Cantorian Diagonal Slash

What is Cantor’s diagonal slash? This is often considered to be an absurd argument from physics point of view. Why is that so? The argument says that “infinity of reals is uncountable, and infinity of integers is countable”, thus giving us two different quantifiable infinities.


What happens if we apply Cantor’s diagonal slash to the integers? How can this be done? Think of the infinite binary tree, which starts at ground level as the trunk and splits in two (bifurcates) as we ascend; if we take the left branch then we assign 0 to the first binary digit, if the right branch then 1. At the next level we do the same….0 if we go left, 1 if we go right…. and we ascend the binary tree all the way to infinity. In this way every possible infinite sequence of binary digits is represented somehow or other (mapped out) by a path up the tree; and every path up the tree corresponds to a unique infinite sequence of binary digits….“the number of routes up the tree is equal to 2n (where n is the number of levels), and the number of nodes (branches) in the tree is equal to (2n)-1.”

Now we can arrange all of these paths in an infinite x infinite binary matrix, of form similar to the infinite x infinite matrix of real numbers that Cantor used for his diagonal slash. What happens if we perform Cantor’s diagonal slash on this infinite binary matrix? According to Cantor, we produce a new infinite binary sequence which is NOT contained within the original matrix (nor is it contained on the infinite binary tree). But how can this be? The matrix contains every possible route up the binary tree, there IS no other route not contained in the matrix. What does this show? That Cantor’s diagonal slash argument is meaningless when applied to infinite matrices.


Metaphysical Exclusions…Speech Act…

….the axiology involved in this analysis is not intrinsically determined by considerations that are merely logical. What logician, what theoretician in general, would have dared to say: B depends logically on A, therefore B is parasitic, nonserious, abnormal, etc.?…All of [those attributes] mark a decline or a pathology, an ethical-ontological determination: i.e. more or less than a mere logical derivation.


What is it, if not an Austinian invocation of Derrida against Searle in trying to portray adjectives like non-serious and abnormal as pathological of language. This is all the more implicated in the language of aetiolation and contagion as pathological in nature. Setting aside the question of logicality, what bothers is the status of ontological-metaphysical questions concerning strategical or methodological operations on a discourse. Derrida answers in the affirmative regarding such a status, for he is firm on the argument of such methodological operations involving decisions as necessarily metaphysical. If this is a metaphysical concern, then it obviously follows that such an exclusion happens to be ontological. This is further criticized by Derrida in terms of a binary of concepts, where invariably one term of the binary gets a higher prerogative, and also in terms of a positive, ideal sense attached to these metaphysical binary oppositions that are regarded as simple, pure, normal and self-identical in themselves. Clearly, the serious/parasitic distinction wrought by Austin is descriptive. But is it axiological and/or evaluative? Yes, since adjectives like aetiolated are rarely used without any evaluative components. Now, if Austin is culpable of metaphysical exclusion, so is Searle, for he fails to expound a general theory of speech acts that would be inclusive of parasitic utterances.

India’s Cashlessness Drive or A Rudderless Cacophony


Is there a plus out of going less-cash dependent rather than  going cashless? Yes, on the negative interest rates issue, these appear to be better than Quantitative Easing to turbocharge an economy from a recession, BUT only in cases of advanced economies and definitely not in the case of an economy that is purportedly to be the fasting growing emerging one according to the whims, fancies and vagaries of WB/IMF statistics. Why is the case?

Presently, the interest rates are zero bound (though India is largely outside the bracket meaning all the more vociferously that this sudden sweep has been misplaced at the very top trickling down to the bottom in treacherous wringing. but imagine for a moment that India too faces this movement of rates towards the ignominious ‘0’), i.e. cannot fall below zero. And then there’s the sacred rule of

Real term interest rate = Nominal Interest Rate – Rate of Inflation

In 2008, with advanced economies like US having less rate of inflation the room to cut interest rates was pretty much restricted considering the US Fed had set a target rate of inflation as 2%. With a less-cash society the Central Bankers can set interest rates to negative which basically means that you need to pay the bank to hold your deposit. Now keep in mind that the debate is still out over whether the three tranches of QE actually did good.

The author (KR) acknowledges that negative interest rates might give rise to strange situations like for example in case of a bond holder – the borrower needs to pay the lender. Legal and administrative issues can arise but they can be handled as the payments due can be deducted from the principal in this case.

There’s one interesting alternative to negative interest rates shared in the book from the academic economic circles – the two currency system.

It calls for identifying as paper currency and currency in electronic form in banking system as two different. And it calls for an exchange rate when a person goes to the bank to deposit his paper currency which will ultimately be recorded in the banking system as an electronic form. This will give rise to three monetary instruments which the Central Bankers can then play with –

  1. Interest rates on electronic currency
  2. Exchange rate b/w Electronic and Paper Currency
  3. Forward (future) exchange rate

As these days the chatter increases about digital or crypto-currencies, Rogoff is of the view that these innovations are admirable but these currencies are at a major disadvantage as the govt. has tremendous power at its disposal to impose its will over them. But eventually, the technology like public ledger will be adopted, and that would eventually be taking off from #Blockchain.

