For the 102nd session of the Philosophical Foundations of Law and Finance, to be held from 6 to 8pm tonight, Friday March 30th 2012, in room 501, University of Westminster campus, we will: (1) collect the LLM dissertation titles from students and (2) examine the causes of the perrenial Great War (making peace between our genetics and our genuine spiritual being) and the ongoing Great Depression (making war between superficial consumerism and our lives).
As a philosophy student studying Plato and Aristotle in Princeton during the Vietnam War, it became obvious to me that a lot of my very brilliant colleagues who'd received princely educations believing that they would become very rich (millionaire-billionaires adjusting for inflation), movie stars, rock stars and presidents, would become relatively average and sedate, if not sedated, and those who did not fall under medication, would become very pissed off, having squandered their God-given talents chasing the meaninglessness of empty suits.
Today, the Arab spring is just one of the global blooms of corrupt political-economic systems where holier than thou public servants have hundreds of billions of dollars of personal wealth while their poor citizen have not even one ounce of zakat, and as the political elite have continuously "bailed out" the bankers in the US and Europe, we have immense bubbles that can be resolved only in terms of debt forgiveness (where bankers take the hit) or more fascistic totalitarianism (where the good taxpaying citizens are debt enslaved). To clarify these choices, we have some beautifully illustrated lectures by David McWilliams of Punk Economics via Zerohedge:
http://www.zerohedge.com/news/how-europe-has-evolved-democracy-bankocracy-and-why-austerity-will-lead-chaos
http://www.zerohedge.com/news/europes-cash-trash-ltro-scam-and-indentured-servitude-citizenry
http://www.zerohedge.com/news/liquidity-and-false-recovery
Enjoy your spring wherever you are and be prepared for another kind of spring coming soon to your door.
Ciao
Joe
Friday 30 March 2012
Monday 26 March 2012
The Consilience of Financial-Economics: Happiness
Title: The Consilience of Financial-Economic: Happiness
In a very brief article by David Sloan Wilson entitled, "A Tale of Two Classics," [New Scientist, 24 March 2012, 30-31], he reviews two influential academic articles:
[ ] Milton Friedman's essay, "The Methodology of Positive Economics," (1953); and
[ ] Stephen Jay Gould and Richard Lewontin's article, "The Spandrels of San Marcos and The Panglossian Paradigm."
The former sets out the classic statement on homo oeconomicus as a species that acts as if the assumptions of orthodox economic theory were true when in the individual cases it is manifestly untrue. This distinction in size is very important and may help explain the differences in the opinion of classical versus behavioural theorists.
The latter is a critique of the use of the argument of adaptation, where theorists fail to distinguish again between different levels of phenomena. Thus, the general adaptive rule that desert animals are all likely to have similar hues for camouflage does not mean that all desert animals are necessarily genetically related. The distinction au fond here is between long-term and proximate cause.
Both papers and D.S. Wilson's own comments warn about what Aristotle first called "metaphysics." Indeed, the concept of cause and its four variations (formal, essential-substantive, efficient and teleological) were practically invented by Aristotle. But the one big point Wilson makes is the need for CONSILIENCE (I believe this term was first coined and made popular by Edward O. Wilson, the great ant-scientist at Harvard). Consilience is the test of an idea in light of its unity with the other sciences.
I find consilience completely absent in business schools and relegated to the fringe in US and UK law schools. This is the main reason why business school and law school curricula appear superficial and are probably marked for obsolescence in the next decade or two. Given what D.S. Wilson says above, it is not difficult to see how the technical financial theology taught in US and European business schools could easily lead to numerous frauds and deceits in the financial industry. The desert is general financial-economic theory and its camouflaged animals are the bad human animals. For example, technical financial textbooks trot out the ideas that "arbitrage" and "net present value" are themselves self-justifying aims within financial theory. These little but significant facts tell us that consilience is utterly lacking in financial theory.
The adjustments required for the benefit of the rest of society should be in the form of regulation, but here, if the game keepers turn a blind eye, the outcome at best will be small pockets of stability for the very rich in a sea of instantaneous instabilities for the rest and mostly poor.
The long-term solution aims at consilience, but without the ancient Platonic ideals of social comity or the modern Bhutanese concept of 'happy economy', we have only ourselves to blame for failing to distinguish proximate from long term causes of misery and happiness.
