1. The brackets [ ] indicate an object.
2. The arrow -> is a morphism, which means some process, transformation, operation or function.
3. B stands for Bailout, and everything implied by that state of the world.
4. [B] means the object of Bailout, which is really just another way of saying Bailout as a state of the world with everything that is implied by that state of the world.
5. We might use [B] or B for the same thing.
6. I stands for Financial Innovation as a state of the world where financial innovation is acceptable, where there is a secondary Market in financial instruments.
7. [I] means the object of financial innovation and all that it means.
8. We write [I]->[B] to mean the financial innovative state of the world is transformed into a world of Bailouts.
9. For our purposes, we can leave out leave out the arrows (although later,we will put them back in) so [I]->[B] can be written as [I][B]. We can simplify further to BI. But for most of the time, in order to remind us of the special states of the world, we will use the bracketed notation.
Got all that?
Now we come to the theoretical parts.
10. If we pars the world into [B] and [I], then we have four possible mega-states of a two state world, as follows:
(1) [I][I]
(2) [I][B]
(3) [B][B]
(4) [B][I]
Note that between two states, we have the morphism of Default.
11. Morphism of Default is the Invariance of Default. It's important to note that we have a special phenomenon which defines the divide between the two objects in each of the mega-states of (1) through (4). That phenomenon is also a morphism and we call it Default. Default is a latent transformation and it is invariant in all four states. for example, notice how default is not only embedded in every contract you enter and perform but also how default must lurk in the shadows of any regime of financial contracts. It cannot go away. Default invariance has nothing to do with whether any particular contract is or is not in default except that each contract has this "quantitative quality" within its particular potentiality (in Aristotelian terms) or coordinate feature as in a Descartean axis. Later we shall see in the "Risk Symmetries Framework" that risk is "Perceived Risk" as the dependent variable to "Definition" which is the independent variable. But we get ahead of ourselves.
12. Invariance of Default leads to the Functor of Default. We shall see that [] objects are categories and the morphism between categories is a functor. So, more properly, where each state of the world [I] or [B] is a category, the functor is Default. Default functors going in the clockwise direction from (1) to (2), (2) to (3), (3) to (4) and (4) to (1) are "free functors" since they tend to add structure. In the anti-clockwise direction, the functors would tend to lose structure and are called forgetful functors.
13. Mini-States Pre- and Post- each State; Critical Key Sequences Ex Ante and Post Hoc. For each state before and each state after default, in other words in the object before and the object after default, we have specific legal and financial elements in some prescribed "order" which we call incremental states or "mini-states." Pre-mini-states to the state [I] is little "i" and written "-[i]", post-mini-state to the state [B] is "[b]+". It is the SEQUENCE of mini-states that correlate to three types of infinite series, which make explicit (1) definitely convergent, (2) definitely divergent and (3) indefinitely divergent phenomena. Having knowledge of which of the three series is involved in the pre- and post-sequence is sufficient to completely describe the structure of the key critical events of CAUSE and EFFECT of any of the States and Mega-States of the Great Cycle of Default. It is important to note that the STRUCTURE of Default has similar patterns through time and space, and that particular personalities and idiosyncrasies are not relevant except as they may be translated into one of three types of infinite series. Any action, behaviour, characteristic which we can name as phenomenon in our epistemology falls within one of the three types of infinity, and it is our ability to determine what type applies and in what sequence pre- and post-state and mega-state that allows us to determine legal and financial structure of the world.
14. Many Steps between Mega-States. The morphism between the mega-states (1), (2), (3), and (4) will simply be "legal and financial transactions" or simply, "transactions."
15. For purposes of study, we can map most any sort of financial regulation as a morphism between different mega-states.
(a) OLA as a Morphism of Potentiality between Mega-State (2) and (3). For example, the Orderly Liquidation Authority of the Dodd-Frank Act is a process of pre-qualification (input criteria) and implementation, from (2) to (3). In other words, from [I][B] -> [B][B]. This two-step process tends to place a resultant emphasis on [B][B], the mega-state (3).
(b) OLA as a Functor of Actuality between Mega-State (2) and (3). A OLA functor of actuality from (2) to (3) results in an acceleration and strengthening of the mega-state (3), which means Bailout to Bailout continues. In other words, governmental control increases geometrically. Fascistic and totalitarian control zooms up and market failure is generally seen in banking failures.
(c) Whistleblower Incentives and Protection (WIP) Provisions of the Dodd-Frank Act.
Exercise: how might WIP fit in the fourfold mega-states?
Answer: next blog.
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