Black Hole Analogue: Extreme Blue Shift Disturbance. Thought of the Day 141.0

One major contribution of the theoretical study of black hole analogues has been to help clarify the derivation of the Hawking effect, which leads to a study of Hawking radiation in a more general context, one that involves, among other features, two horizons. There is an apparent contradiction in Hawking’s semiclassical derivation of black hole evaporation, in that the radiated fields undergo arbitrarily large blue-shifting in the calculation, thus acquiring arbitrarily large masses, which contravenes the underlying assumption that the gravitational effects of the quantum fields may be ignored. This is known as the trans-Planckian problem. A similar issue arises in condensed matter analogues such as the sonic black hole.

Untitled

Sonic horizons in a moving fluid, in which the speed of sound is 1. The velocity profile of the fluid, v(z), attains the value −1 at two values of z; these are horizons for sound waves that are right-moving with respect to the fluid. At the right-hand horizon right-moving waves are trapped, with waves just to the left of the horizon being swept into the supersonic flow region v < −1; no sound can emerge from this region through the horizon, so it is reminiscent of a black hole. At the left-hand horizon right-moving waves become frozen and cannot enter the supersonic flow region; this is reminiscent of a white hole.

Considering the sonic horizons in one-dimensional fluid flow, the velocity profile of the fluid as depicted in the figure above, the two horizons are formed for sound waves that propagate to the right with respect to the fluid. The horizon on the right of the supersonic flow region v < −1 behaves like a black hole horizon for right-moving waves, while the horizon on the left of the supersonic flow region behaves like a white hole horizon for these waves. In such a system, the equation for a small perturbation φ of the velocity potential is

(∂t + ∂zv)(∂t + v∂z)φ − ∂z2φ = 0 —– (1)

In terms of a new coordinate τ defined by

dτ := dt + v/(1 – v2) dz

(1) is the equation φ = 0 of a scalar field in the black-hole-type metric

ds2 = (1 – v2)dτ2 – dz2/(1 – v2)

Each horizon will produce a thermal spectrum of phonons with a temperature determined by the quantity that corresponds to the surface gravity at the horizon, namely the absolute value of the slope of the velocity profile:

kBT = ħα/2π, α := |dv/dz|v=-1 —– (2)

Untitled

Hawking phonons in the fluid flow: Real phonons have positive frequency in the fluid-element frame and for right-moving phonons this frequency (ω − vk) is ω/(1 + v) = k. Thus in the subsonic-flow regions ω (conserved 1 + v for each ray) is positive, whereas in the supersonic-flow region it is negative; k is positive for all real phonons. The frequency in the fluid-element frame diverges at the horizons – the trans-Planckian problem.

The trajectories of the created phonons are formally deduced from the dispersion relation of the sound equation (1). Geometrical acoustics applied to (1) gives the dispersion relation

ω − vk = ±k —– (3)

and the Hamiltonians

dz/dt = ∂ω/∂k = v ± 1 —– (4)

dk/dt = -∂ω/∂z = − v′k —– (5)

The left-hand side of (3) is the frequency in the frame co-moving with a fluid element, whereas ω is the frequency in the laboratory frame; the latter is constant for a time-independent fluid flow (“time-independent Hamiltonian” dω/dt = ∂ω/∂t = 0). Since the Hawking radiation is right-moving with respect to the fluid, we clearly must choose the positive sign in (3) and hence in (4) also. By approximating v(z) as a linear function near the horizons we obtain from (4) and (5) the ray trajectories. The disturbing feature of the rays is the behavior of the wave vector k: at the horizons the radiation is exponentially blue-shifted, leading to a diverging frequency in the fluid-element frame. These runaway frequencies are unphysical since (1) asserts that sound in a fluid element obeys the ordinary wave equation at all wavelengths, in contradiction with the atomic nature of fluids. Moreover the conclusion that this Hawking radiation is actually present in the fluid also assumes that (1) holds at all wavelengths, as exponential blue-shifting of wave packets at the horizon is a feature of the derivation. Similarly, in the black-hole case the equation does not hold at arbitrarily high frequencies because it ignores the gravity of the fields. For the black hole, a complete resolution of this difficulty will require inputs from the gravitational physics of quantum fields, i.e. quantum gravity, but for the dumb hole the physics is available for a more realistic treatment.

