From Posets to Categories. Part 1

A poset (partially ordered set) is a pair (P, ≤), where

P is a set,

is a binary relation on P satisfying the three axioms of partial order:

(i) Reflexive: ∀x ∈ P, x ≤ x

(ii) Antisymmetric: ∀x ,y ∈ P, x ≤ y & y ≤ x ⇒ x = y

(iii) Transitive: ∀x, y, z ∈ P, x ≤ y & y ≤ z ⇒ x ≤ z.

And what does this have to do with category theory?

“x ≤ y” ⇐⇒ “ x → y” “x = y” ⇐⇒ “ x ↔ y”

Given x, y ∈ P,

we say that u ∈ P is a least upper bound of x, y ∈ P if we have x → u & y → u, and for all z ∈ P satisfying x → z & y → z we must have u → z. It is more convenient to express this definition with a picture. We say that u ∈ P is a least upper bound of x, y if for all z ∈ P the following picture holds:

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Dually, we say that l ∈ P is a greatest lower bound of x, y if for all z ∈ P the following picture holds:

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Now suppose that u1, u2 ∈ P are two least upper bounds for x, y. Applying the defininition in both directions gives

u1 → u2 and u2 → u1,

and then from antisymmetry it follows that u1 = u2, which just means that u1 and u2 are indistinguishable within the structure of P. For this reason we can speak of the least upper bound (or “join”) of x, y. If it exists, we denote it by

x ∨ y

Dually, if it exists, we denote the greatest lower bound (or “meet”) by

x ∧ y

The definitions of meet and join are called “universal properties”. Whenever an object defined by a universal property exists, it is automatically unique in a certain canonical sense. However, since the object might not exist, maybe it is better to refer to a universal property as a “characterization,” or a “prescription,” rather than a “definition.”

Let P be a poset. We say that t ∈ P is a top element

if for all z ∈ P the following picture holds:

z —> t

Dually, we say that b ∈ P is a bottom element if for all z ∈ P the following picture holds:

b —> z

For any subset of elements of a poset S ⊆ P we say that the element ⋁ S ∈ P is its join if for all z ∈ P the following diagram is satisfied:

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Dually, we say that ⋀ S ∈ P is the meet of S if for all z ∈ P the following diagram is satisfied:

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If the objects ⋁ S and ⋀ S exist then they are uniquely characterized by their universal properties.

The universal properties in these diagrams will be called the “limit” and “colimit” properties when we move from posets to categories. Note that a limit/colimit diagram looks like a “cone over S”. This is one example of the link between category theory and topology.

Note that all definitions so far are included in this single (pair of) definition(s):

⋁ {x, y} = x∨ y & ⋀ {x, y} = x ∧ y

⋁∅ = 0 & ⋀ ∅ = 1.

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Could Complexity Rehabilitate Mo/PoMo Ethics?

A well known passage from Marie Fleming could be invoked here to acquit complexity from the charges and accusation pertaining to relativism. He says,

Anyone who argues against reason is necessarily caught up in a contradiction: she asserts at the locutionary level that reason does not exist, while demonstrating by way of her performance in argumentative processes that such reason does in fact exist.

Such an absolute statement about complexity would similarly be eaten along its way.

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Taking the locutionary from the above quote, it could be used to adequately distinguish from performative, or logic versus rhetoric. Such a distinction gains credibility, if one is able to locate an Archimedean point to share discourse/s, which, from the point of view of complexity theory would be a space outside the autopoietic system, or, in other words, would be a meta-theoretical framework. Such a framework is skeptically looked upon/at by complexity, which has no qualms in exhibiting an acknowledgement towards performative tensions at work. Such tensions are generative of ethical choices and consequences, since any accessibility to the finality of knowledge is built upon the denial of critical perspective/s, thus shrouding the entire exercise in either a veil of ignorance, or a hubristic pride, or illusory at best.