In a very brief article by David Sloan Wilson entitled, "A Tale of Two Classics," [New Scientist, 24 March 2012, 30-31], he reviews two influential academic articles:
[ ] Milton Friedman's essay, "The Methodology of Positive Economics," (1953); and
[ ] Stephen Jay Gould and Richard Lewontin's article, "The Spandrels of San Marcos and The Panglossian Paradigm."
The former sets out the classic statement on homo oeconomicus as a species that acts as if the assumptions of orthodox economic theory were true when in the individual cases it is manifestly untrue. This distinction in size is very important and may help explain the differences in the opinion of classical versus behavioural theorists.
The latter is a critique of the use of the argument of adaptation, where theorists fail to distinguish again between different levels of phenomena. Thus, the general adaptive rule that desert animals are all likely to have similar hues for camouflage does not mean that all desert animals are necessarily genetically related. The distinction au fond here is between long-term and proximate cause.
Both papers and D.S. Wilson's own comments warn about what Aristotle first called "metaphysics." Indeed, the concept of cause and its four variations (formal, essential-substantive, efficient and teleological) were practically invented by Aristotle. But the one big point Wilson makes is the need for CONSILIENCE (I believe this term was first coined and made popular by Edward O. Wilson, the great ant-scientist at Harvard). Consilience is the test of an idea in light of its unity with the other sciences.
I find consilience completely absent in business schools and relegated to the fringe in US and UK law schools. This is the main reason why business school and law school curricula appear superficial and are probably marked for obsolescence in the next decade or two. Given what D.S. Wilson says above, it is not difficult to see how the technical financial theology taught in US and European business schools could easily lead to numerous frauds and deceits in the financial industry. The desert is general financial-economic theory and its camouflaged animals are the bad human animals. For example, technical financial textbooks trot out the ideas that "arbitrage" and "net present value" are themselves self-justifying aims within financial theory. These little but significant facts tell us that consilience is utterly lacking in financial theory.
The adjustments required for the benefit of the rest of society should be in the form of regulation, but here, if the game keepers turn a blind eye, the outcome at best will be small pockets of stability for the very rich in a sea of instantaneous instabilities for the rest and mostly poor.
The long-term solution aims at consilience, but without the ancient Platonic ideals of social comity or the modern Bhutanese concept of 'happy economy', we have only ourselves to blame for failing to distinguish proximate from long term causes of misery and happiness.
Friday 23 March 2012
Instantaneous Symmetric Risk <=> Dodd Frank Avoidance Scheme
I guess you could make a lot of money helping non-US banks avoid Dodd-Frank Act requirements. See: http://online.wsj.com/article/SB10001424052702303812904577295614224666918.html
Deutsche Bank has always been rather "leveraged" and some estimates say it would have had to come up with between $20 to $40 billion in capital. Instead it gave up its bank holding status so it won't have any FDIC protection. But Title II Orderly Liquidation Authority will be used to liquidate any bank or non-bank posing a systemic risk to the US economy. So the interesting irony here is that by dropping its BHC status and thus lacking federal insurance, hasn't it become instantaneously a danger to the US economy and thus, a target for liquidation? Actually, if I were a benevolent dictator, I'd extract a bit more "taxable value" from Deutsche Bank for making such an obvious avoidance scheme and hold the threat of Title II over its head. Hmm. I doubt severely that the US Fed or the Treasury will consider this argument, but given the powers entrusted them under Title II of the Dodd-Frank Act, they should.
Deutsche Bank has always been rather "leveraged" and some estimates say it would have had to come up with between $20 to $40 billion in capital. Instead it gave up its bank holding status so it won't have any FDIC protection. But Title II Orderly Liquidation Authority will be used to liquidate any bank or non-bank posing a systemic risk to the US economy. So the interesting irony here is that by dropping its BHC status and thus lacking federal insurance, hasn't it become instantaneously a danger to the US economy and thus, a target for liquidation? Actually, if I were a benevolent dictator, I'd extract a bit more "taxable value" from Deutsche Bank for making such an obvious avoidance scheme and hold the threat of Title II over its head. Hmm. I doubt severely that the US Fed or the Treasury will consider this argument, but given the powers entrusted them under Title II of the Dodd-Frank Act, they should.