 

Adjacency of the Possible: Teleology of Autocatalysis. Thought of the Day 140.0

abiogenesisautocatalysis

Given a network of catalyzed chemical reactions, a (sub)set R of such reactions is called:

  1. Reflexively autocatalytic (RA) if every reaction in R is catalyzed by at least one molecule involved in any of the reactions in R;
  2. F-generated (F) if every reactant in R can be constructed from a small “food set” F by successive applications of reactions from R;
  3. Reflexively autocatalytic and F-generated (RAF) if it is both RA and F.

The food set F contains molecules that are assumed to be freely available in the environment. Thus, an RAF set formally captures the notion of “catalytic closure”, i.e., a self-sustaining set supported by a steady supply of (simple) molecules from some food set….

Stuart Kauffman begins with the Darwinian idea of the origin of life in a biological ‘primordial soup’ of organic chemicals and investigates the possibility of one chemical substance to catalyze the reaction of two others, forming new reagents in the soup. Such catalyses may, of course, form chains, so that one reagent catalyzes the formation of another catalyzing another, etc., and self-sustaining loops of reaction chains is an evident possibility in the appropriate chemical environment. A statistical analysis would reveal that such catalytic reactions may form interdependent networks when the rate of catalyzed reactions per molecule approaches one, creating a self-organizing chemical cycle which he calls an ‘autocatalytic set’. When the rate of catalyses per reagent is low, only small local reaction chains form, but as the rate approaches one, the reaction chains in the soup suddenly ‘freeze’ so that what was a group of chains or islands in the soup now connects into one large interdependent network, constituting an ‘autocatalytic set’. Such an interdependent reaction network constitutes the core of the body definition unfolding in Kauffman, and its cyclic character forms the basic precondition for self-sustainment. ‘Autonomous agent’ is an autocatalytic set able to reproduce and to undertake at least one thermodynamic work cycle.

This definition implies two things: reproduction possibility, and the appearance of completely new, interdependent goals in work cycles. The latter idea requires the ability of the autocatalytic set to save energy in order to spend it in its own self-organization, in its search for reagents necessary to uphold the network. These goals evidently introduce a – restricted, to be sure – teleology defined simply by the survival of the autocatalytic set itself: actions supporting this have a local teleological character. Thus, the autocatalytic set may, as it evolves, enlarge its cyclic network by recruiting new subcycles supporting and enhancing it in a developing structure of subcycles and sub-sub-cycles. 

Kauffman proposes that the concept of ‘autonomous agent’ implies a whole new cluster of interdependent concepts. Thus, the autonomy of the agent is defined by ‘catalytic closure’ (any reaction in the network demanding catalysis will get it) which is a genuine Gestalt property in the molecular system as a whole – and thus not in any way derivable from the chemistry of single chemical reactions alone.

Kauffman’s definitions on the basis of speculative chemistry thus entail not only the Kantian cyclic structure, but also the primitive perception and action phases of Uexküll’s functional circle. Thus, Kauffman’s definition of the organism in terms of an ‘autonomous agent’ basically builds on an Uexküllian intuition, namely the idea that the most basic property in a body is metabolism: the constrained, organizing processing of high-energy chemical material and the correlated perception and action performed to localize and utilize it – all of this constituting a metabolic cycle coordinating the organism’s in- and outside, defining teleological action. Perception and action phases are so to speak the extension of the cyclical structure of the closed catalytical set to encompass parts of its surroundings, so that the circle of metabolism may only be completed by means of successful perception and action parts.

The evolution of autonomous agents is taken as the empirical basis for the hypothesis of a general thermodynamic regularity based on non-ergodicity: the Big Bang universe (and, consequently, the biosphere) is not at equilibrium and will not reach equilibrium during the life-time of the universe. This gives rise to Kauffman’s idea of the ‘adjacent possible’. At a given point in evolution, one can define the set of chemical substances which do not exist in the universe – but which is at a distance of one chemical reaction only from a substance already existing in the universe. Biological evolution has, evidently, led to an enormous growth of types of organic macromolecules, and new such substances come into being every day. Maybe there is a sort of chemical potential leading from the actually realized substances and into the adjacent possible which is in some sense driving the evolution? In any case, Kauffman claims the hypothesis that the biosphere as such is supercritical in the sense that there is, in general, more than one action catalyzed by each reagent. Cells, in order not to be destroyed by this chemical storm, must be internally subcritical (even if close to the critical boundary). But if the biosphere as such is, in fact, supercritical, then this distinction seemingly a priori necessitates the existence of a boundary of the agent, protecting it against the environment.