Morality gains significance, since its formulations is often ruptured for want of secure, and certain knowledge, and both of which are not provided for by complexity theory and French theory, according to the accusations labeled against them. Even if, in making choices that are normative in nature, a clear formulation of the ethical is obligated. Lyotard’s underlining conditions of knowledge is often considered unethical, as he admits to the desire for justice to be shrouded in an unknown intellectual territory. Lyotard has Habermas in mind in dealing with this, since for the latter’s communication therapy, what is mandated is clearly consensual agreement on the part of the public to seek out these metaprescriptions as universally valid and as spanning all language games. Habermas is targeted here for deliberately ignoring the diversity inherent in the post-modern society. For Lyotard,

It is the monster formed by the interweaving of various networks of heteromorphous classes of utterances (denotative, prescriptive, performative, technical, evaluative, etc.). there is no reason to think that it could be possible to determine metaprescriptive common to all of these language games or like the revisable consensus like the one in force at a given moment in the scientific community could embrace the totality of metaprescriptions regulating the totality of statements circulating in the social collectivity. As a matter of fact, the contemporary decline of narratives of legitimization – be they traditional or ‘modern’ (the emancipation of humanity, the realization of the idea) – is tied to the abandonment of this belief.

The fight over consensus, if it could be achieved at all, is contentious between Lyotard and Habermas. Obviously, it could be attained, but only locally and should not even vie for universal validity. Lyotard scores a point over Habermas here, because of his emphasis on the permeability of discursive practices dressed with paralogy. Justice, as a subset of ethics in the post-modern society, in order to overcome its status as a problematic, must recognize the heteromorphous nature of language games or phase regimens on the one hand, and consensus as reached must have a local space-time valuation contingently subject to refutation or nullification on the other. Such a diagnosis goes against the crux of modernism’s idea of ethics as founded upon foundational and universal set of rules, and maybe imperatives. Modernism’s idea of ethics is no different, at least in the formative structure from the rule-based analysis, since both demand a strict adherence to the dictates of rules and guidelines. A liberation comes in the form of post-modernism. Bauman sees the post-modern society as not only setting us free, but also pushing us towards a paradoxical situation, where agents have the fullness of moral choice and responsibility, while simultaneously depriving them of the comfort of the universal guidance as promised by modernism. Moral responsibility comes with the loneliness of moral choice. Such paradoxical events or situations facing man in the post-modern society only reinvests faith in agonistics of the network. At the same time, such an aporetic position is too paradoxical to satisfy many. Taking cues from the field of jurisprudence, the works of Druscilla Cornell could help clear the muddy waters here to an extent of a satisfactory resolution. Cornell aims to establish the relationship of the philosophy of the limit, or what she calls the post-structural theory of Derrida in principle, to questions of ethics, law and justice. Cornell shows no inhibitions towards accepting the complexity of relationships governing humans, and in the process accepts Hegel as the vantage point. Hegel criticizes Kant for his abstract idealism, and admits to our constitution within a social structure, which is teleologically headed for perfection. In short, the dialectical process is convergent for Hegel, since it is operative within a social/historical system aiming towards organization. Adorno differs here, since, for him dialectics is always divergent, with stress laid upon differences that characterize between humans as always irreducible to a totalizing organized system. This position of Adorno with its sympathy for difference is much closer to complexity, that at first would seem. Cornell carries further on from there and introduces the work of Luhmann, who is a towering figure in sociology, when it comes to bringing in autopoiesis within the fold. Humans are never allowed to stand outside the system that Luhmann thinks is not only complex, but autopoietic as well. Therefore, on an individual level, the choice element has no role to play, except, accepting the system that would undergo an organization to best suit its survival through a process of evolution, and not transformation. Luhmann’s understanding still prioritizes the present, and has no place for the past or the uncertain future. Cornell considers this a drawback, and makes past as an ingredient in understanding the meaning of an event, on the one hand, and following Derrida, wants to take up responsibility for the future, even if it is unknown. With a structure like this in place, it is possible to evade the rigidity of modernist claims on ethics on the one hand, and fluidity of evasive tendencies towards responsibility on the other. Instead, what Cornell calls for is an acceptance of the present ethical principles in all seriousness. That is to be resistant to change, and awareness of applications of the principles is what is called for. Ethics involves calculation in a responsible manner. In a similar vein, complexity entails irreducibility to calculation, in the sense of coming out with novelistic tendencies involving creativity that is not simply a flight of fancy, but an imagination laden with responsibility. Only, in this regard, could ethics mean not subjecting to any normativity. And, one of the ways to achieve this to obviously shy away from intellectual arrogance.