Wednesday 7 March 2012
From War to Peace and Love Through the Morphism of a Good Massage
The Morphism of Peace and Love => A Good Massage
Alexander, Machiavelli, Sun Tzu, Ghenghis Khan, Tsunetomo and lots of other male dominators from oh so many cultures and periods of history are scary because they USED other human beings as tools for their own ends and because they simply assumed War was inevitable, so they "reasoned," why not just win at whatever the cost which usually meant PRE-EMPTIVE strike. Whatever little bit of DNA-code that "naturally" allows or forces the human species to undertake vast wars against ITSELF should in my opinion be snipped, modified and reconstructed towards that other type of gene which seems to underlie the social-sexual behaviours of Bonobo's. Of course, those religions that support in-group versus out-group mentality through separatist rituals and mystical justification of repression, and thus, are MERELY another manifestation of the SPECIES-KILLER gene, would object violently to this proposal because it would be against their religion. Some enlightened masters figured this "they versus us" mentality is the source of all evil and tried with whatever they had to show others that peace is possible. But this attitude is extremely rare. For example, the founder of Aikido was a master of three martial arts and I studied this art for about 7 years in Honolulu with Yoshioka Sensei. In Aikido, the ethical ideal of no harm to others and yourself is embedded throughout the practice. So, I asked Sensei, "Sensei, you preach 'peace, peace, and love, love' but all we learn in our techniques is only how to kill the other. How can we achieve peace and love when this is all we learn?" His answer is remarkable, "You must learn to stop thinking 'kill, kill' and give your partner a good massage."
Alexander, Machiavelli, Sun Tzu, Ghenghis Khan, Tsunetomo and lots of other male dominators from oh so many cultures and periods of history are scary because they USED other human beings as tools for their own ends and because they simply assumed War was inevitable, so they "reasoned," why not just win at whatever the cost which usually meant PRE-EMPTIVE strike. Whatever little bit of DNA-code that "naturally" allows or forces the human species to undertake vast wars against ITSELF should in my opinion be snipped, modified and reconstructed towards that other type of gene which seems to underlie the social-sexual behaviours of Bonobo's. Of course, those religions that support in-group versus out-group mentality through separatist rituals and mystical justification of repression, and thus, are MERELY another manifestation of the SPECIES-KILLER gene, would object violently to this proposal because it would be against their religion. Some enlightened masters figured this "they versus us" mentality is the source of all evil and tried with whatever they had to show others that peace is possible. But this attitude is extremely rare. For example, the founder of Aikido was a master of three martial arts and I studied this art for about 7 years in Honolulu with Yoshioka Sensei. In Aikido, the ethical ideal of no harm to others and yourself is embedded throughout the practice. So, I asked Sensei, "Sensei, you preach 'peace, peace, and love, love' but all we learn in our techniques is only how to kill the other. How can we achieve peace and love when this is all we learn?" His answer is remarkable, "You must learn to stop thinking 'kill, kill' and give your partner a good massage."
Remember the Parasite: Presentation-Invariance and Degrees of Weakened Equivalence
March 7, 2012
Parasites: Presentation-Invariance and Degrees of Weakened Equivalence
Last night in the seminar on Legal Aspects of International Finance, we had each student read their draft assignments on various aspects of international financial regulations, e.g., the Orderly Liquidation Authority, Whistleblower Incentives and Protection, OTC derivatives under the Dodd -Frank Act, the EC proposal to regulate the OTC derivatives markets, the Volker Rule under Dodd-Frank and the Vickers Report in the UK.
I said to this small but very able group, "I'll be lecturing on Category Theory for the next ten years and the importance of having this view in doing comparative law studies and global financial meditations, and not one student will ever even try to apply these ideas to their work. C'est dommage, what a pity1"
I then said that legal and financial studies are in a quandary because the ambition of both are quite clear, and the honest academic knows quite well that the so-called "theories" in each are not doing their job which is to give a sense of "presentation-invariance structure of theories." [See, Marquis, Jean Pierre (2009) From a Geometric Point of View, at 234.] What does this mean? It means that somehow the idea, and here I must insist on the Platonic concept of idea, simply does not change! It is invariant against all presentations! But this has no meaning at all unless we relax to the nth degree what we mean by equivalence. The clarity coming out of Category Theory is the discovery of a way of showing how we can move from a simple and absolutely intuitive sense of "equals to" as in A = A, to more and more weakened senses of "equivalence," i.e., in order of degrees of weakness, (1) isomorphism, (2) natural transformation, (3) natural isomorphism, (4) adjunction. As we move to weaker and weaker forms of equivalence, we start to realise what we really mean by "identity."