BASEL III: The Deflationary Symbiotic Alliance Between Governments and Banking Sector. Thought of the Day 139.0

basel_reforms

The Bank for International Settlements (BIS) is steering the banks to deal with government debt, since the governments have been running large deficits to deal with the catastrophe of BASEL 2-inspired mortgaged-backed securities collapse. The deficits are ranged anywhere between 3 to 7 per cent of the GDP, and in cases even higher. These deficits were being used to create a floor under growth by stimulating the economy and bailing out financial institutions that got carried away by the wholesale funding of real estate. And this is precisely what BASEL 2 promulgated, i.e. encouraging financial institutions to hold mortgage-backed securities for investments.

In comes the BASEL 3 rules that implore than banks must be in compliance with these regulations. But, who gets to decide these regulations? Actually, banks do, since they then come on board for discussions with the governments, and such negotiations are catered to bail banks out with government deficits in order to oil the engine of economic growth. The logic here underlines the fact that governments can continue to find a godown of sorts for their deficits, while the banks can buy government debt without any capital commitment and make a good spread without the risk, thus serving the interests of the both parties involved mutually. Moreover, for the government, the process is political, as no government would find it acceptable to be objective in its viewership of letting a bubble deflate, because any process of deleveraging would cause the banks to offset their lending orgy, which is detrimental to the engineered economic growth. Importantly, without these deficits, the financial system could go down the deflationary spiral, which might turn out to be a difficult proposition to recover if there isn’t any complicity in rhyme and reason accorded to this particular dysfunctional and symbiotic relationship. So, whats the implication of all this? The more government debt banks hold, the less overall capital they need. And who says so? BASEL 3.

But, the mesh just seems to be building up here. In the same way that banks engineered counterfeit AAA-backed securities that were in fact an improbable financial hoax, how can countries that have government debt/GDP ratio to the tune of 90 – 120 per cent get a Standard&Poor’s ratings of a double-A? They have these ratings because they belong to a apical club that gives their members exclusive rights to a high rating even if they are irresponsible with their issuing of debts. Well, is that this simple? Yes and no. Yes, as is above, and no is merely clothing itself in a bit of an economic jargon, in that these are the countries where the government debt can be held without any capital against it. In other words, if a debt cannot be held, it cannot be issued, and that is the reason why countries are striving for issuing debts that have a zero weighting.

Let us take snippets across gradations of BASEL 1, 2 and 3. In BASEL 1, the unintended consequences were that banks were all buying equity in cross-owned companies. When the unwinding happened, equity just fell apart, since any beginning of a financial crisis is tailored to smash bank equities to begin with. Thats the first wound to rationality. In BASEL 2, banks were told to hold as much AAA-rated paper as they wanted with no capital against it. What happened if these ratings were downgraded? It would trigger a tsunami cutting through pension and insurance schemes to begin with forcing them to sell their papers and pile up huge losses meant to absorbed by capital, which doesn’t exist against these papers. So whatever gets sold is politically cushioned and buffered for by the governments, for the risks cannot be afforded to get any more denser as that explosion would sound the catastrophic death knell for the economy. BASEL 3 doesn’t really help, even if it mandated to hold a concentrated portfolio of government debt without any capital against it, for absorption of losses in case of a crisis hitting would have to exhumed through government bail-outs in scenarios where government debts are a century plus. So, are the banks in-stability, or given to more instability via BASEL 3?  The incentives to ever more hold government securities increase bank exposure to sovereign bonds, adding to existing exposure of government securities via repurchase transactions, investments and trading inventories. A ratings downgrade results in a fall in value of bonds triggering losses. Banks would then face calls for additional collateral, which would drain liquidity, and which would then require additional capital as way of compensation. where would this capital come in from, if not for the governments to source it? One way out would be recapitalization through government debt. On the other hand, the markets are required to hedge against the large holdings of government securities and so short stocks, currencies and insurance companies are all made to stare in the face of volatility that rips through them, of which the net resultant is falling liquidity. So, this vicious cycle would continue to cycle its way through any downgrades. And thats why the deflationary symbiotic alliance between the governments and banking sector isn’t anything more than high-fatigue tolerance….

Conjuncted: Affine Schemes: How Would Functors Carry the Same Information?