What’s an Asset Reconstruction Company, and why does it even matter to NPAs?

As is suggestive of the name, ARCs are required to repackage assets to make them more saleable. But, in the context of bad loans, or non-performing assets, such companies often falter to garner enough firepower to root out the surging menace of NPAs. The Indian context is caused primarily by a systemic rot involving faulty practices of project finance and subsequent difficulties in recoveries on loans. ARCs are constituted to precisely address such hurdles. With their status as centralised agencies, these are programmed to buy up stressed/distressed and non-performing assets and repackage them to sell them to prospective promoters/buyers. ARCs are programmed to buy NPAs at a discounted price, which in turn help the banks and lenders to clean up their sticky balance sheets. ARCs can either be public, private or jointly owned, and are also armed to float bonds to recover dues from borrowers. Even if on paper the concept of an ARC looks robust with scalability to concoct a bad asset with a performing one in order to increase its saleability, in reality, ARCs are prone to failures for lack of buyers for their packages and limited by capital concerns. But, there are challenges galore for ARCs viz. debt aggregation is a far cry, and unless this is done, resolution will always be expeditious; hunt for fresh financial support; and discrepancy between banks and ARCs in pricing of assets, unless reached a commonality would continue to remain a contentious issue.

The whole concept of Asset Reconstruction Companies (ARCs) is closely modelled on the US model of Asset Management Companies (AMCs), and is thus a large industry in itself as far as buying and selling off of debts are concerned. It resembles a time to strike as the ducks are now lined, and the opportunities galore in private equities as ARCs get a chance to own the entire capital structure and reinstall management echelons, all thanks to Budgetary recommendations with a 100% FDI welcomed. But, it still is going a bit too far, and hence let us examine the evolution first.

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The real trigger for ARCs to flourish came with Raghuram Rajan’s exhortation to banks to clean up its mess. A switch of trajectory happened sometime in 2013, when ever greening bad loans was put on to back burner and let ARCs face up. This is where banks were obligated to turnaround loans until then considered unredeemable. Adding to that trigger point is another one banking on Bankruptcy Code, which promises discount to buying off bad debts or distressed assets at a discount pitting them more profitable a venture compared with greenfield projects of similar magnitude.

ARCs are born out of SARFAESI Act, 2002, (The Securitisation and Reconstruction of Financial Assets and Enforcement of Security Interest Act, 2002) and enable the banks to acquire the securities which had been pledged. all of this was achievable without any interference from the jurisdiction of the civil courts thus lending authoritarian power to banks to cope up with NPAs. But regulatory directives prevented the smooth functioning of transactions involving bad debts, thanks to the decrepit system for enforcing securities. Sale of loans to ARCs is however the last resort banks undertake as statutory hurdles and deposed promoters speed break.

Basically, road to recovery is a step by step process involving, Bank selling a bad loan to ARC; ARCs paying 15% upfront, and issuing the remaining 85% as securities in the form of Security Receipts (SRs), which primarily deals with 5% upfront payment as was the case a year back; ARCs initiating the turnaround and in the process earning 1.5% management fee; recovery proceeds thus accrued get shared by the banks and the ARCs; and if the ARCs fail to recover the bad loans for eight years, the investments get written-off. Now, this can be seen as a clear shift from ever greening, or even liberal funding by the government year-on-year, and aptly reminds internal recapitalization as indispensable. Budgetary infusion or capital infusion or recapitalisation is putting capital for the purpose of helping the ailing public sector banks. The very understanding of PSBs would imply such an infusion required from time to time, but the problem lies in its ritualistic nature. On the contrary, if banks were to internally raise funds for recapitalisation, it would indicate a healthy practice. One reason the government does infusion is to meet Basel III norms, as reliance upon internal fund recapitalisation would not let that be accomplished. But, there is a caveat here to be always kept in mind. Written-off doesn’t necessarily mean that defaults and defaulters are not chased. They are undoubtedly sought after, with the only difference being the clean-up of balance sheets for the year such defaults happen for the banks. And, if they don’t write-offs, or alternatively called charge-offs effectuate helping banks not only erase the mess off their balance sheet, but saving them enormous tax liabilities. The real tussle is between charging-off loans and becoming industrious in selling them off. The winner takes it all, which in this case is hedging equivalent to selling off bad debts, and which is promulgated by the RBI and the government in jettisoning this messy baggage.

