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.

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_;μ^;μ = 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:

k_BT = ħα/2π, α := |dv/dz|_v=-1 —– (2)

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.

 

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

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

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?

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|, O_X) 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 h_X of the scheme X as the representable functor defined on the objects as

h_X: (schemes)^op → (sets), h^a_X(A) = Hom(Spec A, X) = A-points of X

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

h^a_X(A) = Hom(Spec A, O(X)) = Hom(O(X), A)

In this case the functor h^a_X 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 h_X and h^a_X are defined on morphisms in the natural way. If φ: T → S is a morphism and ƒ ∈ Hom(S, X), we define h_X(φ)(ƒ) = ƒ ○ φ. Similarly, if ψ: A → Bis a ring morphism and g ∈ Hom(O(X), A), we define h^a_X(ψ)(g) = ψ ○ g. The functors h_X and h^a_X are for a given scheme X not really different but carry the same information. The functor of points h_X of a scheme X is completely determined by its restriction to the category of affine schemes, or equivalently by the functor

h^a_X: (rings) → (sets), h^a_X(A) = Hom(Spec A, X)

Let M = (|M|, O_M) 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

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

h_M is defined on the manifold as

h_M(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 h_X: C^op → (sets) be the representable functors defined on the objects as h_X(T) = Hom(T, X), and on the arrows as h_X(φ)(ƒ) = ƒ . φ, for φ: T → S, ƒ ∈ Hom(T, X)

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

{h_X → F} ⇔ F(X)

The functor

h: C → Fun(C^op, (sets)), X ↦ h_X,

is an equivalence of C with a full subcategory of functors. In particular, h_X ≅ h_Y iff X ≅ Y and the natural transformations h_X → h_Y 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 α_i ∈ F(R_ƒi), with (ƒ_i, i ∈ I) = R, so that α_i and α_j map to the same element in F(R_ƒiƒj) ∀ i and j ∃ a unique element α ∈ F(R) mapping to each α_i, and

F admits a cover by open affine subfunctors, which means that ∃ a family U_i of subfunctors of F, i.e. U_i(R) ⊂ F(R) ∀ R ∈ (rings), U_i = h_Spec Ui, with the property that ∀ natural transformations ƒ: h_Spec A  → F, the functors ƒ^-1(U_i), defined as ƒ^-1(U_i)(R) = ƒ^-1(U_i(R)), are all representable, i.e. ƒ^-1(U_i) = h_Vi, and the V_i 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

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

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

U_ƒ := Spec A \ V(ƒ) = Spec A_ƒ with ƒ ∈ A,

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

U ↦ O_A(U) for each basic open set U = U_ƒ in Spec A.

The assignment

U_ƒ ↦ A_ƒ

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 O_A. Moreover, the stalk at a point p ∈ Spec A, O_A,p is the localization A_p of the ring at the prime p. While the differentiable manifolds are locally modeled, as ringed spaces, by (Rⁿ, C^∞_Rⁿ), 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|, O_X) is a locally ringed space, which is locally isomorphic to affine schemes. In other words, for each x ∈ |X|, ∃ an open set U_x ⊂ |X| such that (U_x, O_X|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

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.

17th Century England – Onwards to Restoration.

In the 17^th century England, the middle class had carried forward their rebellion against absolute monarchy based on divine rights. The Parliament was the representation of this class and its fight. The men who now fought the Stuart Kings were precisely those who had profited from Tudor absolutism, which now began to irritate them. The lower middle class then split from their upper counterpart and rallied Cromwell. So far as the untitled and unmoneyed class was concerned, they stood largely by the throne, although they had as little to gain by the King as by the Parliament. The middle class was so afraid of the poor people as of the King. When the parliamentarians talked of a government based on consent, they had no intention of extending the franchise to the people; it was to be their own consent. Right to property, which they held to be sacred, meant to them the principle that the King had no right to tax them without their consent; it also meant a denial of property to the people who were poor.

Coke, who was appointed the Attorney General (and also the Chief Justice) in 1594, was attacking the divine rights of Kings and he regarded both King and the Parliament, as subject to common law which, to him, was the truly sovereign power in the land. Common law had to be interpreted by the judges. Throughout Europe, absolute state was becoming the order of the day. Louis XI had first subjugated the feudal nobility. The Reformation then enabled the monarchs to better the Church. Henry VIII had claimed jurisdiction and powers, which earlier no British King had done. To the discomfiture of Hobbes, the cursed Puritans had undone the work so artistically done by Henry VIII and the price had to be redesigned so that the fabric may be saved from total destruction in the hands of the rabble. Someone, like Thomas Hobbes agrees with Machiavelli that man is selfish and that human nature is bad but insists that the state could transfer the man into a moral being by the exercise of the master’s rod.  He is indebted to Bodin for his concept of sovereignty, but, unlike Bodin, would impose no limitations of Divine, Natural or Constitutional law on his subjects. He agrees with Grotius that, reason is the basis of law but insists that it must be sovereign’s reason alone. He modifies the Divine Right theory by discarding the divine origin of state and by giving Divine Right to the State instead to the King. Hobbes like Machiavelli, subordinated ethics and religion to politics and was the first prophet of unlimited sovereignty.