GrothMumford

If we go to the generality of schemes, the extra structure overshadows the topological points and leaves out crucial details so that we have little information, without the full knowledge of the sheaf. For example the evaluation of odd functions on topological points is always zero. This implies that the structure sheaf of a supermanifold cannot be reconstructed from its underlying topological space.

The functor of points is a categorical device to bring back our attention to the points of a scheme; however the notion of point needs to be suitably generalized to go beyond the points of the topological space underlying the scheme.

Grothendieck’s idea behind the definition of the functor of points associated to a scheme is the following. If X is a scheme, for each commutative ring A, we can define the set of the A-points of X in analogy to the way the classical geometers used to define the rational or integral points on a variety. The crucial difference is that we do not focus on just one commutative ring A, but we consider the A-points for all commutative rings A. In fact, the scheme we start from is completely recaptured only by the collection of the A-points for every commutative ring A, together with the admissible morphisms.

Let (rings) denote the category of commutative rings and (schemes) the category of schemes.

Let (|X|, OX) be a scheme and let T ∈ (schemes). We call the T-points of X, the set of all scheme morphisms {T → X}, that we denote by Hom(T, X). We then define the functor of points hX of the scheme X as the representable functor defined on the objects as

hX: (schemes)op → (sets), haX(A) = Hom(Spec A, X) = A-points of X

Notice that when X is affine, X ≅ Spec O(X) and we have

haX(A) = Hom(Spec A, O(X)) = Hom(O(X), A)

In this case the functor haX is again representable.

Consider the affine schemes X = Spec O(X) and Y = Spec O(Y). There is a one-to-one correspondence between the scheme morphisms X → Y and the ring morphisms O(X) → O(Y). Both hX and haare defined on morphisms in the natural way. If φ: T → S is a morphism and ƒ ∈ Hom(S, X), we define hX(φ)(ƒ) = ƒ ○ φ. Similarly, if ψ: A → Bis a ring morphism and g ∈ Hom(O(X), A), we define haX(ψ)(g) = ψ ○ g. The functors hX and haare for a given scheme X not really different but carry the same information. The functor of points hof a scheme X is completely determined by its restriction to the category of affine schemes, or equivalently by the functor

haX: (rings) → (sets), haX(A) = Hom(Spec A, X)

Let M = (|M|, OM) be a locally ringed space and let (rspaces) denote the category of locally ringed spaces. We define the functor of points of locally ringed spaces M as the representable functor

hM: (rspaces)op → (sets), hM(T) = Hom(T, M)

hM is defined on the manifold as

hM(φ)(g) = g ○ φ

If the locally ringed space M is a differentiable manifold, then

Hom(M, N) ≅ Hom(C(N), C(M))

This takes us to the theory of Yoneda’s Lemma.

Let C be a category, and let X, Y be objects in C and let hX: Cop → (sets) be the representable functors defined on the objects as hX(T) = Hom(T, X), and on the arrows as hX(φ)(ƒ) = ƒ . φ, for φ: T → S, ƒ ∈ Hom(T, X)

If F: Cop → (sets), then we have a one-to-one correspondence between sets:

{hX → F} ⇔ F(X)

The functor

h: C → Fun(Cop, (sets)), X ↦ hX,

is an equivalence of C with a full subcategory of functors. In particular, hX ≅ hY iff X ≅ Y and the natural transformations hX → hY are in one-to-one correspondence with the morphisms X → Y.

Two schemes (manifolds) are isomorphic iff their functors of points are isomorphic.

The advantages of using the functorial language are many. Morphisms of schemes are just maps between the sets of their A-points, respecting functorial properties. This often simplifies matters, allowing allowing for leaving the sheaves machinery in the background. The problem with such an approach, however, is that not all the functors from (schemes) to (sets) are the functors of points of a scheme, i.e., they are representable.

A functor F: (rings) → (sets) is of the form F(A) = Hom(Spec A, X) for a scheme X iff:

F is local or is a sheaf in Zariski Topology. This means that for each ring R and for every collection αi ∈ F(Rƒi), with (ƒi, i ∈ I) = R, so that αi and αj map to the same element in F(Rƒiƒj) ∀ i and j ∃ a unique element α ∈ F(R) mapping to each αi, and

F admits a cover by open affine subfunctors, which means that ∃ a family Ui of subfunctors of F, i.e. Ui(R) ⊂ F(R) ∀ R ∈ (rings), Ui = hSpec Ui, with the property that ∀ natural transformations ƒ: hSpec A  → F, the functors ƒ-1(Ui), defined as ƒ-1(Ui)(R) = ƒ-1(Ui(R)), are all representable, i.e. ƒ-1(Ui) = hVi, and the Vi form an open covering for Spec A.