Now, I had prepared mentally for this point in the seminar. I knew that my students would look at me as if I were an alien who may or may not have an evil intent on their immediate future. So, I said, "Look, I've been thinking about this for a while, and I think I have an example which you all can understand about how 'weak equivalence' works in the real world. PARASITES."
At this point, I get a look of embarrassed silence. Some look at me in politeness, others are giving me that "yuk" look. I've got their attention, so I continue:
"You all know how parasites work. You walk barefoot in a beautiful paradise, say Hawaii, and you don't mind walking in puddles. But as your foot enters the puddle, a little screw-shaped parasite enters your heel. It burrows deep, gets into your circulatory system, going round and round your blood system, until it lodges idyllically in your liver or your lungs, and there it grows to an enormous size and proliferates seeds of itself, which then are re-deposited to the environment through your faeces."
They grimace at faeces. They don't like me taking them down THAT path, so I take them up the theoretical track.
"So, look at what's going on here. How is it that such a simple small organism is able to travel and adjust to such exotic and hostile environments? Is it intelligent? Does it have some kind of global navigator? Does it depend on the magnetic or coriolli forces of the sun? No. The parasite has a simple linear instruction set which it can simply follow because the environments which it enters are extraordinarily stable over millions of years. So, imagine you are a parasite and this room is the "heel of a human's foot". Your instruction set says something like, "wiggle like hell" when you come into this environment, and this environment is absolutely stable for millions of years because for millions of years the environments of heels are always the SAME. By the way, this is the kind of IDENTITY that we say we must have in Category Theory. Now what? As a parasite, you burrow to the edge of this environment and you break through to the blood circulatory system. Now this environment has also been the same for millions of years, and your instruction set says, "turn off all flagella and float" and wow, you float and float for a couple circulations -- this is like going round the world in a lifeboat for humans -- until you get to a particular chemical environment that "smells like" a liver or a lung, and then and there, "throw anchor." All of these seemingly complex behaviours are reduced to a instruction set where each element corresponds to a particular stable environment. We have an identity of the parasite moving through identical environments for millions of years. This is an example of how IDENTITY works in a WEAKENED EQUIVALENCE. In other words, the parasite through its life cycle shows us an INVARIANCE of PRESENTATION, it will follow a particular path for itself but it is a path that is merely a presentation of a much more general set of equivalent relations. Remember the parasite behaviours from one level and they look "random" but at another level, they are all connected through equivalences, and taken all together those equivalences are invariant."
I got a bunch of "bug eyes" so, I ended this part of the lecture with, "OK, remember the Parasite."
Parasites: Presentation-Invariance and Degrees of Weakened Equivalence
Last night in the seminar on Legal Aspects of International Finance, we had each student read their draft assignments on various aspects of international financial regulations, e.g., the Orderly Liquidation Authority, Whistleblower Incentives and Protection, OTC derivatives under the Dodd -Frank Act, the EC proposal to regulate the OTC derivatives markets, the Volker Rule under Dodd-Frank and the Vickers Report in the UK.
I said to this small but very able group, "I'll be lecturing on Category Theory for the next ten years and the importance of having this view in doing comparative law studies and global financial meditations, and not one student will ever even try to apply these ideas to their work. C'est dommage, what a pity1"
I then said that legal and financial studies are in a quandary because the ambition of both are quite clear, and the honest academic knows quite well that the so-called "theories" in each are not doing their job which is to give a sense of "presentation-invariance structure of theories." [See, Marquis, Jean Pierre (2009) From a Geometric Point of View, at 234.] What does this mean? It means that somehow the idea, and here I must insist on the Platonic concept of idea, simply does not change! It is invariant against all presentations! But this has no meaning at all unless we relax to the nth degree what we mean by equivalence. The clarity coming out of Category Theory is the discovery of a way of showing how we can move from a simple and absolutely intuitive sense of "equals to" as in A = A, to more and more weakened senses of "equivalence," i.e., in order of degrees of weakness, (1) isomorphism, (2) natural transformation, (3) natural isomorphism, (4) adjunction. As we move to weaker and weaker forms of equivalence, we start to realise what we really mean by "identity."
Now, I had prepared mentally for this point in the seminar. I knew that my students would look at me as if I were an alien who may or may not have an evil intent on their immediate future. So, I said, "Look, I've been thinking about this for a while, and I think I have an example which you all can understand about how 'weak equivalence' works in the real world. PARASITES."