Elizabeth (1558 – 1603)

Elizabeth was the daughter of Henry VIII and Anne Boleyn. She ascended to the throne at the age of 25 in 1558 on the death of Queen Mary. She was not only regal but also human. Like her father, she had courage, determination and self-confidence. She was willful and domineering in all matters. Like her mother she was fond of pomp and pleasure. Her great virtue was that she loved the people of England and for their sake she was prepared to make any sacrifices. Her conservative mind made extreme Protestantism suspect to her, separated the foreign policy from any enthusiasm and fitted her to be the real maker of Anglicanism.

When she ascended to the throne, she had to face many difficulties. There was the danger of the civil war in the country. The orthodox Catholics regarded Elizabeth as an usurper and they were prepared to take up arms against her in order to support the cause of Mary Stuart. The Protestants were also bitter. They were determined to carry the Reformation further. There was also a danger of foreign invasion and conquest. A lot of money had been wasted in the French war during the reign of Mary Tudor. The coinage had also been debased. The credit goes to Elizabeth that she not only surmounted all these difficulties but were also able to make her country great and strong.

Religion at her time of ascension

The first great achievement of Elizabeth was her religious settlement. The policy followed by her was that she stopped the burning of the people. The “Act of Supremacy” eliminated the authority of the Pope in England and made Elizabeth the head of the Church of England. She took up the title of “Supreme Governor” and not “Supreme Head” as had been done by her father. The monasteries were dissolved and their lands were passed to the crown. A Book of Common Prayer in English was issued. Extremists among the Catholics and the Protestants were not prepared to reconcile themselves with her religious settlement. However, Elizabeth did not take any strong action against them so long as the people attended the Church. The Church settlement got a setback after 1570, when the Pope issued an excommunication and deposed Elizabeth and declared her to be longer a Queen of England. Her subjects were absolved from their allegiance to her. In 1571, the British Parliament passed an Act, which declared to be high treason for anyone in England to call the Queen a heretic, and usurper or an infidel. The puritans also attacked the Church settlement. They were utterly dissatisfied by the moderate character of it. Most of the ceremonies prescribed by the Church were considered by them to be a relic of Popery and they would like to abolish the same. However, the fact remains that, Elizabeth succeeded in attaining a large unity in the Church and that is the reason why she was successful against Spain, when the Armada attacked England in 1558.

Her foreign policy

The foreign policy of Elizabeth was essentially that of peace. Since England had been weakened in the reigns of Edward VI and Mary Tudor, it was not in her interest to fight against any foreign power in that condition. Her great danger was an invasion from France or Spain, both Catholic countries. However, Elizabeth took advantage of the bitter rivalry going on between France and Spain and was successful in playing off the one against the other. Her foreign policy approach was not dogmatic, but was guided by enlightened national interest. The reign of Elizabeth saw the beginning of English maritime activity. It brought naval supremacy to England.

Her rule in general

Elizabeth can rightly be called as one of the greatest rulers of England. No other ruler was called upon to face so many difficulties and none else faced them so boldly and successfully. She addressed in these words a deputation of both the houses of Parliament: “Though I be a woman, I’ve as good a courage answerable to my place as ever my father had. I’m your anointed Queen. I’ll never be by violence constrained to do anything. I thank God that I’d been endued with such qualities that if I were turned out of the realm in my petticoat, I were able to live in any place in Christendom.” She was the child of the Renaissance rather than that of the Reformation. Skeptical and tolerant in the age of intolerance, she was born and brought up to re-establish the Anglican Church and to evade religious war by a compromise between the Catholics and Protestants.

