

• Every Nation for Itself: Winners and Losers in a G-Zero World. (New York: Portfolio, May 2012). ISBN 978-1-59184-468-6
• The End of the Free Market: Who Wins the War Between States and Corporations. (New York: Portfolio, 2010). ISBN 978-1-59184-301-6
• The Fat Tail: The Power of Political Knowledge for Strategic Investing. (with Preston Keat), (New York: Oxford University Press, 2009; revised paperback, 2010). ISBN 0-19-532855-8
• Managing Strategic Surprise: Lessons from Risk Management & Risk Assessment. (edited with Paul Bracken and David Gordon), (Cambridge: Cambridge University Press, 2008). ISBN 0-521-88315-6
• The J Curve: A New Way to Understand Why Nations Rise and Fall. (Simon & Schuster, 2006; revised paperback, 2007). ISBN 0-7432-7471-7
• New States, New Politics: Building the Post-Soviet Nations. (edited with Raymond Taras), (Cambridge: Cambridge University Press, 1997). ISBN 0-521-57799-3
• Nations and Politics in the Soviet Successor States. (edited with Raymond Taras), (Cambridge: Cambridge University Press, 1993). ISBN 0-521-43860-8
• Soviet Nationalities Problems. (edited with Norman Naimark), (Stanford: Stanford Center for Russian and East European Studies: 1990). ISBN 0-87725-195-9
• Bremmer's books at Google Books
• "The J Curve" official website
• "The Fat Tail" official website
• "The End of the Free Market" official website
• "Every Nation For Itself" official website

Essays[link]

• Five Myths About America's Decline, Washington Post, May 4, 2012
• The Future Belongs to the Flexible, Wall Street Journal, April 27, 2012
• France's What-If Campaign, International Herald Tribune, February 16, 2012
• Far Too Soon to Write Off America, Financial Times,, December 28, 2011
• An Upbeat View of America's 'Bad' Year, with David F. Gordon, International Herald Tribune, December 28, 2011
• Searching the World for Good Governance, International Herald Tribune, November 27, 2011
• Whose Economy Has It Worst?, with Nouriel Roubini, Wall Street Journal, November 12, 2011
• The G-Zero Order, with David F. Gordon, International Herald Tribune, October 26, 2011
• Hungary's New Path is the Hidden Danger to Europe, Financial Times, October 9, 2011
• China's Bumpy Road Ahead, Wall Street Journal, July 9, 2011
• On the Economy, Be Careful What You Wish For, Foreign Policy, July/August 2011
• The Collateral Damage in Pakistan, International Herald Tribune, May 5, 2011
• Washington's Stark Choice: Democracy or Riyadh, Financial Times, March 17, 2011
• Get Ready for a Growth Supercycle, Wall Street Journal, March 2, 2011
• The J Curve Hits the Middle East, Financial Times, February 16, 2011
• A G-Zero World, with Nouriel Roubini, Foreign Affairs, March/April 2011
• Cyberteeth Bared, with Parag Khanna, International Herald Tribune, December 22, 2010
• The Fourth Wave, Foreign Policy, December 2010
• Democracy in Cyberspace, Foreign Affairs, November/December 2010
• Japan's Overblown Anxiety, International Herald Tribune, November 16, 2010
• Paradise Lost: Why Fallen Markets Will Never Be the Same, with Nouriel Roubini, Institutional Investor, September 2010
• BP's Lucky it Spilled in US, not Chinese Waters, USA Today, July 14, 2010
• Sagging Global Growth Requires Us To Act, with Nouriel Roubini, The Financial Times, July 12, 2010
• When the State Battles the Corporation, The International Herald Tribune, June 23, 2010
• Dangerous Insecurity, The International Herald Tribune, May 25, 2010
• As Free Market Democracies Flail, Watch Out for China, USA Today, May 25, 2010
• The Long Shadow of the Invisible Hand, The Wall Street Journal, May 22, 2010
• Fight of the Century, Prospect, April 2010
• At Davos, All the Globalizers are Gone, Washington Post, January 29, 2010
• A Year of US-China Discord, with David Gordon, Project Syndicate, January 2010
• State Capitalism Comes of Age, Foreign Affairs, May/June 2009
• AIG and 'Political Risk', with Sean West, The Wall Street Journal, March 20, 2009
• Outrage is an Unaffordable Luxury, The Washington Post, March 18, 2009
• Expect the World Economy to Suffer through 2009, with Nouriel Roubini, The Wall Street Journal, January 23, 2009
• Reasons to be Gloomy, Slate, September 18, 2008
• Threat or Opportunity? What Sovereign Wealth Funds Mean for US Companies, with Juan Pujadas, The View, Summer 2008
• A Political Scientist in China, Slate, October 5, 2007
• The Dawn of the Next Cold War, Newsweek International, February 26, 2007
• In the Right Direction, The National Interest, Jan/Feb 2007
• Hedging Political Risk in China, with Fareed Zakaria, Harvard Business Review, November 2006
• Lowering the Temperature, Comment is Free, October 20, 2006
• The World is J-Curved, Washington Post, October 1, 2006
• Prices Transform Oil into a Weapon, International Herald Tribune, August 27, 2005
• Managing Risk in an Unstable World, Harvard Business Review, June 2005
• George Kennan's Lessons for the War on Terror, International Herald Tribune, March 24, 2005
• Diary of a Political Scientist, Slate, February 2–6, 2004
• Ian Bremmer’s articles at Project Syndicate