At this point, I get a look of embarrassed silence. Some look at me in politeness, others are giving me that "yuk" look. I've got their attention, so I continue:
"You all know how parasites work. You walk barefoot in a beautiful paradise, say Hawaii, and you don't mind walking in puddles. But as your foot enters the puddle, a little screw-shaped parasite enters your heel. It burrows deep, gets into your circulatory system, going round and round your blood system, until it lodges idyllically in your liver or your lungs, and there it grows to an enormous size and proliferates seeds of itself, which then are re-deposited to the environment through your faeces."
They grimace at faeces. They don't like me taking them down THAT path, so I take them up the theoretical track.
"So, look at what's going on here. How is it that such a simple small organism is able to travel and adjust to such exotic and hostile environments? Is it intelligent? Does it have some kind of global navigator? Does it depend on the magnetic or coriolli forces of the sun? No. The parasite has a simple linear instruction set which it can simply follow because the environments which it enters are extraordinarily stable over millions of years. So, imagine you are a parasite and this room is the "heel of a human's foot". Your instruction set says something like, "wiggle like hell" when you come into this environment, and this environment is absolutely stable for millions of years because for millions of years the environments of heels are always the SAME. By the way, this is the kind of IDENTITY that we say we must have in Category Theory. Now what? As a parasite, you burrow to the edge of this environment and you break through to the blood circulatory system. Now this environment has also been the same for millions of years, and your instruction set says, "turn off all flagella and float" and wow, you float and float for a couple circulations -- this is like going round the world in a lifeboat for humans -- until you get to a particular chemical environment that "smells like" a liver or a lung, and then and there, "throw anchor." All of these seemingly complex behaviours are reduced to a instruction set where each element corresponds to a particular stable environment. We have an identity of the parasite moving through identical environments for millions of years. This is an example of how IDENTITY works in a WEAKENED EQUIVALENCE. In other words, the parasite through its life cycle shows us an INVARIANCE of PRESENTATION, it will follow a particular path for itself but it is a path that is merely a presentation of a much more general set of equivalent relations. Remember the parasite behaviours from one level and they look "random" but at another level, they are all connected through equivalences, and taken all together those equivalences are invariant."
I got a bunch of "bug eyes" so, I ended this part of the lecture with, "OK, remember the Parasite."
Sunday 4 March 2012
Can we go beyond tribal minds?
Can we go beyond the tribal mind?
Thucydides says the preconditions of war are:
(1) colonists (literally, farmers) who set up settlements on other's lands,
(2) bilateral agreements (treaties) of support if one or the other is attacked,
(3) multiple bilateral treaties turn into alliances between members of one group against members of another group, so that
(4) insult, injury or betrayal of one member sets off retaliation but even more importantly,
(5) sussing out and anticipating the consequences of (1) to (4), ANY member looks to other members of an alliance to launch a pre-emptive strike against a member of another alliance. Since membership to an alliance can change by mere threat, a grinding, mutually destructive scenario is primed.
For the great works on war as the reality of the human condition, see:
(a)Thucydides on the History of the Peloponnesian Wars [http://classics.mit.edu/Thucydides/pelopwar.html] and
(b) Gibbon on The History of the Decline and Fall of the Roman Empire [http://www.gutenberg.org/files/25717/25717-h/25717-h.htm].
The great anthropologist Levi-Strauss, after studying tribal wars and classificatory symbolic systems of traditional peoples in South America, use to write: "trade (materials and women) or die." I would say this slogan is somewhat confirmed by Potts' and Hayden's (2008) biological evolutionary thesis in their book, in Sex and Death: How Biology Explains Warfare and Terrorism And Offers a Path to a Safer World.
Thucydides says the preconditions of war are:
(1) colonists (literally, farmers) who set up settlements on other's lands,
(2) bilateral agreements (treaties) of support if one or the other is attacked,
(3) multiple bilateral treaties turn into alliances between members of one group against members of another group, so that
(4) insult, injury or betrayal of one member sets off retaliation but even more importantly,
(5) sussing out and anticipating the consequences of (1) to (4), ANY member looks to other members of an alliance to launch a pre-emptive strike against a member of another alliance. Since membership to an alliance can change by mere threat, a grinding, mutually destructive scenario is primed.