Tudor rule 

Tudor rule was arbitrary and autocratic in nature. It was despotism, under more or less parliamentary forms. Though despots, their rule was not a tyranny. It was popular despotism based upon the assent of the people and it was assented to because in the main it identified itself with national interests. Their rule in nature was of the dictatorship. The rising middle class called for a strong ruler and was ready to overlook his violence and unconstitutional acts if he would maintain peace and order. The policy of the Tudors was to rule with the support of the subservient Parliament. As a result, Parliament was degraded into an instrument of royal will. The Tudors had broken the power of the great nobles. Monarchs could influence elections and so secure the return of members who favoured his views. Thus, as against the sovereign, Parliament had little influence. The Tudors, however, never sought to override the authority of the Parliament. On the contrary, they encouraged the parliamentary action of the commons. Grave and momentous questions were brought before it such as the anti-papal measures, which cut off Pope’s authority in England. As a consequence, the importance of Parliament increased. The commons grew more self-reliant and were gradually fitted to shake off their tutelage to the crown. There was little friction between the Crown and the Parliament. Parliament submitted to royal guidance and the sovereign in its turn never sought to override its legislative authority.

One of the most important characteristics of the Tudor rule was the growth of the strong monarchy built upon the ruins of the feudal system. That was partly due to the decline of the power of the nobility and the invention of the gunpowder. Another important point was the broadening of the people’s minds on account of the Renaissance movement. The new spirit paved the way for the Reformation movement.

James I (1603 – 1625) 

James I ruled from 1603 to 1625. He was born in 1556 and he came to the throne after the expulsion of his mother from Scotland. When his mother was a prisoner in England, he was the King of Scotland. He did nothing to support the cause of his mother. The result was that Elizabeth accepted him as her successor to the throne of England. He had been brought up under rigid Calvinist discipline. He failed as the King of England, even though he was a man of great learning. He was so fond of “unbuttoning his royal stores of wisdom for the benefits of his subjects” that Henry IV of France called him the “wisest fool in Christendom”. He was intolerant to any criticism. He believed that Kings should have supreme authority over all. He believed that people had no right to revolt. “The state of monarchy is the supremest thing on Earth; for Kings are not only God’s lieutenants upon Earth and sit upon God’s throne, but even by God Himself, they are called Gods…it is sedition in subjects to dispute what a King may do in the height of his power. I will not be content that my power be disputed on.” 

Here is an extract from the Vicar of Bray, an old ballad:

                  To teach his flock he never missed,

                  Kings are by God appointed,

                  And damned are they, who do resist,

                  Or touch the Lord’s Anointed.

He had fixed views about politics and the status of Kings. He believed in the Divine Rights of Kings. This view was that Kings were Kings because God made them Kings and they were responsible to God alone for whatever they did and the people had no right to either find fault with them or to challenge their authority. It was this concept of monarchy that was responsible for all his troubles. James I stood for universal peace. He raised the slogan of “Beati Pacifici” (Blessed are the peace makers). His ideas of religious toleration were a cry in the wilderness. In spite of his good intentions, he was a complete failure as a king.

His relations with the Parliament

The relations between James I and the Parliament were not cordial. He believed in the Divine Rights of Kings, but the Parliament claimed certain rights on the basis of tradition, customs and evolutionary growth. Parliament based its rights and privileges on the score of History. Parliament, during the reign of James I, asserted with success its right to impeach the ministers of the King. It protested against the new impositions. It passed its law against monopolies. It asserted its rights to discuss all the affairs of the State although the King strongly protested against the claim. It failed to secure the right of meeting regularly. From these relations, it was clear that the struggle between the two had begun.

Common law

No account of the reign of James I can be complete without a reference to the common law lawyers headed by the Chief Justice Coke. In 1594, Coke was appointed Attorney General. He was a great champion of the common law. His view was that the propriety of all actions must be judged by the common law. There was no place for the Divine Rights of the Kings. The judges alone could resolve the conflicts between the prerogatives and the statutes. The view of Coke was different from that of Bacon who held that judges were lions, but lions under the throne. It was during the reign of James I that many English colonies were established beyond the seas. In 1612, the English East India Company set up its factory at Surat (Gujarat, India). Thus, the beginnings of the future British Empire in India and America were laid during the reign of James I.

Charles I (1625 – 1649)

James I died on the 27^th March 1625 and was succeeded by his second son, Charles I. Charles I loved those who were close near him, but was cold towards others. He was devoted to the Church of England and was punctual in his devotion to it. To Charles I, the Divine Right was the question of his faith, as deeply rooted as his belief in the Church. He was a bad judge of public questions and political men. He viewed them through the lens of his affections. He saw only rebellion in the critics of the Church of England. The reign of Charles I can be divided into four periods. The first four years of his reign from 1625 to 1629 covered the first period. During this period foreign wars were fought but lost and the relations between the King and the Parliament were bitter. The second period was covered by the years from 1629 to 1640. During this period, he ruled without a Parliament. The third period was covered by the years 1640 to 1642. It was also a period of short and long Parliament. The fourth period is covered by the two Civil wars (1642 – 1649). Charles I was executed in January 1649.