This states the conditions we expect for F to be the functor of points of a scheme. Namely, locally, F must look like the functor of points of a scheme, moreover F must be a sheaf, i.e. F must have a gluing property that allows us to patch together the open affine cover.

Hypostatic Abstraction. Thought of the Day 138.0

maxresdefault

Hypostatic abstraction is linguistically defined as the process of making a noun out of an adjective; logically as making a subject out of a predicate. The idea here is that in order to investigate a predicate – which other predicates it is connected to, which conditions it is subjected to, in short to test its possible consequences using Peirce’s famous pragmatic maxim – it is necessary to posit it as a subject for investigation.

Hypostatic abstraction is supposed to play a crucial role in the reasoning process for several reasons. The first is that by making a thing out of a thought, it facilitates the possibility for thought to reflect critically upon the distinctions with which it operates, to control them, reshape them, combine them. Thought becomes emancipated from the prison of the given, in which abstract properties exist only as Husserlian moments, and even if prescission may isolate those moments and induction may propose regularities between them, the road for thought to the possible establishment of abstract objects and the relations between them seems barred. The object created by a hypostatic abstraction is a thing, but it is of course no actually existing thing, rather it is a scholastic ens rationis, it is a figment of thought. It is a second intention thought about a thought – but this does not, in Peirce’s realism, imply that it is necessarily fictitious. In many cases it may indeed be, but in other cases we may hit upon an abstraction having real existence:

Putting aside precisive abstraction altogether, it is necessary to consider a little what is meant by saying that the product of subjectal abstraction is a creation of thought. (…) That the abstract subject is an ens rationis, or creation of thought does not mean that it is a fiction. The popular ridicule of it is one of the manifestations of that stoical (and Epicurean, but more marked in stoicism) doctrine that existence is the only mode of being which came in shortly before Descartes, in concsequence of the disgust and resentment which progressive minds felt for the Dunces, or Scotists. If one thinks of it, a possibility is a far more important fact than any actuality can be. (…) An abstraction is a creation of thought; but the real fact which is important in this connection is not that actual thinking has caused the predicate to be converted into a subject, but that this is possible. The abstraction, in any important sense, is not an actual thought but a general type to which thought may conform.

The seemingly scepticist pragmatic maxim never ceases to surprise: if we take all possible effects we can conceive an object to have, then our conception of those effects is identical with our conception of that object, the maxim claims – but if we can conceive of abstract properties of the objects to have effects, then they are part of our conception of it, and hence they must possess reality as well. An abstraction is a possible way for an object to behave – and if certain objects do in fact conform to this behavior, then that abstraction is real; it is a ‘real possibility’ or a general object. If not, it may still retain its character of possibility. Peirce’s definitions of hypostatic abstractions now and then confuse this point. When he claims that

An abstraction is a substance whose being consists in the truth of some proposition concerning a more primary substance,

then the abstraction’s existence depends on the truth of some claim concerning a less abstract substance. But if the less abstract substance in question does not exist, and the claim in question consequently will be meaningless or false, then the abstraction will – following that definition – cease to exist. The problem is only that Peirce does not sufficiently clearly distinguish between the really existing substances which abstractive expressions may refer to, on the one hand, and those expressions themselves, on the other. It is the same confusion which may make one shuttle between hypostatic abstraction as a deduction and as an abduction. The first case corresponds to there actually existing a thing with the quality abstracted, and where we consequently may expect the existence of a rational explanation for the quality, and, correlatively, the existence of an abstract substance corresponding to the supposed ens rationis – the second case corresponds to the case – or the phase – where no such rational explanation and corresponding abstract substance has yet been verified. It is of course always possible to make an abstraction symbol, given any predicate – whether that abstraction corresponds to any real possibility is an issue for further investigation to estimate. And Peirce’s scientific realism makes him demand that the connections to actual reality of any abstraction should always be estimated (The Essential Peirce):

every kind of proposition is either meaningless or has a Real Secondness as its object. This is a fact that every reader of philosophy should carefully bear in mind, translating every abstractly expressed proposition into its precise meaning in reference to an individual experience.