For the great works on war as the reality of the human condition, see:
(a)Thucydides on the History of the Peloponnesian Wars [http://classics.mit.edu/Thucydides/pelopwar.html] and
(b) Gibbon on The History of the Decline and Fall of the Roman Empire [http://www.gutenberg.org/files/25717/25717-h/25717-h.htm].
The great anthropologist Levi-Strauss, after studying tribal wars and classificatory symbolic systems of traditional peoples in South America, use to write: "trade (materials and women) or die." I would say this slogan is somewhat confirmed by Potts' and Hayden's (2008) biological evolutionary thesis in their book, in Sex and Death: How Biology Explains Warfare and Terrorism And Offers a Path to a Safer World.
Friday 2 March 2012
Naive Category Theory is Sufficient to Subsume Asymmetric Bias; Clear the Way to Adjunctions in Law and Finance
1. Today, in my Facebook, I wrote:
An example of "asymmetric bias" is where one group of people feel they are following a correct procedure and therefore, are immune from justice. In the new category theory of law and finance, this is the MISTAKE of confusing translational symmetry (eg procedure) for justice (eg rotational symmetry). An example of this bias can found in the ISDA Determinations Committee view of the "voluntary 70% nonpayment" of bonds as a "non-default." To understand why this determination is actually an asymmetric bias, you might ask yourself, "when has a banker ever treated you as being not in default when you failed to pay 70% of the debt due and payable?" The answer establishes a bilateral symmetry. Now imagine multiplying this question out to all members of society and receiving answers. If the answer is basically the same, then you will have a sense of the rotational symmetry. Biases form part of a transformational group that define the space. With category theory, we can "conceptually calculate" an instantiation of the space that is "presentation-invariant" of the theory. Sounds vague, but it is actually rigorously fun and exciting once you get the hang of it, like skiing. For the latest on the defensiveness of the ISDA determinations committee, see: http://www.zerohedge.com/news/isdas-take-lack-greek-cds-trigger-we-think-credit-eventdc-process-fair-transparent-and-well-tes
2. If you've bothered to follow the argument in this blog re a Category Theory of Law and Finance, you will note that I have tried to show how a few formalism coming from what is now called Category Theory may be applied to: (1) the Arrow-Debreu-Sharpe (ADS) Model of the Financial Contract (FC) can be thought of as the fundamental unit of the law and finance universe with the quadrangle sketch with the four objects t0 ("t zero") for initial conditions, infinite contingent states of the world (Inf-C), Pay, and t1 ("t one") as the "maturity condition" when payment is due and payable. Let's label the morphisms between the objects, f, g, h and i, so that:
f: t0, Inf-C
g: Inf-C, P
h: t1, P
i: t0, t1
It's a lot easier to see what's going on if you draw the morphisms, so it looks like a "square."
Inf-C -------->P
/\ /\
| |
| |
t0----------> t1
3. The above ADS Model is a brilliant reduction of the complex law and finance phenomena since it captures most of the important and significant features of the basic unit of behaviours in the financial markets, including primary (eg, prospectus disclosures under a 1933 Securities Act regime) and secondary (eg, ongoing reporting requirements under a 1934 Securities Exchange Act regime) behaviours. But there is one big issue that it tends to pass over and that is, the phenomenon of Default.
4. Default is a fact of life. In Aristotelian terms, default is at least a "potential-actuality." I would go so far as to assert that its primary substance is commingled with primary matter in the classical sense of undifferentiated matter, where really no distinctions can be made except for that it is an ingredient that makes up the world. This undifferentiated quality links it to Uncertainty, and Uncertainty is basically the same thing as saying "infinite contingent states of the world.". So,in terms of a Category Theory diagram (which uses equinal morphisms) we have:
Default --> Potential-Actuality --> Primary Substance --> The Undifferentiated --> Uncertainty --> Infinite States of the World
5. Default Invariance. I guess my contribution to the Category Theory of Law and Finance is that the ADS Model is insufficient to capture the legal and financial reality. To be even more precise, the ADS Model fails to show the presentation-invariance of the general structure in which financial contracts exist. This is an enormous claim! And it is an example of the philosophical importance of Category Theory in general. So, in order to correct the model so that it is ontologically and epistemologically coherent, we MUST add "not-pay" as a possible alternative object to "pay." Now this change may sound trivial, but it cleaves the universe of possibilities and gives us the "presentation-invariance" that we need for a fundamental unit of legal and financial space. In simpler terms, we can now do conceptual calculations that take account more of the space that constitute legal and financial reality. From this foundation, we can connect to:
(1) Akerloff (1970) where
(a) Part 1 of his paper where information asymmetry favouring the seller leads to market failure is simply the morphism from not-pay and where
(b) Part 2 of his paper where information asymmetry favouring the buyer never leads to market failure corresponds to the morphism from pay [sorry, this thought deserves a simple diagram and a couple thousand words of explanation];
(2) Hohfeld's Legal Conceptions where
(a) Jural Opposites and
(b) Jual Correlatives
form the Category of Legal Relations, which act as a sort for the various legal interpretations of Financial Contracts [again, apologies, this thought deserves an essay unto itself];
(3) Default Invariance implemented into
(a) the Great Cycle of Default which is the four phase mega-states of the world of law and finance (recall previous notes on the definition of Financial Innovation [I] and Bailout [B], where we have the ordered qaudtuple, [I][I], [I][B], [B][B] and [B][I], and where various regulatory proposals can be mapped as morphisms from one phase to another) eg,
(i) the Orderly Liquidation Authority of Title II of the Dodd-Frank Act is a morphism from [I][B] to [B][B], and
(ii) the Whistleblower Incentives Orotection of the Dodd-Frank Act is a morphism from [B][B] to [I][I].