Relations with the Parliament 

The fundamental dispute between the King and the Parliament was that the Parliament was determined to become the sovereign of the country and was not prepared to allow the King to do whatever he wanted to do. The execution of Charles I shocked the people. The people were not in favour of Parliament going to such an extreme. The dignified behaviour of the King at the time of his execution also excited universal admiration. There was a strong reaction in favour of the monarch. Many called him the martyr who died for the Church of England. There were others who gave him the credit for having died for the laws and liberties of the English men. A few days after his death, a book entitled “Sikon Basilike” was published. It purported to give the views of the King on Government. It was felt that the dictatorship of the army was no guarantee to safeguard the popular institutions of England and the liberties of the people. The army could fight but could not reconstruct society. This execution was followed by military despotism, which was as bad as the tyranny of the King himself. The question has been asked whether the execution of Charles I was justified or not. From the legal point of view, there was no justification for trying the King as no process could be issued against the monarch. Moreover, the members of the court were partisans and did not come up to the ideal of impartiality as required by the judges. The only justification for the execution of Charles I was moral and political. Cromwell was right in saying that it was a cruel necessity. It was cruel because it was an extreme measure involving the execution of the King. It was a necessity because without it there would have been no liberty for Englishmen. Charles I was not at all prepared to accept any limitations on his powers. He was given many opportunities both by the Parliament and the army to come to reasonable compromise but he was declared dishonest by these very bodies and hence it was difficult to come to any sort of an agreement with him. The Parliament and the army always thought of him as extremely cynical and his dealings with these two constitutional bodies were inherently insincere in nature and thus no wonder such an insincere man was put to death.

Commonwealth 

The Commonwealth was established in England on January 4, 1649 by a proclamation by the Rump Parliament that “the people are, under God, the origin of all just power…that the commons of England in Parliament assembled, being chosen by and representing the people have the supreme power in this nation”. On February 5, the Rump decided that the House of Lords, being dangerous and useless, should be abolished. On February 6, it was resolved that “it hath been found by experience and this House doth declare that the office of the King in this nation and to have power thereof in any single person, is unnecessary and burdensome and dangerous to the liberty, safety and public interest of the people of this nation and thereof ought to be abolished”. On March 17 and 19, 1649, two Acts were passed by which the offices of the King and the House of Lords were abolished. Thus the House of Commons became the sole governing body of England. The chief organ of administration of the Commonwealth was the Council of the State. It was annually chosen by the Parliament. The council was concerned with the army, the navy, foreign affairs etc. In July 1649, was passed the “Treason Act”, which made it treasonable for anyone who published maliciously that “the Government is usurped or unlawful or that the Commons assembled in Parliament are not the supreme authority of this nation”. In September 1649, was passed the “Press Act” which muzzled the freedom of the press. The publication of any printed material without a license from the Government was forbidden. A special court of justice consisting of 12 judges was established to liquidate the enemies of the Commonwealth.

The members of the Parliament were Presbyterians and they insisted on imposing “certain fundamentals before a man should be free to propagate his opinions”. Cromwell was in favour of religious toleration for all except the Roman Catholics. Certain changes were introduced in the Church whereby it became less Presbyterian. It lost its autonomy and became subordinate to the State. Rump Parliament was “the first English Government to appreciate the importance of sea power”. It also was responsible for England a great sea power. The Rump Parliament also attended to foreign trade and the overseas empire of England. In 1651, was passed the “Navigation Act”. This Act was intended to strike a blow at the commercial power of Holland and no wonder it aroused the indignation of that country. The Rump had become unpopular with the army because it was a small body, which did not represent the whole nation. Moreover, many of its members were guilty of favouritism and corruption. Cromwell and his army urged the dissolution of the Parliament but the Rump refused to be dissolved. Cromwell could not tolerate the pride ambition and self-seeking of the members of the Parliament. On April 20, 1653, Cromwell himself went to the House of the Commons and turned out the members of the House and had the doors locked. The same afternoon, the Council of State also fell before military violence. After the dissolution of the Rump, Cromwell set up a new council of State which recommended that a Parliament of saints composed of 140 Godly men, 129 from England, 5 from Scotland and 6 from Ireland be summoned. This Parliament met in 1653. it is also known as Barebone’s Parliament. This Parliament was a unique one and it passed many laws like the solemnization of marriage a civil institution, public registration of births, marriages and death. Another law provided for the better custody of insanes. But this Parliament too failed. Cromwell was essentially a reluctant and an apologetic dictator. Lambert drew up a constitutional document called the “Instrument of Government”. It was the first and the last written English constitution. By this instrument, Cromwell was made Lord Protector for life with Council of State to help him. England, Scotland and Ireland were to be united in a single commonwealth with a Parliament representing the three countries. Parliament consisting of one House was to possess the legislative power and was to be elected every three years by a reformed electorate. This instrument gave Cromwell a limited monarchy for life. While the peculiarity of the English constitution was that it was flexible and unwritten, but the instrument tried to make it rigid and written.