Is India following the playbook in The Curse of Cash? On motivation, yes, absolutely. A central theme of the book is that whereas advanced country citizens still use cash extensively (amounting to about 10% of the value of all transactions in the United States), the vast bulk of physical currency is held in the underground economy, fueling tax evasion and crime of all sorts. Moreover, most of this cash is held in the form of large denomination notes such as the US $100 that are increasingly unimportant in legal, tax-compliant transactions. Ninety-five percent of Americans never hold $100s, yet for every man, woman and child there are 34 of them. Paper currency is also a key driver of illegal immigration and corruption. The European Central Bank recently began phasing out the 500 euro mega-note over these concerns, partly because of the terrorist attacks in Paris.


On implementation, however, India’s approach is radically different, in two fundamental ways. First, I argue for a very gradual phase-out, in which citizens would have up to seven years to exchange their currency, but with the exchange made less convenient over time. This is the standard approach in currency exchanges. For example this is how the European swapped out legacy national currencies (e.g the deutschmark and the French franc) during the introduction of the physical euro fifteen years ago. India has given people 50 days, and the notes are of very limited use in the meantime. The idea of taking big notes out of circulation at short notice is hardly new, it was done in Europe after World War II for example, but as a peacetime move it is extremely radical. Back in the 1970s, James Henry suggested an idea like this for the United States. Here is what I say there about doing a fast swap for the United States instead of the very gradual one I recommend:

 “(A very fast) swap plan absolutely merits serious discussion, but there might be significant problems even if the government only handed out small bills for the old big bills. First, there are formidable logistical problems to doing anything quickly, since at least 40% of U.S. currency is held overseas. Moreover, there is a fine line between a snap currency exchange and a debt default, especially for a highly developed economy in peacetime. Foreign dollar holders especially would feel this way. Finally, any exchange at short notice would be extremely unfair to people who acquired their big bills completely legally but might not keep tabs on the news.

In general, a slow gradual currency swap would be far less disruptive in an advanced economy, and would leave room for dealing with unanticipated and unintended consequences. One idea, detailed in The Curse of Cash, is to allow people to exchange their expiring large bills relatively conveniently for the first few years (still subject to standard anti-money-laundering reporting requirements), then over time make it more inconvenient by accepting the big notes at ever fewer locations and with ever stronger reporting requirements.

Second, my approach eliminates large notes entirely. Instead of eliminating the large notes, India is exchanging them for new ones, and also introducing a larger, 2000-rupee note, which are also being given in exchange for the old notes.


The idea in The Curse of Cash of eliminating large notes and not replacing them is not aimed at developing countries, where the share of people without effective access to banking is just too large. In the book I explain how a major part of any plan to phase out large notes must include a significant component for financial inclusion. In the United States, the poor do not really rely heavily on $100 bills (virtually no one in the legal economy does) and as long as smaller bills are around, the phase out of large notes should not be too much of a problem, However, the phaseout of large notes is golden opportunity to advance financial inclusion, in the first instance by giving low income individuals access to free basic debt accounts. The government could use these accounts to make transfers, which would in turn be a major cost saving measure. But in the US, only 8% of the population is unbanked. In Colombia, the number is closer to 50% and, by some accounts, it is near 90% in India. Indeed, the 500 rupee note in India is like the $10 or $20 bill in the US and is widely used by all classes, so India’s maneuver is radically different than my plan. (That said, I appreciate that the challenges are both different and greater, and the long-run potential upside also much higher.)

Indeed, developing countries share some of the same problems and the corruption and counterfeiting problem is often worse. Simply replacing old notes with new ones does have a lot of beneficial effects similar to eliminating large notes. Anyone turning in large amounts of cash still becomes very vulnerable to legal and tax authorities. Indeed that is Modi’s idea. And criminals have to worry that if the government has done this once, it can do it again, making large notes less desirable and less liquid. And replacing notes is also a good way to fight counterfeiting—as The Curse of Cash explains, it is a constant struggle for governments to stay ahead of counterfeiters, as for example in the case of the infamous North Korean $100 supernote.

Will Modi’s plan work? Despite apparent huge holes in the planning (for example, the new notes India is printing are a different size and do not fit the ATM machines), many economists feel it could still have large positive effects in the long-run, shaking up the corruption, tax evasion, and crime that has long crippled the country. But the long-run gains depend on implementation, and it could take years to know how history will view this unprecedented move.


In The Curse of Cash, I argue that it will likely be necessary to have a physical currency into the far distant future, but that society should try to better calibrate the use of cash. What is happening in India is an extremely ambitious step in that direction, of a staggering scale that is immediately affecting 1.2 billion people. The short run costs are unfolding, but the long-run effects on India may well prove more than worth them, but it is very hard to know for sure at this stage.

The long quote is by none other than Rogoff himself on the viability of the Indian drive.

Kordela’s Surplus and Ballardian Fiction of the Political Ambiguity Within Accelerationism: Note Quote

Kiorana Kordela in Surplus makes a point that resonates accelerationism, albeit in a narrower sense. She critiques post-modern ‘neo-Spinozism’, notably Negri and Hardt’s Empire for the assumption that replicating and reinforcing the structures of capital, far from supporting it, amounts to accelerating the advent of its end as an exploitative and an oppressive system. This is the Ballardian fictional political ambiguity treading an uneasy line between the critique and an ecstatic celebration of the liberating power of capitalism. In trying to exceed reality along Deleuzean lines of flight, his extra-wordly dematerialization of crime becomes an all-too material replication of the tendencies of capitalism itself. The point is to distinguish the strategy of subtraction from the strategy of transgression, for only then there is a strategy towards accelerationism, a higher-level recuperation at that.