These "regulatory highways" tend to accelerate transitions from one phase to another, AND there are
(4) Opetopes, that is, morphisms on morphisms between these regulatory highways which have a n-category characteristics--I.e., I suppose, at the crazy complex legal and financial level of decision-making, we have the miraculous opetopes (Many-to-One) morphisms.
Ok, got that?
6. To check that we are on the same page, you might try "sketching" all the items stated in paragraph 5 above. There's actually a whole school of Category Theory by C. Ehresmann which developed the concept of esquisse (sketch) that systematically developed sketches as the rigorous syntactics and semantics of the theory. [See, Marquis, Jean-Pierre (2009) p. 225.]
7. Now, we have been using a Naive form of Category Theory, that is, up to isomorphisms of objects where the diagrams commute to at least one "cone.". That is, where we have the objects, A, B and C, we have the following morphisms: f: A->B, g:B->C, and h:A->C, h = gf. But really, where Category Theory proper makes itself fantastically useful is when we can show that we have ADJUNCTIONS.
8. An adjunction, in one simple (but not exact) version, is merely an equivalence of functors between categories. If anyone can show that adjunctions exist in law and finance, then that person or group of people deserve at least one Nobel Prize. At this point in time, I have a couple ideas of why there is no objection to have adjunctions in law and finance systems. But to PROVE the positive of this statement....well, that would be really amazing!
An example of "asymmetric bias" is where one group of people feel they are following a correct procedure and therefore, are immune from justice. In the new category theory of law and finance, this is the MISTAKE of confusing translational symmetry (eg procedure) for justice (eg rotational symmetry). An example of this bias can found in the ISDA Determinations Committee view of the "voluntary 70% nonpayment" of bonds as a "non-default." To understand why this determination is actually an asymmetric bias, you might ask yourself, "when has a banker ever treated you as being not in default when you failed to pay 70% of the debt due and payable?" The answer establishes a bilateral symmetry. Now imagine multiplying this question out to all members of society and receiving answers. If the answer is basically the same, then you will have a sense of the rotational symmetry. Biases form part of a transformational group that define the space. With category theory, we can "conceptually calculate" an instantiation of the space that is "presentation-invariant" of the theory. Sounds vague, but it is actually rigorously fun and exciting once you get the hang of it, like skiing. For the latest on the defensiveness of the ISDA determinations committee, see: http://www.zerohedge.com/news/isdas-take-lack-greek-cds-trigger-we-think-credit-eventdc-process-fair-transparent-and-well-tes
2. If you've bothered to follow the argument in this blog re a Category Theory of Law and Finance, you will note that I have tried to show how a few formalism coming from what is now called Category Theory may be applied to: (1) the Arrow-Debreu-Sharpe (ADS) Model of the Financial Contract (FC) can be thought of as the fundamental unit of the law and finance universe with the quadrangle sketch with the four objects t0 ("t zero") for initial conditions, infinite contingent states of the world (Inf-C), Pay, and t1 ("t one") as the "maturity condition" when payment is due and payable. Let's label the morphisms between the objects, f, g, h and i, so that:
f: t0, Inf-C
g: Inf-C, P
h: t1, P
i: t0, t1
It's a lot easier to see what's going on if you draw the morphisms, so it looks like a "square."