Cromwell

Cromwell was one of the greatest figures in the History of England. He was born in 1599 at Huntington. He was a son of a country gentleman and was educated in a college in Cambridge. He emerged as a leader of his country when she was plunged in a Civil war on account of the conflict between the King and the Parliament. He not only won victories for the Parliament but also restored law and order in the country. Cromwell was the first pronounced imperialist in the history of England. His objective was to extend the power of England overseas and he did not hesitate to use all possible means to achieve that end. In his foreign policy, he showed zeal for Protestantism, but while doing so, he did not ignore the trade and commerce of his country. He was himself a Republican, but circumstances forced him to act as a military despot. He tried to govern by a system involving the division of power between himself and the Parliament. When he failed in that objective, he ruled despotically. He levied taxes without the sanction of the Parliament. He imprisoned people without trial. As a matter of fact, he set up a military tyranny. He wished for the Parliament to be supreme and did not wish to take up the title of the King. His faith in God was both a source of his strength and his weakness. In all that he did, whether good or evil, in the three kingdoms, his conviction was that God would support him in everything that he undertook. What he judged to be necessary for the present, that he thought to be predestined for the future. His victories seemed to him, not the result of the means, which he employed, but proofs that his policies were also the will of the Divine. Although he is regarded by some as the greatest patriot and by others as the greatest traitor, he was without doubt one of the greatest men of his country. He possessed military capacity of a very high order. He organized and maintained an army, which was so efficient that he did not meet with any defeat. Oliver Cromwell died on September 3,1658. When his strong hand was removed, the country was plunged into confusion. The Levellers stood for a Republic in which the common people were to rule without Lords, Priests or Lawyers. They had a very treatment from Oliver Cromwell but now they felt that they could do whatever they pleased. Another set known as the Fifth Monarchy Men was led by Harrison. They foretold the immediate end of the world. According to their reading of Daniel, the four monarchies of antiquity, Babylonia, Persia, Greece, and Rome were to be succeeded by the fifth monarchy, now at hand, the reign of Christ and his Saints.

Oliver Cromwell had named his son Richard Cromwell to succeed as the Lord Protector. He lacked political capacity and had no advisers. The gulf between Richard and the army was widening. In order to strengthen his position, Richard decided to summon the Parliament and the members of the Parliament were hostile to the army. The army did not like the law, which forbade the army officers from having political meetings. Parliament was dissolved by force in April 1659 and the Rump was recalled. Richard resigned his charge. About the period between 1649 and 1660, monarchy had gone and the House of Lords was established as “useless and dangerous”. This “freedom” was to rise to a climax of Puritan democracy, to decline by reaction into military dictatorship and at last to expire through faction. But it left a legacy. Puritanism released an energy, which called for liberty in religion and every department of life with efficiency greater than anything England had seen. It took long strides towards union with Scotland and Ireland. Its administrative machinery pointed towards the cabinet and its economic doctrine led to the capitalist Britain of the next two centuries.

Restoration

The Restoration of Charles II to the throne of England in 1660 was not merely the restoration of the King but also of Parliament, the Anglican Church, the historic law courts and the old system of local governments in the country. It is wrong to say that the monarchy that was restored was the unlimited and absolute monarchy of Charles I and James I. The “Triennial Act” of 1641 had not been repealed and it meant that the King could not carry on Government without calling a Parliament at least once in three years. Thus, the “Triennial Act” put a check on the power of the King. The result was that Charles II had to be less arbitrary and act according to the law. The very fact that Parliament had made Charles II, the King of England implied that in the last resort Parliament could also unmake him. The Divine Right of Kings to rule was practically dead. A point of conflict between the first two Stuart Kings and the Parliament was the question of taxation. Charles I had levied taxes without the consent of the Parliament. Now it was clearly understood that new taxes could be levied only with the consent of the Parliament. It is clear that although monarchy was restored, it was restored with a difference. Restoration gave to Parliament its old form and organization, which had so radically been changed during the Commonwealth period. The two Houses of the Parliament were restored and the House of Commons became more powerful than the House of Lords. Charles II never questioned the privileges of the Parliament. As a matter of fact, most of his important laws were passed through the Parliament.