Arsenic-Tolerant GFAJ-1

The bacterium — strain GFAJ-1 of the Halomonadaceae family of Gammaproteobacteria, not only grows but also incorporates arsenic molecules into its DNA, in place of phosphorus. NASA has aliens…

What about arsenic, in the form of the arsenate ion, subbing for phosphate ions inside the cell? After all, arsenic is the downstairs neighbor to phosphorus on the periodic table of the elements, and phosphate and arsenate are chemical cousins. That similarity contributes to arsenic’s toxicity, arsenate masquerades as the nutrient phosphate and thus gains access to the body’s metabolic system. Just why the bacterium has a penchant for arsenic is not yet clear. Perhaps some life-forms evolved in an arsenic-rich environment and later migrated to a more typical region of Earth, where phosphorus is far more abundant.

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Hyman Minsky, Karl Polanyi, Deleterious Markets and if there is any Alt-Right to them? Apparently No.

Karl Polanyi has often highlighted on the insight about the predicaments of the market. these perils realize that when the markets are left to their own devices, they are enough o cause attrition to the social relations and fabric. However, the social consequences of financial instability can be understood only by employing a Polanyian perspective on how processes of commodification and market expansion jeopardize social institutions. For someone like Hyman Minsky, equilibrium and stability are elusive conditions in markets with debt contracts. His financial instability hypothesis suggests that capitalist economies lead, through their own dynamics, to “the development over historical time of liability structures that cannot be validated by market-determined cash flows or asset values”. According to Minsky, a stable period generates optimistic expectations. Increased confidence and positive expectations of future income streams cause economic actors to decrease margins of safety in their investment decisions. This feeds a surge in economic activity and profits, which turns into a boom as investments are financed by higher degrees of indebtedness. As the economic boom matures, an increasing number of financial intermediaries and firms switch from hedge finance to speculative and Ponzi finance. Minsky argued that economists, misreading Keynes, downplay the role of financial institutions. In particular, he argued that financial innovation can create economic euphoria for a while before destabilizing the economy and hurling it into crises rivaling the Great Depression. Minsky’s insights are evident in the effects of innovations in mortgages and mortgage securities. Actors using speculative and Ponzi finance are vulnerable to macroeconomic volatility and interest rate fluctuations. A boom ends when movements in short-term and long-term interest rates render the liability structures of speculative and Ponzi finance unsustainable. The likelihood of a financial crisis (as opposed to a business cycle) depends on the preponderance of speculative and Ponzi finance in the economy under question.

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Minsky regularly criticized economists for failing to grasp Keynes’s ideas. In his book Stabilizing an Unstable Economy Minsky argued that while economists assimilated some of Keynes’s insights into standard economic theory, they failed to grasp the connection between the financial and real sectors. Specifically, he argued that finance is missing from macroeconomic theory, with its focus on capital structure, asset-liability management, agency theory, and contracts. He wrote:

Keynes’s theory revolves around bankers and businessmen making deals on Wall Street … One of the peculiarities of the neoclassical theory that preceded Keynes and the neoclassical synthesis that now predominates economic theory is that neither allows the activities that take place on Wall Street to have any significant impact upon the coordination or lack of coordination of the economy…

Minsky’s work on financial crises builds on Keynes’s insights, using terms such as “euphoric economy”, and “unrealistic euphoric expectations with respect to costs, markets, and their development over time”. Yet Minsky considered the issues of rational prices and market efficiency as only the tip of an iceberg. His broad framework addresses issues related to the lending practices by financial institutions, central bank policy, fiscal policy, the efficacy of financial market regulation, employment policy, and income distribution. Financial institutions, such as banks, become increasingly innovative in their use of financial products when the business cycle expands, boosting their leverage and funding projects with ever increasing risk. Minsky’s words on financial innovation are striking, as if foretelling the recent crisis.