Inf-C -------->P
/\ /\
| |
| |
t0----------> t1
3. The above ADS Model is a brilliant reduction of the complex law and finance phenomena since it captures most of the important and significant features of the basic unit of behaviours in the financial markets, including primary (eg, prospectus disclosures under a 1933 Securities Act regime) and secondary (eg, ongoing reporting requirements under a 1934 Securities Exchange Act regime) behaviours. But there is one big issue that it tends to pass over and that is, the phenomenon of Default.
4. Default is a fact of life. In Aristotelian terms, default is at least a "potential-actuality." I would go so far as to assert that its primary substance is commingled with primary matter in the classical sense of undifferentiated matter, where really no distinctions can be made except for that it is an ingredient that makes up the world. This undifferentiated quality links it to Uncertainty, and Uncertainty is basically the same thing as saying "infinite contingent states of the world.". So,in terms of a Category Theory diagram (which uses equinal morphisms) we have:
Default --> Potential-Actuality --> Primary Substance --> The Undifferentiated --> Uncertainty --> Infinite States of the World
5. Default Invariance. I guess my contribution to the Category Theory of Law and Finance is that the ADS Model is insufficient to capture the legal and financial reality. To be even more precise, the ADS Model fails to show the presentation-invariance of the general structure in which financial contracts exist. This is an enormous claim! And it is an example of the philosophical importance of Category Theory in general. So, in order to correct the model so that it is ontologically and epistemologically coherent, we MUST add "not-pay" as a possible alternative object to "pay." Now this change may sound trivial, but it cleaves the universe of possibilities and gives us the "presentation-invariance" that we need for a fundamental unit of legal and financial space. In simpler terms, we can now do conceptual calculations that take account more of the space that constitute legal and financial reality. From this foundation, we can connect to:
(1) Akerloff (1970) where
(a) Part 1 of his paper where information asymmetry favouring the seller leads to market failure is simply the morphism from not-pay and where
(b) Part 2 of his paper where information asymmetry favouring the buyer never leads to market failure corresponds to the morphism from pay [sorry, this thought deserves a simple diagram and a couple thousand words of explanation];
(2) Hohfeld's Legal Conceptions where
(a) Jural Opposites and
(b) Jual Correlatives
form the Category of Legal Relations, which act as a sort for the various legal interpretations of Financial Contracts [again, apologies, this thought deserves an essay unto itself];
(3) Default Invariance implemented into
(a) the Great Cycle of Default which is the four phase mega-states of the world of law and finance (recall previous notes on the definition of Financial Innovation [I] and Bailout [B], where we have the ordered qaudtuple, [I][I], [I][B], [B][B] and [B][I], and where various regulatory proposals can be mapped as morphisms from one phase to another) eg,
(i) the Orderly Liquidation Authority of Title II of the Dodd-Frank Act is a morphism from [I][B] to [B][B], and
(ii) the Whistleblower Incentives Orotection of the Dodd-Frank Act is a morphism from [B][B] to [I][I].
These "regulatory highways" tend to accelerate transitions from one phase to another, AND there are
(4) Opetopes, that is, morphisms on morphisms between these regulatory highways which have a n-category characteristics--I.e., I suppose, at the crazy complex legal and financial level of decision-making, we have the miraculous opetopes (Many-to-One) morphisms.
Ok, got that?
6. To check that we are on the same page, you might try "sketching" all the items stated in paragraph 5 above. There's actually a whole school of Category Theory by C. Ehresmann which developed the concept of esquisse (sketch) that systematically developed sketches as the rigorous syntactics and semantics of the theory. [See, Marquis, Jean-Pierre (2009) p. 225.]
7. Now, we have been using a Naive form of Category Theory, that is, up to isomorphisms of objects where the diagrams commute to at least one "cone.". That is, where we have the objects, A, B and C, we have the following morphisms: f: A->B, g:B->C, and h:A->C, h = gf. But really, where Category Theory proper makes itself fantastically useful is when we can show that we have ADJUNCTIONS.
8. An adjunction, in one simple (but not exact) version, is merely an equivalence of functors between categories. If anyone can show that adjunctions exist in law and finance, then that person or group of people deserve at least one Nobel Prize. At this point in time, I have a couple ideas of why there is no objection to have adjunctions in law and finance systems. But to PROVE the positive of this statement....well, that would be really amazing!
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