Restoration of the Church

Restoration was also the restoration of the Church of England. The Parliament, which was elected in 1661 after the dissolution of the convention Parliament, was predominantly Anglican in nature. The Presbyterian element had disappeared altogether. The so-called Cavalier Parliament ended the work of the Presbyterian majority and restored the Anglican Church to its former position. The “Act of Uniformity” of 1662 provided that all clergymen and teachers were to declare their acceptance of the Anglican Prayer Book. The “Conventicle Act” of 1664 forbade under severe penalties, attendance of any public worship, which was not of Anglican form, of more than four persons, unless they belonged to the same family. The “Test Act” of 1673 provided that all civil and military officers were to take the oath of allegiance and accept the supremacy of the Church of England. In 1679, was passed the “Parliamentary Test Act” which provided that no person was to be a Member of Parliament unless he belonged to the Church of England. 1679 was also the year of Hobbes’ death. It is clear that the Anglican Church was established as a State Church, but with the difference that the headship of the Church no longer belonged to the King as a prerogative right. The leadership of the Church lay with the King-in-Parliament. As has been rightly put by Sir D. L. Keir that the restoration of monarchy in 1660 was especially a return to Government by Law. In this period, the legislative union with Scotland and Ireland was dissolved.

The reign of Charles II

During the reign of Charles II, some constitutional progress was made. The system of appropriation of supplies was established. While granting money to the King, the Parliament laid down the specific purpose for which the money was granted. The responsibility of the Ministers of Parliament was also secured to some extent. During the reign of Charles II, parliamentary parties with definite political programmes were formed and that also added to the strength of the Parliament. The passing of the “Habeas Corpus Act” in 1679 has become a cornerstone of the liberties of the people of England. The Parliament, which placed Charles II on the throne, was known as the Convention Parliament because it was summoned without a royal writ. The lands of the Royalists, which were confiscated, were restored. The Royal revenue was fixed at a fixed sum. Feudal dues and purveyance were abolished. A permanent excise tax was granted to the King as a compensation for the loss of his feudal revenues. The Convention Parliament was dissolved in 1661 and fresh elections were held. The new Parliament, which met in 1661, sat for 18 years and is known as the Cavalier Parliament. It was so called because the cavalier spirit was present among its members. This Parliament was royalist in nature in politics and Anglican in religion. It hated the Puritans and stood for the strengthening of the Church of England. It is true that during the reign of Charles II, the court was corrupt and there were pleasures all around. However, during this period, humanity and refinement spread rapidly in England. Literature, art and science, architecture and etiquette and fashions were copied from the court off Louis XIV, the grand monarch of France. One of the most notable men of this age wasIsaac Newton (1642 – 1727). There were great strides made in the disciplines of Astronomy, Physics, Chemistry and Medicine.

Bacteria’s Perception-Action Circle: Materiality of the Ontological. Thought of the Day 136.0

The unicellular organism has thin filaments protruding from its cell membrane, and in the absence of any stimuli, it simply wanders randomly around by changing between two characteristical movement patterns. One is performed by rotating the flagella counterclockwise. In that case, they form a bundle which pushes the cell forward along a curved path, a ‘run’ of random duration with these runs interchanging with ‘tumbles’ where the flagella shifts to clockwise rotation, making them work independently and hence moving the cell erratically around with small net displacement. The biased random walk now consists in the fact than in the presence of a chemical attractant, the runs happening to carry the cell closer to the attractant are extended, while runs in other directions are not. The sensation of the chemical attractant is performed temporally rather than spatially, because the cell moves too rapidly for concentration comparisons between its two ends to be possible. A chemical repellant in the environment gives rise to an analogous behavioral structure – now the biased random walk takes the cell away from the repellant. The bias saturates very quickly – which is what prevents the cell from continuing in a ‘false’ direction, because a higher concentration of attractant will now be needed to repeat the bias. The reception system has three parts, one detecting repellants such as leucin, the other detecting sugars, the third oxygen and oxygen-like substances.

The cell’s behavior forms a primitive, if full-fledged example of von Uexküll’s functional circle connecting specific perception signs and action signs. Functional circle behavior is thus no privilege for animals equipped with central nervous systems (CNS). Both types of signs involve categorization. First, the sensory receptors of the bacterium evidently are organized after categorization of certain biologically significant chemicals, while most chemicals that remain insignificant for the cell’s metabolism and survival are ignored. The self-preservation of metabolism and cell structure is hence the ultimate regulator which is supported by the perception-action cycles described. The categorization inherent in the very structure of the sensors is mirrored in the categorization of act types. Three act types are outlined: a null-action, composed of random running and tumbling, and two mirroring biased variants triggered by attractants and repellants, respectively. Moreover, a negative feed-back loop governed by quick satiation grants that the window of concentration shifts to which the cell is able to react appropriately is large – it so to speak calibrates the sensory system so that it does not remain blinded by one perception and does not keep moving the cell forward on in one selected direction. This adaptation of the system grants that it works in a large scale of different attractor/repellor concentrations. These simple signals at stake in the cell’s functional circle display an important property: at simple biological levels, the distinction between signs and perception vanish – that distinction is supposedly only relevant for higher CNS-based animals. Here, the signals are based on categorical perception – a perception which immediately categorizes the entity perceived and thus remains blind to internal differences within the category.