This warning is directed, of course, towards empirical abstractions which require the support of particular instances to be pragmatically relevant but could hardly hold for mathematical abstraction. But in any case hypostatic abstraction is necessary for the investigation, be it in pure or empirical scenarios.

Affine Schemes

1-s2.0-S0022404915000730-fx001

Let us associate to any commutative ring A its spectrum, that is the topological space Spec A. As a set, Spec A consists of all the prime ideals in A. For each subset S A we define as closed sets in Spec A:

V(S) := {p ∈ Spec A | S ⊂ p} ⊂ Spec A

If X is an affine variety, defined over an algebraically closed field, and O(X) is its coordinate ring, we have that the points of the topological space underlying X are in one-to-one correspondence with the maximal ideals in O(X).

We also define the basic open sets in Spec A as

Uƒ := Spec A \ V(ƒ) = Spec Aƒ with ƒ ∈ A,

where Aƒ = A[ƒ-1] is the localization of A obtained by inverting the element ƒ. The collection of the basic open sets Uƒ, ∀ ƒ ∈ A forms a base for Zariski topology. Next, we define the structure sheaf OA on the topological space Spec A. In order to do this, it is enough to give an assignment

U ↦ OA(U) for each basic open set U = Uƒ in Spec A.

The assignment

Uƒ ↦ Aƒ

defines a B-sheaf on the topological space Spec A and it extends uniquely to a sheaf of commutative rings on Spec A, called the structure sheaf and denoted by OA. Moreover, the stalk at a point p ∈ Spec A, OA,p is the localization Ap of the ring at the prime p. While the differentiable manifolds are locally modeled, as ringed spaces, by (Rn, CRn), the schemes are geometric objects modeled by the spectrum of commutative rings.

Affine scheme is a locally ringed space isomorphic to Spec A for some commutative ring A. We say that X is a scheme if X = (|X|, OX) is a locally ringed space, which is locally isomorphic to affine schemes. In other words, for each x ∈ |X|, ∃ an open set Ux ⊂ |X| such that (Ux, OX|Ux) is an affine scheme. A morphism of schemes is just a morphism of locally ringed spaces.

There is an equivalence of categories between the category of affine schemes (aschemes) and the category of commutative rings (rings). This equivalence is defined on the objects by

(rings)op → (aschemes), A Spec A

In particular a morphism of commutative rings A → B contravariantly to a morphism Spec B → Spec A of the corresponding affine superschemes.

Since any affine variety X is completely described by the knowledge of its coordinate ring O(X), we can associate uniquely to an affine variety X, the affine scheme Spec O(X). A morphism between algebraic varieties determines uniquely a morphism between the corresponding schemes. In the language of categories, we say we have a fully faithful functor from the category of algebraic varieties to the category of schemes.

Conjuncted: Balance of Payments in a Dirty Float System, or Why Central Banks Find It Ineligible to Conduct Independent Monetary Policies? Thought of the Day

Exchange_rate_arrangements_map

Screen Shot 2018-01-19 at 10.40.54 AM

If the rate of interest is partly a monetary phenomenon, money will have real effects working through variations in investment expenditure and the capital stock. Secondly, if there are unemployed resources, the impact of increases in the money supply will first be on output, and not on prices. It was, indeed, Keynes’s view expressed in his General Theory that throughout history the propensity to save has been greater than the propensity to invest, and that pervasive uncertainty and the desire for liquidity has in general kept the rate of interest too high. Given the prevailing economic conditions of the 1930s when Keynes was writing, it was no accident that he should have devoted part of the General Theory to a defence of mercantilism as containing important germs of truth:

What I want is to do justice to schools of thought which the classicals have treated as imbeciles for the last hundred years and, above all, to show that I am not really being so great an innovator, except as against the classical school, but have important predecessors, and am returning to an age-long tradition of common sense.

The mercantilists recognised, like Keynes, that the rate of interest is determined by monetary conditions, and that it could be too high to secure full employment, and in relation to the needs of growth. As Keynes put it in the General Theory:

mercantilist thought never supposed as later economists did [for example, Ricardo, and even Alfred Marshall] that there was a self-adjusting tendency by which the rate of interest would be established at the appropriate level [for full employment].