Blogs[link]

• Bremmer Davos blog for the Financial Times
• Bremmer's "The Call" blog on ForeignPolicy.com
• Bremmer's blog on Reuters

Interviews[link]

• Ian Bremmer on Charlie Rose
• Bremmer interviews on The Daily Show
• PWC interview with Bremmer, CEOs
• PWC interview with Bremmer on political risk
• Mckinsey Quarterly interview with Bremmer
• Bremmer at the Council on Foreign Relations
• Bremmer interviews in The Big Think
• Bremmer interview in Newsweek
• Bremmer's J Curve in the Daily Telegraph
• Bremmer's End of the Free Market in the Daily Telegraph
• The J Curve on BBC Newsnight
• SFO interview with Bremmer
• Foreign Policy Association interview with Bremmer
• Barrons interview with Bremmer
• Financial Times interview with Bremmer
• Reuters interview with Bremmer
• Foreign Policy interview with Bremmer and Nouriel Roubini
• Spears interview with Bremmer
• Strategy & Business interview with Bremmer
• The Big Interview with Bremmer on The Wall Street Journal
• Bremmer interview in the Washington Post
• Bremmer guest hosts CNBC Squawk Box

Testimony[link]

• Appearances on C-SPAN
• Congressional Ways & Means Committee, US-China relations

Research[link]

Ian Bremmer's research interests include:

• International political economy;
• Geoeconomics and geopolitics;
• States in transition and global emerging markets;
• US foreign policy

Current appointments[link]

• Senior Fellow, World Policy Institute
• Adjunct Professor, School for International and Public Affairs, Columbia University
• Founding Chair, Global Agenda Council on Geopolitical Risk, World Economic Forum
• Member, Council on Foreign Relations
• Member, International Institute for Strategic Studies

References[link]

External links[link]

Wikiquote has a collection of quotations related to: Ian Bremmer

Ian Bremmer[link]

• Bremmer webpage
• Bremmer bio at Eurasia Group
• Ian Bremmer on Facebook
• Ian Bremmer on Twitter
• RSA Vision webcasts - Ian Bremmer on "The Fat Tail"
• Bremmer's op-ed commentaries on Project Syndicate.

Eurasia Group[link]

• Official website
• Economist profile of Eurasia Group
• Google News on Eurasia Group