The mechanism by which the cell identifies sugar, is partly identical to what goes on in human taste buds. Sensation of sugar gradients must, of course, differ from the consumption of it – while the latter, of course, destroys the sugar molecule, the former merely reads an ‘active site’ on the outside of the macromolecule. E . Coli – exactly like us – may be fooled by artificial sweeteners bearing the same ‘active site’ on their outer perimeter, even if being completely different chemicals (this is, of course, the secret behind such sweeteners, they are not sugars and hence do not enter the digestion process carrying the energy of carbohydrates). This implies that E . coli may be fooled. Bacteria may not lie, but a simpler process than lying (which presupposes two agents and the ability of being fooled) is, in fact, being fooled (presupposing, in turn, only one agent and an ambiguous environment). E . coli has the ability to categorize a series of sugars – but, by the same token, the ability to categorize a series of irrelevant substances along with them. On the one hand, the ability to recognize and categorize an object by a surface property only (due to the weak van der Waal-bonds and hydrogen bonds to the ‘active site’, in contrast to the strong covalent bonds holding the molecule together) facilitates perception economy and quick action adaptability. On the other hand, the economy involved in judging objects from their surface only has an unavoidable flip side: it involves the possibility of mistake, of being fooled by allowing impostors in your categorization. So in the perception-action circle of a bacterium, some of the self-regulatory stability of a metabolism involving categorized signal and action involvement with the surroundings form intercellular communication in multicellular organisms to reach out to complicated perception and communication in higher animals.

The Biological Kant. Note Quote.

The biological treatise takes as its object the realm of physics left out of Kant’s critical demarcations of scientific, that is, mathematical and mechanistic, physics. Here, the main idea was that scientifically understandable Nature was defined by lawfulness. In his Metaphysical Foundations of Natural Science, this idea was taken further in the following claim:

I claim, however, that there is only as much proper science to be found in any special doctrine on nature as there is mathematics therein, and further ‘a pure doctrine on nature about certain things in nature (doctrine on bodies and doctrine on minds) is only possible by means of mathematics’.

The basic idea is thus to identify Nature’s lawfulness with its ability to be studied by means of mathematical schemata uniting understanding and intuition. The central schema, to Kant, was numbers, so apt to be used in the understanding of mechanically caused movement. But already here, Kant is very well aware of a whole series of aspects of spontaneuosly experienced Nature is left out of sight by the concentration on matter in movement, and he calls for these further realms of Nature to be studied by a continuation of the Copernican turn, by the mind’s further study of the utmost limits of itself. Why do we spontaneously see natural purposes, in Nature? Purposiveness is wholly different from necessity, crucial to Kant’s definition of Nature. There is no reason in the general concept of Nature (as lawful) to assume that nature’s objects may serve each other as purposes. Nevertheless, we do not stop assuming just that. But what we do when we ascribe purposes to Nature is using the faculties of mind in another way than in science, much closer to the way we use them in the appreciation of beauty and art, the object of the first part of the book immediately before the treatment of teleological judgment. This judgment is characterized by a central distinction, already widely argued in this first part of the book: the difference between determinative and reflective judgments, respectively. While the judgment used scientifically to decide whether a specific case follows a certain rule in explanation by means of a derivation from a principle, and thus constitutes the objectivity of the object in question – the judgment which is reflective lacks all these features. It does not proceed by means of explanation, but by mere analogy; it is not constitutive, but merely regulative; it does not prove anything but merely judges, and it has no principle of reason to rest its head upon but the very act of judging itself. These ideas are now elaborated throughout the critic of teleological judgment.

In the section Analytik der teleologischen Urteilskraft, Kant gradually approaches the question: first is treated the merely formal expediency: We may ascribe purposes to geometry in so far as it is useful to us, just like rivers carrying fertile soils with them for trees to grow in may be ascribed purposes; these are, however, merely contingent purposes, dependent on an external telos. The crucial point is the existence of objects which are only possible as such in so far as defined by purposes:

That its form is not possible after mere natural laws, that is, such things which may not be known by us through understanding applied to objects of the senses; on the contrary that even the empirical knowledge about them, regarding their cause and effect, presupposes concepts of reason.