It was David Ricardo, in his The Principles of Political Economy and Taxation, who accepted and developed Say’s law of markets that supply creates its own demand, and who for the first time expounded the theory of comparative advantage, which laid the early foundations for orthodox trade and growth theory that has prevailed ever since. Ricardian trade theory, however, is real theory relating to the reallocation of real resources through trade which ignores the monetary aspects of trade; that is, the balance between exports and imports as trade takes place. In other words, it ignores the balance of payments effects of trade that arises as a result of trade specialization, and the feedback effects that the balance of payments can have on the real economy. Moreover, continuous full employment is assumed because supply creates its own demand through variations in the real rate of interest. These aspects question the prevalence of Ricardian theory in orthodox trade and growth theory to a large extent in today’s scenario. But in relation to trade, as Keynes put it:

free trade assumes that if you throw men out of work in one direction you re-employ them in another. As soon as that link in the chain is broken the whole of the free trade argument breaks down.

In other words, the real income gains from specialization may be offset by the real income losses from unemployment. Now, suppose that payments deficits arise in the process of international specialization and the freeing of trade, and the rate of interest has to be raised to attract foreign capital inflows to finance them. Or suppose deficits cannot be financed and income has to be deflated to reduce imports. The balance of payments consequences of trade may offset the real income gains from trade.

This raises the question of why the orthodoxy ignores the balance of payments? There are several reasons, both old and new, that all relate to the balance of payments as a self-adjusting process, or simply as a mirror image of autonomous capital flows, with no income adjustment implied. Until the First World War, the mechanism was the gold standard. The balance of payments was supposed to be self-equilibrating because countries in surplus, accumulating gold, would lose competitiveness through rising prices (Hume’s quantity theory of money), and countries in deficit losing gold would gain competitiveness through falling prices. The balance of payments was assumed effectively to look after itself through relative price adjustments without any change in income or output. After the external gold standard collapsed in 1931, the theory of flexible exchange rates was developed, and it was shown that if the real exchange rate is flexible, and the so-called Marshall–Lerner condition is satisfied (i.e. the sum of the price elasticities of demand for exports and imports is greater than unity), the balance of payments will equilibrate; again, without income adjustment.

In modern theory, balance of payments deficits are assumed to be inherently temporary as the outcome of inter-temporal decisions by private agents concerning consumption. Deficits are the outcome of rational decisions to consume now and pay later. Deficits are merely a form of consumption smoothing, and present no difficulty for countries. And then there is the Panglossian view that the current account of the balance of payments is of no consequence at all because it simply reflects the desire of foreigners to invest in a country. Current account deficits should be seen as a sign of economic success, not as a weakness.

It is not difficult to question how balance of payments looks after itself, or does not have consequences for long-run growth. As far as the old gold standard mechanism is concerned, instead of the price levels of deficit and surplus countries moving in opposite directions, there was a tendency in the nineteenth century for the price levels of countries to move together in the same direction. In practice, it was not movements in relative prices that equilibrated the balance of payments but expenditure and output changes associated with interest rate differentials. Interest rates rose in deficit countries which deflated demand and output, and fell in surplus countries stimulating demand.

On the question of flexible exchange rates as an equilibrating device, a distinction first needs to be made between the nominal exchange rate and the real exchange rate. It is easy for countries to adjust the nominal rate, but not so easy to adjust the real rate because competitors may “price to market” or retaliate, and domestic prices may rise with a nominal devaluation. Secondly, the Marshall–Lerner condition then has to be satisfied for the balance of payments to equilibrate. This may not be the case in the short run, or because of the nature of goods exported and imported by a particular country. The international evidence over the past almost half a century years since the breakdown of the Bretton Woods fixed exchange rate system suggests that exchange rate changes are not an efficient balance of payments adjustment weapon. Currencies appreciate and depreciate and still massive global imbalances of payments remain.

On the inter-temporal substitution effect, it is wrong to give the impression that inter-temporal shifts in consumption behaviour do not have real effects, particularly if interest rates have to rise to finance deficits caused by more consumption in the present if countries do not want their exchange rate to depreciate. On the view that deficits are a sign of success, an important distinction needs to be made between types of capital inflows. If the capital flows are autonomous, such as foreign direct investment, the argument is plausible, but if they are “accommodating” in the form of loans from the banking system or the sale of securities to foreign governments and international organizations, the probable need to raise interest rates will again have real effects by reducing investment and output domestically.