Over an expansion, new financial instruments and new ways of financing activity develop. Typically, defects of the new ways and the new institutions are revealed when the crunch comes.

Commercial banks sponsored conduits to finance long-term assets through special purpose entities such as structured investment vehicles (SIVs), something similar to the Indian version of Special Purpose Vehicles (SPVs). These were off balance sheet entities, subjecting them to lower regulatory capital requirements. Special purpose entities used commercial paper to raise funds they then used to buy mortgages and mortgage securities. In effect, banks relied on Minsky-type speculative and Ponzi financing, borrowing short-term and using these borrowed funds to buy long-term assets. Wrote Minsky,

The standard analysis of banking has led to a game that is played by central banks, henceforth to be called the authorities, and profit-seeking banks. In this game, the authorities impose interest rates and reserve regulations and operate in money markets to get what they consider to be the right amount of money, and the banks invent and innovate in order to circumvent the authorities. The authorities may constrain the rate of growth of the reserve base, but the banking and financial structure determines the efficacy of reserves…This is an unfair game. The entrepreneurs of the banking community have much more at stake than the bureaucrats of the central banks. In the postwar period, the initiative has been with the banking community, and the authorities have been “surprised” by changes in the way financial markets operate. The profit-seeking bankers almost always win their game with the authorities, but, in winning, the banking community destabilizes the economy; the true losers are those who are hurt by unemployment and inflation.

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Combining Hyman Minsky’s insights on financial fragility with a Polanyian focus on commodification offers a distinct perspective on the causes and consequences of the foreclosure crisis. First, following Polanyi, we should expect to find commodity fiction applied to arenas of social life previously isolated from markets to be at the heart of the recent financial crisis. Second, following Minsky, the transformations caused by novel uses of commodity fiction should be among the primary causes of financial fragility. Finally, in line with a Polanyian focus on the effects of supply-demand-price mechanism, the price fluctuations caused by financial fragility should disrupt existing social relations and institutions in a significant manner. So, how does this all peter down to alt-right? Right-wing libertarianism is basically impossible. The “free” market as we know it today needs the state to be implemented – without reading Polanyi, you just know for example that without the force of the state, you just can’t have private property or all the legal arrangements that underpin property, labour and money. So it wouldn’t work anyway. Polanyi’s point is that if we want democracy to survive, we need to beware of financial overlords and their ideological allies peddling free-market utopias. And if democracy even stinks of stability, then stability is destabilizing as Minsky would have had it, thus corroborating the cross-purposes between the two thinkers in question, at least to the point of a beginning.

Drake Equation and Astrobiology

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The Drake equation is one of those rare mathematical beasts that has leaked into the public consciousness. It estimates the number of extraterrestrial civilisations that we might be able to detect today or in the near future. Frank Drake attempted to quantify the number by asking what fraction of stars have planets, what fraction of these might be habitable, then the fraction of these on which life actually evolves and the fraction of these on which life becomes intelligent and so on. Many of these numbers are little more than wild guesses. For example, the number of ET civilisations we can detect now is hugely sensitive to the fraction that destroy themselves with their own technology, through nuclear war for example. Obviously we have no way of knowing this figure. Of the many uncertainties in the Drake equation, one term is traditionally thought of as relatively reliable. That is the probability of life emerging on a planet in a habitable zone. On Earth, life arose about 3.8 billion years ago, just a few million years after the planet had cooled sufficiently to allow it. Astrobiologists naturally argue that because life arose so quickly here, it must be pretty likely to emerge in other places where conditions allow.