The idea here is that in order to conceive of objects which may not be explained with reference to understanding and its (in this case, mechanical) concepts only, these must be grasped by the non-empirical ideas of reason itself. If causes are perceived as being interlinked in chains, then such contingencies are to be thought of only as small causal circles on the chain, that is, as things being their own cause. Hence Kant’s definition of the Idea of a natural purpose:

an object exists as natural purpose, when it is cause and effect of itself.

This can be thought as an idea without contradiction, Kant maintains, but not conceived. This circularity (the small causal circles) is a very important feature in Kant’s tentative schematization of purposiveness. Another way of coining this Idea is – things as natural purposes are organized beings. This entails that naturally purposeful objects must possess a certain spatio-temporal construction: the parts of such a thing must be possible only through their relation to the whole – and, conversely, the parts must actively connect themselves to this whole. Thus, the corresponding idea can be summed up as the Idea of the Whole which is necessary to pass judgment on any empirical organism, and it is very interesting to note that Kant sums up the determination of any part of a Whole by all other parts in the phrase that a natural purpose is possible only as an organized and self-organizing being. This is probably the very birth certificate of the metaphysics of self-organization. It is important to keep in mind that Kant does not feel any vitalist temptation at supposing any organizing power or any autonomy on the part of the whole which may come into being only by this process of self-organization between its parts. When Kant talks about the forming power in the formation of the Whole, it is thus nothing outside of this self-organization of its parts.

This leads to Kant’s final definition: an organized being is that in which all that is alternating is ends and means. This idea is extremely important as a formalization of the idea of teleology: the natural purposes do not imply that there exists given, stable ends for nature to pursue, on the contrary, they are locally defined by causal cycles, in which every part interchangeably assumes the role of ends and means. Thus, there is no absolute end in this construal of nature’s teleology; it analyzes teleology formally at the same time as it relativizes it with respect to substance. Kant takes care to note that this maxim needs not be restricted to the beings – animals – which we spontaneously tend to judge as purposeful. The idea of natural purposes thus entails that there might exist a plan in nature rendering processes which we have all reasons to disgust purposeful for us. In this vision, teleology might embrace causality – and even aesthetics:

Also natural beauty, that is, its harmony with the free play of our epistemological faculties in the experience and judgment of its appearance can be seen in the way of objective purposivity of nature in its totality as system, in which man is a member.

An important consequence of Kant’s doctrine is that their teleology is so to speak secularized in two ways: (1) it is formal, and (2) it is local. It is formal because self-organization does not ascribe any special, substantial goal for organisms to pursue – other than the sustainment of self-organization. Thus teleology is merely a formal property in certain types of systems. This is why teleology is also local – it is to be found in certain systems when the causal chain form loops, as Kant metaphorically describes the cycles involved in self-organization – it is no overarching goal governing organisms from the outside. Teleology is a local, bottom-up, process only.

Kant does not in any way doubt the existence of organized beings, what is at stake is the possibility of dealing with them scientifically in terms of mechanics. Even if they exist as a given thing in experience, natural purposes can not receive any concept. This implies that biology is evident in so far as the existence of organisms cannot be doubted. Biology will never rise to the heights of science, its attempts at doing so are beforehand delimited, all scientific explanations of organisms being bound to be mechanical. Following this line of argument, it corresponds very well to present-day reductionism in biology, trying to take all problems of phenotypical characters, organization, morphogenesis, behavior, ecology, etc. back to the biochemistry of genetics. But the other side of the argument is that no matter how successful this reduction may prove, it will never be able to reduce or replace the teleological point of view necessary in order to understand the organism as such in the first place.

Evidently, there is something deeply unsatisfactory in this conclusion which is why most biologists have hesitated at adopting it and cling to either full-blown reductionism or to some brand of vitalism, subjecting themselves to the dangers of ‘transcendental illusion’ and allowing for some Goethe-like intuitive idea without any schematization. Kant tries to soften up the question by philosophical means by establishing an crossing over from metaphysics to physics, or, from the metaphysical constraints on mechanical physics and to physics in its empirical totality, including the organized beings of biology. Pure mechanics leaves physics as a whole unorganized, and this organization is sought to be established by means of mediating concepts’. Among them is the formative power, which is not conceived of in a vitalist substantialist manner, but rather a notion referring to the means by which matter manages to self-organize. It thus comprehends not only biological organization, but macrophysic solid matter physics as well. Here, he adds an important argument to the critic of judgment:

Because man is conscious of himself as a self-moving machine, without being able to further understand such a possibility, he can, and is entitled to, introduce a priori organic-moving forces of bodies into the classification of bodies in general and thus to distinguish mere mechanical bodies from self-propelled organic bodies.